diff --git a/examples/beambeam_multibunch/000_multibunch_2d.py b/examples/beambeam_multibunch/000_multibunch_2d.py new file mode 100644 index 000000000..4099f7375 --- /dev/null +++ b/examples/beambeam_multibunch/000_multibunch_2d.py @@ -0,0 +1,163 @@ +# copyright ############################### # +# This file is part of the Xtrack Package. # +# Copyright (c) CERN, 2024. # +# ######################################### # + +""" +Multi-bunch coherent (2D) beam-beam example. + +Two counter-rotating beams are each represented by several bunches, with one +macroparticle per bunch (the macroparticle holds the bunch centroid, its +longitudinal position `zeta` and its population through `weight`). + +The element `BeamBeamBiGaussianMultibunch2D` applies, to every bunch of one +beam, the transverse (dipole) beam-beam kick produced by the opposing bunch it +meets: a particle (bunch) at `zeta` interacts with the opposing bunch located +at `zeta + zeta_offset`. With `zeta_offset = 0` and both beams sharing the same +longitudinal grid, bunch `i` of beam 1 collides with bunch `i` of beam 2. + +Each turn we: + 1) snapshot both beams into the opposing element (`update_from_other_beam`) + BEFORE applying any kick, so both beams are kicked using the bunch + positions at the same turn (strong-strong simultaneity); + 2) apply the beam-beam kicks; + 3) transport both beams with a simple linear one-turn map. +""" + +import numpy as np +import matplotlib.pyplot as plt + +import xpart as xp +import xtrack as xt +import xfields as xf + +# ---------------------------------------------------------------------------- +# Beam / machine parameters +# ---------------------------------------------------------------------------- +p0c = 7e12 # 7 TeV protons +mass0 = xp.PROTON_MASS_EV + +n_bunches = 4 # bunches per beam +bunch_spacing_zeta = 0.75 # m, spacing between bunches in zeta +bunch_intensity = 1.2e11 # real charges per bunch + +# Per-bunch normalized emittances and beta functions at the IP. Here we give +# each bunch a slightly different horizontal emittance to show the per-bunch +# treatment (bunch 0 the smallest, bunch 3 the largest). +nemitt_x = np.array([1.8e-6, 2.0e-6, 2.2e-6, 2.5e-6]) # m rad +nemitt_y = 2.0e-6 * np.ones(n_bunches) # m rad +betx_ip = 1.0 * np.ones(n_bunches) # m +bety_ip = 1.0 * np.ones(n_bunches) # m + +gamma0 = p0c / mass0 # ultrarelativistic: beta*gamma ~ gamma +beta0_rel = np.sqrt(1 - 1 / gamma0**2) + +qx, qy = 0.31, 0.32 # transverse tunes of the one-turn map +beta_x, beta_y = 1.0, 1.0 # m, beta functions of the one-turn map + +# Reference horizontal size (bunch 0), only used to scale the plots / offset +sigma_x = np.sqrt(nemitt_x[0] / (beta0_rel * gamma0) * betx_ip[0]) + +n_turns = 2048 + +# ---------------------------------------------------------------------------- +# Build the two multi-bunch beams (1 macroparticle = 1 bunch) +# ---------------------------------------------------------------------------- +zeta_bunches = np.arange(n_bunches) * bunch_spacing_zeta + +def make_beam(x0, y0): + p = xp.Particles( + p0c=p0c, mass0=mass0, q0=1.0, + x=x0 * np.ones(n_bunches), + y=y0 * np.ones(n_bunches), + zeta=zeta_bunches.copy(), + weight=bunch_intensity, # bunch population + ) + return p + +# Give the two beams a small initial transverse offset so that the coherent +# beam-beam force drives the bunch centroids. +beam1 = make_beam(x0=0.5 * sigma_x, y0=0.0) +beam2 = make_beam(x0=-0.5 * sigma_x, y0=0.0) + +# ---------------------------------------------------------------------------- +# Beam-beam elements (one per beam: it kicks "its" beam using the other one) +# ---------------------------------------------------------------------------- +common_bb_kwargs = dict( + zeta_offset=0.0, # head-on: bunch i meets bunch i + zeta_match_tol=1e-6, + other_beam_q0=1.0, + other_beam_beta0=beta0_rel, + # per-bunch transverse sizes (sigma = sqrt(beta * nemitt / gamma0)) + other_beam_sigma_x=np.sqrt(betx_ip * nemitt_x / gamma0), + other_beam_sigma_y=np.sqrt(bety_ip * nemitt_y / gamma0), +) + +# The opposing beam is passed as a Particles object (each active macroparticle +# is one bunch); `num_bunches` and the initial bunch centroids are taken from it. +bb_on_beam1 = xf.BeamBeamBiGaussianMultibunch2D( + other_particles=beam2, **common_bb_kwargs) # other = beam2 +bb_on_beam2 = xf.BeamBeamBiGaussianMultibunch2D( + other_particles=beam1, **common_bb_kwargs) # other = beam1 + +# Report the per-bunch transverse sizes derived from the emittances and betas. +print('opposing bunch sigma_x [um]:', bb_on_beam1.other_beam_sigma_x * 1e6) +print('opposing bunch sigma_y [um]:', bb_on_beam1.other_beam_sigma_y * 1e6) + +# ---------------------------------------------------------------------------- +# Simple linear one-turn maps (transverse rotation by the tune) +# ---------------------------------------------------------------------------- +otm1 = xt.LineSegmentMap(qx=qx, qy=qy, betx=beta_x, bety=beta_y) +otm2 = xt.LineSegmentMap(qx=qx, qy=qy, betx=beta_x, bety=beta_y) + +# ---------------------------------------------------------------------------- +# Tracking loop +# ---------------------------------------------------------------------------- +rec_x1 = np.zeros((n_turns, n_bunches)) +rec_x2 = np.zeros((n_turns, n_bunches)) + +for turn in range(n_turns): + # 1) snapshot both beams BEFORE kicking either of them + bb_on_beam1.update_from_other_beam(beam2) + bb_on_beam2.update_from_other_beam(beam1) + + # 2) beam-beam kicks + bb_on_beam1.track(beam1) + bb_on_beam2.track(beam2) + + # 3) linear transport + otm1.track(beam1) + otm2.track(beam2) + + # record bunch centroids + rec_x1[turn] = beam1.x + rec_x2[turn] = beam2.x + +# ---------------------------------------------------------------------------- +# Plot +# ---------------------------------------------------------------------------- +fig, axs = plt.subplots(2, 1, figsize=(8, 6), sharex=True) +for ib in range(n_bunches): + axs[0].plot(rec_x1[:, ib] / sigma_x, label=f'bunch {ib}') + axs[1].plot(rec_x2[:, ib] / sigma_x, label=f'bunch {ib}') +axs[0].set_ylabel('beam 1 x / $\\sigma_x$') +axs[1].set_ylabel('beam 2 x / $\\sigma_x$') +axs[1].set_xlabel('turn') +axs[0].legend(ncol=n_bunches, fontsize=8) +axs[0].set_title('Coherent multi-bunch beam-beam (2D)') + +# Coherent beam-beam tune spectra of all bunches of beam 1 +fig2, ax2 = plt.subplots(figsize=(8, 4)) +freqs = np.fft.rfftfreq(n_turns) +for ib in range(n_bunches): + spectrum = np.abs(np.fft.rfft(rec_x1[:, ib] - rec_x1[:, ib].mean())) + ax2.plot(freqs, spectrum, label=f'bunch {ib}') +ax2.axvline(qx % 1, color='k', ls='--', label='unperturbed $q_x$') +ax2.set_xlabel('tune') +ax2.set_ylabel('amplitude') +ax2.set_title('Spectra of beam 1 bunches (x)') +ax2.legend() +ax2.set_xlim(0.28, 0.34) + +plt.tight_layout() +plt.show() diff --git a/examples/beambeam_multibunch/001_twiss_multibunch.py b/examples/beambeam_multibunch/001_twiss_multibunch.py new file mode 100644 index 000000000..e6267d963 --- /dev/null +++ b/examples/beambeam_multibunch/001_twiss_multibunch.py @@ -0,0 +1,173 @@ +# copyright ############################### # +# This file is part of the Xtrack Package. # +# Copyright (c) CERN, 2024. # +# ######################################### # + +""" +Per-bunch closed solution of a multi-bunch beam with `twiss_multibunch`. + +Each bunch of a multi-bunch beam sits at a distinct longitudinal position +`zeta` and, through the `BeamBeamBiGaussianMultibunch2D` element, sees a +different opposing bunch. Its closed orbit and optics (in particular the tunes) +therefore differ from bunch to bunch. `line.twiss_multibunch(...)` fixes `zeta` +to each bunch position in turn and returns the corresponding periodic solution. + +The example has two parts: + A) per-bunch tune footprint of a beam colliding head-on with an opposing beam + whose bunches have (slightly) different emittances; + B) self-consistent per-bunch closed orbit of two colliding beams that are + transversely separated, obtained by iterating `twiss_multibunch` on each + beam while updating the opposing-beam centroids. +""" + +import numpy as np +import matplotlib.pyplot as plt + +import xpart as xp +import xtrack as xt +import xfields as xf + +# ---------------------------------------------------------------------------- +# Beam / machine parameters +# ---------------------------------------------------------------------------- +p0c = 7e12 +mass0 = xp.PROTON_MASS_EV +gamma0 = p0c / mass0 +beta0_rel = np.sqrt(1 - 1 / gamma0**2) + +n_bunches = 8 +bunch_spacing_zeta = 0.75 +bunch_intensity = 2.0e11 + +# Per-bunch normalized emittances (a small bunch-by-bunch spread) +nemitt_x = np.linspace(1.8e-6, 2.6e-6, n_bunches) +nemitt_y = 2.0e-6 * np.ones(n_bunches) +betx_ip = 1.0 * np.ones(n_bunches) +bety_ip = 1.0 * np.ones(n_bunches) + +qx0, qy0 = 0.31, 0.32 + +zeta_bunches = np.arange(n_bunches) * bunch_spacing_zeta + +# ============================================================================ +# Part A: per-bunch tune footprint (head-on, opposing beam on axis) +# ============================================================================ +opposing = xp.Particles( + p0c=p0c, mass0=mass0, q0=1.0, + x=np.zeros(n_bunches), y=np.zeros(n_bunches), + zeta=zeta_bunches.copy(), weight=bunch_intensity) + +bb = xf.BeamBeamBiGaussianMultibunch2D( + other_particles=opposing, zeta_offset=0.0, zeta_match_tol=1e-6, + other_beam_q0=1.0, other_beam_beta0=beta0_rel, + other_beam_sigma_x=np.sqrt(betx_ip * nemitt_x / gamma0), + other_beam_sigma_y=np.sqrt(bety_ip * nemitt_y / gamma0)) + +otm = xt.LineSegmentMap(qx=qx0, qy=qy0, betx=1.0, bety=1.0, + longitudinal_mode='frozen') +line = xt.Line(elements=[otm, bb], element_names=['otm', 'bb']) +line.particle_ref = xp.Particles(p0c=p0c, mass0=mass0, q0=1.0) + +mbtw = line.twiss_multibunch(zeta_bunches=zeta_bunches) + +print('Per-bunch tunes:') +for ib in range(n_bunches): + print(f' bunch {ib}: qx={mbtw.qx[ib]:.6f} qy={mbtw.qy[ib]:.6f} ' + f'(beam-beam dQx={mbtw.qx[ib]-qx0:+.2e})') + +# ============================================================================ +# Part B: self-consistent per-bunch closed orbit of two separated beams +# ============================================================================ +# The two beams are horizontally separated at the IP (e.g. a long-range-like +# offset), so every bunch receives a dipole beam-beam kick and develops a +# closed-orbit distortion. The orbit of one beam depends on the orbit of the +# other, so we iterate to self-consistency. +# Separation of a few beam sigmas, so the (per-bunch) beam-beam dipole kick is +# significant and bunch-dependent (bunches differ in size through nemitt_x). +sigma_x_ref = np.sqrt(betx_ip[0] * nemitt_x.mean() / gamma0) +separation = 4.0 * sigma_x_ref # nominal horizontal separation [m] + + +def make_line(x_ref): + # A one-turn map whose reference (closed) orbit is offset by `x_ref`, plus + # the beam-beam element (opposing beam filled in during the iteration). + otm = xt.LineSegmentMap(qx=qx0, qy=qy0, betx=1.0, bety=1.0, + x_ref=x_ref, longitudinal_mode='frozen') + bb = xf.BeamBeamBiGaussianMultibunch2D( + num_bunches=n_bunches, zeta_offset=0.0, zeta_match_tol=1e-6, + other_beam_q0=1.0, other_beam_beta0=beta0_rel, + other_beam_sigma_x=np.sqrt(betx_ip * nemitt_x / gamma0), + other_beam_sigma_y=np.sqrt(bety_ip * nemitt_y / gamma0)) + ln = xt.Line(elements=[otm, bb], element_names=['otm', 'bb']) + ln.particle_ref = xp.Particles(p0c=p0c, mass0=mass0, q0=1.0) + return ln, bb + + +line1, bb1 = make_line(x_ref=+separation / 2) +line2, bb2 = make_line(x_ref=-separation / 2) + + +def co_particles(mbtw, weight): + # Build a Particles object with the per-bunch closed orbit at the bb element + # (each active macroparticle = one bunch), to feed the opposing element. + x = np.array([tw['x', 'bb'] for tw in mbtw]) + y = np.array([tw['y', 'bb'] for tw in mbtw]) + return xp.Particles(p0c=p0c, mass0=mass0, q0=1.0, + x=x, y=y, zeta=zeta_bunches.copy(), weight=weight) + + +# Initial guess: both beams on their bare reference orbit (+/- separation/2) +x1 = np.full(n_bunches, +separation / 2) +x2 = np.full(n_bunches, -separation / 2) + +n_iter = 8 +history = np.zeros((n_iter, n_bunches)) +for it in range(n_iter): + # opposing centroids from the other beam's current closed orbit + bb1.update_from_other_beam(xp.Particles( + p0c=p0c, mass0=mass0, q0=1.0, x=x2, y=np.zeros(n_bunches), + zeta=zeta_bunches.copy(), weight=bunch_intensity)) + bb2.update_from_other_beam(xp.Particles( + p0c=p0c, mass0=mass0, q0=1.0, x=x1, y=np.zeros(n_bunches), + zeta=zeta_bunches.copy(), weight=bunch_intensity)) + + mbtw1 = line1.twiss_multibunch(zeta_bunches=zeta_bunches) + mbtw2 = line2.twiss_multibunch(zeta_bunches=zeta_bunches) + + x1 = np.array([tw['x', 'bb'] for tw in mbtw1]) + x2 = np.array([tw['x', 'bb'] for tw in mbtw2]) + history[it] = x1 + print(f'iter {it}: beam1 per-bunch closed orbit x [um] = ' + f'{np.array2string(x1 * 1e6, precision=2)}') + +print('\nConverged beam1 per-bunch closed orbit x [um]:', x1 * 1e6) +print('(bare reference orbit was %.1f um)' % (separation / 2 * 1e6)) + +# ---------------------------------------------------------------------------- +# Plots +# ---------------------------------------------------------------------------- +fig, axs = plt.subplots(1, 2, figsize=(11, 4)) + +# Part A: tune footprint vs bunch +axs[0].plot(range(n_bunches), mbtw.qx, 'o-', label='$q_x$') +axs[0].plot(range(n_bunches), mbtw.qy, 's-', label='$q_y$') +axs[0].axhline(qx0, color='C0', ls='--', alpha=0.5) +axs[0].axhline(qy0, color='C1', ls='--', alpha=0.5) +axs[0].set_xlabel('bunch index') +axs[0].set_ylabel('tune') +axs[0].set_title('Part A: per-bunch tunes\n(head-on, per-bunch emittance)') +axs[0].legend() + +# Part B: convergence of the per-bunch closed orbit +for ib in range(n_bunches): + axs[1].plot(range(n_iter), history[:, ib] * 1e6, '.-', + label=f'bunch {ib}' if ib in (0, n_bunches - 1) else None) +axs[1].axhline(separation / 2 * 1e6, color='k', ls='--', + label='bare reference') +axs[1].set_xlabel('iteration') +axs[1].set_ylabel('beam1 closed orbit x [$\\mu$m]') +axs[1].set_title('Part B: self-consistent\nper-bunch closed orbit') +axs[1].legend(fontsize=8) + +plt.tight_layout() +plt.show() diff --git a/examples/lhc_multibunch_bb/000_lhc_multibunch_bb.py b/examples/lhc_multibunch_bb/000_lhc_multibunch_bb.py new file mode 100644 index 000000000..b8e5109ec --- /dev/null +++ b/examples/lhc_multibunch_bb/000_lhc_multibunch_bb.py @@ -0,0 +1,80 @@ +# copyright ############################### # +# This file is part of the Xtrack Package. # +# Copyright (c) CERN, 2024. # +# ######################################### # + +""" +Multi-bunch beam-beam on the FULL (thick) LHC lattice in collisions (6.8 TeV, +fully squeezed R2025aRP 15 cm flat optics, end-of-levelling knobs). + +Head-on and long-range beam-beam elements (BeamBeamBiGaussianMultibunch2D) are +installed at IP1/2/5/8 and the per-bunch closed solution (closed orbit + tunes) +of the two multi-bunch beams is found self-consistently. See ``lhc_mb_common.py`` +for the model (encounter geometry, convolved sizes, closed-orbit + survey +separation) which follows pytrain / TRAIN. The beams collide head-on at +IP1/IP5 (levelling offsets at IP2/IP8), so the effect is head-on + BBLR. + +This "direct" variant twisses the full thick line (no sector-map reduction). +The companion example ``002_multibunch_sectormaps_collisions.py`` replaces +the arcs by second-order maps (much faster). +""" +import os + +import matplotlib.pyplot as plt + +import lhc_mb_common as mb + +sim = mb.LHCMultibunchBB.collision() + +N_ITER = int(os.environ.get('LHC_NITER', '3')) +ALL_BUNCHES = os.environ.get('LHC_ALL', '0') == '1' # False -> bounded subset +WINDOW = int(os.environ.get('LHC_WINDOW', '48')) + +# ---------------------------------------------------------------------------- +env, line_b1, line_b2 = sim.load() +slot_len = line_b1.get_length() / sim.N_SLOTS +b_h_dist = slot_len / 2.0 + +sim.install_markers(line_b1, mirror=False, b_h_dist=b_h_dist) +sim.install_markers(line_b2, mirror=True, b_h_dist=b_h_dist) + +geom, meta = sim.compute_geometry(line_b1, line_b2, b_h_dist, slot_len) +for ip in sim.ips: + print(f' IP{ip}: head-on offset = {geom[f"bb_ip{ip}_ho"]["offset"]} slots') + +# Filling: bounded subset with all-IP pairings +scheme_b1, scheme_b2 = mb.load_scheme() +if ALL_BUNCHES: + slots_b1, slots_b2 = mb.all_filled_slots(scheme_b1, scheme_b2) +else: + slots_b1, slots_b2 = sim.windowed_slots(scheme_b1, scheme_b2, WINDOW) +print(f' populated bunches: B1 = {len(slots_b1)}, B2 = {len(slots_b2)}') + +# Install beam-beam elements in the full lines +bb_b1 = sim.install_bb(line_b1, False, len(slots_b2)) +bb_b2 = sim.install_bb(line_b2, True, len(slots_b1)) + +print('Self-consistent solve on the full thick lattice:') +import time +t0 = time.time() +mbtw_b1, mbtw_b2 = sim.solve_self_consistent( + line_b1, line_b2, bb_b1, bb_b2, slots_b1, slots_b2, n_iter=N_ITER) +print(f' solve time ({len(slots_b1)}+{len(slots_b2)} bunches, {N_ITER} iters): ' + f'{time.time() - t0:.1f} s') + +dqx_b1 = mb.wrap_frac_tune(mbtw_b1.qx - meta['bare_qx_b1']) +print(f"\nB1 tune shift: dqx in [{dqx_b1.min():.2e}, {dqx_b1.max():.2e}]") + +df_b1 = mb.results_dataframe(mbtw_b1, slots_b1, meta['bare_qx_b1'], meta['bare_qy_b1'], + ip='ip1', reverse=False) +df_b2 = mb.results_dataframe(mbtw_b2, slots_b2, meta['bare_qx_b2'], meta['bare_qy_b2'], + ip='ip1', reverse=True) +out_b1 = os.path.join(mb.HERE, 'results_b1_coll_full.pkl') +out_b2 = os.path.join(mb.HERE, 'results_b2_coll_full.pkl') +df_b1.to_pickle(out_b1) +df_b2.to_pickle(out_b2) +print(f'saved {out_b1}\nsaved {out_b2}') + +mb.plot_results(slots_b1, mbtw_b1, meta['bare_qx_b1'], meta['bare_qy_b1'], + title_suffix=' [full thick lattice, collision]') +plt.show() diff --git a/examples/lhc_multibunch_bb/001_multibunch_sectormaps_injection.py b/examples/lhc_multibunch_bb/001_multibunch_sectormaps_injection.py new file mode 100644 index 000000000..707fae090 --- /dev/null +++ b/examples/lhc_multibunch_bb/001_multibunch_sectormaps_injection.py @@ -0,0 +1,118 @@ +# copyright ############################### # +# This file is part of the Xtrack Package. # +# Copyright (c) CERN, 2024. # +# ######################################### # + +""" +Multi-bunch beam-beam on the LHC at injection, sped up with second-order maps. + +Same physics as ``000_lhc_multibunch_bb.py`` (long-range beam-beam at injection +-- separation bumps kept on, so no head-on collisions -- with per-bunch +self-consistent closed solution), but the machine between the beam-beam +encounters is replaced by second-order Taylor maps: + + reduced line = [ map(arc), BB, map(arc), BB, ... ] + +The beam-beam elements stay EXACT; only the arcs are approximated (to second +order, as in pytrain's sector maps). The reduced line has ~a few hundred +elements instead of ~13000. +""" + +import os +import time +import matplotlib.pyplot as plt + +import lhc_mb_common as mb + +sim = mb.LHCMultibunchBB.injection() + +N_ITER = int(os.environ.get('LHC_NITER', '3')) +ALL_BUNCHES = os.environ.get('LHC_ALL', '1') == '1' # False -> bounded subset +WINDOW = int(os.environ.get('LHC_WINDOW', '48')) + +# ---------------------------------------------------------------------------- +# Load, install markers, get per-encounter geometry (cached) +# ---------------------------------------------------------------------------- +env, line_b1, line_b2 = sim.load() +slot_len = line_b1.get_length() / sim.N_SLOTS +b_h_dist = slot_len / 2.0 + +sim.install_markers(line_b1, mirror=False, b_h_dist=b_h_dist) +sim.install_markers(line_b2, mirror=True, b_h_dist=b_h_dist) + +geom, meta = sim.compute_geometry(line_b1, line_b2, b_h_dist, slot_len) + +# ---------------------------------------------------------------------------- +# Timing comparison and reduced-line construction +# ---------------------------------------------------------------------------- +print(' building second-order maps between the beam-beam markers...') +red_b1 = line_b1.get_line_with_second_order_maps(split_at=sim.marker_names_b1) +red_b2 = line_b2.get_line_with_second_order_maps(split_at=sim.marker_names_b2) +for rl in (red_b1, red_b2): + rl.twiss_default['method'] = '4d' + rl.build_tracker(_context=sim.context) + +# Timing comparison (warm: compile each kernel once before timing) +line_b1.twiss(); red_b1.twiss() +t0 = time.time(); line_b1.twiss(); t_full = time.time() - t0 +t0 = time.time(); tw_red = red_b1.twiss(); t_red = time.time() - t0 +print(f' one full-lattice twiss: {t_full:.3f} s ({len(line_b1.element_names)} elements)') +print(f' one reduced-line twiss: {t_red:.3f} s ({len(red_b1.element_names)} elements)' + f' -> speed-up x{t_full/t_red:.1f}') +# The reduced line reproduces the FRACTIONAL tunes (its integer tune is not +# meaningful -- the maps carry phase advance only modulo 2 pi). +print(f' fractional tunes reduced/full: ' + f'qx {tw_red.qx % 1:.5f} / {meta["bare_qx_b1"] % 1:.5f} ' + f'qy {tw_red.qy % 1:.5f} / {meta["bare_qy_b1"] % 1:.5f}') + +# ---------------------------------------------------------------------------- +# Filling: all bunches (feasible thanks to the fast reduced twiss) +# ---------------------------------------------------------------------------- +scheme_b1, scheme_b2 = mb.load_scheme() +if ALL_BUNCHES: + slots_b1, slots_b2 = mb.all_filled_slots(scheme_b1, scheme_b2) +else: + slots_b1, slots_b2 = sim.windowed_slots(scheme_b1, scheme_b2, WINDOW) +print(f' populated bunches: B1 = {len(slots_b1)}, B2 = {len(slots_b2)}') + +# Install beam-beam elements in the reduced lines (markers were kept) +bb_b1 = sim.install_bb(red_b1, False, len(slots_b2)) +bb_b2 = sim.install_bb(red_b2, True, len(slots_b1)) + +print('Self-consistent solve on the reduced (second-order-map) lines:') +t0 = time.time() +mbtw_b1, mbtw_b2 = sim.solve_self_consistent( + red_b1, red_b2, bb_b1, bb_b2, slots_b1, slots_b2, n_iter=N_ITER) +print(f' solve time ({len(slots_b1)}+{len(slots_b2)} bunches, {N_ITER} iters): {time.time() - t0:.1f} s') + +# Optional: per-bunch optics (dynamic beta*) and global quantities (tunes, chromaticity, coupling) +COMPUTE_OPTICS_PARAMS = os.environ.get('COMPUTE_OPTICS_PARAMS', '1') == '1' +if COMPUTE_OPTICS_PARAMS: + import numpy as np + print('Final mode="fast" twiss (per-bunch optics + global quantities):') + t0 = time.time() + mbtw_b1 = red_b1.twiss_multibunch( + zeta_bunches=np.array(slots_b1) * sim.ZETA_PER_SLOT, mode='fast') + mbtw_b2 = red_b2.twiss_multibunch( + zeta_bunches=np.array(slots_b2) * sim.ZETA_PER_SLOT, mode='fast') + print(f' final twiss (both beams): {time.time() - t0:.1f} s') + +# Reference the tune shift to each reduced line's own bare tune (on the +# fractional-tune circle: fast-mode twiss returns fractional tunes) +tw_red2 = red_b2.twiss() +dqx_b1 = mb.wrap_frac_tune(mbtw_b1.qx - tw_red.qx) +print(f"\nB1 tune shift: dqx in [{dqx_b1.min():.2e}, {dqx_b1.max():.2e}]") + +# Save per-bunch results of both beams as DataFrames +df_b1 = mb.results_dataframe(mbtw_b1, slots_b1, tw_red.qx, tw_red.qy, ip='ip1', reverse=False) +df_b2 = mb.results_dataframe(mbtw_b2, slots_b2, tw_red2.qx, tw_red2.qy, ip='ip1', reverse=True) +out_b1 = os.path.join(mb.HERE, 'results_b1.pkl') +out_b2 = os.path.join(mb.HERE, 'results_b2.pkl') +df_b1.to_pickle(out_b1) +df_b2.to_pickle(out_b2) +print(f'saved {out_b1}\nsaved {out_b2}') + +mb.plot_results(slots_b1, mbtw_b1, tw_red.qx, tw_red.qy, title_suffix=' [second-order maps]') +if COMPUTE_OPTICS_PARAMS: + mb.plot_global_quantities(slots_b1, mbtw_b1, slots_b2, mbtw_b2) +plt.show() diff --git a/examples/lhc_multibunch_bb/002_multibunch_sectormaps_collisions.py b/examples/lhc_multibunch_bb/002_multibunch_sectormaps_collisions.py new file mode 100644 index 000000000..847930089 --- /dev/null +++ b/examples/lhc_multibunch_bb/002_multibunch_sectormaps_collisions.py @@ -0,0 +1,98 @@ +# copyright ############################### # +# This file is part of the Xtrack Package. # +# Copyright (c) CERN, 2024. # +# ######################################### # + +""" +Multi-bunch beam-beam on the LHC in COLLISION (6.8 TeV, fully squeezed +R2025aRP 15 cm flat optics, levelling-style knobs), with second-order maps. + +Scenario following LHC 2025/2026 physics at end of levelling: head-on collisions +at IP1/IP5 (flat optics, H crossing in 1, V crossing in 5, separations off), +levelling offsets at IP2/IP8, spectrometers/solenoids on, octupoles powered, +tunes/chromaticity matched to 62.316/60.322 and Q' = 10. 1.1e11 p/bunch, +2.3 um normalized emittance, full 2460-bunch filling scheme. + +The flattened collision optics and the pytrain reference are provided in +``test_data/lhc_2024`` (regenerate with +``test_data/lhc_2024/pytrain/regenerate_collision.py``, pytrain venv + +cpymad + acc-models-lhc checkout). +""" + +import os +import time +import numpy as np +import matplotlib.pyplot as plt + +import lhc_mb_common as mb + +sim = mb.LHCMultibunchBB.collision() + +N_ITER = int(os.environ.get('LHC_NITER', '4')) +ALL_BUNCHES = os.environ.get('LHC_ALL', '1') == '1' +WINDOW = int(os.environ.get('LHC_WINDOW', '48')) +COMPUTE_OPTICS_PARAMS = os.environ.get('COMPUTE_OPTICS_PARAMS', '1') == '1' + +# ---------------------------------------------------------------------------- +env, line_b1, line_b2 = sim.load() +slot_len = line_b1.get_length() / sim.N_SLOTS +b_h_dist = slot_len / 2.0 + +sim.install_markers(line_b1, mirror=False, b_h_dist=b_h_dist) +sim.install_markers(line_b2, mirror=True, b_h_dist=b_h_dist) + +geom, meta = sim.compute_geometry(line_b1, line_b2, b_h_dist, slot_len) +print(f' bare tunes B1 {meta["bare_qx_b1"]:.5f}/{meta["bare_qy_b1"]:.5f} ' + f'B2 {meta["bare_qx_b2"]:.5f}/{meta["bare_qy_b2"]:.5f}') + +print(' building second-order maps between the beam-beam markers...') +red_b1 = line_b1.get_line_with_second_order_maps(split_at=sim.marker_names_b1) +red_b2 = line_b2.get_line_with_second_order_maps(split_at=sim.marker_names_b2) +for rl in (red_b1, red_b2): + rl.twiss_default['method'] = '4d' + rl.build_tracker(_context=sim.context) +tw_red = red_b1.twiss() +tw_red2 = red_b2.twiss() + +scheme_b1, scheme_b2 = mb.load_scheme() +if ALL_BUNCHES: + slots_b1, slots_b2 = mb.all_filled_slots(scheme_b1, scheme_b2) +else: + slots_b1, slots_b2 = sim.windowed_slots(scheme_b1, scheme_b2, WINDOW) +print(f' populated bunches: B1 = {len(slots_b1)}, B2 = {len(slots_b2)}') + +bb_b1 = sim.install_bb(red_b1, False, len(slots_b2)) +bb_b2 = sim.install_bb(red_b2, True, len(slots_b1)) + +print('Self-consistent solve (head-on + long-range):') +t0 = time.time() +mbtw_b1, mbtw_b2 = sim.solve_self_consistent( + red_b1, red_b2, bb_b1, bb_b2, slots_b1, slots_b2, n_iter=N_ITER) +print(f' solve time ({len(slots_b1)}+{len(slots_b2)} bunches, {N_ITER} iters): ' + f'{time.time() - t0:.1f} s') + +if COMPUTE_OPTICS_PARAMS: + print('Final mode="fast" twiss (per-bunch optics + global quantities):') + t0 = time.time() + mbtw_b1 = red_b1.twiss_multibunch( + zeta_bunches=np.array(slots_b1) * sim.ZETA_PER_SLOT, mode='fast') + mbtw_b2 = red_b2.twiss_multibunch( + zeta_bunches=np.array(slots_b2) * sim.ZETA_PER_SLOT, mode='fast') + print(f' final twiss (both beams): {time.time() - t0:.1f} s') + +dqx_b1 = mb.wrap_frac_tune(mbtw_b1.qx - tw_red.qx) +print(f"\nB1 tune shift: dqx in [{dqx_b1.min():.2e}, {dqx_b1.max():.2e}]") + +df_b1 = mb.results_dataframe(mbtw_b1, slots_b1, tw_red.qx, tw_red.qy, + ip='ip1', reverse=False) +df_b2 = mb.results_dataframe(mbtw_b2, slots_b2, tw_red2.qx, tw_red2.qy, + ip='ip1', reverse=True) +df_b1.to_pickle(os.path.join(mb.HERE, 'results_b1_coll.pkl')) +df_b2.to_pickle(os.path.join(mb.HERE, 'results_b2_coll.pkl')) +print('saved results_b1_coll.pkl / results_b2_coll.pkl') + +mb.plot_results(slots_b1, mbtw_b1, tw_red.qx, tw_red.qy, + title_suffix=' [collision, 6.8 TeV]') +if COMPUTE_OPTICS_PARAMS: + mb.plot_global_quantities(slots_b1, mbtw_b1, slots_b2, mbtw_b2) +plt.show() diff --git a/examples/lhc_multibunch_bb/003_compare_results_pytrain.py b/examples/lhc_multibunch_bb/003_compare_results_pytrain.py new file mode 100644 index 000000000..f293330c4 --- /dev/null +++ b/examples/lhc_multibunch_bb/003_compare_results_pytrain.py @@ -0,0 +1,116 @@ +# copyright ############################### # +# This file is part of the Xtrack Package. # +# Copyright (c) CERN, 2024. # +# ######################################### # + +""" +Plot the per-bunch beam-beam results of both beams for BOTH scenarios: + +* injection (BBLR only), saved by ``001_multibunch_sectormaps_injection.py`` + as ``results_b{1,2}.pkl``; +* collision (6.8 TeV squeezed, head-on + BBLR), saved by + ``002_multibunch_sectormaps_collisions.py`` as ``results_b{1,2}_coll.pkl``. + +One figure per scenario. Top row: per-bunch tune offsets (beam-beam tune +shift) dqx, dqy for B1 and B2. Bottom row: per-bunch closed-orbit offsets +(deviation from the beam-averaged orbit, which removes the common +crossing/separation bump) dx, dy at IP1. + +The pytrain references from +``test_data/lhc_2024/pytrain/pytrain_{injection,collision}.json`` (the same +data the regression test ``test_lhc_multibunch_train.py`` checks against) are +overlaid. Scenarios whose xsuite result files are missing are skipped. +""" + +import os +import json + +import numpy as np +import pandas as pd +import matplotlib.pyplot as plt + +HERE = os.path.dirname(os.path.abspath(__file__)) +PYTRAIN_DIR = os.path.join(HERE, '..', '..', 'test_data', 'lhc_2024', + 'pytrain') + +SCENARIOS = [ + # (title, xsuite suffix, scenario key, tune-panel ylim or None) + ('LHC injection multi-bunch beam-beam (BBLR)', '', 'injection', (-4, 4)), + ('LHC collision 6.8 TeV multi-bunch beam-beam (head-on + BBLR)', + '_coll', 'collision', None), +] + + +def load(name): + path = os.path.join(HERE, name) + return pd.read_pickle(path) if os.path.exists(path) else None + + +def load_pytrain(scenario): + """pytrain reference from the test-data JSON, as per-beam DataFrames with + the same columns/index as the xsuite result pickles.""" + path = os.path.join(PYTRAIN_DIR, f'pytrain_{scenario}.json') + if not os.path.exists(path): + return None, None + with open(path) as fid: + ref = json.load(fid) + + def beam_df(beam): + dd = ref[beam] + return pd.DataFrame( + {kk: dd[kk] for kk in + ('qx', 'qy', 'dqx', 'dqy', 'x', 'y', 'dx', 'dy')}, + index=pd.Index(dd['slots'], name='slot')) + + return beam_df('b1'), beam_df('b2') + + +def plot_scenario(title, df_b1, df_b2, pt_b1, pt_b2, tune_ylim): + fig, axs = plt.subplots(2, 2, figsize=(13, 8), sharex=True) + + def panel(ax, col, scale, ylabel, panel_title): + if pt_b1 is not None: + bb = np.full((3564,), np.nan) + bb[pt_b1.index] = pt_b1[col] * scale + ax.plot(bb, '-', ms=3, color='C2', alpha=1, label='B1 pytrain') + bb = np.full((3564,), np.nan) + bb[pt_b2.index] = pt_b2[col] * scale + ax.plot(bb, '-', ms=3, color='C3', alpha=1, label='B2 pytrain') + ax.plot(df_b1.index, df_b1[col] * scale, '.', ms=3, color='C0', + label='B1 xsuite') + ax.plot(df_b2.index, df_b2[col] * scale, '.', ms=3, color='C1', + label='B2 xsuite') + ax.set_ylabel(ylabel) + ax.set_title(panel_title) + ax.legend(ncol=2, fontsize=8) + + panel(axs[0, 0], 'dqx', 1e3, r'$\Delta q_x$ [$10^{-3}$]', + r'Per-bunch beam-beam tune offset $\Delta q_x$') + panel(axs[0, 1], 'dqy', 1e3, r'$\Delta q_y$ [$10^{-3}$]', + r'Per-bunch beam-beam tune offset $\Delta q_y$') + panel(axs[1, 0], 'dx', 1e6, r'orbit offset x at IP1 [$\mu$m]', + 'Per-bunch beam-beam closed-orbit offset (x)') + panel(axs[1, 1], 'dy', 1e6, r'orbit offset y at IP1 [$\mu$m]', + 'Per-bunch beam-beam closed-orbit offset (y)') + if pt_b1 is not None and tune_ylim is not None: + # pytrain tune tails can be large (unconverged in slicing) + axs[0, 0].set_ylim(*tune_ylim) + axs[0, 1].set_ylim(*tune_ylim) + axs[1, 0].set_xlabel('25 ns slot') + axs[1, 1].set_xlabel('25 ns slot') + + plt.suptitle(title + ': xsuite vs pytrain' if pt_b1 is not None else title) + plt.tight_layout() + return fig + + +for title, xs_suffix, scenario, tune_ylim in SCENARIOS: + df_b1 = load(f'results_b1{xs_suffix}.pkl') + df_b2 = load(f'results_b2{xs_suffix}.pkl') + if df_b1 is None or df_b2 is None: + print(f'skipping "{title}" (results_b*{xs_suffix}.pkl not found)') + continue + pt_b1, pt_b2 = load_pytrain(scenario) + plot_scenario(title, df_b1, df_b2, pt_b1, pt_b2, tune_ylim) + +plt.show() diff --git a/examples/lhc_multibunch_bb/004_multibunch_sectormaps_dyn_beta_collisions.py b/examples/lhc_multibunch_bb/004_multibunch_sectormaps_dyn_beta_collisions.py new file mode 100644 index 000000000..88e36282c --- /dev/null +++ b/examples/lhc_multibunch_bb/004_multibunch_sectormaps_dyn_beta_collisions.py @@ -0,0 +1,151 @@ +# copyright ############################### # +# This file is part of the Xtrack Package. # +# Copyright (c) CERN, 2024. # +# ######################################### # + +""" +Impact of DYNAMIC BETA on the multi-bunch beam-beam closed solution in the +LHC collision scenario (6.8 TeV squeezed flat optics, head-on + BBLR). + +The beam-beam elements take the effective (convolved) transverse sizes of +the colliding bunch pairs. By default these are STATIC, computed once from +the bare optics: ``sigma^2 = (beta_b1 + beta_b2) * nemitt / gamma0``. But +head-on beam-beam changes the per-bunch beta functions at the encounters +(dynamic beta, ~10% spread of beta* in this scenario), which in turn changes +the sizes, the kicks, and hence the per-bunch closed solution. + +This script solves the same machine twice: + +1. static sizes (as ``002_multibunch_sectormaps_collisions.py``); +2. ``dynamic_beta=True``: at every iteration the per-bunch effective sizes + of all encounters are recomputed from the LIVE per-bunch betas of both + beams (requires the optics-carrying mode='fast' twiss in the loop). + +and compares per-bunch tunes, orbits and beta* at IP1. + +By default the MULTI-THREADED CPU kernels (OpenMP) are used (set +``LHC_OMP=0`` for serial, ``LHC_OMP=`` for a specific thread count; see +``005_multibunch_openmp.py`` for the speed-up measurement). +""" + +import os +import time +import numpy as np +import matplotlib.pyplot as plt + +import xobjects as xo +import lhc_mb_common as mb + +# multi-threaded CPU kernels by default in this demo +omp = os.environ.get('LHC_OMP', 'auto') +sim = mb.LHCMultibunchBB.collision(context=( + xo.ContextCpu() if omp == 'serial' + else xo.ContextCpu(omp_num_threads='auto' if omp == 'auto' else int(omp)))) + +N_ITER = int(os.environ.get('LHC_NITER', '3')) + +# ---------------------------------------------------------------------------- +# Build the machine (as in 002) +# ---------------------------------------------------------------------------- +env, line_b1, line_b2 = sim.load() +slot_len = line_b1.get_length() / sim.N_SLOTS +b_h_dist = slot_len / 2.0 + +sim.install_markers(line_b1, mirror=False, b_h_dist=b_h_dist) +sim.install_markers(line_b2, mirror=True, b_h_dist=b_h_dist) +geom, meta = sim.compute_geometry(line_b1, line_b2, b_h_dist, slot_len) + +print(' building second-order maps between the beam-beam markers...') +red_b1 = line_b1.get_line_with_second_order_maps(split_at=sim.marker_names_b1) +red_b2 = line_b2.get_line_with_second_order_maps(split_at=sim.marker_names_b2) +for rl in (red_b1, red_b2): + rl.twiss_default['method'] = '4d' + rl.build_tracker(_context=sim.context) +tw_red = red_b1.twiss() +tw_red2 = red_b2.twiss() + +scheme_b1, scheme_b2 = mb.load_scheme() +slots_b1, slots_b2 = mb.all_filled_slots(scheme_b1, scheme_b2) +print(f' populated bunches: B1 = {len(slots_b1)}, B2 = {len(slots_b2)}') + +bb_b1 = sim.install_bb(red_b1, False, len(slots_b2)) +bb_b2 = sim.install_bb(red_b2, True, len(slots_b1)) + +# ---------------------------------------------------------------------------- +# Solve with static sizes, then with dynamic beta +# ---------------------------------------------------------------------------- +results = {} +for label, dynamic_beta in (('static', False), ('dynamic beta', True)): + print(f'Self-consistent solve ({label}):') + t0 = time.time() + # twiss_mode='fast' in both runs (dynamic_beta forces it anyway) so the + # returned tables carry the per-bunch optics and the cost is comparable + mbtw_b1, mbtw_b2 = sim.solve_self_consistent( + red_b1, red_b2, bb_b1, bb_b2, slots_b1, slots_b2, + n_iter=N_ITER, twiss_mode='fast', dynamic_beta=dynamic_beta) + print(f' solve time ({N_ITER} iters): {time.time() - t0:.1f} s') + results[label] = (mbtw_b1, mbtw_b2) + +# ---------------------------------------------------------------------------- +# Compare per-bunch tunes, orbit and beta* at IP1 (B1) +# ---------------------------------------------------------------------------- +mk_b1 = mb.marker_name('bb_ip1_ho', False) + + +def extract(mbtw): + return dict( + qx=np.asarray(mbtw.qx_frac), qy=np.asarray(mbtw.qy_frac), + x=mbtw['x', mk_b1], + betx=mbtw['betx', mk_b1], + bety=mbtw['bety', mk_b1], + ) + + +stat = extract(results['static'][0]) +dyn = extract(results['dynamic beta'][0]) + +df_b1 = mb.results_dataframe(results['dynamic beta'][0], slots_b1, + tw_red.qx, tw_red.qy, ip='ip1', reverse=False) +df_b2 = mb.results_dataframe(results['dynamic beta'][1], slots_b2, + tw_red2.qx, tw_red2.qy, ip='ip1', reverse=True) +df_b1.to_pickle(os.path.join(mb.HERE, 'results_b1_coll_dynbeta.pkl')) +df_b2.to_pickle(os.path.join(mb.HERE, 'results_b2_coll_dynbeta.pkl')) +print('saved results_b1_coll_dynbeta.pkl / results_b2_coll_dynbeta.pkl') + +dqx = mb.wrap_frac_tune(dyn['qx'] - stat['qx']) +dqy = mb.wrap_frac_tune(dyn['qy'] - stat['qy']) +print(f"\nDynamic-beta impact (B1):") +print(f" tune change dqx in [{dqx.min():+.2e}, {dqx.max():+.2e}] " + f"(rms {dqx.std():.2e})") +print(f" tune change dqy in [{dqy.min():+.2e}, {dqy.max():+.2e}] " + f"(rms {dqy.std():.2e})") +print(f" orbit change at IP1: rms {np.std(dyn['x'] - stat['x'])*1e9:.1f} nm") +print(f" betx* at IP1: static [{stat['betx'].min():.4f}, " + f"{stat['betx'].max():.4f}] m, dynamic [{dyn['betx'].min():.4f}, " + f"{dyn['betx'].max():.4f}] m") + +fig, axs = plt.subplots(3, 1, figsize=(10, 9), sharex=True) + +axs[0].plot(slots_b1, dqx * 1e3, '.', ms=3, label=r'$\Delta q_x$') +axs[0].plot(slots_b1, dqy * 1e3, '.', ms=3, label=r'$\Delta q_y$') +axs[0].set_ylabel(r'tune change [$10^{-3}$]') +axs[0].set_title('Per-bunch effect of dynamic beta on the closed solution ' + '(B1, collision)') +axs[0].legend() + +axs[1].plot(slots_b1, (dyn['x'] - stat['x']) * 1e9, '.', ms=3, label='x') +axs[1].set_ylabel('orbit change at IP1 [nm]') +axs[1].legend() + +axs[2].plot(slots_b1, stat['betx'], '.', ms=3, label=r'$\beta_x^*$ static') +axs[2].plot(slots_b1, dyn['betx'], '.', ms=3, + label=r'$\beta_x^*$ dynamic beta') +axs[2].plot(slots_b1, stat['bety'], '.', ms=3, label=r'$\beta_y^*$ static') +axs[2].plot(slots_b1, dyn['bety'], '.', ms=3, + label=r'$\beta_y^*$ dynamic beta') +axs[2].set_ylabel(r'$\beta^*$ at IP1 [m]') +axs[2].set_xlabel('25 ns slot') +axs[2].legend(ncol=2, fontsize=8) + +plt.tight_layout() +plt.show() diff --git a/examples/lhc_multibunch_bb/005_multibunch_openmp.py b/examples/lhc_multibunch_bb/005_multibunch_openmp.py new file mode 100644 index 000000000..1bd3967da --- /dev/null +++ b/examples/lhc_multibunch_bb/005_multibunch_openmp.py @@ -0,0 +1,86 @@ +# copyright ############################### # +# This file is part of the Xtrack Package. # +# Copyright (c) CERN, 2024. # +# ######################################### # + +""" +Multi-threaded (OpenMP) CPU kernels for the multi-bunch beam-beam machinery. + +Builds the collision machine on second-order maps (as +``002_multibunch_sectormaps_collisions.py``), populates the beam-beam +elements with one self-consistent iteration, then times the batched +multibunch twiss of beam 1 -- both the orbit-only ``fast_orbit`` mode (used +in the solver loop) and the optics-carrying ``fast`` mode -- with the SERIAL +and the MULTI-THREADED CPU kernels, and reports the speed-up. + +All the multibunch examples accept the environment variable ``LHC_OMP`` +(unset/``0`` -> serial kernels; ``auto`` or a thread count -> OpenMP +kernels); prebuilt kernels exist for both flavours, so no compilation is +triggered either way. Here ``LHC_OMP`` defaults to ``auto``. +""" + +import os +import time +import numpy as np + +import xobjects as xo +import lhc_mb_common as mb + +omp = os.environ.get('LHC_OMP', 'auto') +ctx_mt = xo.ContextCpu(omp_num_threads='auto' if omp == 'auto' else int(omp)) +sim = mb.LHCMultibunchBB.collision(context=ctx_mt) +n_threads = os.cpu_count() if ctx_mt.omp_num_threads == 'auto' \ + else ctx_mt.omp_num_threads +print(f'multi-threaded context: {ctx_mt.omp_num_threads} ' + f'({n_threads} threads)') + +# ---------------------------------------------------------------------------- +# Build the machine (as in 002) and populate the beam-beam elements +# ---------------------------------------------------------------------------- +env, line_b1, line_b2 = sim.load() +slot_len = line_b1.get_length() / sim.N_SLOTS +b_h_dist = slot_len / 2.0 + +sim.install_markers(line_b1, mirror=False, b_h_dist=b_h_dist) +sim.install_markers(line_b2, mirror=True, b_h_dist=b_h_dist) +geom, meta = sim.compute_geometry(line_b1, line_b2, b_h_dist, slot_len) + +print(' building second-order maps between the beam-beam markers...') +red_b1 = line_b1.get_line_with_second_order_maps(split_at=sim.marker_names_b1) +red_b2 = line_b2.get_line_with_second_order_maps(split_at=sim.marker_names_b2) +for rl in (red_b1, red_b2): + rl.twiss_default['method'] = '4d' + rl.build_tracker(_context=sim.context) + +scheme_b1, scheme_b2 = mb.load_scheme() +slots_b1, slots_b2 = mb.all_filled_slots(scheme_b1, scheme_b2) +print(f' populated bunches: B1 = {len(slots_b1)}, B2 = {len(slots_b2)}') + +bb_b1 = sim.install_bb(red_b1, False, len(slots_b2)) +bb_b2 = sim.install_bb(red_b2, True, len(slots_b1)) + +print('Populating the beam-beam elements (one solve iteration):') +sim.solve_self_consistent(red_b1, red_b2, bb_b1, bb_b2, + slots_b1, slots_b2, n_iter=1) + +# ---------------------------------------------------------------------------- +# Timing: batched multibunch twiss of B1, serial vs multi-threaded kernels +# ---------------------------------------------------------------------------- +zeta_b1 = np.array(slots_b1) * sim.ZETA_PER_SLOT +contexts = (('serial', xo.ContextCpu()), + (f'openmp ({n_threads} threads)', ctx_mt)) + +print(f'\nBatched multibunch twiss of B1 ({len(slots_b1)} bunches):') +for mode in ('fast_orbit', 'fast'): + timings = [] + for label, ctx in contexts: + red_b1.discard_tracker() + red_b1.build_tracker(_context=ctx) + red_b1.twiss_multibunch(zeta_bunches=zeta_b1[:16], mode=mode, + show_progress=False) # warm-up + t0 = time.time() + red_b1.twiss_multibunch(zeta_bunches=zeta_b1, mode=mode, + show_progress=False) + timings.append(time.time() - t0) + print(f' mode={mode!r:13s} {label:22s}: {timings[-1]:7.1f} s') + print(f' mode={mode!r:13s} speed-up: x{timings[0] / timings[1]:.2f}') diff --git a/examples/lhc_multibunch_bb/006_multibunch_footprint.py b/examples/lhc_multibunch_bb/006_multibunch_footprint.py new file mode 100644 index 000000000..5ac49b1bb --- /dev/null +++ b/examples/lhc_multibunch_bb/006_multibunch_footprint.py @@ -0,0 +1,243 @@ +# copyright ############################### # +# This file is part of the Xtrack Package. # +# Copyright (c) CERN, 2024. # +# ######################################### # + +""" +Tune FOOTPRINTS of different bunch families in the LHC collision scenario +(6.8 TeV squeezed flat optics, head-on + BBLR), with the per-bunch +self-consistent multi-bunch beam-beam closed solution. + +Workflow (multi-threaded OpenMP kernels by default, ``LHC_OMP=0`` for +serial): + +1. Solve the multi-bunch problem on the sector-map machine (as in + ``002``/``004``): 2 iterations with the orbit-only ``fast_orbit`` twiss, + then 2 more with ``dynamic_beta=True`` (per-bunch effective sizes + recomputed from the live betas each iteration; the element state carries + over between the two calls, so this continues the same iteration). +2. Transfer the converged solution back to the FULL THICK lattice of beam 1: + the same multi-bunch beam-beam lenses are installed at the (still + present) encounter markers and loaded with the final per-bunch orbits + and dynamic sizes of beam 2, plus the (bunch-averaged) dynamic own sizes + of beam 1. +3. Generate tune footprints on this thick lattice for 12 equidistant + bunches along the longest train (first and last included), covering the + PACMAN transition from the train head through the fully-surrounded + center to the tail. Each footprint tracks particles with ``zeta`` frozen at the + bunch's slot label, so the multi-bunch lenses apply that bunch's actual + encounters (head-on + long-range, around its own closed orbit). Before + tracking, the lenses are switched to ``coherent=False``: the footprint + particles are INDIVIDUAL protons that see the field of the opposing + bunches with their own sizes (incoherent, weak-strong), while the closed + solution was obtained with the coherent rigid-bunch (convolved-size) + kicks. The footprints use the linear rescale on the ``beambeam_scale`` + knob (bound to the ``scale_strength`` of all lenses at installation, as + in the xfields beam-beam config tools): computed at weak beam-beam and + extrapolated linearly to full strength, which avoids resonance-distorted + footprints. The footprints are computed on THREE variants of the machine + (same converged lenses) and plotted side by side with the execution + times compared: + + - the full thick lattice; + - a second-order-map line that keeps the lattice octupoles (MO) as + exact thick elements between the maps, retaining most of the lattice + amplitude detuning (which is 3rd order, hence absent from the maps + themselves) at a fraction of the thick tracking cost; + - the plain second-order-map line, whose arcs carry NO amplitude + detuning -- its footprint isolates the beam-beam contribution and is + the cheapest to track. +""" + +import os +import re +import time +import numpy as np +import matplotlib.pyplot as plt + +import xobjects as xo +import xtrack as xt +import lhc_mb_common as mb + +# multi-threaded CPU kernels by default in this demo +omp = os.environ.get('LHC_OMP', 'auto') +sim = mb.LHCMultibunchBB.collision(context=( + xo.ContextCpu() if omp in ('0', '', 'serial') + else xo.ContextCpu(omp_num_threads='auto' if omp == 'auto' else int(omp)))) + +# ---------------------------------------------------------------------------- +# Build the machine (as in 002/004) +# ---------------------------------------------------------------------------- +env, line_b1, line_b2 = sim.load() +slot_len = line_b1.get_length() / sim.N_SLOTS +b_h_dist = slot_len / 2.0 + +sim.install_markers(line_b1, mirror=False, b_h_dist=b_h_dist) +sim.install_markers(line_b2, mirror=True, b_h_dist=b_h_dist) +geom, meta = sim.compute_geometry(line_b1, line_b2, b_h_dist, slot_len) + +# lattice octupoles (MO), kept exact in the third footprint variant to +# retain the lattice amplitude detuning (split elements are excluded from +# the maps, so splitting at them preserves them exactly) +mo_names = [nn for nn in line_b1.element_names if re.match(r'^mo\.', nn)] + +print(' building second-order maps between the beam-beam markers...') +red_b1 = line_b1.get_line_with_second_order_maps(split_at=sim.marker_names_b1) +red_b2 = line_b2.get_line_with_second_order_maps(split_at=sim.marker_names_b2) +print(f' ... and a variant keeping the {len(mo_names)} lattice octupoles ' + 'of beam 1 exact...') +red_mo_b1 = line_b1.get_line_with_second_order_maps( + split_at=sim.marker_names_b1 + mo_names) +for rl in (red_b1, red_b2, red_mo_b1): + rl.twiss_default['method'] = '4d' + rl.build_tracker(_context=sim.context) + +scheme_b1, scheme_b2 = mb.load_scheme() +slots_b1, slots_b2 = mb.all_filled_slots(scheme_b1, scheme_b2) +print(f' populated bunches: B1 = {len(slots_b1)}, B2 = {len(slots_b2)}') + +bb_b1 = sim.install_bb(red_b1, False, len(slots_b2)) +bb_b2 = sim.install_bb(red_b2, True, len(slots_b1)) + +# ---------------------------------------------------------------------------- +# 1) Self-consistent solve: 2 iterations orbit-only, 2 with dynamic beta +# ---------------------------------------------------------------------------- +print('Self-consistent solve (2 iterations fast_orbit):') +t0 = time.time() +sim.solve_self_consistent(red_b1, red_b2, bb_b1, bb_b2, + slots_b1, slots_b2, n_iter=2) +print('Self-consistent solve (2 more iterations with dynamic beta):') +mbtw_b1, mbtw_b2 = sim.solve_self_consistent( + red_b1, red_b2, bb_b1, bb_b2, slots_b1, slots_b2, n_iter=2, + dynamic_beta=True) +print(f' total solve time: {time.time() - t0:.1f} s') + +# ---------------------------------------------------------------------------- +# 2) Transfer the converged solution to the full thick lattice of beam 1 +# ---------------------------------------------------------------------------- +print('Installing the converged lenses on the full thick lattice (B1) and ' + 'on the maps+MO line...') +bb_thick_b1 = sim.install_bb(line_b1, False, len(slots_b2)) +bb_mo_b1 = sim.install_bb(red_mo_b1, False, len(slots_b2)) +sizes_b2 = sim.compute_sigmas(mbtw_b2, sim.marker_names_b2) +sizes_b1 = sim.compute_sigmas(mbtw_b1, sim.marker_names_b1) +for bb_dict in (bb_thick_b1, bb_mo_b1): + sim.update_opposing(bb_dict, mbtw_b2, slots_b2, sim.marker_names_b2, + sigmas_other=sizes_b2, sigmas_own=sizes_b1) + +zeta_b1 = np.array(slots_b1) * sim.ZETA_PER_SLOT + +# ---------------------------------------------------------------------------- +# 3) Footprints for the bunch families of the longest train +# ---------------------------------------------------------------------------- +# longest contiguous filled run of beam 1 +filled = np.asarray(scheme_b1) > 0 +best_len = best_start = cur_len = cur_start = 0 +for s in range(sim.N_SLOTS): + if filled[s]: + cur_start = s if cur_len == 0 else cur_start + cur_len += 1 + if cur_len > best_len: + best_len, best_start = cur_len, cur_start + else: + cur_len = 0 +train = list(range(best_start, best_start + best_len)) +print(f' longest train: {best_len} bunches starting at slot {best_start}') + +# 12 equidistant bunches along the train (first and last included) +pos_in_train = np.round(np.linspace(0, len(train) - 1, 12)).astype(int) +family = [(train[k], f'train bunch {k + 1}') for k in pos_in_train] + +# cross-check the transferred lattices on the family bunches +zeta_fam = np.array([sl for sl, _ in family]) * sim.ZETA_PER_SLOT +idx_fam = np.searchsorted(slots_b1, [sl for sl, _ in family]) +for label, transferred in (('thick', line_b1), ('maps+MO', red_mo_b1)): + mb_check = transferred.twiss_multibunch( + zeta_bunches=zeta_fam, mode='fast_orbit', show_progress=False) + dq_check = mb.wrap_frac_tune( + mb_check.qx - np.asarray(mbtw_b1.qx)[idx_fam]) + print(f' transfer check ({label} vs sector maps, family bunches): ' + f'max |dqx| = {np.max(np.abs(dq_check)):.2e}') + +# incoherent footprints: individual particles see the field of the opposing +# bunches with their OWN sizes (weak-strong), not the convolved coherent +# kick used for the rigid-bunch closed solution. NOTE: switched only AFTER +# the transfer check above, which must reproduce the (coherent) sector-map +# solution. +for bb in (list(bb_thick_b1.values()) + list(bb_mo_b1.values()) + + list(bb_b1.values())): + bb.coherent = False + +# Footprints on the full thick lattice, on the maps+MO line (exact +# octupoles between the maps -> keeps most of the lattice amplitude +# detuning) and on the plain second-order-map line (2nd-order Taylor arcs +# carry NO amplitude detuning -- its footprint contains only the (exact) +# beam-beam nonlinearity), all with the converged incoherent lenses. +LINES = (('thick', line_b1), ('maps+MO', red_mo_b1), ('maps', red_b1)) +SUFFIX = {'thick': '', 'maps+MO': '_mapmo', 'maps': '_map'} +print('Footprints (thick lattice vs maps + exact MO vs plain maps):') +footprints = {} +timing = {tag: 0.0 for tag, _ in LINES} +for sl, label in family: + fp = {} + for tag, line in LINES: + t0 = time.time() + # linear rescale on the beam-beam strength (as in the xmask + # footprint example): the footprint is computed at weak beam-beam + # (beambeam_scale = v0 and v0 + dv) and extrapolated linearly to + # the actual strength, avoiding resonance-distorted footprints. + fp[tag] = line.get_footprint( + nemitt_x=sim.nemitt, nemitt_y=sim.nemitt, + r_range=(0.3, 6), theta_range=(0.15, np.pi / 2 - 0.15), + freeze_longitudinal=True, zeta0=sl * sim.ZETA_PER_SLOT, + linear_rescale_on_knobs=[xt.LinearRescale( + knob_name='beambeam_scale', v0=0.0, dv=0.1)]) + fp[tag + '_t'] = time.time() - t0 + timing[tag] += fp[tag + '_t'] + footprints[sl] = dict(label=label) + for tag, _ in LINES: + footprints[sl]['qx' + SUFFIX[tag]] = fp[tag].qx + footprints[sl]['qy' + SUFFIX[tag]] = fp[tag].qy + print(f' slot {sl:4d} ({label:14s}): ' + + ' / '.join(f'{tag} {fp[tag + "_t"]:5.1f} s' for tag, _ in LINES) + + f' qx [{fp["thick"].qx.min():.4f}, {fp["thick"].qx.max():.4f}]') +print('footprint time: ' + + ', '.join(f'{tag} {timing[tag]:.0f} s' for tag, _ in LINES) + + ' -> speed-up vs thick: ' + + ', '.join(f'{tag} x{timing["thick"] / timing[tag]:.1f}' + for tag, _ in LINES[1:])) + +import pandas as pd +pd.to_pickle(footprints, os.path.join(mb.HERE, 'footprints_coll.pkl')) +print('saved footprints_coll.pkl') + +# ---------------------------------------------------------------------------- +# Plot: footprints colored by the bunch position in the train +# ---------------------------------------------------------------------------- +from matplotlib.cm import ScalarMappable +from matplotlib.colors import Normalize + +fig, axes = plt.subplots( + 1, 3, figsize=(18, 6.5), sharex=True, sharey=True) +cmap = plt.get_cmap('viridis') +norm = Normalize(vmin=1, vmax=len(train)) +for ax, suffix, title in ((axes[0], '', 'full thick lattice'), + (axes[1], '_mapmo', 'second-order maps\n' + '+ exact MO octupoles'), + (axes[2], '_map', 'second-order maps\n' + '(no lattice/octupole detuning)')): + for k, (sl, _) in zip(pos_in_train, family): + fp = footprints[sl] + color = cmap(norm(k + 1)) + ax.plot(fp['qx' + suffix], fp['qy' + suffix], color=color, lw=1) + ax.plot(fp['qx' + suffix].T, fp['qy' + suffix].T, color=color, lw=1) + ax.set_xlabel(r'$q_x$') + ax.set_title(title) +axes[0].set_ylabel(r'$q_y$') +fig.suptitle('Per-bunch tune footprints, LHC collision (head-on + BBLR)') +fig.colorbar(ScalarMappable(norm=norm, cmap=cmap), ax=list(axes), + label='bunch position in train') +plt.tight_layout() +plt.show() + + diff --git a/examples/lhc_multibunch_bb/lhc_mb_common.py b/examples/lhc_multibunch_bb/lhc_mb_common.py new file mode 100644 index 000000000..b587c6296 --- /dev/null +++ b/examples/lhc_multibunch_bb/lhc_mb_common.py @@ -0,0 +1,599 @@ +# copyright ############################### # +# This file is part of the Xtrack Package. # +# Copyright (c) CERN, 2024. # +# ######################################### # + +""" +Shared helpers for the LHC multi-bunch beam-beam examples and the regression +test ``xtrack/tests/test_lhc_multibunch_train.py``. + +The examples install 2D beam-beam elements +(``xfields.BeamBeamBiGaussianMultibunch2D``) for head-on and long-range (LR) +encounters at IP1/2/5/8 and find the per-bunch closed solution of the two +multi-bunch beams self-consistently -- either on the full thick lines or on +reduced lines where the arcs between the encounters are second-order Taylor +maps. + +All scenario configuration (beam momentum, bunch intensity, emittance, optics +file, IP set, number of LR encounters) lives in an :class:`LHCMultibunchBB` +instance; use the presets ``LHCMultibunchBB.injection()`` / +``LHCMultibunchBB.collision()``. The module holds no mutable state, so it can +be imported normally from several scenarios in one process. + +Model (following pytrain / TRAIN): + +* Encounter geometry: LR encounter ``n`` sits at ``n * b_h_dist`` from the IP, + ``b_h_dist = L / n_slots / 2`` (half a 25 ns slot). Beam-1 bunch ``b1`` meets + beam-2 bunch ``b2 = b1 + offset`` with + ``offset = round(2 * (s_marker - s_IP1) / slot_len)`` (mod n_slots) -> 0 at + IP1 and IP5, ~891 at IP2, ~2670 at IP8. +* Coherent (rigid-bunch) kick with the convolved pair size: + ``sigma_eff = sqrt(eps_n * (beta_b1 + beta_b2) / gamma)``, obtained by the + elements (``coherent=True``) from each beam's own sizes + ``sigma = sqrt(eps_n * beta / gamma)``. +* Beam separation = closed-orbit difference (crossing AND separation bumps, from + the live twiss) PLUS the geometric survey separation of the two rings. The + latter is ~0 in the common vacuum chamber and rises through the recombination + region to the 194 mm arc separation, which is what makes the LR encounters + beyond ~D1 negligible. + +The per-bunch macroparticle is labelled by its 25 ns slot through +``zeta = slot * ZETA_PER_SLOT``; the ``zeta_offset`` of each element encodes the +encounter slot offset so ``twiss_multibunch`` pairs the right bunches. +""" + +import os +import json +import numpy as np +from scipy.constants import c as clight + + +import xobjects as xo +import xtrack as xt +import xfields as xf + +HERE = os.path.dirname(os.path.abspath(__file__)) +DATA = os.path.join(HERE, '..', '..', 'test_data', 'lhc_2024') +SCHEME_FILE = os.path.join(DATA, '25ns_2460b_2448_2092_2239_144bpi_20inj.json') + + +def marker_name(name, mirror): + return name + ('_b2' if mirror else '_b1') + + +def wrap_frac_tune(v): + """Tune difference on the fractional-tune circle, wrapped to (-0.5, 0.5] + (fast-mode twiss returns fractional tunes while the bare reference may + carry an integer part).""" + return (np.asarray(v) + 0.5) % 1.0 - 0.5 + + +class LHCMultibunchBB: + """One multi-bunch beam-beam scenario: beam parameters, optics file and + encounter layout, plus all the machinery to build and solve it. + + Use the presets:: + + sim = LHCMultibunchBB.injection() # 450 GeV, BBLR only + sim = LHCMultibunchBB.collision() # 6.8 TeV squeezed, head-on + BBLR + + ``ips`` / ``nparasitic`` default from the environment variables + ``LHC_IPS`` / ``LHC_NPAR`` (falling back to 1,2,5,8 / 45). + + ``context`` selects the CPU context for all trackers and beam-beam + elements; default from the environment variable ``LHC_OMP`` (unset/``0`` + -> serial; a thread count or ``auto`` -> multi-threaded OpenMP kernels, + e.g. ``LHC_OMP=auto``). Prebuilt kernels exist for both flavours. + """ + + N_SLOTS = 3564 + ZETA_PER_SLOT = 25e-9 * clight # per-bunch zeta spacing [m] + + def __init__(self, p0c, bunch_intensity, nemitt, optics_file, + ips=None, nparasitic=None, context=None): + if context is None: + omp = os.environ.get('LHC_OMP', '0') + if omp in ('0', '', 'serial'): + context = xo.ContextCpu() + else: + context = xo.ContextCpu( + omp_num_threads=('auto' if omp == 'auto' else int(omp))) + self.context = context + if ips is None: + ips = [int(v) for v in + os.environ.get('LHC_IPS', '1,2,5,8').split(',')] + if nparasitic is None: + nparasitic = int(os.environ.get('LHC_NPAR', '45')) + self.p0c = p0c + energy = np.sqrt(p0c**2 + xt.PROTON_MASS_EV**2) + self.gamma0 = energy / xt.PROTON_MASS_EV + self.beta0 = p0c / energy + self.bunch_intensity = bunch_intensity + self.nemitt = nemitt + self.optics_file = optics_file + self.geom = None # set by compute_geometry + self.meta = None + self.ips = list(ips) + self.nparasitic = nparasitic + self.enc_names = [n for n, _, _ in self.encounter_specs()] + self.marker_names_b1 = [marker_name(n, False) for n in self.enc_names] + self.marker_names_b2 = [marker_name(n, True) for n in self.enc_names] + + @classmethod + def injection(cls, **kwargs): + """LHC injection: 450 GeV, 1.8e11 p/bunch, 1.5 um. The nominal + injection optics are used as-is: the separation bumps are kept ON (as + at real injection), so the beams DO NOT collide head-on and the + effect is long-range only (BBLR). The head-on elements are still + installed but act as "long-range" at the full IP separation.""" + return cls(p0c=450e9, bunch_intensity=1.8e11, nemitt=1.5e-6, + optics_file=os.path.join(DATA, 'injection_optics.madx'), + **kwargs) + + @classmethod + def collision(cls, **kwargs): + """LHC collision: 6.8 TeV, 1.1e11 p/bunch, 2.3 um, fully squeezed + R2025aRP 15 cm flat optics with end-of-levelling knobs, tunes/chroma + matched to 62.316/60.322, Q' = 10 (head-on at IP1/5 + BBLR). + + The squeezed optics of acc-models-lhc generate their knobs via MAD-X + matching, which xsuite cannot execute directly. Instead the FLATTENED + optics ``collision_optics_15cm_flat_2026.madx`` (the complete numeric + MAD-X global-variable state after optics + knobs + matching, produced + by ``test_data/lhc_2024/pytrain/regenerate_collision.py``) is loaded + on top of the sequence, exactly like ``injection_optics.madx``.""" + return cls(p0c=6800e9, bunch_intensity=1.1e11, nemitt=2.3e-6, + optics_file=os.path.join( + DATA, 'collision_optics_15cm_flat_2026.madx'), + **kwargs) + + # ------------------------------------------------------------------ + # Encounter bookkeeping + # ------------------------------------------------------------------ + def encounter_specs(self): + """Yield (name, ip, signed_n); signed_n == 0 is the head-on + encounter.""" + for ip in self.ips: + yield f'bb_ip{ip}_ho', ip, 0 + for n in range(1, self.nparasitic + 1): + yield f'bb_ip{ip}_r{n:02d}', ip, +n + yield f'bb_ip{ip}_l{n:02d}', ip, -n + + # ------------------------------------------------------------------ + # Loading + # ------------------------------------------------------------------ + def load(self): + """Load both LHC beams (sequence + this scenario's optics file). + Returns (env, line_b1, line_b2); the beam-2 line is reversed.""" + env = xt.load(os.path.join(DATA, 'lhc.seq'), format='madx', + reverse_lines=['lhcb2']) + env.lhcb1.particle_ref = xt.Particles(mass0=xt.PROTON_MASS_EV, + p0c=self.p0c) + env.lhcb2.particle_ref = xt.Particles(mass0=xt.PROTON_MASS_EV, + p0c=self.p0c) + env.vars.load(self.optics_file) + for ln in (env.lhcb1, env.lhcb2): + ln.twiss_default['method'] = '4d' + # no IP at the s=0 boundary (IP1 is at s=0 otherwise) + ln.cycle(name_first_element='ip3', inplace=True) + ln.build_tracker(_context=self.context) + return env, env.lhcb1, env.lhcb2 + + def install_markers(self, line, mirror, b_h_dist): + """Install the beam-beam markers. For the reversed beam-2 line the + left/right side is mirrored so a given marker name is the same + physical point in both beams.""" + env = line.env + places = [] + for name, ip, sn in self.encounter_specs(): + at = (-sn if mirror else sn) * b_h_dist + 1e-6 + places.append(env.place( + env.new(marker_name(name, mirror), xt.Marker), + at=at, from_=f'ip{ip}')) + line.insert(places) + + # ------------------------------------------------------------------ + # Encounter geometry (offset, convolved betas, survey separation) + # ------------------------------------------------------------------ + @staticmethod + def _survey_positions(sv, names): + r = sv.rows[names] + return np.stack([r.X, r.Y, r.Z], axis=1) # (n, 3) + + def compute_geometry(self, line_b1, line_b2, b_h_dist, slot_len): + """Compute per-encounter offset, convolved betas and geometric survey + separation (twiss + survey of both full beams, ~10 s with prebuilt + kernels).""" + print(' twiss + survey of both beams...') + tw1 = line_b1.twiss() + tw2 = line_b2.twiss() + sv1 = line_b1.survey() + sv2 = line_b2.survey() + + s_ip1 = tw1['s', 'ip1'] + # survey position of each IP for both beams (looked up once per IP) + ip_pos1 = {ip: np.array([sv1['X', f'ip{ip}'], sv1['Y', f'ip{ip}'], + sv1['Z', f'ip{ip}']]) for ip in self.ips} + ip_pos2 = {ip: np.array([sv2['X', f'ip{ip}'], sv2['Y', f'ip{ip}'], + sv2['Z', f'ip{ip}']]) for ip in self.ips} + m1 = self._survey_positions(sv1, self.marker_names_b1) + m2 = self._survey_positions(sv2, self.marker_names_b2) + + length = line_b1.get_length() + geom = {} + for j, (name, ip, sn) in enumerate(self.encounter_specs()): + n1, n2 = self.marker_names_b1[j], self.marker_names_b2[j] + s_marker = tw1['s', n1] + offset = int(round(2 * (s_marker - s_ip1) / slot_len)) % self.N_SLOTS + # Geometric (survey) separation of the two rings at this + # encounter, in beam 1's frame. Beam-2 survey is rotated 180 deg + # about the vertical (X,Z -> -X,-Z), then the SIGNED horizontal + # separation is obtained as in TRAIN/pytrain: the horizontal- + # plane distance times a sign from the direction of the + # separation vector relative to the ring azimuth (2*pi*s/L). + # This sign flips between IP1/IP5 and IP2/IP8 because the latter + # are rotated in the global frame -- it must be right for the + # long-range orbit. + s1 = m1[j] - ip_pos1[ip] + s2 = m2[j] - ip_pos2[ip] + s2 = np.array([-s2[0], s2[1], -s2[2]]) + d = s1 - s2 + ang = np.arctan2(d[2], d[0]) - 2 * np.pi * s_marker / length + ang = (ang + np.pi) % (2 * np.pi) - np.pi + xsign = 1.0 if abs(ang) <= np.pi / 2 else -1.0 + sep_x = float(np.hypot(d[0], d[2]) * xsign) + sep_y = float(d[1]) + geom[name] = dict( + ip=ip, + offset=offset, + betx_b1=float(tw1['betx', n1]), + bety_b1=float(tw1['bety', n1]), + betx_b2=float(tw2['betx', n2]), + bety_b2=float(tw2['bety', n2]), + sep_x=sep_x, sep_y=sep_y, + ) + meta = dict(bare_qx_b1=float(tw1.qx), bare_qy_b1=float(tw1.qy), + bare_qx_b2=float(tw2.qx), bare_qy_b2=float(tw2.qy)) + self.geom = geom + self.meta = meta + return geom, meta + + # ------------------------------------------------------------------ + # Filling scheme + # ------------------------------------------------------------------ + def windowed_slots(self, scheme_b1, scheme_b2, window): + """A bounded subset: a reference window plus the windows it collides + with at every distinct head-on offset (so all IPs get realistic + pairings).""" + ho_offsets = sorted({self.geom[f'bb_ip{ip}_ho']['offset'] + for ip in self.ips}) + # Use the longest contiguous filled run of beam 1 as the reference + # window (the filling is made of batches separated by gaps, so a + # window may be shorter than requested). Its LR/IP partners in beam 2 + # may or may not be filled -> realistic PACMAN structure at the + # window edges. + filled = scheme_b1 > 0 + best_len = best_start = cur_len = cur_start = 0 + for s in range(self.N_SLOTS): + if filled[s]: + cur_start = s if cur_len == 0 else cur_start + cur_len += 1 + if cur_len > best_len: + best_len, best_start = cur_len, cur_start + else: + cur_len = 0 + window = min(window, best_len) + ref_start = best_start + cand = set() + for o in ho_offsets: + for shift in (o, -o): + for k in range(window): + cand.add((ref_start + shift + k) % self.N_SLOTS) + return (sorted(s for s in cand if scheme_b1[s]), + sorted(s for s in cand if scheme_b2[s])) + + # ------------------------------------------------------------------ + # Beam-beam element installation and self-consistent solve + # ------------------------------------------------------------------ + def install_bb(self, line, mirror, n_other): + """Install one beam-beam element per encounter. + Returns {enc_name: element}.""" + env = line.env + places = [] + names = [] + for name, ip, sn in self.encounter_specs(): + e = self.geom[name] + # beam1 pairs b2 = b1 + offset (zeta_offset=+offset); + # beam2 pairs b1 = b2 - offset (zeta_offset=-offset) + zoff = (-e['offset'] if mirror else e['offset']) \ + * self.ZETA_PER_SLOT + # coherent (rigid-bunch) kick: the element convolves this beam's + # own size with each opposing bunch's size, sigma_eff^2 = + # sigma_own^2 + sigma_other^2 (statically equivalent to the + # previous (beta_b1 + beta_b2) * nemitt / gamma0) + own, oth = ('b2', 'b1') if mirror else ('b1', 'b2') + bb = xf.BeamBeamBiGaussianMultibunch2D( + num_bunches=max(n_other, 1), + zeta_offset=zoff, zeta_match_tol=0.4 * self.ZETA_PER_SLOT, + # ring is periodic in slots; encounter offsets are stored mod + # N_SLOTS, so the pairing must wrap around the ring + zeta_period=self.N_SLOTS * self.ZETA_PER_SLOT, + other_beam_q0=1.0, other_beam_beta0=self.beta0, + coherent=True, + sigma_x=np.sqrt(e[f'betx_{own}'] * self.nemitt / self.gamma0), + sigma_y=np.sqrt(e[f'bety_{own}'] * self.nemitt / self.gamma0), + other_beam_sigma_x=np.sqrt( + e[f'betx_{oth}'] * self.nemitt / self.gamma0), + other_beam_sigma_y=np.sqrt( + e[f'bety_{oth}'] * self.nemitt / self.gamma0), + _context=line._context) + elname = marker_name(name, mirror) + '_bb' + places.append(env.place(elname, bb, at=marker_name(name, mirror))) + names.append((name, elname)) + line.insert(places) + # 'beambeam_scale' knob scaling the strength of all lenses of this + # line (as in the xfields beam-beam config tools), e.g. for footprints + # with linear rescale on the beam-beam strength + line.vars['beambeam_scale'] = 1.0 + for name, elname in names: + line.element_refs[elname].scale_strength = line.vars['beambeam_scale'] + return {name: line[elname] for name, elname in names} + + def compute_sigmas(self, mbtw, marker_names): + """Per-encounter transverse sizes of a beam's bunches from their + LIVE per-bunch beta functions (dynamic beta). Returns (sigma_x, + sigma_y), each of shape (n_bunches, n_encounters). The convolution + of the two beams' sizes is done inside the elements + (``coherent=True``).""" + eg = self.nemitt / self.gamma0 # same convention as the static case + # mbtw['betx', names] resolves the marker rows once and slices the + # numpy columns of all bunch tables (fast multi-element access) + sigma_x = np.sqrt(mbtw['betx', marker_names] * eg) + sigma_y = np.sqrt(mbtw['bety', marker_names] * eg) + return sigma_x, sigma_y + + def update_opposing(self, bb_dict, mbtw_other, slots_other, + marker_names_other, sigmas_other=None, + sigmas_own=None, weights_other=None): + """Write the opposing beam's per-bunch orbit + geometric survey + separation into the beam-beam elements, in the frame of the line that + holds them; optionally also update the sizes (dynamic beta): + ``sigmas_other`` = the opposing bunches' per-bunch sizes + (n_other, n_enc), ``sigmas_own`` = this beam's bunch sizes + (n_own, n_enc) -- the elements hold ONE own size per encounter, so + the bunch AVERAGE is stored (the bunch-by-bunch resolution enters + through the opposing beam's per-bunch sizes of the partner + elements). ``weights_other`` optionally gives the opposing bunches' + populations (default: the scenario's ``bunch_intensity`` for all). + + Between the two (opposite-parity) beam lines x flips and y does not. + Matching TRAIN/pytrain (beam1 sees the opponent at co - sep, beam2 at + co + sep), and accounting for the beam-2 line x-flip, the survey + separation enters as ``-sep_x`` in x for BOTH beams.""" + # mbtw['x', names] resolves the marker rows once and slices the + # numpy columns of all bunch tables (fast multi-element access) + xs = -mbtw_other['x', marker_names_other] + ys = mbtw_other['y', marker_names_other] + zeta_other = np.array(slots_other) * self.ZETA_PER_SLOT + # NOTE: encounter slot offsets are stored mod N_SLOTS (a left LR at + # -n is stored as N_SLOTS-n; the IP2/IP8 pairings wrap around the + # ring for part of the bunches). The elements handle this via their + # `zeta_period` (set in install_bb), which makes the pairing periodic + # in the bunch-label axis. + # one reusable Particles object (same zeta/weight for all encounters) + if weights_other is None: + weights_other = self.bunch_intensity + p = xt.Particles(p0c=self.p0c, mass0=xt.PROTON_MASS_EV, q0=1.0, + x=np.zeros(len(zeta_other)), + y=np.zeros(len(zeta_other)), + zeta=zeta_other, weight=weights_other) + for j, name in enumerate(self.enc_names): + p.x[:] = xs[:, j] - self.geom[name]['sep_x'] + p.y[:] = ys[:, j] - self.geom[name]['sep_y'] + kw = {} + if sigmas_other is not None: + kw = dict(other_beam_sigma_x=sigmas_other[0][:, j], + other_beam_sigma_y=sigmas_other[1][:, j]) + bb = bb_dict[name] + if sigmas_own is not None: + bb.sigma_x = sigmas_own[0][:, j].mean() + bb.sigma_y = sigmas_own[1][:, j].mean() + bb.update_from_other_beam(p, **kw) + + def solve_self_consistent(self, line_b1, line_b2, bb_b1, bb_b2, + slots_b1, slots_b2, n_iter=3, chrom=False, + twiss_mode='fast_orbit', show_progress=True, + dynamic_beta=False, + weights_b1=None, weights_b2=None): + """Iterate twiss_multibunch on both beams, feeding each beam's + per-bunch closed orbit into the other beam's elements. Returns + (mbtw_b1, mbtw_b2). + + The iteration only feeds back orbits, so by default the orbit-only + fast twiss is used (roughly half the cost of the optics-carrying + default); pass ``twiss_mode='fast'`` to get optics in the returned tables. + + With ``dynamic_beta=True`` the per-bunch effective (convolved) sizes + of every encounter are recomputed at each iteration from the LIVE + per-bunch beta functions of both beams (dynamic beta) instead of + staying at their static values. This requires the optics-carrying + twiss, so mode='fast' is forced.""" + if dynamic_beta and twiss_mode == 'fast_orbit': + twiss_mode = 'fast' + zeta_b1 = np.array(slots_b1) * self.ZETA_PER_SLOT + zeta_b2 = np.array(slots_b2) * self.ZETA_PER_SLOT + mbtw_b1 = mbtw_b2 = None + for it in range(n_iter): + mbtw_b1 = line_b1.twiss_multibunch( + zeta_bunches=zeta_b1, chrom=chrom, mode=twiss_mode, + show_progress=show_progress) + mbtw_b2 = line_b2.twiss_multibunch( + zeta_bunches=zeta_b2, chrom=chrom, mode=twiss_mode, + show_progress=show_progress) + sizes_b1 = sizes_b2 = None + if dynamic_beta: + # per-bunch sizes of each beam at ITS OWN markers: used both + # as the opposing-beam sizes of the other beam's elements and + # (bunch-averaged) as the own sizes of this beam's elements + sizes_b1 = self.compute_sigmas(mbtw_b1, + self.marker_names_b1) + sizes_b2 = self.compute_sigmas(mbtw_b2, + self.marker_names_b2) + self.update_opposing(bb_b1, mbtw_b2, slots_b2, + self.marker_names_b2, + sigmas_other=sizes_b2, sigmas_own=sizes_b1, + weights_other=weights_b2) + self.update_opposing(bb_b2, mbtw_b1, slots_b1, + self.marker_names_b1, + sigmas_other=sizes_b1, sigmas_own=sizes_b2, + weights_other=weights_b1) + if show_progress: + print(f' iteration {it}: ' + f'B1 qx spread {np.ptp(mbtw_b1.qx):.2e}, ' + f'B2 qx spread {np.ptp(mbtw_b2.qx):.2e}') + return mbtw_b1, mbtw_b2 + + +# ---------------------------------------------------------------------------- +# Filling scheme (scenario-independent) +# ---------------------------------------------------------------------------- +def load_scheme(): + with open(SCHEME_FILE) as fid: + scheme = json.load(fid) + return np.array(scheme['schemebeam1']), np.array(scheme['schemebeam2']) + + +def all_filled_slots(scheme_b1, scheme_b2): + return (sorted(np.where(scheme_b1 > 0)[0].tolist()), + sorted(np.where(scheme_b2 > 0)[0].tolist())) + + +# ---------------------------------------------------------------------------- +# Results as a DataFrame +# ---------------------------------------------------------------------------- +def results_dataframe(mbtw, slots, bare_qx, bare_qy, ip='ip1', reverse=False): + """Per-bunch results as a pandas DataFrame, indexed by 25 ns slot. + + Columns: qx, qy (per-bunch tunes), dqx, dqy (beam-beam tune shift vs the + bare tune), x, y (closed orbit at the head-on marker of ``ip``, in the + physical frame -- for the reversed beam-2 line pass ``reverse=True`` to flip + x). ``dx``/``dy`` are the per-bunch orbit deviations from the beam average. + """ + import pandas as pd + marker = marker_name(f'bb_{ip}_ho', reverse) + x = mbtw['x', marker] * (-1.0 if reverse else 1.0) + y = mbtw['y', marker] + + df = pd.DataFrame({ + 'slot': np.asarray(slots), + 'qx': mbtw.qx, 'qy': mbtw.qy, + 'dqx': wrap_frac_tune(mbtw.qx - bare_qx), + 'dqy': wrap_frac_tune(mbtw.qy - bare_qy), + 'x': x, 'y': y, + 'dx': x - x.mean(), 'dy': y - y.mean(), + }).set_index('slot') + return df + + +# ---------------------------------------------------------------------------- +# Plot +# ---------------------------------------------------------------------------- +def plot_results(slots_b1, mbtw_b1, bare_qx, bare_qy, title_suffix=''): + import matplotlib.pyplot as plt + qx0, qy0 = bare_qx, bare_qy + co_x = mbtw_b1['x', marker_name('bb_ip1_ho', False)] + co_y = mbtw_b1['y', marker_name('bb_ip1_ho', False)] + # per-bunch orbit deviation from the bunch-averaged orbit (removes the common + # crossing/separation-bump orbit, leaving the bunch-by-bunch beam-beam part) + dco_x = (co_x - co_x.mean()) * 1e6 + dco_y = (co_y - co_y.mean()) * 1e6 + fig, axs = plt.subplots(2, 1, figsize=(9, 7)) + axs[0].plot(slots_b1, wrap_frac_tune(mbtw_b1.qx - qx0) * 1e3, '.', + label=r'$\Delta q_x$') + axs[0].plot(slots_b1, wrap_frac_tune(mbtw_b1.qy - qy0) * 1e3, '.', + label=r'$\Delta q_y$') + axs[0].set_xlabel('25 ns slot') + axs[0].set_ylabel(r'beam-beam tune shift [$10^{-3}$]') + axs[0].set_title('LHC: per-bunch beam-beam tune shift (B1)' + + title_suffix) + axs[0].legend() + axs[1].plot(slots_b1, dco_x, '.', label='x') + axs[1].plot(slots_b1, dco_y, '.', label='y') + axs[1].set_xlabel('25 ns slot') + axs[1].set_ylabel('orbit dev. from mean at IP1 [$\\mu$m]') + axs[1].set_title('Per-bunch beam-beam closed-orbit deviation at IP1 (B1)') + axs[1].legend() + plt.tight_layout() + return fig + + +def plot_global_quantities(slots_b1, mbtw_b1, slots_b2, mbtw_b2): + """Bunch-by-bunch orbit at IP1, beta* at IP1, tunes, chromaticity and + coupling |C-| of both beams, from mode='fast' MultiBunchTwiss results + (which carry per-bunch optics and global quantities).""" + import matplotlib.pyplot as plt + mk = {False: marker_name('bb_ip1_ho', False), + True: marker_name('bb_ip1_ho', True)} + + def at_ip1(mbtw, col, mirror): + return mbtw[col, mk[mirror]] + + fig, axs = plt.subplots(3, 2, figsize=(13, 10), sharex=True) + + ax = axs[0, 0] # orbit deviation at IP1 (physical frame for both beams) + for slots, mbtw, mirror, lab in [(slots_b1, mbtw_b1, False, 'B1'), + (slots_b2, mbtw_b2, True, 'B2')]: + sgn = -1.0 if mirror else 1.0 + x = sgn * at_ip1(mbtw, 'x', mirror) + y = at_ip1(mbtw, 'y', mirror) + ax.plot(slots, (x - x.mean()) * 1e6, '.', ms=3, label=f'{lab} x') + ax.plot(slots, (y - y.mean()) * 1e6, '.', ms=3, label=f'{lab} y') + ax.set_ylabel(r'orbit dev. at IP1 [$\mu$m]') + ax.set_title('Per-bunch closed-orbit deviation at IP1') + ax.legend(ncol=2, fontsize=8) + + ax = axs[0, 1] # beta* at IP1 + for slots, mbtw, mirror, lab in [(slots_b1, mbtw_b1, False, 'B1'), + (slots_b2, mbtw_b2, True, 'B2')]: + ax.plot(slots, at_ip1(mbtw, 'betx', mirror), '.', ms=3, + label=fr'{lab} $\beta_x^*$') + ax.plot(slots, at_ip1(mbtw, 'bety', mirror), '.', ms=3, + label=fr'{lab} $\beta_y^*$') + ax.set_ylabel(r'$\beta^*$ at IP1 [m]') + ax.set_title('Per-bunch $\\beta^*$ at IP1 (dynamic beta)') + ax.legend(ncol=2, fontsize=8) + + ax = axs[1, 0] # fractional tunes + for slots, mbtw, lab in [(slots_b1, mbtw_b1, 'B1'), + (slots_b2, mbtw_b2, 'B2')]: + ax.plot(slots, mbtw.qx_frac, '.', ms=3, label=f'{lab} $q_x$') + ax.plot(slots, mbtw.qy_frac, '.', ms=3, label=f'{lab} $q_y$') + ax.set_ylabel('fractional tune') + ax.set_title('Per-bunch tunes') + ax.legend(ncol=2, fontsize=8) + + ax = axs[1, 1] # chromaticity + for slots, mbtw, lab in [(slots_b1, mbtw_b1, 'B1'), + (slots_b2, mbtw_b2, 'B2')]: + ax.plot(slots, mbtw.dqx, '.', ms=3, label=f"{lab} $q'_x$") + ax.plot(slots, mbtw.dqy, '.', ms=3, label=f"{lab} $q'_y$") + ax.set_ylabel("chromaticity $q'$") + ax.set_title('Per-bunch chromaticity') + ax.legend(ncol=2, fontsize=8) + + ax = axs[2, 0] # coupling + for slots, mbtw, lab in [(slots_b1, mbtw_b1, 'B1'), + (slots_b2, mbtw_b2, 'B2')]: + ax.plot(slots, mbtw.c_minus, '.', ms=3, label=lab) + ax.set_xlabel('25 ns slot') + ax.set_ylabel('$|C^-|$') + ax.set_title('Per-bunch coupling (closest tune approach)') + ax.legend(fontsize=8) + + axs[2, 1].axis('off') + axs[1, 1].set_xlabel('25 ns slot') + axs[1, 1].tick_params(labelbottom=True) + plt.suptitle('Per-bunch optics & global quantities ' + '(mode="fast" multibunch twiss)') + plt.tight_layout() + return fig diff --git a/test_data/lhc_2024/25ns_2460b_2448_2092_2239_144bpi_20inj.json b/test_data/lhc_2024/25ns_2460b_2448_2092_2239_144bpi_20inj.json new file mode 100644 index 000000000..019fb54c1 --- /dev/null +++ b/test_data/lhc_2024/25ns_2460b_2448_2092_2239_144bpi_20inj.json @@ -0,0 +1 @@ +{"AGK":32781,"schemeGroup":"PHYSICS FILLS 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\ No newline at end of file diff --git a/test_data/lhc_2024/collision_optics_15cm_flat_2026.madx b/test_data/lhc_2024/collision_optics_15cm_flat_2026.madx new file mode 100644 index 000000000..ae63c1c72 --- /dev/null +++ b/test_data/lhc_2024/collision_optics_15cm_flat_2026.madx @@ -0,0 +1,3271 @@ +! Flattened LHC collision optics, 6.8 TeV, R2025aRP_A15cmC15cmA10mL200cm_Flat +! (acc-models-lhc branch 2026) with end-of-levelling knobs and tunes/chroma +! matched to 62.316/60.322, Q'=10. Generated by +! test_data/lhc_2024/pytrain/regenerate_collision.py + +pi := 3.141592653589793 ; +twopi := 6.283185307179586 ; +degrad := 57.29577951308232 ; +raddeg := 0.017453292519943295 ; +e := 2.718281828459045 ; +amu0 := 1.2566370614359173e-06 ; +emass := 0.00051099895 ; +mumass := 0.1056583755 ; +nmass := 0.93956542052 ; +umass := 0.93149410242 ; +pmass := 0.93827208816 ; +clight := 299792458.0 ; +qelect := 1.602176634e-19 ; +hbar := 6.582119569e-25 ; +erad := 2.8179403262e-15 ; +prad := 1.5346982671888944e-18 ; +twiss_tol := 1e-06 ; +lhclength := 26658.8832 ; +sep_arc := 0.194 ; +sep_ir3 := 0.224 ; +sep_ir4 := 0.42 ; +sep_ir7 := 0.224 ; +ip1ofs.b1 := 0.0 ; +ip1ofs.b2 := 0.0 ; +ip2ofs.b1 := 154.0 ; +ip2ofs.b2 := -154.0 ; +ip3ofs.b1 := 0.0 ; +ip3ofs.b2 := 0.0 ; +ip4ofs.b1 := -154.0 ; +ip4ofs.b2 := 154.0 ; +ip5ofs.b1 := -308.0 ; +ip5ofs.b2 := 308.0 ; +ip6ofs.b1 := -154.0 ; +ip6ofs.b2 := 154.0 ; +ip7ofs.b1 := 0.0 ; +ip7ofs.b2 := 0.0 ; +ip8ofs.b1 := 154.0 ; +ip8ofs.b2 := -154.0 ; +dsep1 := 85.913 ; +dsep2 := 63.295 ; +dsep3 := 26.493 ; +dsep4 := 71.901 ; +dsep5 := 85.913 ; +dsep7 := 39.7395 ; +dsep8 := 63.295 ; +aip1 := 0.0011290486746249162 ; +aip2 := 0.0015325053173680238 ; +aip3 := 0.0005661872342565977 ; +aip4 := 0.0015716041079483997 ; +aip5 := 0.0011290486746249162 ; +aip7 := 0.00037745817857865875 ; +aip8 := 0.0015325053173680238 ; +pip1 := 0.0 ; +pip1.l1 := 26658.8832 ; +pip2 := 3332.3604 ; +pip3 := 6664.7208 ; +pip4 := 9997.0812 ; +pip5 := 13329.4416 ; +pip6 := 16661.802 ; +pip7 := 19994.1624 ; +pip8 := 23315.3028 ; +hrf200 := 17820.0 ; +hrf400 := 35640.0 ; +a.mb := 0.005099988074009404 ; +ab.a12 := 0.005099988074009404 ; +ab.a23 := 0.005099988074009404 ; +ab.a34 := 0.005099988074009404 ; +ab.a45 := 0.005099988074009404 ; +ab.a56 := 0.005099988074009404 ; +ab.a67 := 0.005099988074009404 ; +ab.a78 := 0.005099988074009404 ; +ab.a81 := 0.005099988074009404 ; +l.acsca := 0.0 ; +l.acsph001 := 0.5125 ; +l.acsph002 := 0.5825 ; +l.adtkh := 0.0 ; +l.adtkv := 0.0 ; +l.apwl := 0.0 ; +l.bbcwb := 0.0 ; +l.bbcwe := 0.0 ; +l.bbcwi := 0.0 ; +l.bbcwt := 0.0 ; +l.bctdc := 0.0 ; +l.bctfr := 0.0 ; +l.bgcac := 0.0 ; +l.bgvca001 := 0.0 ; +l.bgvca003 := 0.0 ; +l.bgvca004 := 0.0 ; +l.bplh := 0.0 ; +l.bplv := 0.0 ; +l.bplx := 0.0 ; +l.bpm := 0.0 ; +l.bpmcs := 0.0 ; +l.bpmr := 0.0 ; +l.bpmra := 0.0 ; +l.bpmsa := 0.0 ; +l.bpmse := 0.0 ; +l.bpmsi002 := 0.0 ; +l.bpmsw002 := 0.0 ; +l.bpmsx002 := 0.0 ; +l.bpmsx003 := 0.0 ; +l.bpmsx004 := 0.0 ; +l.bpmsy002 := 0.0 ; +l.bpms_003 := 0.0 ; +l.bpmwa := 0.0 ; +l.bpmwb := 0.0 ; +l.bpmwc := 0.0 ; +l.bpmwe003 := 0.0 ; +l.bpmwe007 := 0.0 ; +l.bpmwe008 := 0.0 ; +l.bpmwe009 := 0.0 ; +l.bpmwf := 0.0 ; +l.bpmwg := 0.0 ; +l.bpmwi := 0.0 ; +l.bpmwj := 0.0 ; +l.bpmwt := 0.0 ; +l.bpmw_010 := 0.0 ; +l.bpmw_013 := 0.0 ; +l.bpmw_014 := 0.0 ; +l.bpmw_015 := 0.0 ; +l.bpmya := 0.0 ; +l.bpmyb := 0.0 ; +l.bpm_a := 0.0 ; +l.bptdh := 0.0 ; +l.bptdj := 0.0 ; +l.bptdv := 0.0 ; +l.bptuh := 0.0 ; +l.bptuj := 0.0 ; +l.bptut := 0.0 ; +l.bptuv := 0.0 ; +l.bptx := 0.0 ; +l.bqkh := 0.0 ; +l.bqkv := 0.0 ; +l.bqsh := 0.0 ; +l.bqsv := 0.0 ; +l.brana := 0.0 ; +l.branc := 0.0 ; +l.brand := 0.0 ; +l.bsrtm := 0.0 ; +l.bsrtmb := 0.0 ; +l.bsrto001 := 0.0 ; +l.bsrto002 := 0.0 ; +l.bsrtr := 0.0 ; +l.btvm := 0.0 ; +l.btvse := 0.0 ; +l.btvsi084 := 0.0 ; +l.btvsi088 := 0.5 ; +l.btvss074 := 0.0 ; +l.btvss075 := 0.75 ; +l.btvst064 := 0.0 ; +l.btvst065 := 0.0 ; +l.bws := 0.0 ; +l.dfbaa := 2.175 ; +l.dfbab := 2.675 ; +l.dfbac := 2.175 ; +l.dfbad := 2.675 ; +l.dfbae := 2.175 ; +l.dfbaf := 2.675 ; +l.dfbag := 2.175 ; +l.dfbah := 2.675 ; +l.dfbai := 2.175 ; +l.dfbaj := 2.675 ; +l.dfbak := 2.175 ; +l.dfbal := 2.675 ; +l.dfbam := 2.175 ; +l.dfban := 2.675 ; +l.dfbao := 2.175 ; +l.dfbap := 2.675 ; +l.dfbxa := 3.09 ; +l.dfbxb := 3.09 ; +l.dfbxc := 2.853 ; +l.dfbxd := 2.853 ; +l.dfbxe := 3.09 ; +l.dfbxf := 3.09 ; +l.dfbxg := 2.853 ; +l.dfbxh := 2.853 ; +l.leal := 12.7747 ; +l.lear := 12.7747 ; +l.lebl := 12.7747 ; +l.lebr := 12.7747 ; +l.lecl := 12.7747 ; +l.ledr := 13.7167 ; +l.leel := 13.7167 ; +l.lefl := 13.7167 ; +l.legr := 13.7167 ; +l.lehr := 13.7167 ; +l.leir := 13.7167 ; +l.lejl := 10.12 ; +l.lenla := 2.156 ; +l.lenra := 2.156 ; +l.lepla := 5.30935 ; +l.leplb := 5.30935 ; +l.lepra := 5.30935 ; +l.leprb := 5.30935 ; +l.mb := 14.3 ; +l.mbas2 := 3.0 ; +l.mbaw := 4.5406 ; +l.mbcs2 := 6.5 ; +l.mbls2 := 6.05 ; +l.mblw := 5.0 ; +l.mbrb := 9.45 ; +l.mbrc := 9.45 ; +l.mbrs := 9.45 ; +l.mbw := 3.4 ; +l.mbwmd := 2.62 ; +l.mbx := 9.45 ; +l.mbxw := 3.4 ; +l.mbxwh := 3.4 ; +l.mbxws := 0.78 ; +l.mbxwt := 1.53 ; +l.mcbch := 0.904 ; +l.mcbcv := 0.904 ; +l.mcbcv_unplugged := 0.904 ; +l.mcbh := 0.647 ; +l.mcbh_unplugged := 0.647 ; +l.mcbv := 0.647 ; +l.mcbv_unplugged := 0.647 ; +l.mcbwh := 1.7 ; +l.mcbwv := 1.7 ; +l.mcbxh := 0.45 ; +l.mcbxh_unplugged := 0.45 ; +l.mcbxv := 0.48 ; +l.mcbyh := 0.899 ; +l.mcbyv := 0.899 ; +l.mcd := 0.066 ; +l.mcd_unplugged := 0.066 ; +l.mco := 0.066 ; +l.mcosx := 0.138 ; +l.mcosx_unplugged := 0.138 ; +l.mcox := 0.137 ; +l.mcox_unplugged := 0.137 ; +l.mco_unplugged := 0.066 ; +l.mcs := 0.11 ; +l.mcssx := 0.132 ; +l.mcssx_unplugged := 0.132 ; +l.mcsx := 0.576 ; +l.mcs_unplugged := 0.11 ; +l.mctx := 0.615 ; +l.mgmwh := 0.5263 ; +l.mgmwh003 := 0.5263 ; +l.mgmwv := 0.5263 ; +l.mgmwv003 := 0.5263 ; +l.mkd := 1.348 ; +l.mkima02a := 0.0 ; +l.mkima192 := 0.0 ; +l.mkima193 := 0.0 ; +l.mkima262 := 0.0 ; +l.mkqa := 1.583 ; +l.mo := 0.32 ; +l.mo_unplugged := 0.32 ; +l.mq := 3.1 ; +l.mqm := 3.4 ; +l.mqmc := 2.4 ; +l.mqml := 4.8 ; +l.mqs := 0.32 ; +l.mqsx := 0.223 ; +l.mqt := 0.32 ; +l.mqtlh := 1.3 ; +l.mqtli := 1.3 ; +l.mqt_unplugged := 0.32 ; +l.mqwa := 3.108 ; +l.mqwb := 3.108 ; +l.mqxa := 6.37 ; +l.mqxb := 5.5 ; +l.mqy := 3.4 ; +l.ms := 0.369 ; +l.msda := 4.088 ; +l.msdb := 4.088 ; +l.msdb2 := 2.044 ; +l.msdc := 4.088 ; +l.msia := 4.0 ; +l.msib := 4.0 ; +l.mss := 0.369 ; +l.mss_unplugged := 0.369 ; +l.mu := 0.14 ; +l.omk := 0.0 ; +l.tanal := 3.492 ; +l.tanar := 3.492 ; +l.tanb := 0.605 ; +l.tanc := 3.492 ; +l.tas := 1.8 ; +l.tasb := 1.2 ; +l.tcapa019 := 1.0 ; +l.tcapa020 := 1.0 ; +l.tcapb := 0.2 ; +l.tcapc := 0.6 ; +l.tcapd := 0.626 ; +l.tccp := 0.07 ; +l.tccs := 0.004 ; +l.tcdd := 1.0 ; +l.tcddm := 1.0 ; +l.tcdqa := 0.0 ; +l.tcdqm := 1.05 ; +l.tcdsa := 3.012 ; +l.tcdsb := 3.012 ; +l.tcl := 1.0 ; +l.tcla := 1.0 ; +l.tcld := 0.6 ; +l.tclia := 1.0 ; +l.tclib := 1.0 ; +l.tclim := 0.5 ; +l.tcp := 0.6 ; +l.tcpc_002 := 0.0 ; +l.tcppm := 0.6 ; +l.tcsg := 1.0 ; +l.tcsp := 1.0 ; +l.tcspm := 1.0 ; +l.tctph := 1.0 ; +l.tctpv := 1.0 ; +l.tctwh := 1.0 ; +l.tctwv := 1.0 ; +l.tdisa := 1.565 ; +l.tdisb := 1.565 ; +l.tdisc := 1.565 ; +l.x1zdc001 := 0.6 ; +l.x1zdc002 := 0.3 ; +l.x2zdc001 := 1.5 ; +l.x2zdc002 := 1.5 ; +l.x5fca := 0.0 ; +l.x5fcb := 0.0 ; +l.x5zdc001 := 0.775 ; +l.x5zdc002 := 0.125 ; +l.xrph := 0.0 ; +l.xrpv := 0.0 ; +l.xrpv_003 := 0.013 ; +r0 := 0.0 ; +ds := 0.0004946988431789122 ; +ad1.l2 := 0.0015325053173680238 ; +ad1.l8 := 0.0015325053173680238 ; +ad1.lr1 := 0.00018817477910415268 ; +ad1.lr5 := 0.00018817477910415268 ; +ad1.r2 := 0.0015325053173680238 ; +ad1.r8 := 0.0015325053173680238 ; +ad2.l1 := 0.0011290486746249162 ; +ad2.l2 := 0.0015325053173680238 ; +ad2.l5 := 0.0011290486746249162 ; +ad2.l8 := 0.0015325053173680238 ; +ad2.r1 := 0.0011290486746249162 ; +ad2.r2 := 0.0015325053173680238 ; +ad2.r5 := 0.0011290486746249162 ; +ad2.r8 := 0.0015325053173680238 ; +ad3.l4 := 0.0015716041079483997 ; +ad3.lr3 := 0.0001887290780855326 ; +ad3.lr7 := 0.00018872908928932938 ; +ad3.r4 := 0.0015716041079483997 ; +ad4.l4 := 0.0015716041079483997 ; +ad4.lr3 := 0.0001887290780855326 ; +ad4.lr7 := 0.00018872908928932938 ; +ad4.r4 := 0.0015716041079483997 ; +ad34.lr3 := 0.0001887290780855326 ; +ad34.lr7 := 0.00018872908928932938 ; +kmax_mb := 8.3274 ; +kmax_mbaw := 0.6792 ; +kmax_mblw := 1.1 ; +kmax_mbrb_4.5k := 3.88 ; +kmax_mbrc_4.5k := 3.8 ; +kmax_mbrs_4.5k := 3.88 ; +kmax_mbw := 1.42 ; +kmax_mbwmd := 1.345 ; +kmax_mbx := 3.8 ; +kmax_mbxw := 1.282 ; +kmax_mbxwh := 1.24 ; +kmax_mbxws := 1.1 ; +kmax_mbxwt := 1.68 ; +kmax_mcbch := 3.11 ; +kmax_mcbch_4.5k := 2.33 ; +kmax_mcbcv := 3.11 ; +kmax_mcbcv_4.5k := 2.33 ; +kmax_mcbh := 2.93 ; +kmax_mcbv := 2.93 ; +kmax_mcbwh := 1.1 ; +kmax_mcbwv := 1.1 ; +kmax_mcbxh := 3.35 ; +kmax_mcbxv := 3.26 ; +kmax_mcbyh_4.5k := 2.5 ; +kmax_mcbyv_4.5k := 2.5 ; +kmax_mcd := 28800000.0 ; +kmax_mco := 48900.0 ; +kmax_mcosx := 58080.0 ; +kmax_mcox := 55380.0 ; +kmax_mcs := 3260.0 ; +kmax_mcssx := 754.0 ; +kmax_mcsx := 208.0 ; +kmax_mctx := 847200000.0 ; +kmax_mo := 378600.0 ; +kmax_mq := 223.0 ; +kmax_mqm := 200.0 ; +kmax_mqm_4.5k := 160.0 ; +kmax_mqmc := 200.0 ; +kmax_mqml := 200.0 ; +kmax_mqml_4.5k := 160.0 ; +kmax_mqs := 123.0 ; +kmax_mqsx := 80.0 ; +kmax_mqt := 123.0 ; +kmax_mqtlh_4.5k := 90.0 ; +kmax_mqtli := 125.0 ; +kmax_mqwa := 35.0 ; +kmax_mqwb := 30.0 ; +kmax_mqxa := 205.0 ; +kmax_mqxb := 205.0 ; +kmax_mqy_4.5k := 160.0 ; +kmax_ms := 8860.0 ; +kmax_msda := 0.8 ; +kmax_msdb := 0.99 ; +kmax_msdb2 := 0.99 ; +kmax_msdc := 1.17 ; +kmax_msia := 0.76 ; +kmax_msib := 1.13 ; +kmax_mss := 8860.0 ; +kmin_mb := 0.246 ; +kmin_mbaw := -0.6792 ; +kmin_mblw := -1.1 ; +kmin_mbrb_4.5k := 0.126 ; +kmin_mbrc_4.5k := 0.104 ; +kmin_mbrs_4.5k := 0.132 ; +kmin_mbw := 0.036 ; +kmin_mbwmd := 0.037 ; +kmin_mbx := 0.131 ; +kmin_mbxw := 0.031 ; +kmin_mbxwh := -1.24 ; +kmin_mbxws := -1.1 ; +kmin_mbxwt := 0.042 ; +kmin_mcbch := -3.11 ; +kmin_mcbch_4.5k := -2.33 ; +kmin_mcbcv := -3.11 ; +kmin_mcbcv_4.5k := -2.33 ; +kmin_mcbh := -2.93 ; +kmin_mcbv := -2.93 ; +kmin_mcbwh := -1.1 ; +kmin_mcbwv := -1.1 ; +kmin_mcbxh := -3.35 ; +kmin_mcbxv := -3.26 ; +kmin_mcbyh_4.5k := -2.5 ; +kmin_mcbyv_4.5k := -2.5 ; +kmin_mcd := -28800000.0 ; +kmin_mco := -48900.0 ; +kmin_mcosx := -58080.0 ; +kmin_mcox := -55380.0 ; +kmin_mcs := -3260.0 ; +kmin_mcssx := -754.0 ; +kmin_mcsx := -208.0 ; +kmin_mctx := -847200000.0 ; +kmin_mo := -378600.0 ; +kmin_mq := 6.575 ; +kmin_mqm := 4.453 ; +kmin_mqm_4.5k := 4.455 ; +kmin_mqmc := 4.453 ; +kmin_mqml := 4.453 ; +kmin_mqml_4.5k := 4.455 ; +kmin_mqs := -123.0 ; +kmin_mqsx := -80.0 ; +kmin_mqt := -123.0 ; +kmin_mqtlh_4.5k := -90.0 ; +kmin_mqtli := -125.0 ; +kmin_mqwa := 1.873 ; +kmin_mqwb := -30.0 ; +kmin_mqxa := 5.71 ; +kmin_mqxb := 5.999 ; +kmin_mqy_4.5k := 3.546 ; +kmin_ms := -8860.0 ; +kmin_msda := 0.021 ; +kmin_msdb := 0.026 ; +kmin_msdb2 := 0.026 ; +kmin_msdc := 0.031 ; +kmin_msia := 0.04 ; +kmin_msib := 0.059 ; +kmin_mss := -8860.0 ; +imax_mb := 11850.0 ; +imax_mbaw := 6000.0 ; +imax_mblw := 5850.0 ; +imax_mbrb_4.5k := 6150.0 ; +imax_mbrc_4.5k := 4400.0 ; +imax_mbrs_4.5k := 5860.0 ; +imax_mbw := 720.0 ; +imax_mbwmd := 550.0 ; +imax_mbx := 5800.0 ; +imax_mbxw := 750.0 ; +imax_mbxwh := 750.0 ; +imax_mbxws := 780.0 ; +imax_mbxwt := 600.0 ; +imax_mcbch := 100.0 ; +imax_mcbch_4.5k := 80.0 ; +imax_mcbcv := 100.0 ; +imax_mcbcv_4.5k := 80.0 ; +imax_mcbh := 55.0 ; +imax_mcbv := 55.0 ; +imax_mcbwh := 500.0 ; +imax_mcbwv := 500.0 ; +imax_mcbxh := 550.0 ; +imax_mcbxv := 550.0 ; +imax_mcbyh_4.5k := 72.0 ; +imax_mcbyv_4.5k := 72.0 ; +imax_mcd := 550.0 ; +imax_mco := 100.0 ; +imax_mcosx := 100.0 ; +imax_mcox := 100.0 ; +imax_mcs := 550.0 ; +imax_mcssx := 100.0 ; +imax_mcsx := 100.0 ; +imax_mctx := 80.0 ; +imax_mo := 550.0 ; +imax_mq := 11870.0 ; +imax_mqm := 5390.0 ; +imax_mqm_4.5k := 4310.0 ; +imax_mqmc := 5390.0 ; +imax_mqml := 5390.0 ; +imax_mqml_4.5k := 4310.0 ; +imax_mqs := 550.0 ; +imax_mqsx := 550.0 ; +imax_mqt := 550.0 ; +imax_mqtlh_4.5k := 400.0 ; +imax_mqtli := 550.0 ; +imax_mqwa := 710.0 ; +imax_mqwb := 600.0 ; +imax_mqxa := 7180.0 ; +imax_mqxb := 11960.0 ; +imax_mqy_4.5k := 3610.0 ; +imax_ms := 550.0 ; +imax_msda := 880.0 ; +imax_msdb := 880.0 ; +imax_msdb2 := 880.0 ; +imax_msdc := 880.0 ; +imax_msia := 950.0 ; +imax_msib := 950.0 ; +imax_mss := 550.0 ; +acbch10.l1b1 := 0.0 ; +acbch10.l2b2 := 0.0 ; +acbch10.l3b1 := 0.0 ; +acbch10.l4b2 := 0.0 ; +acbch10.l5b1 := 0.0 ; +acbch10.l6b2 := 0.0 ; +acbch10.l7b1 := 0.0 ; +acbch10.l8b2 := 0.0 ; +acbch10.r1b2 := 0.0 ; +acbch10.r2b1 := 0.0 ; +acbch10.r3b2 := 0.0 ; +acbch10.r4b1 := 0.0 ; +acbch10.r5b2 := 0.0 ; +acbch10.r6b1 := 0.0 ; +acbch10.r7b2 := 0.0 ; +acbch10.r8b1 := 0.0 ; +acbch5.l1b2 := 1.0842700856988e-05 ; +acbch5.l5b2 := 0.0 ; +acbch5.l8b1 := 0.0 ; +acbch5.r1b1 := 1.295964687348e-05 ; +acbch5.r2b2 := 0.0 ; +acbch5.r5b1 := 0.0 ; +acbch6.l1b1 := -1.316591303352e-05 ; +acbch6.l2b2 := -0.0 ; +acbch6.l3b1 := 0.0 ; +acbch6.l5b1 := 0.0 ; +acbch6.l7b1 := 0.0 ; +acbch6.l8b2 := -0.0 ; +acbch6.r1b2 := -1.476337150188e-05 ; +acbch6.r2b1 := -0.0 ; +acbch6.r3b2 := 0.0 ; +acbch6.r5b2 := 0.0 ; +acbch6.r7b2 := 0.0 ; +acbch6.r8b1 := -0.0 ; +acbch7.l1b2 := -0.0 ; +acbch7.l2b1 := -0.0 ; +acbch7.l3b2 := 0.0 ; +acbch7.l4b1 := 0.0 ; +acbch7.l5b2 := -0.0 ; +acbch7.l7b2 := 0.0 ; +acbch7.l8b1 := -0.0 ; +acbch7.r1b1 := 0.0 ; +acbch7.r2b2 := -0.0 ; +acbch7.r3b1 := 0.0 ; +acbch7.r4b2 := 0.0 ; +acbch7.r5b1 := -0.0 ; +acbch7.r7b1 := 0.0 ; +acbch7.r8b2 := -0.0 ; +acbch8.l1b1 := -0.0 ; +acbch8.l2b2 := 0.0 ; +acbch8.l3b1 := 0.0 ; +acbch8.l4b2 := 0.0 ; +acbch8.l5b1 := -0.0 ; +acbch8.l6b2 := 0.0 ; +acbch8.l7b1 := 0.0 ; +acbch8.l8b2 := 0.0 ; +acbch8.r1b2 := -0.0 ; +acbch8.r2b1 := 0.0 ; +acbch8.r3b2 := 0.0 ; +acbch8.r4b1 := 0.0 ; +acbch8.r5b2 := -0.0 ; +acbch8.r6b1 := 0.0 ; +acbch8.r7b2 := 0.0 ; +acbch8.r8b1 := 0.0 ; +acbch9.l1b2 := 0.0 ; +acbch9.l2b1 := 0.0 ; +acbch9.l3b2 := 0.0 ; +acbch9.l4b1 := 0.0 ; +acbch9.l5b2 := 0.0 ; +acbch9.l6b1 := 0.0 ; +acbch9.l7b2 := 0.0 ; +acbch9.l8b1 := 0.0 ; +acbch9.r1b1 := 0.0 ; +acbch9.r2b2 := 0.0 ; +acbch9.r3b1 := 0.0 ; +acbch9.r4b2 := 0.0 ; +acbch9.r5b1 := 0.0 ; +acbch9.r6b2 := 0.0 ; +acbch9.r7b1 := 0.0 ; +acbch9.r8b2 := 0.0 ; +acbchs5.l8b1 := 5.9369115921800004e-08 ; +acbchs5.l8b2 := 3.11670901518e-07 ; +acbchs5.r2b1 := -2.28101950779e-06 ; +acbchs5.r2b2 := -3.74705525253e-07 ; +acbcv10.l1b2 := 0.0 ; +acbcv10.l2b1 := 0.0 ; +acbcv10.l3b2 := 0.0 ; +acbcv10.l4b1 := 0.0 ; +acbcv10.l5b2 := 0.0 ; +acbcv10.l6b1 := 0.0 ; +acbcv10.l7b2 := 0.0 ; +acbcv10.l8b1 := 0.0 ; +acbcv10.r1b1 := 0.0 ; +acbcv10.r2b2 := 0.0 ; +acbcv10.r3b1 := 0.0 ; +acbcv10.r4b2 := 0.0 ; +acbcv10.r5b1 := 0.0 ; +acbcv10.r6b2 := 0.0 ; +acbcv10.r7b1 := 0.0 ; +acbcv10.r8b2 := 0.0 ; +acbcv5.l1b1 := 0.0 ; +acbcv5.l5b1 := 2.8389354735360003e-07 ; +acbcv5.l8b2 := 0.0 ; +acbcv5.r1b2 := 0.0 ; +acbcv5.r2b1 := 0.0 ; +acbcv5.r5b2 := 2.3728216473599998e-07 ; +acbcv6.l1b2 := 0.0 ; +acbcv6.l2b1 := -0.0 ; +acbcv6.l3b2 := 0.0 ; +acbcv6.l5b2 := -2.6868279747479997e-05 ; +acbcv6.l7b2 := 0.0 ; +acbcv6.l8b1 := -0.0 ; +acbcv6.r1b1 := 0.0 ; +acbcv6.r2b2 := -0.0 ; +acbcv6.r3b1 := 0.0 ; +acbcv6.r5b1 := -2.4734786800559998e-05 ; +acbcv6.r7b1 := 0.0 ; +acbcv6.r8b2 := -0.0 ; +acbcv7.l1b1 := -0.0 ; +acbcv7.l2b2 := -0.0 ; +acbcv7.l3b1 := 0.0 ; +acbcv7.l4b2 := 0.0 ; +acbcv7.l5b1 := -0.0 ; +acbcv7.l7b1 := 0.0 ; +acbcv7.l8b2 := -0.0 ; +acbcv7.r1b2 := -0.0 ; +acbcv7.r2b1 := -0.0 ; +acbcv7.r3b2 := 0.0 ; +acbcv7.r4b1 := 0.0 ; +acbcv7.r5b2 := -0.0 ; +acbcv7.r7b2 := 0.0 ; +acbcv7.r8b1 := -0.0 ; +acbcv8.l1b2 := 0.0 ; +acbcv8.l2b1 := 0.0 ; +acbcv8.l3b2 := 0.0 ; +acbcv8.l4b1 := 0.0 ; +acbcv8.l5b2 := -0.0 ; +acbcv8.l6b1 := 0.0 ; +acbcv8.l7b2 := 0.0 ; +acbcv8.l8b1 := 0.0 ; +acbcv8.r1b1 := 0.0 ; +acbcv8.r2b2 := 0.0 ; +acbcv8.r3b1 := 0.0 ; +acbcv8.r4b2 := 0.0 ; +acbcv8.r5b1 := -0.0 ; +acbcv8.r6b2 := 0.0 ; +acbcv8.r7b1 := 0.0 ; +acbcv8.r8b2 := 0.0 ; +acbcv9.l1b1 := 0.0 ; +acbcv9.l2b2 := 0.0 ; +acbcv9.l3b1 := 0.0 ; +acbcv9.l4b2 := 0.0 ; +acbcv9.l5b1 := 0.0 ; +acbcv9.l6b2 := 0.0 ; +acbcv9.l7b1 := 0.0 ; +acbcv9.l8b2 := 0.0 ; +acbcv9.r1b2 := 0.0 ; +acbcv9.r2b1 := 0.0 ; +acbcv9.r3b2 := 0.0 ; +acbcv9.r4b1 := 0.0 ; +acbcv9.r5b2 := 0.0 ; +acbcv9.r6b1 := 0.0 ; +acbcv9.r7b2 := 0.0 ; +acbcv9.r8b1 := 0.0 ; +acbcvs5.l8b1 := -1.6203906462688e-05 ; +acbcvs5.l8b2 := 3.1012739572713096e-05 ; +acbcvs5.r2b1 := 4.07226985828e-05 ; +acbcvs5.r2b2 := -2.48710392874e-05 ; +acbh11.l1b2 := 0.0 ; +acbh11.l2b1 := 0.0 ; +acbh11.l3b2 := 0.0 ; +acbh11.l4b1 := 0.0 ; +acbh11.l5b2 := 0.0 ; +acbh11.l6b1 := 0.0 ; +acbh11.l7b2 := 0.0 ; +acbh11.l8b1 := 0.0 ; +acbh11.r1b1 := 0.0 ; +acbh11.r2b2 := 0.0 ; +acbh11.r3b1 := 0.0 ; +acbh11.r4b2 := 0.0 ; +acbh11.r5b1 := 0.0 ; +acbh11.r6b2 := 0.0 ; +acbh11.r7b1 := 0.0 ; +acbh11.r8b2 := 0.0 ; +acbh12.l1b1 := 0.0 ; +acbh12.l2b2 := 0.0 ; +acbh12.l3b1 := 0.0 ; +acbh12.l4b2 := 0.0 ; +acbh12.l5b1 := 0.0 ; +acbh12.l6b2 := 0.0 ; +acbh12.l7b1 := 0.0 ; +acbh12.l8b2 := 0.0 ; +acbh12.r1b2 := -0.0 ; +acbh12.r2b1 := 0.0 ; +acbh12.r3b2 := 0.0 ; +acbh12.r4b1 := 0.0 ; +acbh12.r5b2 := -0.0 ; +acbh12.r6b1 := 0.0 ; +acbh12.r7b2 := 0.0 ; +acbh12.r8b1 := 0.0 ; +acbh13.l1b2 := 0.0 ; +acbh13.l2b1 := 0.0 ; +acbh13.l3b2 := 0.0 ; +acbh13.l4b1 := 0.0 ; +acbh13.l5b2 := 0.0 ; +acbh13.l6b1 := 0.0 ; +acbh13.l7b2 := 0.0 ; +acbh13.l8b1 := 0.0 ; +acbh13.r1b1 := -0.0 ; +acbh13.r2b2 := 0.0 ; +acbh13.r3b1 := 0.0 ; +acbh13.r4b2 := 0.0 ; +acbh13.r5b1 := -0.0 ; +acbh13.r6b2 := 0.0 ; +acbh13.r7b1 := 0.0 ; +acbh13.r8b2 := 0.0 ; +acbh14.l1b1 := 0.0 ; +acbh14.l2b2 := 0.0 ; +acbh14.l3b1 := 0.0 ; +acbh14.l4b2 := 0.0 ; +acbh14.l5b1 := 0.0 ; +acbh14.l6b2 := 0.0 ; +acbh14.l7b1 := 0.0 ; +acbh14.l8b2 := 0.0 ; +acbh14.r1b2 := 0.0 ; +acbh14.r2b1 := 0.0 ; +acbh14.r3b2 := 0.0 ; +acbh14.r4b1 := 0.0 ; +acbh14.r5b2 := 0.0 ; +acbh14.r6b1 := 0.0 ; +acbh14.r7b2 := 0.0 ; +acbh14.r8b1 := 0.0 ; +acbh15.l1b2 := -0.0 ; +acbh15.l2b1 := 0.0 ; +acbh15.l3b2 := 0.0 ; +acbh15.l4b1 := 0.0 ; +acbh15.l5b2 := -0.0 ; +acbh15.l6b1 := 0.0 ; +acbh15.l7b2 := 0.0 ; +acbh15.l8b1 := 0.0 ; +acbh15.r1b1 := 0.0 ; +acbh15.r2b2 := 0.0 ; +acbh15.r3b1 := 0.0 ; +acbh15.r4b2 := 0.0 ; +acbh15.r5b1 := 0.0 ; +acbh15.r6b2 := 0.0 ; +acbh15.r7b1 := 0.0 ; +acbh15.r8b2 := 0.0 ; +acbh16.l1b1 := 0.0 ; +acbh16.l2b2 := 0.0 ; +acbh16.l3b1 := 0.0 ; +acbh16.l4b2 := 0.0 ; +acbh16.l5b1 := 0.0 ; +acbh16.l6b2 := 0.0 ; +acbh16.l7b1 := 0.0 ; +acbh16.l8b2 := 0.0 ; +acbh16.r1b2 := 0.0 ; +acbh16.r2b1 := 0.0 ; +acbh16.r3b2 := 0.0 ; +acbh16.r4b1 := 0.0 ; +acbh16.r5b2 := 0.0 ; +acbh16.r6b1 := 0.0 ; +acbh16.r7b2 := 0.0 ; +acbh16.r8b1 := 0.0 ; +acbh17.l1b2 := 0.0 ; +acbh17.l2b1 := 0.0 ; +acbh17.l3b2 := 0.0 ; +acbh17.l4b1 := 0.0 ; +acbh17.l5b2 := 0.0 ; +acbh17.l6b1 := 0.0 ; +acbh17.l7b2 := 0.0 ; +acbh17.l8b1 := 0.0 ; +acbh17.r1b1 := 0.0 ; +acbh17.r2b2 := 0.0 ; +acbh17.r3b1 := 0.0 ; +acbh17.r4b2 := 0.0 ; +acbh17.r5b1 := 0.0 ; +acbh17.r6b2 := 0.0 ; +acbh17.r7b1 := 0.0 ; +acbh17.r8b2 := 0.0 ; +acbh18.l1b1 := 0.0 ; +acbh18.l2b2 := 0.0 ; +acbh18.l3b1 := 0.0 ; +acbh18.l4b2 := 0.0 ; +acbh18.l5b1 := 0.0 ; +acbh18.l6b2 := 0.0 ; +acbh18.l7b1 := 0.0 ; +acbh18.l8b2 := 0.0 ; +acbh18.r1b2 := 0.0 ; +acbh18.r2b1 := 0.0 ; +acbh18.r3b2 := 0.0 ; +acbh18.r4b1 := 0.0 ; +acbh18.r5b2 := 0.0 ; +acbh18.r6b1 := 0.0 ; +acbh18.r7b2 := 0.0 ; +acbh18.r8b1 := 0.0 ; +acbh19.l1b2 := 0.0 ; +acbh19.l2b1 := 0.0 ; +acbh19.l3b2 := 0.0 ; +acbh19.l4b1 := 0.0 ; +acbh19.l5b2 := 0.0 ; +acbh19.l6b1 := 0.0 ; +acbh19.l7b2 := 0.0 ; +acbh19.l8b1 := 0.0 ; +acbh19.r1b1 := 0.0 ; +acbh19.r2b2 := 0.0 ; +acbh19.r3b1 := 0.0 ; +acbh19.r4b2 := 0.0 ; +acbh19.r5b1 := 0.0 ; +acbh19.r6b2 := 0.0 ; +acbh19.r7b1 := 0.0 ; +acbh19.r8b2 := 0.0 ; +acbh20.l1b1 := 0.0 ; +acbh20.l2b2 := 0.0 ; +acbh20.l3b1 := 0.0 ; +acbh20.l4b2 := 0.0 ; +acbh20.l5b1 := 0.0 ; +acbh20.l6b2 := 0.0 ; +acbh20.l7b1 := 0.0 ; +acbh20.l8b2 := 0.0 ; +acbh20.r1b2 := 0.0 ; +acbh20.r2b1 := 0.0 ; +acbh20.r3b2 := 0.0 ; +acbh20.r4b1 := 0.0 ; +acbh20.r5b2 := 0.0 ; +acbh20.r6b1 := 0.0 ; +acbh20.r7b2 := 0.0 ; +acbh20.r8b1 := 0.0 ; +acbh21.l1b2 := 0.0 ; +acbh21.l2b1 := 0.0 ; +acbh21.l3b2 := 0.0 ; +acbh21.l4b1 := 0.0 ; +acbh21.l5b2 := 0.0 ; +acbh21.l6b1 := 0.0 ; +acbh21.l7b2 := 0.0 ; +acbh21.l8b1 := 0.0 ; +acbh21.r1b1 := 0.0 ; +acbh21.r2b2 := 0.0 ; +acbh21.r3b1 := 0.0 ; +acbh21.r4b2 := 0.0 ; +acbh21.r5b1 := 0.0 ; +acbh21.r6b2 := 0.0 ; +acbh21.r7b1 := 0.0 ; +acbh21.r8b2 := 0.0 ; +acbh22.l1b1 := 0.0 ; +acbh22.l2b2 := 0.0 ; +acbh22.l3b1 := 0.0 ; +acbh22.l4b2 := 0.0 ; +acbh22.l5b1 := 0.0 ; +acbh22.l6b2 := 0.0 ; +acbh22.l7b1 := 0.0 ; +acbh22.l8b2 := 0.0 ; +acbh22.r1b2 := 0.0 ; +acbh22.r2b1 := 0.0 ; +acbh22.r3b2 := 0.0 ; +acbh22.r4b1 := 0.0 ; +acbh22.r5b2 := 0.0 ; +acbh22.r6b1 := 0.0 ; +acbh22.r7b2 := 0.0 ; +acbh22.r8b1 := 0.0 ; +acbh23.l1b2 := 0.0 ; +acbh23.l2b1 := 0.0 ; +acbh23.l3b2 := 0.0 ; +acbh23.l4b1 := 0.0 ; +acbh23.l5b2 := 0.0 ; +acbh23.l6b1 := 0.0 ; +acbh23.l7b2 := 0.0 ; +acbh23.l8b1 := 0.0 ; +acbh23.r1b1 := 0.0 ; +acbh23.r2b2 := 0.0 ; +acbh23.r3b1 := 0.0 ; +acbh23.r4b2 := 0.0 ; +acbh23.r5b1 := 0.0 ; +acbh23.r6b2 := 0.0 ; +acbh23.r7b1 := 0.0 ; +acbh23.r8b2 := 0.0 ; +acbh24.l1b1 := 0.0 ; +acbh24.l2b2 := 0.0 ; +acbh24.l3b1 := 0.0 ; +acbh24.l4b2 := 0.0 ; +acbh24.l5b1 := 0.0 ; +acbh24.l6b2 := 0.0 ; +acbh24.l7b1 := 0.0 ; +acbh24.l8b2 := 0.0 ; +acbh24.r1b2 := 0.0 ; +acbh24.r2b1 := 0.0 ; +acbh24.r3b2 := 0.0 ; +acbh24.r4b1 := 0.0 ; +acbh24.r5b2 := 0.0 ; +acbh24.r6b1 := 0.0 ; +acbh24.r7b2 := 0.0 ; +acbh24.r8b1 := 0.0 ; +acbh25.l1b2 := 0.0 ; +acbh25.l2b1 := 0.0 ; +acbh25.l3b2 := 0.0 ; +acbh25.l4b1 := 0.0 ; +acbh25.l5b2 := 0.0 ; +acbh25.l6b1 := 0.0 ; +acbh25.l7b2 := 0.0 ; +acbh25.l8b1 := 0.0 ; +acbh25.r1b1 := 0.0 ; +acbh25.r2b2 := 0.0 ; +acbh25.r3b1 := 0.0 ; +acbh25.r4b2 := 0.0 ; +acbh25.r5b1 := 0.0 ; +acbh25.r6b2 := 0.0 ; +acbh25.r7b1 := 0.0 ; +acbh25.r8b2 := 0.0 ; +acbh26.l1b1 := 0.0 ; +acbh26.l2b2 := 0.0 ; +acbh26.l3b1 := 0.0 ; +acbh26.l4b2 := 0.0 ; +acbh26.l5b1 := 0.0 ; +acbh26.l6b2 := 0.0 ; +acbh26.l7b1 := 0.0 ; +acbh26.l8b2 := 0.0 ; +acbh26.r1b2 := 0.0 ; +acbh26.r2b1 := 0.0 ; +acbh26.r3b2 := 0.0 ; +acbh26.r4b1 := 0.0 ; +acbh26.r5b2 := 0.0 ; +acbh26.r6b1 := 0.0 ; +acbh26.r7b2 := 0.0 ; +acbh26.r8b1 := 0.0 ; +acbh27.l1b2 := 0.0 ; +acbh27.l2b1 := 0.0 ; +acbh27.l3b2 := 0.0 ; +acbh27.l4b1 := 0.0 ; +acbh27.l5b2 := 0.0 ; +acbh27.l6b1 := 0.0 ; +acbh27.l7b2 := 0.0 ; +acbh27.l8b1 := 0.0 ; +acbh27.r1b1 := 0.0 ; +acbh27.r2b2 := 0.0 ; +acbh27.r3b1 := 0.0 ; +acbh27.r4b2 := 0.0 ; +acbh27.r5b1 := 0.0 ; +acbh27.r6b2 := 0.0 ; +acbh27.r7b1 := 0.0 ; +acbh27.r8b2 := 0.0 ; +acbh28.l1b1 := 0.0 ; +acbh28.l2b2 := 0.0 ; +acbh28.l3b1 := 0.0 ; +acbh28.l4b2 := 0.0 ; +acbh28.l5b1 := 0.0 ; +acbh28.l6b2 := 0.0 ; +acbh28.l7b1 := 0.0 ; +acbh28.l8b2 := 0.0 ; +acbh28.r1b2 := 0.0 ; +acbh28.r2b1 := 0.0 ; +acbh28.r3b2 := 0.0 ; +acbh28.r4b1 := 0.0 ; +acbh28.r5b2 := 0.0 ; +acbh28.r6b1 := 0.0 ; +acbh28.r7b2 := 0.0 ; +acbh28.r8b1 := 0.0 ; +acbh29.l1b2 := 0.0 ; +acbh29.l2b1 := 0.0 ; +acbh29.l3b2 := 0.0 ; +acbh29.l4b1 := 0.0 ; +acbh29.l5b2 := 0.0 ; +acbh29.l6b1 := 0.0 ; +acbh29.l7b2 := 0.0 ; +acbh29.l8b1 := 0.0 ; +acbh29.r1b1 := 0.0 ; +acbh29.r2b2 := 0.0 ; +acbh29.r3b1 := 0.0 ; +acbh29.r4b2 := 0.0 ; +acbh29.r5b1 := 0.0 ; +acbh29.r6b2 := 0.0 ; +acbh29.r7b1 := 0.0 ; +acbh29.r8b2 := 0.0 ; +acbh30.l1b1 := 0.0 ; +acbh30.l2b2 := 0.0 ; +acbh30.l3b1 := 0.0 ; +acbh30.l4b2 := 0.0 ; +acbh30.l5b1 := 0.0 ; +acbh30.l6b2 := 0.0 ; +acbh30.l7b1 := 0.0 ; +acbh30.l8b2 := 0.0 ; +acbh30.r1b2 := 0.0 ; +acbh30.r2b1 := 0.0 ; +acbh30.r3b2 := 0.0 ; +acbh30.r4b1 := 0.0 ; +acbh30.r5b2 := 0.0 ; +acbh30.r6b1 := 0.0 ; +acbh30.r7b2 := 0.0 ; +acbh30.r8b1 := 0.0 ; +acbh31.l1b2 := 0.0 ; +acbh31.l2b1 := 0.0 ; +acbh31.l3b2 := 0.0 ; +acbh31.l4b1 := 0.0 ; +acbh31.l5b2 := 0.0 ; +acbh31.l6b1 := 0.0 ; +acbh31.l7b2 := 0.0 ; +acbh31.l8b1 := 0.0 ; +acbh31.r1b1 := 0.0 ; +acbh31.r2b2 := 0.0 ; +acbh31.r3b1 := 0.0 ; +acbh31.r4b2 := 0.0 ; +acbh31.r5b1 := 0.0 ; +acbh31.r6b2 := 0.0 ; +acbh31.r8b2 := 0.0 ; +acbh32.l1b1 := 0.0 ; +acbh32.l2b2 := 0.0 ; +acbh32.l3b1 := 0.0 ; +acbh32.l4b2 := 0.0 ; +acbh32.l5b1 := 0.0 ; +acbh32.l6b2 := 0.0 ; +acbh32.l7b1 := 0.0 ; +acbh32.l8b2 := 0.0 ; +acbh32.r1b2 := 0.0 ; +acbh32.r2b1 := 0.0 ; +acbh32.r3b2 := 0.0 ; +acbh32.r4b1 := 0.0 ; +acbh32.r5b2 := 0.0 ; +acbh32.r6b1 := 0.0 ; +acbh32.r7b2 := 0.0 ; +acbh32.r8b1 := 0.0 ; +acbh33.l1b2 := 0.0 ; +acbh33.l2b1 := 0.0 ; +acbh33.l3b2 := 0.0 ; +acbh33.l4b1 := 0.0 ; +acbh33.l5b2 := 0.0 ; +acbh33.l6b1 := 0.0 ; +acbh33.l7b2 := 0.0 ; +acbh33.l8b1 := 0.0 ; +acbh33.r1b1 := 0.0 ; +acbh33.r2b2 := 0.0 ; +acbh33.r3b1 := 0.0 ; +acbh33.r4b2 := 0.0 ; +acbh33.r5b1 := 0.0 ; +acbh33.r6b2 := 0.0 ; +acbh33.r7b1 := 0.0 ; +acbh33.r8b2 := 0.0 ; +acbh34.l1b1 := 0.0 ; +acbh34.l2b2 := 0.0 ; +acbh34.l3b1 := 0.0 ; +acbh34.l4b2 := 0.0 ; +acbh34.l5b1 := 0.0 ; +acbh34.l6b2 := 0.0 ; +acbh34.l7b1 := 0.0 ; +acbh34.l8b2 := 0.0 ; +acbv11.l1b1 := 0.0 ; +acbv11.l2b2 := 0.0 ; +acbv11.l3b1 := 0.0 ; +acbv11.l4b2 := 0.0 ; +acbv11.l5b1 := 0.0 ; +acbv11.l6b2 := 0.0 ; +acbv11.l7b1 := 0.0 ; +acbv11.l8b2 := 0.0 ; +acbv11.r1b2 := 0.0 ; +acbv11.r2b1 := 0.0 ; +acbv11.r3b2 := 0.0 ; +acbv11.r4b1 := 0.0 ; +acbv11.r5b2 := 0.0 ; +acbv11.r6b1 := 0.0 ; +acbv11.r7b2 := 0.0 ; +acbv11.r8b1 := 0.0 ; +acbv12.l1b2 := 0.0 ; +acbv12.l2b1 := 0.0 ; +acbv12.l3b2 := -0.0 ; +acbv12.l4b1 := 0.0 ; +acbv12.l5b2 := 0.0 ; +acbv12.l6b1 := 0.0 ; +acbv12.l7b2 := 0.0 ; +acbv12.l8b1 := 0.0 ; +acbv12.r1b1 := 0.0 ; +acbv12.r2b2 := 0.0 ; +acbv12.r3b1 := 0.0 ; +acbv12.r4b2 := 0.0 ; +acbv12.r5b1 := 0.0 ; +acbv12.r6b2 := 0.0 ; +acbv12.r7b1 := -0.0 ; +acbv12.r8b2 := 0.0 ; +acbv13.l1b1 := 0.0 ; +acbv13.l2b2 := 0.0 ; +acbv13.l3b1 := 0.0 ; +acbv13.l4b2 := 0.0 ; +acbv13.l5b1 := 0.0 ; +acbv13.l6b2 := 0.0 ; +acbv13.l7b1 := 0.0 ; +acbv13.l8b2 := -0.0 ; +acbv13.r1b2 := 0.0 ; +acbv13.r2b1 := -0.0 ; +acbv13.r3b2 := 0.0 ; +acbv13.r4b1 := 0.0 ; +acbv13.r5b2 := 0.0 ; +acbv13.r6b1 := 0.0 ; +acbv13.r7b2 := 0.0 ; +acbv13.r8b1 := 0.0 ; +acbv14.l1b2 := 0.0 ; +acbv14.l2b1 := 0.0 ; +acbv14.l3b2 := -0.0 ; +acbv14.l4b1 := 0.0 ; +acbv14.l5b2 := 0.0 ; +acbv14.l6b1 := 0.0 ; +acbv14.l7b2 := 0.0 ; +acbv14.l8b1 := 0.0 ; +acbv14.r1b1 := 0.0 ; +acbv14.r2b2 := 0.0 ; +acbv14.r3b1 := 0.0 ; +acbv14.r4b2 := 0.0 ; +acbv14.r5b1 := 0.0 ; +acbv14.r6b2 := 0.0 ; +acbv14.r7b1 := -0.0 ; +acbv14.r8b2 := 0.0 ; +acbv15.l1b1 := 0.0 ; +acbv15.l2b2 := -0.0 ; +acbv15.l3b1 := -0.0 ; +acbv15.l4b2 := 0.0 ; +acbv15.l5b1 := 0.0 ; +acbv15.l6b2 := -0.0 ; +acbv15.l7b1 := 0.0 ; +acbv15.l8b2 := -0.0 ; +acbv15.r1b2 := -0.0 ; +acbv15.r2b1 := -0.0 ; +acbv15.r3b2 := 0.0 ; +acbv15.r4b1 := 0.0 ; +acbv15.r5b2 := -0.0 ; +acbv15.r6b1 := 0.0 ; +acbv15.r7b2 := 0.0 ; +acbv15.r8b1 := 0.0 ; +acbv16.l1b2 := 0.0 ; +acbv16.l2b1 := -0.0 ; +acbv16.l3b2 := 0.0 ; +acbv16.l4b1 := 0.0 ; +acbv16.l5b2 := 0.0 ; +acbv16.l6b1 := -0.0 ; +acbv16.l7b2 := 0.0 ; +acbv16.l8b1 := 0.0 ; +acbv16.r1b1 := 0.0 ; +acbv16.r2b2 := 0.0 ; +acbv16.r3b1 := 0.0 ; +acbv16.r4b2 := 0.0 ; +acbv16.r5b1 := 0.0 ; +acbv16.r6b2 := 0.0 ; +acbv16.r7b1 := -0.0 ; +acbv16.r8b2 := 0.0 ; +acbv17.l1b1 := 0.0 ; +acbv17.l2b2 := 0.0 ; +acbv17.l3b1 := -0.0 ; +acbv17.l4b2 := 0.0 ; +acbv17.l5b1 := 0.0 ; +acbv17.l6b2 := 0.0 ; +acbv17.l7b1 := 0.0 ; +acbv17.l8b2 := 0.0 ; +acbv17.r1b2 := 0.0 ; +acbv17.r2b1 := 0.0 ; +acbv17.r3b2 := 0.0 ; +acbv17.r4b1 := 0.0 ; +acbv17.r5b2 := 0.0 ; +acbv17.r6b1 := 0.0 ; +acbv17.r7b2 := 0.0 ; +acbv17.r8b1 := 0.0 ; +acbv18.l1b2 := 0.0 ; +acbv18.l2b1 := 0.0 ; +acbv18.l3b2 := 0.0 ; +acbv18.l4b1 := 0.0 ; +acbv18.l5b2 := 0.0 ; +acbv18.l6b1 := 0.0 ; +acbv18.l7b2 := 0.0 ; +acbv18.l8b1 := 0.0 ; +acbv18.r1b1 := 0.0 ; +acbv18.r2b2 := 0.0 ; +acbv18.r3b1 := 0.0 ; +acbv18.r4b2 := 0.0 ; +acbv18.r5b1 := 0.0 ; +acbv18.r6b2 := 0.0 ; +acbv18.r7b1 := 0.0 ; +acbv18.r8b2 := 0.0 ; +acbv19.l1b1 := 0.0 ; +acbv19.l2b2 := 0.0 ; +acbv19.l3b1 := 0.0 ; +acbv19.l4b2 := 0.0 ; +acbv19.l5b1 := 0.0 ; +acbv19.l6b2 := 0.0 ; +acbv19.l7b1 := 0.0 ; +acbv19.l8b2 := 0.0 ; +acbv19.r1b2 := 0.0 ; +acbv19.r2b1 := 0.0 ; +acbv19.r3b2 := 0.0 ; +acbv19.r4b1 := 0.0 ; +acbv19.r5b2 := 0.0 ; +acbv19.r6b1 := 0.0 ; +acbv19.r7b2 := 0.0 ; +acbv19.r8b1 := 0.0 ; +acbv20.l1b2 := 0.0 ; +acbv20.l2b1 := 0.0 ; +acbv20.l3b2 := 0.0 ; +acbv20.l4b1 := 0.0 ; +acbv20.l5b2 := 0.0 ; +acbv20.l6b1 := 0.0 ; +acbv20.l7b2 := 0.0 ; +acbv20.l8b1 := 0.0 ; +acbv20.r1b1 := 0.0 ; +acbv20.r2b2 := 0.0 ; +acbv20.r3b1 := 0.0 ; +acbv20.r4b2 := 0.0 ; +acbv20.r5b1 := 0.0 ; +acbv20.r6b2 := 0.0 ; +acbv20.r7b1 := 0.0 ; +acbv20.r8b2 := 0.0 ; +acbv21.l1b1 := 0.0 ; +acbv21.l2b2 := 0.0 ; +acbv21.l3b1 := 0.0 ; +acbv21.l4b2 := 0.0 ; +acbv21.l5b1 := 0.0 ; +acbv21.l6b2 := 0.0 ; +acbv21.l7b1 := 0.0 ; +acbv21.l8b2 := 0.0 ; +acbv21.r1b2 := 0.0 ; +acbv21.r2b1 := 0.0 ; +acbv21.r3b2 := 0.0 ; +acbv21.r4b1 := 0.0 ; +acbv21.r5b2 := 0.0 ; +acbv21.r6b1 := 0.0 ; +acbv21.r7b2 := 0.0 ; +acbv21.r8b1 := 0.0 ; +acbv22.l1b2 := 0.0 ; +acbv22.l2b1 := 0.0 ; +acbv22.l3b2 := 0.0 ; +acbv22.l4b1 := 0.0 ; +acbv22.l5b2 := 0.0 ; +acbv22.l6b1 := 0.0 ; +acbv22.l7b2 := 0.0 ; +acbv22.l8b1 := 0.0 ; +acbv22.r1b1 := 0.0 ; +acbv22.r2b2 := 0.0 ; +acbv22.r3b1 := 0.0 ; +acbv22.r4b2 := 0.0 ; +acbv22.r5b1 := 0.0 ; +acbv22.r6b2 := 0.0 ; +acbv22.r7b1 := 0.0 ; +acbv22.r8b2 := 0.0 ; +acbv23.l1b1 := 0.0 ; +acbv23.l2b2 := 0.0 ; +acbv23.l3b1 := 0.0 ; +acbv23.l4b2 := 0.0 ; +acbv23.l5b1 := 0.0 ; +acbv23.l6b2 := 0.0 ; +acbv23.l7b1 := 0.0 ; +acbv23.l8b2 := 0.0 ; +acbv23.r1b2 := 0.0 ; +acbv23.r2b1 := 0.0 ; +acbv23.r3b2 := 0.0 ; +acbv23.r4b1 := 0.0 ; +acbv23.r5b2 := 0.0 ; +acbv23.r6b1 := 0.0 ; +acbv23.r7b2 := 0.0 ; +acbv23.r8b1 := 0.0 ; +acbv24.l1b2 := 0.0 ; +acbv24.l2b1 := 0.0 ; +acbv24.l3b2 := 0.0 ; +acbv24.l4b1 := 0.0 ; +acbv24.l5b2 := 0.0 ; +acbv24.l6b1 := 0.0 ; +acbv24.l7b2 := 0.0 ; +acbv24.l8b1 := 0.0 ; +acbv24.r1b1 := 0.0 ; +acbv24.r2b2 := 0.0 ; +acbv24.r3b1 := 0.0 ; +acbv24.r4b2 := 0.0 ; +acbv24.r5b1 := 0.0 ; +acbv24.r6b2 := 0.0 ; +acbv24.r7b1 := 0.0 ; +acbv24.r8b2 := 0.0 ; +acbv25.l1b1 := 0.0 ; +acbv25.l2b2 := 0.0 ; +acbv25.l3b1 := 0.0 ; +acbv25.l4b2 := 0.0 ; +acbv25.l5b1 := 0.0 ; +acbv25.l6b2 := 0.0 ; +acbv25.l7b1 := 0.0 ; +acbv25.l8b2 := 0.0 ; +acbv25.r1b2 := 0.0 ; +acbv25.r2b1 := 0.0 ; +acbv25.r3b2 := 0.0 ; +acbv25.r4b1 := 0.0 ; +acbv25.r5b2 := 0.0 ; +acbv25.r6b1 := 0.0 ; +acbv25.r7b2 := 0.0 ; +acbv25.r8b1 := 0.0 ; +acbv26.l1b2 := 0.0 ; +acbv26.l2b1 := 0.0 ; +acbv26.l3b2 := 0.0 ; +acbv26.l4b1 := 0.0 ; +acbv26.l5b2 := 0.0 ; +acbv26.l6b1 := 0.0 ; +acbv26.l7b2 := 0.0 ; +acbv26.l8b1 := 0.0 ; +acbv26.r1b1 := 0.0 ; +acbv26.r2b2 := 0.0 ; +acbv26.r3b1 := 0.0 ; +acbv26.r4b2 := 0.0 ; +acbv26.r6b2 := 0.0 ; +acbv26.r7b1 := 0.0 ; +acbv26.r8b2 := 0.0 ; +acbv27.l1b1 := 0.0 ; +acbv27.l2b2 := 0.0 ; +acbv27.l3b1 := 0.0 ; +acbv27.l4b2 := 0.0 ; +acbv27.l5b1 := 0.0 ; +acbv27.l6b2 := 0.0 ; +acbv27.l7b1 := 0.0 ; +acbv27.l8b2 := 0.0 ; +acbv27.r1b2 := 0.0 ; +acbv27.r2b1 := 0.0 ; +acbv27.r3b2 := 0.0 ; +acbv27.r4b1 := 0.0 ; +acbv27.r5b2 := 0.0 ; +acbv27.r6b1 := 0.0 ; +acbv27.r7b2 := 0.0 ; +acbv27.r8b1 := 0.0 ; +acbv28.l1b2 := 0.0 ; +acbv28.l2b1 := 0.0 ; +acbv28.l3b2 := 0.0 ; +acbv28.l4b1 := 0.0 ; +acbv28.l5b2 := 0.0 ; +acbv28.l6b1 := 0.0 ; +acbv28.l7b2 := 0.0 ; +acbv28.l8b1 := 0.0 ; +acbv28.r1b1 := 0.0 ; +acbv28.r2b2 := 0.0 ; +acbv28.r3b1 := 0.0 ; +acbv28.r4b2 := 0.0 ; +acbv28.r5b1 := 0.0 ; +acbv28.r6b2 := 0.0 ; +acbv28.r7b1 := 0.0 ; +acbv28.r8b2 := 0.0 ; +acbv29.l1b1 := 0.0 ; +acbv29.l2b2 := 0.0 ; +acbv29.l3b1 := 0.0 ; +acbv29.l4b2 := 0.0 ; +acbv29.l5b1 := 0.0 ; +acbv29.l6b2 := 0.0 ; +acbv29.l7b1 := 0.0 ; +acbv29.l8b2 := 0.0 ; +acbv29.r1b2 := 0.0 ; +acbv29.r2b1 := 0.0 ; +acbv29.r3b2 := 0.0 ; +acbv29.r4b1 := 0.0 ; +acbv29.r5b2 := 0.0 ; +acbv29.r6b1 := 0.0 ; +acbv29.r7b2 := 0.0 ; +acbv29.r8b1 := 0.0 ; +acbv30.l1b2 := 0.0 ; +acbv30.l2b1 := 0.0 ; +acbv30.l3b2 := 0.0 ; +acbv30.l4b1 := 0.0 ; +acbv30.l5b2 := 0.0 ; +acbv30.l6b1 := 0.0 ; +acbv30.l7b2 := 0.0 ; +acbv30.l8b1 := 0.0 ; +acbv30.r1b1 := 0.0 ; +acbv30.r2b2 := 0.0 ; +acbv30.r3b1 := 0.0 ; +acbv30.r4b2 := 0.0 ; +acbv30.r5b1 := 0.0 ; +acbv30.r6b2 := 0.0 ; +acbv30.r7b1 := 0.0 ; +acbv30.r8b2 := 0.0 ; +acbv31.l1b1 := 0.0 ; +acbv31.l2b2 := 0.0 ; +acbv31.l3b1 := 0.0 ; +acbv31.l4b2 := 0.0 ; +acbv31.l5b1 := 0.0 ; +acbv31.l6b2 := 0.0 ; +acbv31.l7b1 := 0.0 ; +acbv31.l8b2 := 0.0 ; +acbv31.r1b2 := 0.0 ; +acbv31.r2b1 := 0.0 ; +acbv31.r3b2 := 0.0 ; +acbv31.r4b1 := 0.0 ; +acbv31.r5b2 := 0.0 ; +acbv31.r6b1 := 0.0 ; +acbv31.r7b2 := 0.0 ; +acbv31.r8b1 := 0.0 ; +acbv32.l1b2 := 0.0 ; +acbv32.l2b1 := 0.0 ; +acbv32.l3b2 := 0.0 ; +acbv32.l4b1 := 0.0 ; +acbv32.l5b2 := 0.0 ; +acbv32.l6b1 := 0.0 ; +acbv32.l7b2 := 0.0 ; +acbv32.l8b1 := 0.0 ; +acbv32.r1b1 := 0.0 ; +acbv32.r2b2 := 0.0 ; +acbv32.r3b1 := 0.0 ; +acbv32.r4b2 := 0.0 ; +acbv32.r5b1 := 0.0 ; +acbv32.r6b2 := 0.0 ; +acbv32.r7b1 := 0.0 ; +acbv32.r8b2 := 0.0 ; +acbv33.l1b1 := 0.0 ; +acbv33.l2b2 := 0.0 ; +acbv33.l3b1 := 0.0 ; +acbv33.l4b2 := 0.0 ; +acbv33.l5b1 := 0.0 ; +acbv33.l6b2 := 0.0 ; +acbv33.l7b1 := 0.0 ; +acbv33.l8b2 := 0.0 ; +acbv33.r1b2 := 0.0 ; +acbv33.r2b1 := 0.0 ; +acbv33.r3b2 := 0.0 ; +acbv33.r4b1 := 0.0 ; +acbv33.r5b2 := 0.0 ; +acbv33.r6b1 := 0.0 ; +acbv33.r7b2 := 0.0 ; +acbv33.r8b1 := 0.0 ; +acbv34.l1b2 := 0.0 ; +acbv34.l2b1 := 0.0 ; +acbv34.l3b2 := 0.0 ; +acbv34.l4b1 := 0.0 ; +acbv34.l5b2 := 0.0 ; +acbv34.l6b1 := 0.0 ; +acbv34.l7b2 := 0.0 ; +acbv34.l8b1 := 0.0 ; +acbwh4.l3b1 := 0.0 ; +acbwh4.l7b1 := 0.0 ; +acbwh4.r3b2 := 0.0 ; +acbwh4.r7b2 := 0.0 ; +acbwh5.l3b2 := 0.0 ; +acbwh5.l7b2 := 0.0 ; +acbwh5.r3b1 := 0.0 ; +acbwh5.r7b1 := 0.0 ; +acbwv4.l3b2 := 0.0 ; +acbwv4.l7b2 := 0.0 ; +acbwv4.r3b1 := 0.0 ; +acbwv4.r7b1 := 0.0 ; +acbwv5.l3b1 := 0.0 ; +acbwv5.l7b1 := 0.0 ; +acbwv5.r3b2 := 0.0 ; +acbwv5.r7b2 := 0.0 ; +acbxh1.l1 := 4.70588235294e-06 ; +acbxh1.l2 := 0.0 ; +acbxh1.l5 := 0.0 ; +acbxh1.l8 := -1.6e-07 ; +acbxh1.r1 := -4.70588235294e-06 ; +acbxh1.r2 := -8e-07 ; +acbxh1.r5 := 0.0 ; +acbxh1.r8 := -1.6e-07 ; +acbxh2.l1 := 4.70588235294e-06 ; +acbxh2.l2 := -1.2000000000000002e-06 ; +acbxh2.l5 := 0.0 ; +acbxh2.l8 := -1.6e-07 ; +acbxh2.r1 := -4.70588235294e-06 ; +acbxh2.r2 := -8e-07 ; +acbxh2.r5 := 0.0 ; +acbxh2.r8 := -1.6e-07 ; +acbxh3.l1 := 4.70588235294e-06 ; +acbxh3.l2 := -1.2000000000000002e-06 ; +acbxh3.l5 := 0.0 ; +acbxh3.l8 := -1.6e-07 ; +acbxh3.r1 := -4.70588235294e-06 ; +acbxh3.r2 := -8e-07 ; +acbxh3.r5 := 0.0 ; +acbxh3.r8 := -1.6e-07 ; +acbxv1.l1 := 0.0 ; +acbxv1.l2 := 1.588235294118e-05 ; +acbxv1.l5 := -3.203334516228e-06 ; +acbxv1.l8 := 1.596235294118e-05 ; +acbxv1.r1 := 0.0 ; +acbxv1.r2 := -1.588235294118e-05 ; +acbxv1.r5 := 3.203334516228e-06 ; +acbxv1.r8 := -1.580235294118e-05 ; +acbxv2.l1 := 0.0 ; +acbxv2.l2 := 1.588235294118e-05 ; +acbxv2.l5 := -3.203334516228e-06 ; +acbxv2.l8 := 1.596235294118e-05 ; +acbxv2.r1 := 0.0 ; +acbxv2.r2 := -1.588235294118e-05 ; +acbxv2.r5 := 3.203334516228e-06 ; +acbxv2.r8 := -1.580235294118e-05 ; +acbxv3.l1 := 0.0 ; +acbxv3.l2 := 1.588235294118e-05 ; +acbxv3.l5 := -3.203334516228e-06 ; +acbxv3.l8 := 1.596235294118e-05 ; +acbxv3.r1 := 0.0 ; +acbxv3.r2 := -1.588235294118e-05 ; +acbxv3.r5 := 3.203334516228e-06 ; +acbxv3.r8 := -1.580235294118e-05 ; +acbyh4.l1b1 := 0.0 ; +acbyh4.l2b2 := 0.0 ; +acbyh4.l5b1 := 0.0 ; +acbyh4.l6b2 := 0.0 ; +acbyh4.l8b2 := 0.0 ; +acbyh4.r1b2 := 0.0 ; +acbyh4.r2b1 := 0.0 ; +acbyh4.r5b2 := 0.0 ; +acbyh4.r6b1 := 0.0 ; +acbyh4.r8b1 := 0.0 ; +acbyh5.l2b1 := 0.0 ; +acbyh5.l4b1 := 0.0 ; +acbyh5.l6b1 := 0.0 ; +acbyh5.r4b2 := 0.0 ; +acbyh5.r6b2 := 0.0 ; +acbyh5.r8b2 := 0.0 ; +acbyh6.l4b2 := 0.0 ; +acbyh6.r4b1 := 0.0 ; +acbyhs4.l1b1 := -1.7232931704719998e-05 ; +acbyhs4.l1b2 := 3.074389646208e-05 ; +acbyhs4.l2b1 := -7.91967278401e-07 ; +acbyhs4.l2b2 := -1.7015654059700002e-07 ; +acbyhs4.l5b1 := 0.0 ; +acbyhs4.l5b2 := 0.0 ; +acbyhs4.l8b1 := -2.6938133605e-07 ; +acbyhs4.l8b2 := -4.2483020780800004e-08 ; +acbyhs4.r1b1 := 2.8357432467e-05 ; +acbyhs4.r1b2 := -1.5870051014279998e-05 ; +acbyhs4.r2b1 := 7.80265136087e-07 ; +acbyhs4.r2b2 := 1.4952949307e-06 ; +acbyhs4.r5b1 := 0.0 ; +acbyhs4.r5b2 := 0.0 ; +acbyhs4.r8b1 := 4.65399586048e-08 ; +acbyhs4.r8b2 := 2.70329631946e-07 ; +acbyhs5.l2b1 := 1.3488786884000001e-07 ; +acbyhs5.l2b2 := 1.6718877448e-06 ; +acbyhs5.r8b1 := -3.12487393302e-07 ; +acbyhs5.r8b2 := -5.77454301616e-08 ; +acbyv4.l1b2 := 0.0 ; +acbyv4.l2b1 := 0.0 ; +acbyv4.l5b2 := 0.0 ; +acbyv4.l6b1 := 0.0 ; +acbyv4.l8b1 := 0.0 ; +acbyv4.r1b1 := 0.0 ; +acbyv4.r2b2 := 0.0 ; +acbyv4.r5b1 := 0.0 ; +acbyv4.r6b2 := 0.0 ; +acbyv4.r8b2 := 0.0 ; +acbyv5.l2b2 := 0.0 ; +acbyv5.l4b2 := 0.0 ; +acbyv5.l6b2 := 0.0 ; +acbyv5.r4b1 := 0.0 ; +acbyv5.r6b1 := 0.0 ; +acbyv5.r8b1 := 0.0 ; +acbyv6.l4b1 := 0.0 ; +acbyv6.r4b2 := 0.0 ; +acbyvs4.l1b1 := 0.0 ; +acbyvs4.l1b2 := 0.0 ; +acbyvs4.l2b1 := -6.1438986027e-05 ; +acbyvs4.l2b2 := 3.8651833291e-05 ; +acbyvs4.l5b1 := 3.214300975884e-05 ; +acbyvs4.l5b2 := -1.91816609292e-06 ; +acbyvs4.l8b1 := -6.0552633350458795e-05 ; +acbyvs4.l8b2 := 4.1788013979548e-05 ; +acbyvs4.r1b1 := 0.0 ; +acbyvs4.r1b2 := 0.0 ; +acbyvs4.r2b1 := 2.86287250536e-05 ; +acbyvs4.r2b2 := -5.61975766496e-05 ; +acbyvs4.r5b1 := -4.1929457053919994e-06 ; +acbyvs4.r5b2 := 3.2194661811360004e-05 ; +acbyvs4.r8b1 := 4.238845055962e-05 ; +acbyvs4.r8b2 := -6.081927369695391e-05 ; +acbyvs5.l2b1 := -1.6137596230080002e-05 ; +acbyvs5.l2b2 := 3.1627412875799996e-05 ; +acbyvs5.r8b1 := 3.0778705554841394e-05 ; +acbyvs5.r8b2 := -1.6858945490443002e-05 ; +kb.a12 := 0.00035664252265800027 ; +kb.a23 := 0.00035664252265800027 ; +kb.a34 := 0.00035664252265800027 ; +kb.a45 := 0.00035664252265800027 ; +kb.a56 := 0.00035664252265800027 ; +kb.a67 := 0.00035664252265800027 ; +kb.a78 := 0.00035664252265800027 ; +kb.a81 := 0.00035664252265800027 ; +kcd.a12b1 := 0.0 ; +kcd.a12b2 := 0.0 ; +kcd.a23b1 := 0.0 ; +kcd.a23b2 := 0.0 ; +kcd.a34b1 := 0.0 ; +kcd.a34b2 := 0.0 ; +kcd.a45b1 := 0.0 ; +kcd.a45b2 := 0.0 ; +kcd.a56b1 := 0.0 ; +kcd.a56b2 := 0.0 ; +kcd.a67b1 := 0.0 ; +kcd.a67b2 := 0.0 ; +kcd.a78b1 := 0.0 ; +kcd.a78b2 := 0.0 ; +kcd.a81b1 := 0.0 ; +kcd.a81b2 := 0.0 ; +kco.a12b1 := 0.0 ; +kco.a12b2 := 0.0 ; +kco.a23b1 := 0.0 ; +kco.a23b2 := 0.0 ; +kco.a34b1 := 0.0 ; +kco.a34b2 := 0.0 ; +kco.a45b1 := 0.0 ; +kco.a45b2 := 0.0 ; +kco.a56b1 := 0.0 ; +kco.a56b2 := 0.0 ; +kco.a67b1 := 0.0 ; +kco.a67b2 := 0.0 ; +kco.a78b1 := 0.0 ; +kco.a81b1 := 0.0 ; +kco.a81b2 := 0.0 ; +kcosx3.l5 := 0.0 ; +kcosx3.l8 := 0.0 ; +kcosx3.r1 := 0.0 ; +kcosx3.r2 := 0.0 ; +kcosx3.r5 := 0.0 ; +kcosx3.r8 := 0.0 ; +kcox3.l1 := 0.0 ; +kcox3.l5 := 0.0 ; +kcox3.l8 := 0.0 ; +kcox3.r1 := 0.0 ; +kcox3.r2 := 0.0 ; +kcox3.r5 := 0.0 ; +kcox3.r8 := 0.0 ; +kcs.a12b1 := 0.0 ; +kcs.a12b2 := 0.0 ; +kcs.a23b1 := 0.0 ; +kcs.a23b2 := 0.0 ; +kcs.a34b1 := 0.0 ; +kcs.a34b2 := 0.0 ; +kcs.a45b1 := 0.0 ; +kcs.a45b2 := 0.0 ; +kcs.a56b1 := 0.0 ; +kcs.a56b2 := 0.0 ; +kcs.a67b1 := 0.0 ; +kcs.a67b2 := 0.0 ; +kcs.a78b1 := 0.0 ; +kcs.a81b1 := 0.0 ; +kcs.a81b2 := 0.0 ; +kcssx3.l1 := 0.0 ; +kcssx3.l5 := 0.0 ; +kcssx3.l8 := 0.0 ; +kcssx3.r1 := 0.0 ; +kcssx3.r2 := 0.0 ; +kcssx3.r5 := 0.0 ; +kcssx3.r8 := 0.0 ; +kcsx3.l1 := 0.0 ; +kcsx3.l2 := 0.0 ; +kcsx3.l5 := 0.0 ; +kcsx3.l8 := 0.0 ; +kcsx3.r1 := 0.0 ; +kcsx3.r2 := 0.0 ; +kcsx3.r5 := 0.0 ; +kcsx3.r8 := 0.0 ; +kctx3.l1 := 0.0 ; +kctx3.l2 := 0.0 ; +kctx3.l5 := 0.0 ; +kctx3.l8 := 0.0 ; +kctx3.r1 := 0.0 ; +kctx3.r2 := 0.0 ; +kctx3.r5 := 0.0 ; +kctx3.r8 := 0.0 ; +kd1.l2 := 0.00016216987485375914 ; +kd1.l8 := 0.00016216987485375914 ; +kd1.lr1 := 5.5345523265927265e-05 ; +kd1.lr5 := 5.5345523265927265e-05 ; +kd1.r2 := 0.00016216987485375914 ; +kd1.r8 := 0.00016216987485375914 ; +kd2.l1 := 0.00011947605022485886 ; +kd2.l2 := 0.00016216987485375914 ; +kd2.l5 := 0.00011947605022485886 ; +kd2.l8 := 0.00016216987485375914 ; +kd2.r1 := 0.00011947605022485886 ; +kd2.r2 := 0.00016216987485375914 ; +kd2.r5 := 0.00011947605022485886 ; +kd2.r8 := 0.00016216987485375914 ; +kd3.l4 := 0.00016630731301041268 ; +kd3.r4 := 0.00016630731301041268 ; +kd34.lr3 := 5.550855237809782e-05 ; +kd34.lr7 := 5.5508555673332175e-05 ; +kd4.l4 := 0.00016630731301041268 ; +kd4.r4 := 0.00016630731301041268 ; +kgmwh.l4b1 := 0.0 ; +kgmwh.r4b2 := 0.0 ; +kgmwv.l4b1 := 0.0 ; +kgmwv.r4b2 := 0.0 ; +kmsd.lr6b1 := 0.0 ; +kmsd.lr6b2 := 0.0 ; +kod.a12b1 := -12.0 ; +kod.a12b2 := -12.0 ; +kod.a23b1 := -12.0 ; +kod.a23b2 := -12.0 ; +kod.a34b1 := -12.0 ; +kod.a34b2 := -12.0 ; +kod.a45b1 := -12.0 ; +kod.a45b2 := -12.0 ; +kod.a56b1 := -12.0 ; +kod.a56b2 := -12.0 ; +kod.a67b1 := -12.0 ; +kod.a67b2 := -12.0 ; +kod.a78b1 := -12.0 ; +kod.a78b2 := -12.0 ; +kod.a81b1 := -12.0 ; +kod.a81b2 := -12.0 ; +kof.a12b1 := -12.0 ; +kof.a12b2 := -12.0 ; +kof.a23b1 := -12.0 ; +kof.a23b2 := -12.0 ; +kof.a34b1 := -12.0 ; +kof.a34b2 := -12.0 ; +kof.a45b1 := -12.0 ; +kof.a45b2 := -12.0 ; +kof.a56b1 := -12.0 ; +kof.a56b2 := -12.0 ; +kof.a67b1 := -12.0 ; +kof.a67b2 := -12.0 ; +kof.a78b1 := -12.0 ; +kof.a78b2 := -12.0 ; +kof.a81b1 := -12.0 ; +kof.a81b2 := -12.0 ; +kq10.l1b1 := 0.00700860812387 ; +kq10.l1b2 := -0.00636538961371 ; +kq10.l2b1 := -0.00650242152136 ; +kq10.l2b2 := 0.0072588362848 ; +kq10.l4b1 := -0.0064225164082 ; +kq10.l4b2 := 0.00709556309292 ; +kq10.l5b1 := 0.00693976087987 ; +kq10.l5b2 := -0.00597407396939 ; +kq10.l6b1 := -0.00726838129116 ; +kq10.l6b2 := 0.00702250703926 ; +kq10.l8b1 := -0.00546045671952 ; +kq10.l8b2 := 0.00744652582177 ; +kq10.r1b1 := -0.00655583035397 ; +kq10.r1b2 := 0.00704690672034 ; +kq10.r2b1 := 0.00725081656956 ; +kq10.r2b2 := -0.00602861966554 ; +kq10.r4b1 := 0.0073878095146 ; +kq10.r4b2 := -0.00626964430262 ; +kq10.r5b1 := -0.00670640881105 ; +kq10.r5b2 := 0.00688694469597 ; +kq10.r6b1 := 0.00716126130553 ; +kq10.r6b2 := -0.0080306245298 ; +kq10.r8b1 := 0.0073214736068 ; +kq10.r8b2 := -0.00624440225311 ; +kq4.l1b1 := 0.00312291549797 ; +kq4.l1b2 := -0.00300687604856 ; +kq4.l2b1 := -0.00311615911087 ; +kq4.l2b2 := 0.00353734311324 ; +kq4.l5b1 := 0.0 ; +kq4.l5b2 := 0.0 ; +kq4.l6b1 := -0.004881414734 ; +kq4.l6b2 := 0.00548430944549 ; +kq4.l8b1 := -0.00286476925196 ; +kq4.l8b2 := 0.00292733462422 ; +kq4.lr3 := 0.001241284 ; +kq4.lr7 := 0.001313827241 ; +kq4.r1b1 := -0.00312291549797 ; +kq4.r1b2 := 0.00300687604856 ; +kq4.r2b1 := 0.00311615911087 ; +kq4.r2b2 := -0.00353734311324 ; +kq4.r5b1 := 0.0 ; +kq4.r5b2 := 0.0 ; +kq4.r6b1 := 0.00566534309841 ; +kq4.r6b2 := -0.00483383773 ; +kq4.r8b1 := 0.00286475613898 ; +kq4.r8b2 := -0.00292733491476 ; +kq5.l1b1 := -0.00192526664202 ; +kq5.l1b2 := 0.00151785504855 ; +kq5.l2b1 := 0.00423659837335 ; +kq5.l2b2 := -0.00372377548478 ; +kq5.l4b1 := 0.00405252361677 ; +kq5.l4b2 := -0.00411216466298 ; +kq5.l5b1 := -0.00145984259988 ; +kq5.l5b2 := 0.00142576695347 ; +kq5.l6b1 := 0.00700183002334 ; +kq5.l6b2 := -0.0071260057831 ; +kq5.l8b1 := 0.00343796139347 ; +kq5.l8b2 := -0.00275410686666 ; +kq5.lr3 := -0.001303924 ; +kq5.lr7 := -0.001335536573 ; +kq5.r1b1 := 0.00175027259607 ; +kq5.r1b2 := -0.00171791530294 ; +kq5.r2b1 := -0.00409616587176 ; +kq5.r2b2 := 0.00433019149416 ; +kq5.r4b1 := -0.00375790746424 ; +kq5.r4b2 := 0.00506948884112 ; +kq5.r5b1 := 0.00139426423318 ; +kq5.r5b2 := -0.00145981368003 ; +kq5.r6b1 := -0.00665647589556 ; +kq5.r6b2 := 0.00647794896186 ; +kq5.r8b1 := -0.00257052998287 ; +kq5.r8b2 := 0.0027956452864 ; +kq6.l1b1 := 0.000322580645161 ; +kq6.l1b2 := -0.000322580645161 ; +kq6.l2b1 := -0.00498664552197 ; +kq6.l2b2 := 0.00443116968533 ; +kq6.l3b1 := 0.002652066007 ; +kq6.l3b2 := -0.002474368718 ; +kq6.l4b1 := -0.00505611443371 ; +kq6.l4b2 := 0.00579472683419 ; +kq6.l5b1 := 0.00129332627241 ; +kq6.l5b2 := -0.00209479693559 ; +kq6.l7b1 := 0.003323803831 ; +kq6.l7b2 := -0.002780522858 ; +kq6.l8b1 := -0.00623618595857 ; +kq6.l8b2 := 0.0059703636487 ; +kq6.r1b1 := -0.000322580645161 ; +kq6.r1b2 := 0.000322580645161 ; +kq6.r2b1 := 0.00411010229043 ; +kq6.r2b2 := -0.00429254133907 ; +kq6.r3b1 := -0.002482840022 ; +kq6.r3b2 := 0.002675674759 ; +kq6.r4b1 := 0.00471220468233 ; +kq6.r4b2 := -0.00610086821587 ; +kq6.r5b1 := -0.00142573432983 ; +kq6.r5b2 := 0.00141140131543 ; +kq6.r7b1 := -0.002818210593 ; +kq6.r7b2 := 0.003302618961 ; +kq6.r8b1 := 0.00489334127546 ; +kq6.r8b2 := -0.00553260392415 ; +kq7.l1b1 := -0.00732300847786 ; +kq7.l1b2 := 0.00698477081774 ; +kq7.l2b1 := 0.00757723534787 ; +kq7.l2b2 := -0.00781096124829 ; +kq7.l4b1 := 0.00724071437865 ; +kq7.l4b2 := -0.00489893431741 ; +kq7.l5b1 := -0.00687981898945 ; +kq7.l5b2 := 0.00679497165889 ; +kq7.l8b1 := 0.00833106686491 ; +kq7.l8b2 := -0.00649247188092 ; +kq7.r1b1 := 0.00697608185623 ; +kq7.r1b2 := -0.00735911001315 ; +kq7.r2b1 := -0.00623620489135 ; +kq7.r2b2 := 0.00718492231168 ; +kq7.r4b1 := -0.00479427633356 ; +kq7.r4b2 := 0.00454157044397 ; +kq7.r5b1 := 0.00678205875524 ; +kq7.r5b2 := -0.00707735039586 ; +kq7.r8b1 := -0.00754512077678 ; +kq7.r8b2 := 0.00690495498755 ; +kq8.l1b1 := 0.00788991770585 ; +kq8.l1b2 := -0.00773094109684 ; +kq8.l2b1 := -0.00547415660079 ; +kq8.l2b2 := 0.00726632325962 ; +kq8.l4b1 := -0.00521992706363 ; +kq8.l4b2 := 0.00848005711303 ; +kq8.l5b1 := 0.00779228623922 ; +kq8.l5b2 := -0.00798051852319 ; +kq8.l6b1 := -0.00535026952088 ; +kq8.l6b2 := 0.00855121449088 ; +kq8.l8b1 := -0.00681816325179 ; +kq8.l8b2 := 0.00794197718102 ; +kq8.r1b1 := -0.0074437564601 ; +kq8.r1b2 := 0.00779814963993 ; +kq8.r2b1 := 0.00637606547308 ; +kq8.r2b2 := -0.0051645684354 ; +kq8.r4b1 := 0.00854230395036 ; +kq8.r4b2 := -0.00794369107791 ; +kq8.r5b1 := -0.0078081316648 ; +kq8.r5b2 := 0.00768860064574 ; +kq8.r6b1 := 0.00695471260443 ; +kq8.r6b2 := -0.00509873591832 ; +kq8.r8b1 := 0.00773968137743 ; +kq8.r8b2 := -0.00582188688679 ; +kq9.l1b1 := -0.00665580761999 ; +kq9.l1b2 := 0.00659840160344 ; +kq9.l2b1 := 0.00686932877059 ; +kq9.l2b2 := -0.00710505528087 ; +kq9.l4b1 := 0.00708860135363 ; +kq9.l4b2 := -0.00486100822584 ; +kq9.l5b1 := -0.00680637331579 ; +kq9.l5b2 := 0.00661092573379 ; +kq9.l6b1 := 0.00675292925701 ; +kq9.l6b2 := -0.00609193540023 ; +kq9.l8b1 := 0.00659755076164 ; +kq9.l8b2 := -0.00692505440628 ; +kq9.r1b1 := 0.00655277610103 ; +kq9.r1b2 := -0.00652937903272 ; +kq9.r2b1 := -0.00560807487271 ; +kq9.r2b2 := 0.00642104864045 ; +kq9.r4b1 := -0.00601048960123 ; +kq9.r4b2 := 0.00618134058962 ; +kq9.r5b1 := 0.00663208680717 ; +kq9.r5b2 := -0.00647878067718 ; +kq9.r6b1 := -0.00743798469507 ; +kq9.r6b2 := 0.0071271134909 ; +kq9.r8b1 := -0.00732077378701 ; +kq9.r8b2 := 0.00691086647423 ; +kqd.a12 := -0.008704755521 ; +kqd.a23 := -0.008553534086 ; +kqd.a34 := -0.008553534086 ; +kqd.a45 := -0.008704755521 ; +kqd.a56 := -0.008704755521 ; +kqd.a67 := -0.008859670695 ; +kqd.a78 := -0.008859670695 ; +kqd.a81 := -0.008704755521 ; +kqf.a12 := 0.008703299539 ; +kqf.a23 := 0.008740037422 ; +kqf.a34 := 0.008740037422 ; +kqf.a45 := 0.008703299539 ; +kqf.a56 := 0.008703299539 ; +kqf.a67 := 0.008772193705 ; +kqf.a78 := 0.008772193705 ; +kqf.a81 := 0.008703299539 ; +kqs.a12b2 := 0.0 ; +kqs.a23b1 := 0.0 ; +kqs.a34b2 := 0.0 ; +kqs.a45b1 := 0.0 ; +kqs.a56b2 := 0.0 ; +kqs.a67b1 := 0.0 ; +kqs.a78b2 := 0.0 ; +kqs.a81b1 := 0.0 ; +kqs.l1b2 := 0.0 ; +kqs.l2b1 := 0.0 ; +kqs.l3b2 := 0.0 ; +kqs.l4b1 := 0.0 ; +kqs.l5b2 := 0.0 ; +kqs.l6b1 := 0.0 ; +kqs.l7b2 := 0.0 ; +kqs.l8b1 := 0.0 ; +kqs.r1b1 := 0.0 ; +kqs.r2b2 := 0.0 ; +kqs.r3b1 := 0.0 ; +kqs.r4b2 := 0.0 ; +kqs.r5b1 := 0.0 ; +kqs.r6b2 := 0.0 ; +kqs.r7b1 := 0.0 ; +kqs.r8b2 := 0.0 ; +kqsx3.l1 := 0.0 ; +kqsx3.l2 := 0.0 ; +kqsx3.l5 := 0.0 ; +kqsx3.l8 := 0.0 ; +kqsx3.r1 := 0.0 ; +kqsx3.r2 := 0.0 ; +kqsx3.r5 := 0.0 ; +kqsx3.r8 := 0.0 ; +kqt12.l1b1 := -0.00143083258734 ; +kqt12.l1b2 := -0.000325227714244 ; +kqt12.l2b1 := -0.00109195520976 ; +kqt12.l2b2 := -0.00269819806703 ; +kqt12.l3b1 := 0.002842766616 ; +kqt12.l3b2 := 0.0009184540534 ; +kqt12.l4b1 := -0.00446769308961 ; +kqt12.l4b2 := 0.00069246893483 ; +kqt12.l5b1 := -0.000647050353316 ; +kqt12.l5b2 := 0.0023120589152 ; +kqt12.l6b1 := 0.00485986 ; +kqt12.l6b2 := 0.00452024371773 ; +kqt12.l7b1 := 0.00203869506 ; +kqt12.l7b2 := -0.0007051995313 ; +kqt12.l8b1 := 0.0033446005693 ; +kqt12.l8b2 := 9.2106190523e-05 ; +kqt12.r1b1 := -0.00151289884607 ; +kqt12.r1b2 := -0.00200803683076 ; +kqt12.r2b1 := -0.00032796038178 ; +kqt12.r2b2 := -0.00102754643448 ; +kqt12.r3b1 := 0.005 ; +kqt12.r3b2 := 0.002803576421 ; +kqt12.r4b1 := 0.00135649591107 ; +kqt12.r4b2 := 0.00330900795741 ; +kqt12.r5b1 := 0.00209923575817 ; +kqt12.r5b2 := -0.00111224427396 ; +kqt12.r6b1 := 0.00434021912796 ; +kqt12.r6b2 := -0.00237170163011 ; +kqt12.r7b1 := 0.0004148555029 ; +kqt12.r7b2 := -0.001386201846 ; +kqt12.r8b1 := -0.00348450981695 ; +kqt12.r8b2 := 0.0018122934551 ; +kqt13.l1b1 := 0.00135409675323 ; +kqt13.l1b2 := -0.00076912190119 ; +kqt13.l2b1 := 0.00298656247064 ; +kqt13.l2b2 := 0.00197892845905 ; +kqt13.l3b1 := -0.0006353716883 ; +kqt13.l3b2 := -0.00508018044 ; +kqt13.l4b1 := 0.00425385066958 ; +kqt13.l4b2 := 0.00157628963465 ; +kqt13.l5b1 := 0.00248701379072 ; +kqt13.l5b2 := -0.00042419606692 ; +kqt13.l6b1 := -0.00255213268089 ; +kqt13.l6b2 := -0.00403581373824 ; +kqt13.l7b1 := -0.0006470475605 ; +kqt13.l7b2 := -0.0006066477367 ; +kqt13.l8b1 := 0.000440117562444 ; +kqt13.l8b2 := 0.00328564029195 ; +kqt13.r1b1 := -0.0005768561773 ; +kqt13.r1b2 := 5.79181985044e-05 ; +kqt13.r2b1 := -0.00188002995876 ; +kqt13.r2b2 := 0.000716766597545 ; +kqt13.r3b1 := -0.004566289657 ; +kqt13.r3b2 := -0.0006320554999 ; +kqt13.r4b1 := 0.000883130547885 ; +kqt13.r4b2 := -0.00380676238123 ; +kqt13.r5b1 := -0.000689293727623 ; +kqt13.r5b2 := -0.00120130527148 ; +kqt13.r6b1 := 0.00474575921675 ; +kqt13.r6b2 := -0.00171561672252 ; +kqt13.r7b1 := 0.0001634702097 ; +kqt13.r7b2 := -0.0005855719594 ; +kqt13.r8b1 := 0.0035863414186 ; +kqt13.r8b2 := 0.00212540538422 ; +kqt4.l3 := 0.000688713 ; +kqt4.l7 := 0.000331689344 ; +kqt4.r3 := 0.000688713 ; +kqt4.r7 := 0.000331689344 ; +kqt5.l3 := 0.000972084 ; +kqt5.l7 := 0.0 ; +kqt5.r3 := 0.000972084 ; +kqt5.r7 := 0.0 ; +kqtd.a12b1 := 0.0 ; +kqtd.a12b2 := 0.0 ; +kqtd.a23b1 := 0.0008927411619395262 ; +kqtd.a23b2 := -0.0009388527411689877 ; +kqtd.a34b1 := 0.0008927411619395262 ; +kqtd.a34b2 := -0.0009388527411689877 ; +kqtd.a45b1 := 0.0 ; +kqtd.a45b2 := 0.0 ; +kqtd.a56b1 := 0.0 ; +kqtd.a56b2 := 0.0 ; +kqtd.a67b1 := -0.0009563572501604738 ; +kqtd.a67b2 := 0.0009102456709310123 ; +kqtd.a78b1 := -0.0009563572501604738 ; +kqtd.a78b2 := 0.0009102456709310123 ; +kqtd.a81b1 := 0.0 ; +kqtd.a81b2 := 0.0 ; +kqtf.a12b1 := 0.0 ; +kqtf.a12b2 := 0.0 ; +kqtf.a23b1 := -0.0007255160177301116 ; +kqtf.a23b2 := 0.000818486802342172 ; +kqtf.a34b1 := -0.0007255160177301116 ; +kqtf.a34b2 := 0.000818486802342172 ; +kqtf.a45b1 := 0.0 ; +kqtf.a45b2 := 0.0 ; +kqtf.a56b1 := 0.0 ; +kqtf.a56b2 := 0.0 ; +kqtf.a67b1 := 0.0008075949215698883 ; +kqtf.a67b2 := -0.0007146241369578281 ; +kqtf.a78b1 := 0.0008075949215698883 ; +kqtf.a78b2 := -0.0007146241369578281 ; +kqtf.a81b1 := 0.0 ; +kqtf.a81b2 := 0.0 ; +kqtl10.l3b1 := 0.000915285061 ; +kqtl10.l3b2 := 0.002148878916 ; +kqtl10.l7b1 := 0.004691498433 ; +kqtl10.l7b2 := 0.0001562433692 ; +kqtl10.r3b1 := 0.002852811764 ; +kqtl10.r3b2 := 0.0008518391125 ; +kqtl10.r7b1 := 0.0002340065042 ; +kqtl10.r7b2 := 0.004512070106 ; +kqtl11.l1b1 := 0.00209577285148 ; +kqtl11.l1b2 := -0.000551966548775 ; +kqtl11.l2b1 := 0.000813186941482 ; +kqtl11.l2b2 := 0.000912186409724 ; +kqtl11.l3b1 := -0.0003385236565 ; +kqtl11.l3b2 := -0.003413909006 ; +kqtl11.l4b1 := 0.000890141753735 ; +kqtl11.l4b2 := 0.00174183628307 ; +kqtl11.l5b1 := 0.000518401969416 ; +kqtl11.l5b2 := -0.000414206599249 ; +kqtl11.l6b1 := -0.00164112606056 ; +kqtl11.l6b2 := 0.00366884795937 ; +kqtl11.l7b1 := 0.001093003815 ; +kqtl11.l7b2 := 0.0003606025949 ; +kqtl11.l8b1 := -0.000441115007306 ; +kqtl11.l8b2 := -0.00288225606369 ; +kqtl11.r1b1 := -0.000337440106718 ; +kqtl11.r1b2 := 0.00220940586933 ; +kqtl11.r2b1 := -0.00124738378526 ; +kqtl11.r2b2 := 0.000577201139727 ; +kqtl11.r3b1 := -0.003631233322 ; +kqtl11.r3b2 := 0.001101610357 ; +kqtl11.r4b1 := -0.00408878647421 ; +kqtl11.r4b2 := 0.000870099001824 ; +kqtl11.r5b1 := -5.77786860222e-05 ; +kqtl11.r5b2 := 0.00129910498052 ; +kqtl11.r6b1 := -0.00161931273746 ; +kqtl11.r6b2 := 0.00184708467003 ; +kqtl11.r7b1 := -0.0001295175717 ; +kqtl11.r7b2 := 0.001319200255 ; +kqtl11.r8b1 := 0.00117225511051 ; +kqtl11.r8b2 := 7.82569661701e-05 ; +kqtl7.l3b1 := -0.001994900585 ; +kqtl7.l3b2 := 0.0007669052266 ; +kqtl7.l7b1 := 0.0003072313601 ; +kqtl7.l7b2 := 0.003911098692 ; +kqtl7.r3b1 := 0.0009102712091 ; +kqtl7.r3b2 := -0.002815536674 ; +kqtl7.r7b1 := 0.004117753828 ; +kqtl7.r7b2 := 0.0003079132134 ; +kqtl8.l3b1 := 0.0001293067741 ; +kqtl8.l3b2 := 0.002193623326 ; +kqtl8.l7b1 := 0.0005356315382 ; +kqtl8.l7b2 := 0.001413280626 ; +kqtl8.r3b1 := 0.002507454641 ; +kqtl8.r3b2 := -0.0001487395702 ; +kqtl8.r7b1 := 0.001800612514 ; +kqtl8.r7b2 := 0.00139274871 ; +kqtl9.l3b1 := -0.00471507917 ; +kqtl9.l3b2 := 8.471983894e-06 ; +kqtl9.l7b1 := 0.0001046498316 ; +kqtl9.l7b2 := 0.003635160604 ; +kqtl9.r3b1 := -7.46685541e-05 ; +kqtl9.r3b2 := -0.003969478967 ; +kqtl9.r7b1 := 0.003165157368 ; +kqtl9.r7b2 := 6.92028108e-05 ; +kqx.l1 := -0.00877140926768 ; +kqx.l2 := 0.008779857141 ; +kqx.l5 := 0.00858472622569 ; +kqx.l8 := 0.008779857141 ; +kqx.r1 := 0.00877140926768 ; +kqx.r2 := -0.008779857141 ; +kqx.r5 := -0.00858472622569 ; +kqx.r8 := -0.008779857141 ; +ksd1.a12b1 := -0.0973708023456 ; +ksd1.a12b2 := -0.30346350451 ; +ksd1.a23b1 := -0.15908087957536246 ; +ksd1.a23b2 := -0.1691358101437286 ; +ksd1.a34b1 := -0.15908087957536246 ; +ksd1.a34b2 := -0.1691358101437286 ; +ksd1.a45b1 := -0.0973708023456 ; +ksd1.a45b2 := -0.288896194719 ; +ksd1.a56b1 := -0.0973708023456 ; +ksd1.a56b2 := -0.262194737522 ; +ksd1.a67b1 := -0.15908087957536246 ; +ksd1.a67b2 := -0.1691358101437286 ; +ksd1.a78b1 := -0.15908087957536246 ; +ksd1.a78b2 := -0.1691358101437286 ; +ksd1.a81b1 := -0.0973708023456 ; +ksd1.a81b2 := -0.338046329195 ; +ksd2.a12b1 := -0.331716054064 ; +ksd2.a12b2 := -0.097762026909 ; +ksd2.a23b1 := -0.15908087957536246 ; +ksd2.a23b2 := -0.1691358101437286 ; +ksd2.a34b1 := -0.15908087957536246 ; +ksd2.a34b2 := -0.1691358101437286 ; +ksd2.a45b1 := -0.299706767852 ; +ksd2.a45b2 := -0.097762026909 ; +ksd2.a56b1 := -0.330585957973 ; +ksd2.a56b2 := -0.097762026909 ; +ksd2.a67b1 := -0.15908087957536246 ; +ksd2.a67b2 := -0.1691358101437286 ; +ksd2.a78b1 := -0.15908087957536246 ; +ksd2.a78b2 := -0.1691358101437286 ; +ksd2.a81b1 := -0.302163103647 ; +ksd2.a81b2 := -0.097762026909 ; +ksf1.a12b1 := 0.201212405992 ; +ksf1.a12b2 := 0.0592526249753 ; +ksf1.a23b1 := 0.08547443947858442 ; +ksf1.a23b2 := 0.10098349428092675 ; +ksf1.a34b1 := 0.08547443947858442 ; +ksf1.a34b2 := 0.10098349428092675 ; +ksf1.a45b1 := 0.200816993632 ; +ksf1.a45b2 := 0.0592526249753 ; +ksf1.a56b1 := 0.200057162122 ; +ksf1.a56b2 := 0.0592526249753 ; +ksf1.a67b1 := 0.08547443947858442 ; +ksf1.a67b2 := 0.10098349428092675 ; +ksf1.a78b1 := 0.08547443947858442 ; +ksf1.a78b2 := 0.10098349428092675 ; +ksf1.a81b1 := 0.222099037836 ; +ksf1.a81b2 := 0.0592526249753 ; +ksf2.a12b1 := 0.0591207281691 ; +ksf2.a12b2 := 0.173687616539 ; +ksf2.a23b1 := 0.08547443947858442 ; +ksf2.a23b2 := 0.10098349428092675 ; +ksf2.a34b1 := 0.08547443947858442 ; +ksf2.a34b2 := 0.10098349428092675 ; +ksf2.a45b1 := 0.0591207281691 ; +ksf2.a45b2 := 0.185302570675 ; +ksf2.a56b1 := 0.0591207281691 ; +ksf2.a56b2 := 0.200071563609 ; +ksf2.a67b1 := 0.08547443947858442 ; +ksf2.a67b2 := 0.10098349428092675 ; +ksf2.a78b1 := 0.08547443947858442 ; +ksf2.a78b2 := 0.10098349428092675 ; +ksf2.a81b1 := 0.0591207281691 ; +ksf2.a81b2 := 0.15764507901 ; +kss.a12b1 := 0.0 ; +kss.a12b2 := 0.0 ; +kss.a23b1 := 0.0 ; +kss.a23b2 := 0.0 ; +kss.a34b2 := 0.0 ; +kss.a45b1 := 0.0 ; +kss.a45b2 := 0.0 ; +kss.a56b1 := 0.0 ; +kss.a56b2 := 0.0 ; +kss.a67b1 := 0.0 ; +kss.a67b2 := 0.0 ; +kss.a78b1 := 0.0 ; +kss.a78b2 := 0.0 ; +kss.a81b1 := 0.0 ; +kss.a81b2 := 0.0 ; +ktqx1.l1 := 6.17780576399e-05 ; +ktqx1.l2 := 0.0 ; +ktqx1.l5 := 0.0 ; +ktqx1.l8 := 0.0 ; +ktqx1.r1 := -6.17780576399e-05 ; +ktqx1.r2 := 0.0 ; +ktqx1.r5 := 0.0 ; +ktqx1.r8 := 0.0 ; +ktqx2.l1 := -1.21636619723e-05 ; +ktqx2.l2 := 0.0 ; +ktqx2.l5 := 0.000264468113933 ; +ktqx2.l8 := 0.0 ; +ktqx2.r1 := 1.21636619723e-05 ; +ktqx2.r2 := 0.0 ; +ktqx2.r5 := -0.000264468113933 ; +ktqx2.r8 := 0.0 ; +nrj := 6800.0 ; +arc_squeeze := 1.0 ; +betx_ip1 := 0.51 ; +bety_ip1 := 0.153 ; +betx_ip5 := 0.153 ; +bety_ip5 := 0.51 ; +rx_ip1 := 1.0 ; +ry_ip1 := 3.333333 ; +rx_ip5 := 3.333333 ; +ry_ip5 := 1.0 ; +on_x1 := 0.0 ; +on_sep1 := 0.0 ; +on_oh1 := 0.0 ; +on_ov1 := 0.0 ; +phi_ir1 := 0.0 ; +on_sep1_h := 0.0 ; +on_sep1_v := 0.0 ; +on_x1_h := 120.0 ; +on_x1_v := 0.0 ; +on_x5 := 0.0 ; +on_sep5 := 0.0 ; +on_oh5 := 0.0 ; +on_ov5 := 0.0 ; +phi_ir5 := -90.0 ; +on_sep5_h := 0.0 ; +on_sep5_v := 0.0 ; +on_x5_h := 0.0 ; +on_x5_v := -120.0 ; +on_x2h := 0.0 ; +on_sep2h := -0.1 ; +on_x2v := 200.0 ; +on_sep2v := 0.0 ; +on_a2 := 0.0 ; +on_o2 := 0.0 ; +on_oh2 := 0.0 ; +on_ov2 := 0.0 ; +phi_ir2 := 90.0 ; +on_x8h := 0.0 ; +on_sep8h := -0.02 ; +on_x8v := 200.0 ; +on_sep8v := 0.01 ; +on_a8 := 0.0 ; +on_o8 := 0.0 ; +on_oh8 := 0.0 ; +on_ov8 := 0.0 ; +phi_ir8 := 180.0 ; +on_disp := 1.0 ; +abas := 8.817425235294117e-05 ; +abls := 2.2043563088235292e-05 ; +abcs := 0.00017634850470588234 ; +kd3.lr3 := 5.550855237809782e-05 ; +kd4.lr3 := 5.550855237809782e-05 ; +kd3.lr7 := 5.5508555673332175e-05 ; +kd4.lr7 := 5.5508555673332175e-05 ; +ksumd2.l1b2 := 0.00011947605022485886 ; +ksumd2.l2b2 := 0.00016216987485375914 ; +ksumd2.l5b2 := 0.00011947605022485886 ; +ksumd2.l8b2 := 0.00016216987485375914 ; +ksumd2.r1b2 := 0.00011947605022485886 ; +ksumd2.r2b2 := 0.00016216987485375914 ; +ksumd2.r5b2 := 0.00011947605022485886 ; +ksumd2.r8b2 := 0.00016216987485375914 ; +acbxv1.l1x := 3.92156862745e-08 ; +acbxv1.l1s := -8e-06 ; +acbxv1.r1x := -3.92156862745e-08 ; +acbxv1.r1s := -8e-06 ; +acbxh1.l1x := 3.92156862745e-08 ; +acbxh1.l1s := 8e-06 ; +acbxh1.r1x := -3.92156862745e-08 ; +acbxh1.r1s := 8e-06 ; +acbxv2.l1x := 3.92156862745e-08 ; +acbxv2.l1s := -8e-06 ; +acbxv2.r1x := -3.92156862745e-08 ; +acbxv2.r1s := -8e-06 ; +acbxh2.l1x := 3.92156862745e-08 ; +acbxh2.l1s := 8e-06 ; +acbxh2.r1x := -3.92156862745e-08 ; +acbxh2.r1s := 8e-06 ; +acbxv3.l1x := 3.92156862745e-08 ; +acbxv3.l1s := -8e-06 ; +acbxv3.r1x := -3.92156862745e-08 ; +acbxv3.r1s := -8e-06 ; +acbxh3.l1x := 3.92156862745e-08 ; +acbxh3.l1s := 8e-06 ; +acbxh3.r1x := -3.92156862745e-08 ; +acbxh3.r1s := 8e-06 ; +acbyvs4.l1b1x := -2.55359028125e-07 ; +acbyvs4.l1b1s := -2.28169370618e-05 ; +acbyvs4.l1b1ov := 3.49564681638e-05 ; +acbyvs4.r1b1x := 1.34856462356e-07 ; +acbyvs4.r1b1s := -6.3292474954e-10 ; +acbyvs4.r1b1ov := 2.86008891915e-05 ; +acbcv5.l1b1x := -9.07189087589e-08 ; +acbcv5.l1b1s := 1.08413589033e-05 ; +acbcv5.l1b1ov := 3.26224069977e-05 ; +acbcv6.r1b1x := 1.22997829661e-07 ; +acbcv6.r1b1s := -6.91716300209e-06 ; +acbcv6.r1b1ov := 2.66911932673e-05 ; +acbyhs4.l1b1x := -1.43607764206e-07 ; +acbyhs4.l1b1s := 4.92875028224e-07 ; +acbyhs4.l1b1oh := 3.05767392353e-05 ; +acbyhs4.r1b1x := 2.36311937225e-07 ; +acbyhs4.r1b1s := 2.50914475755e-05 ; +acbyhs4.r1b1oh := 3.26564219051e-05 ; +acbch6.l1b1x := -1.09715941946e-07 ; +acbch6.l1b1s := 6.17015417152e-06 ; +acbch6.l1b1oh := 2.85351147983e-05 ; +acbch5.r1b1x := 1.07997057279e-07 ; +acbch5.r1b1s := -1.29051137599e-05 ; +acbch5.r1b1oh := 3.0475935998e-05 ; +acbch8.l1b1oh := -1.37214280824e-05 ; +acbcv7.l1b1ov := -4.20490585637e-05 ; +acbch7.r1b1oh := -4.34308688424e-05 ; +acbcv8.r1b1ov := -1.34179876587e-05 ; +acbyvs4.l1b2x := 1.44420715251e-07 ; +acbyvs4.l1b2s := 5.3850815308e-07 ; +acbyvs4.l1b2ov := 2.92486799849e-05 ; +acbyvs4.r1b2x := -2.37186310979e-07 ; +acbyvs4.r1b2s := 2.49886659291e-05 ; +acbyvs4.r1b2ov := 3.23325629437e-05 ; +acbcv6.l1b2x := 1.12742451933e-07 ; +acbcv6.l1b2s := 6.34042030229e-06 ; +acbcv6.l1b2ov := 2.72957307398e-05 ; +acbcv5.r1b2x := -1.08124353054e-07 ; +acbcv5.r1b2s := -1.29213950297e-05 ; +acbcv5.r1b2ov := 3.01737012643e-05 ; +acbyhs4.l1b2x := 2.56199137184e-07 ; +acbyhs4.l1b2s := -2.27150314952e-05 ; +acbyhs4.l1b2oh := 3.67418155631e-05 ; +acbyhs4.r1b2x := -1.32250425119e-07 ; +acbyhs4.r1b2s := 1.45838803623e-07 ; +acbyhs4.r1b2oh := 2.93786031881e-05 ; +acbch5.l1b2x := 9.03558404749e-08 ; +acbch5.l1b2s := 1.07970802636e-05 ; +acbch5.l1b2oh := 3.42885458427e-05 ; +acbch6.r1b2x := -1.23028095849e-07 ; +acbch6.r1b2s := -6.9188052562e-06 ; +acbch6.r1b2oh := 2.74169789046e-05 ; +acbcv8.l1b2ov := -1.42319581869e-05 ; +acbch7.l1b2oh := -4.08737944726e-05 ; +acbcv7.r1b2ov := -4.37126614107e-05 ; +acbch8.r1b2oh := -1.31793646838e-05 ; +acbxv1.l5x := 2.66944543019e-08 ; +acbxv1.l5s := 8e-06 ; +acbxv1.r5x := -2.66944543019e-08 ; +acbxv1.r5s := 8e-06 ; +acbxh1.l5x := 2.66944543019e-08 ; +acbxh1.l5s := -8e-06 ; +acbxh1.r5x := -2.66944543019e-08 ; +acbxh1.r5s := -8e-06 ; +acbxv2.l5x := 2.66944543019e-08 ; +acbxv2.l5s := 8e-06 ; +acbxv2.r5x := -2.66944543019e-08 ; +acbxv2.r5s := 8e-06 ; +acbxh2.l5x := 2.66944543019e-08 ; +acbxh2.l5s := -8e-06 ; +acbxh2.r5x := -2.66944543019e-08 ; +acbxh2.r5s := -8e-06 ; +acbxv3.l5x := 2.66944543019e-08 ; +acbxv3.l5s := 8e-06 ; +acbxv3.r5x := -2.66944543019e-08 ; +acbxv3.r5s := 8e-06 ; +acbxh3.l5x := 2.66944543019e-08 ; +acbxh3.l5s := -8e-06 ; +acbxh3.r5x := -2.66944543019e-08 ; +acbxh3.r5s := -8e-06 ; +acbyvs4.l5b1x := -2.67858414657e-07 ; +acbyvs4.l5b1s := 6.51082065215e-06 ; +acbyvs4.l5b1ov := 3.56084422744e-05 ; +acbyvs4.r5b1x := 3.49412142116e-08 ; +acbyvs4.r5b1s := 1.08736707496e-05 ; +acbyvs4.r5b1ov := 3.25754515974e-05 ; +acbcv5.l5b1x := -2.36577956128e-09 ; +acbcv5.l5b1s := 9.81143327659e-07 ; +acbcv5.l5b1ov := 3.32308484652e-05 ; +acbcv6.r5b1x := 2.06123223338e-07 ; +acbcv6.r5b1s := -2.60824218087e-06 ; +acbcv6.r5b1ov := 3.0400372119e-05 ; +acbyhs4.l5b1x := -1.55167344069e-08 ; +acbyhs4.l5b1s := -1.11192796839e-05 ; +acbyhs4.l5b1oh := 3.23115441362e-05 ; +acbyhs4.r5b1x := 2.6828218597e-07 ; +acbyhs4.r5b1s := -6.68905454466e-06 ; +acbyhs4.r5b1oh := 3.50220877347e-05 ; +acbch6.l5b1x := -2.23399568237e-07 ; +acbch6.l5b1s := 2.82676284938e-06 ; +acbch6.l5b1oh := 3.01540858933e-05 ; +acbch5.r5b1x := 1.98031233603e-09 ; +acbch5.r5b1s := -8.19481650341e-07 ; +acbch5.r5b1oh := 3.26836451165e-05 ; +acbch8.l5b1oh := -1.35821096188e-05 ; +acbcv7.l5b1ov := -4.68678811378e-05 ; +acbch7.r5b1oh := -5.27048227381e-05 ; +acbcv8.r5b1ov := -1.48420056291e-05 ; +acbyvs4.l5b2x := 1.5984717441e-08 ; +acbyvs4.l5b2s := -1.11135425323e-05 ; +acbyvs4.l5b2ov := 2.97073944275e-05 ; +acbyvs4.r5b2x := -2.68288848428e-07 ; +acbyvs4.r5b2s := -6.68933418481e-06 ; +acbyvs4.r5b2ov := 3.44899966963e-05 ; +acbcv6.l5b2x := 2.23902331229e-07 ; +acbcv6.l5b2s := 2.83321551092e-06 ; +acbcv6.l5b2ov := 2.77238165857e-05 ; +acbcv5.r5b2x := -1.9773513728e-09 ; +acbcv5.r5b2s := -8.2005041927e-07 ; +acbcv5.r5b2ov := 3.21870820674e-05 ; +acbyhs4.l5b2x := 2.67850935485e-07 ; +acbyhs4.l5b2s := 6.51060816059e-06 ; +acbyhs4.l5b2oh := 3.69068184796e-05 ; +acbyhs4.r5b2x := -3.38778684671e-08 ; +acbyhs4.r5b2s := 1.08869443521e-05 ; +acbyhs4.r5b2oh := 3.30123611105e-05 ; +acbch5.l5b2x := 2.37137719294e-09 ; +acbch5.l5b2s := 9.81298645472e-07 ; +acbch5.l5b2oh := 3.44425314305e-05 ; +acbch6.r5b2x := -2.05106549804e-07 ; +acbch6.r5b2s := -2.59529025544e-06 ; +acbch6.r5b2oh := 3.08081089616e-05 ; +acbcv8.l5b2ov := -1.4991174988e-05 ; +acbch7.l5b2oh := -4.37872604563e-05 ; +acbcv7.r5b2ov := -5.34605699162e-05 ; +acbch8.r5b2oh := -1.44159703538e-05 ; +abxwt.l2 := -7.953104239642468e-05 ; +abwmd.l2 := 0.00015158986592583645 ; +abaw.r2 := -0.00013747535326976272 ; +abxwt.r2 := 6.541652974035096e-05 ; +acbxv1.l2x := 7.94117647059e-08 ; +acbxv1.l2s := 8e-06 ; +acbxv1.r2x := -7.94117647059e-08 ; +acbxv1.r2s := 8e-06 ; +acbxh1.l2x := 0.0 ; +acbxh1.l2s := 0.0 ; +acbxh1.r2x := -7.94117647059e-08 ; +acbxh1.r2s := 8e-06 ; +acbxv2.l2x := 7.94117647059e-08 ; +acbxv2.l2s := 8e-06 ; +acbxv2.r2x := -7.94117647059e-08 ; +acbxv2.r2s := 8e-06 ; +acbxh2.l2x := 1.19117647059e-07 ; +acbxh2.l2s := 1.2e-05 ; +acbxh2.r2x := -7.94117647059e-08 ; +acbxh2.r2s := 8e-06 ; +acbxv3.l2x := 7.94117647059e-08 ; +acbxv3.l2s := 8e-06 ; +acbxv3.r2x := -7.94117647059e-08 ; +acbxv3.r2s := 8e-06 ; +acbxh3.l2x := 1.19117647059e-07 ; +acbxh3.l2s := 1.2e-05 ; +acbxh3.r2x := -7.94117647059e-08 ; +acbxh3.r2s := 8e-06 ; +acbyvs4.l2b1x := -3.07194930135e-07 ; +acbyvs4.l2b1s := -1.56290054124e-06 ; +acbyvs4.l2b1o := 4.69607420532e-05 ; +acbyvs4.l2b1ov := 1.42221999242e-05 ; +acbyvs4.r2b1x := 1.43143625268e-07 ; +acbyvs4.r2b1s := 1.47560490812e-05 ; +acbyvs4.r2b1o := 0.000101930078648 ; +acbyvs4.r2b1ov := 3.44374941727e-05 ; +acbyvs5.l2b1x := -8.06879811504e-08 ; +acbyvs5.l2b1s := 1.50314791552e-05 ; +acbyvs5.l2b1o := -4.46405844704e-05 ; +acbyvs5.l2b1ov := -4.04951724612e-07 ; +acbcvs5.r2b1x := 2.03613492914e-07 ; +acbcvs5.r2b1s := -3.79024589843e-06 ; +acbcvs5.r2b1o := -5.22956704207e-05 ; +acbcvs5.r2b1ov := -6.33664993151e-06 ; +acbyhs4.l2b1x := -2.62176404352e-07 ; +acbyhs4.l2b1s := 7.91967278401e-06 ; +acbyhs4.l2b1a := 5.10849463344e-07 ; +acbyhs4.l2b1oh := 3.20333854219e-05 ; +acbyhs4.r2b1x := 2.7368729816e-07 ; +acbyhs4.r2b1s := -7.80265136087e-06 ; +acbyhs4.r2b1a := -4.53848429188e-07 ; +acbyhs4.r2b1oh := 1.37287747067e-05 ; +acbyhs5.l2b1x := -1.46683004517e-07 ; +acbyhs5.l2b1s := -1.3488786884e-06 ; +acbyhs5.l2b1a := -5.50087257838e-07 ; +acbyhs5.l2b1oh := -6.01546179864e-06 ; +acbchs5.r2b1x := 1.22457864576e-07 ; +acbchs5.r2b1s := 2.28101950779e-05 ; +acbchs5.r2b1a := 1.02130113904e-06 ; +acbchs5.r2b1oh := 2.26861392054e-06 ; +acbch6.r2b1oh := -1.2812097434e-05 ; +acbcv6.l2b1ov := -1.32725763986e-05 ; +acbch7.l2b1oh := -1.53462919616e-05 ; +acbcv7.r2b1ov := -1.64980326944e-05 ; +acbyvs4.l2b2x := 1.93259166455e-07 ; +acbyvs4.l2b2s := -1.382315375e-05 ; +acbyvs4.l2b2o := 8.90585145945e-05 ; +acbyvs4.l2b2ov := 3.47982783653e-05 ; +acbyvs4.r2b2x := -2.80987883248e-07 ; +acbyvs4.r2b2s := 6.44504373579e-06 ; +acbyvs4.r2b2o := 6.14597613496e-05 ; +acbyvs4.r2b2ov := 1.26991240468e-05 ; +acbyvs5.l2b2x := 1.58137064379e-07 ; +acbyvs5.l2b2s := 2.94370693308e-06 ; +acbyvs5.l2b2o := -4.06156033031e-05 ; +acbyvs5.l2b2ov := -1.36155756772e-06 ; +acbcvs5.r2b2x := -1.24355196437e-07 ; +acbcvs5.r2b2s := -2.31662954506e-05 ; +acbcvs5.r2b2o := -6.87994117717e-05 ; +acbcvs5.r2b2ov := -2.64029425983e-06 ; +acbyhs4.l2b2x := 3.33152655809e-07 ; +acbyhs4.l2b2s := 1.70156540597e-06 ; +acbyhs4.l2b2a := 1.02485745325e-07 ; +acbyhs4.l2b2oh := 1.24735320344e-05 ; +acbyhs4.r2b2x := -1.32487387699e-07 ; +acbyhs4.r2b2s := -1.4952949307e-05 ; +acbyhs4.r2b2a := -7.57940504524e-07 ; +acbyhs4.r2b2oh := 3.60507473978e-05 ; +acbyhs5.l2b2x := 7.13500357922e-08 ; +acbyhs5.l2b2s := -1.6718877448e-05 ; +acbyhs5.l2b2a := -6.94687786667e-07 ; +acbyhs5.l2b2oh := -8.00373020488e-06 ; +acbchs5.r2b2x := -2.01331646311e-07 ; +acbchs5.r2b2s := 3.74705525253e-06 ; +acbchs5.r2b2a := 6.77373856816e-07 ; +acbchs5.r2b2oh := -7.30145399095e-06 ; +acbch6.l2b2oh := -1.16406679536e-05 ; +acbcv6.r2b2ov := -1.18511970726e-05 ; +acbch7.r2b2oh := -1.72708968383e-05 ; +acbcv7.l2b2ov := -1.66708742308e-05 ; +abxws.l8 := -4.7025174878201355e-05 ; +abxwh.l8 := 0.00018599576311349546 ; +ablw.r8 := -0.00018599576311349546 ; +abxws.r8 := 4.7025174878201355e-05 ; +acbxv1.l8x := 7.94117647059e-08 ; +acbxv1.l8s := 8e-06 ; +acbxv1.r8x := -7.94117647059e-08 ; +acbxv1.r8s := 8e-06 ; +acbxh1.l8x := 7.94117647059e-08 ; +acbxh1.l8s := 8e-06 ; +acbxh1.r8x := -7.94117647059e-08 ; +acbxh1.r8s := 8e-06 ; +acbxv2.l8x := 7.94117647059e-08 ; +acbxv2.l8s := 8e-06 ; +acbxv2.r8x := -7.94117647059e-08 ; +acbxv2.r8s := 8e-06 ; +acbxh2.l8x := 7.94117647059e-08 ; +acbxh2.l8s := 8e-06 ; +acbxh2.r8x := -7.94117647059e-08 ; +acbxh2.r8s := 8e-06 ; +acbxv3.l8x := 7.94117647059e-08 ; +acbxv3.l8s := 8e-06 ; +acbxv3.r8x := -7.94117647059e-08 ; +acbxv3.r8s := 8e-06 ; +acbxh3.l8x := 7.94117647059e-08 ; +acbxh3.l8s := 8e-06 ; +acbxh3.r8x := -7.94117647059e-08 ; +acbxh3.r8s := 8e-06 ; +acbyvs4.l8b1x := -3.02642618865e-07 ; +acbyvs4.l8b1s := -2.41095774588e-06 ; +acbyvs4.l8b1a := 2.12444583864e-07 ; +acbyvs4.l8b1ov := 1.62259163913e-05 ; +acbyvs4.r8b1x := 2.1126785665e-07 ; +acbyvs4.r8b1s := 1.3487922962e-05 ; +acbyvs4.r8b1a := -4.92968277231e-07 ; +acbyvs4.r8b1ov := 2.85153548031e-05 ; +acbcvs5.l8b1x := -8.17812900575e-08 ; +acbcvs5.l8b1s := 1.52351548812e-05 ; +acbcvs5.l8b1a := -6.82140373546e-07 ; +acbcvs5.l8b1ov := -5.8119610897e-06 ; +acbyvs5.r8b1x := 1.54036896887e-07 ; +acbyvs5.r8b1s := -2.86738225586e-06 ; +acbyvs5.r8b1a := 5.18290107292e-07 ; +acbyvs5.r8b1ov := 6.78664886546e-06 ; +acbyhs4.l8b1x := -2.12217344413e-07 ; +acbyhs4.l8b1s := 1.34690668025e-05 ; +acbyhs4.l8b1o := 8.41799144029e-05 ; +acbyhs4.l8b1oh := 3.29312989032e-05 ; +acbyhs4.r8b1x := 3.03083663425e-07 ; +acbyhs4.r8b1s := -2.32699793024e-06 ; +acbyhs4.r8b1o := 4.92286709868e-05 ; +acbyhs4.r8b1oh := 1.42213688836e-05 ; +acbchs5.l8b1x := -1.59496997383e-07 ; +acbchs5.l8b1s := -2.96845579609e-06 ; +acbchs5.l8b1o := -4.0960372816e-05 ; +acbchs5.l8b1oh := 1.61827789277e-06 ; +acbyhs5.r8b1x := 8.38803411375e-08 ; +acbyhs5.r8b1s := 1.56243696651e-05 ; +acbyhs5.r8b1o := -4.64000469737e-05 ; +acbyhs5.r8b1oh := -3.20579608282e-06 ; +acbch6.r8b1oh := -1.32718008471e-05 ; +acbcv6.l8b1ov := -1.51425036977e-05 ; +acbch7.l8b1oh := -1.57764569991e-05 ; +acbcv7.r8b1ov := -1.36609026625e-05 ; +acbyvs4.l8b2x := 2.09616003538e-07 ; +acbyvs4.l8b2s := -1.35186728052e-05 ; +acbyvs4.l8b2a := 4.9852642683e-07 ; +acbyvs4.l8b2ov := 3.40724684736e-05 ; +acbyvs4.r8b2x := -3.04202387622e-07 ; +acbyvs4.r8b2s := 2.12038274461e-06 ; +acbyvs4.r8b2a := -1.99434349216e-07 ; +acbyvs4.r8b2ov := 1.40667018538e-05 ; +acbcvs5.l8b2x := 1.54919507241e-07 ; +acbcvs5.l8b2s := 2.88381245131e-06 ; +acbcvs5.l8b2a := -5.212599268e-07 ; +acbcvs5.l8b2ov := 6.64294388388e-06 ; +acbyvs5.r8b2x := -8.35168046046e-08 ; +acbyvs5.r8b2s := -1.55584569523e-05 ; +acbyvs5.r8b2a := 6.96615933347e-07 ; +acbyvs5.r8b2ov := -2.60995153799e-06 ; +acbyhs4.l8b2x := 3.04172651654e-07 ; +acbyhs4.l8b2s := 2.12415103904e-06 ; +acbyhs4.l8b2o := 4.86262759046e-05 ; +acbyhs4.l8b2oh := 1.57507211976e-05 ; +acbyhs4.r8b2x := -2.09669705381e-07 ; +acbyhs4.r8b2s := -1.35164815973e-05 ; +acbyhs4.r8b2o := 8.48341727668e-05 ; +acbyhs4.r8b2oh := 2.69254708427e-05 ; +acbchs5.l8b2x := 8.36611917093e-08 ; +acbchs5.l8b2s := -1.55835450759e-05 ; +acbchs5.l8b2o := -4.62788201924e-05 ; +acbchs5.l8b2oh := -9.76612874088e-06 ; +acbyhs5.r8b2x := -1.55134922464e-07 ; +acbyhs5.r8b2s := 2.88727150808e-06 ; +acbyhs5.r8b2o := -3.98401497529e-05 ; +acbyhs5.r8b2oh := 6.120646841e-06 ; +acbch6.l8b2oh := -1.46990375289e-05 ; +acbcv6.r8b2ov := -1.31274610135e-05 ; +acbch7.r8b2oh := -1.28992340746e-05 ; +acbcv7.l8b2ov := -1.63231591717e-05 ; +dqx.b1 := 0.0 ; +dqy.b1 := 0.0 ; +dqx.b1_sq := 0.006035999986715323 ; +dqy.b1_sq := 0.0020682142638924587 ; +dqx.b2 := 0.0 ; +dqy.b2 := 0.0 ; +dqx.b2_sq := 0.00603791838964124 ; +dqy.b2_sq := 0.0020664113754588435 ; +dqpx.b1 := 0.0 ; +dqpy.b1 := 0.0 ; +dqpx.b1_sq := 10.723817194638977 ; +dqpy.b1_sq := 9.73508224720886 ; +on_qpbump.b1 := 0.0 ; +dqpx.b2 := 0.0 ; +dqpy.b2 := 0.0 ; +dqpx.b2_sq := 11.319659171849773 ; +dqpy.b2_sq := 9.993662778137592 ; +on_qpbump.b2 := 0.0 ; +cmrs.b1 := 0.0 ; +cmis.b1 := 0.0 ; +cmrs.b1_sq := 0.0 ; +cmis.b1_sq := 0.0 ; +ona2_b1 := 0.0 ; +cmrs.b2 := 0.0 ; +cmis.b2 := 0.0 ; +cmrs.b2_sq := 0.0 ; +cmis.b2_sq := 0.0 ; +ona2_b2 := 0.0 ; +ona3_b1 := 0.0 ; +kss.a34b1 := 0.0 ; +ona3_b2 := 0.0 ; +dqxdjy.b1 := 0.0 ; +dqxdjy.b1_sq := 0.0 ; +kof.b1 := -12.0 ; +kod.b1 := -12.0 ; +dqxdjy.b2 := 0.0 ; +dqxdjy.b2_sq := 0.0 ; +kof.b2 := -12.0 ; +kod.b2 := -12.0 ; +acbh14.r8b1x := 0.0 ; +acbh14.r8b1s := -0.0 ; +acbh16.r8b1x := 6.05936278156e-08 ; +acbh16.r8b1s := -1.32004722096e-06 ; +acbh14.l1b1x := -3.65599835187e-10 ; +acbh14.l1b1s := 7.59455525633e-09 ; +acbh12.l1b1x := -6.08972558823e-08 ; +acbh12.l1b1s := 1.32666705728e-06 ; +acbh13.r1b1x := -4.94827132742e-08 ; +acbh13.r1b1s := -4.00412295344e-07 ; +acbh15.r1b1x := -3.74154871573e-12 ; +acbh15.r1b1s := 1.01542958792e-10 ; +acbh15.l2b1x := 4.94816743106e-08 ; +acbh15.l2b1s := 4.00416148323e-07 ; +acbh13.l2b1x := 0.0 ; +acbh13.l2b1s := -0.0 ; +acbv13.r8b1x := 0.0 ; +acbv13.r8b1s := -0.0 ; +acbv15.r8b1x := -5.42594725414e-08 ; +acbv15.r8b1s := -3.55401004311e-07 ; +acbv15.l1b1x := -1.21120127141e-10 ; +acbv15.l1b1s := -9.06654905652e-10 ; +acbv13.l1b1x := 5.41571548078e-08 ; +acbv13.l1b1s := 3.54706073002e-07 ; +acbv12.r1b1x := 6.68039311533e-08 ; +acbv12.r1b1s := -1.40274818458e-06 ; +acbv14.r1b1x := 1.79265823862e-10 ; +acbv14.r1b1s := -3.35839704142e-09 ; +acbv16.l2b1x := -6.66068445864e-08 ; +acbv16.l2b1s := 1.39848949504e-06 ; +acbv14.l2b1x := 0.0 ; +acbv14.l2b1s := -0.0 ; +acbh14.r4b1x := 0.0 ; +acbh14.r4b1s := 0.0 ; +acbh16.r4b1x := 4.94014874903e-08 ; +acbh16.r4b1s := 3.96983890326e-07 ; +acbh14.l5b1x := -6.41612418731e-10 ; +acbh14.l5b1s := -5.10215565392e-09 ; +acbh12.l5b1x := -4.9999322642e-08 ; +acbh12.l5b1s := -4.01918316705e-07 ; +acbh13.r5b1x := -7.20685824088e-08 ; +acbh13.r5b1s := 1.55188375091e-06 ; +acbh15.r5b1x := -1.16530481615e-11 ; +acbh15.r5b1s := -2.26824889682e-10 ; +acbh15.l6b1x := 7.20654569447e-08 ; +acbh15.l6b1s := -1.55182576152e-06 ; +acbh13.l6b1x := 0.0 ; +acbh13.l6b1s := 0.0 ; +acbv13.r4b1x := 0.0 ; +acbv13.r4b1s := 0.0 ; +acbv15.r4b1x := -7.83497118351e-08 ; +acbv15.r4b1s := 1.65038328903e-06 ; +acbv15.l5b1x := -1.72053046773e-10 ; +acbv15.l5b1s := 4.11272567731e-09 ; +acbv13.l5b1x := 7.80787530395e-08 ; +acbv13.l5b1s := -1.64454998754e-06 ; +acbv12.r5b1x := 4.76607605737e-08 ; +acbv12.r5b1s := 2.92024506696e-07 ; +acbv14.r5b1x := 1.48575215661e-10 ; +acbv14.r5b1s := 7.91225257179e-10 ; +acbv16.l6b1x := -4.74916139828e-08 ; +acbv16.l6b1s := -2.9095097663e-07 ; +acbv14.l6b1x := 0.0 ; +acbv14.l6b1s := 0.0 ; +acbh13.r8b2x := 0.0 ; +acbh13.r8b2s := -0.0 ; +acbh15.r8b2x := 6.99555667429e-08 ; +acbh15.r8b2s := -3.69901862471e-07 ; +acbh15.l1b2x := -6.09415416138e-12 ; +acbh15.l1b2s := -1.25882623584e-10 ; +acbh13.l1b2x := -6.98822851836e-08 ; +acbh13.l1b2s := 3.69592329956e-07 ; +acbh12.r1b2x := -8.44648273813e-08 ; +acbh12.r1b2s := -1.73593502127e-06 ; +acbh14.r1b2x := 1.55026283892e-10 ; +acbh14.r1b2s := 3.85926183238e-09 ; +acbh16.l2b2x := 8.44427562899e-08 ; +acbh16.l2b2s := 1.73559725823e-06 ; +acbh14.l2b2x := 0.0 ; +acbh14.l2b2s := -0.0 ; +acbv14.r8b2x := 0.0 ; +acbv14.r8b2s := -0.0 ; +acbv16.r8b2x := -6.42200327004e-08 ; +acbv16.r8b2s := -1.34672112642e-06 ; +acbv14.l1b2x := 3.07495861075e-10 ; +acbv14.l1b2s := 5.85146001587e-09 ; +acbv12.l1b2x := 6.45042723842e-08 ; +acbv12.l1b2s := 1.35291251237e-06 ; +acbv13.r1b2x := 5.31848415516e-08 ; +acbv13.r1b2s := -3.48435109163e-07 ; +acbv15.r1b2x := -1.16602930285e-10 ; +acbv15.r1b2s := 9.47052962716e-10 ; +acbv15.l2b2x := -5.31839218509e-08 ; +acbv15.l2b2s := 3.48501646502e-07 ; +acbv13.l2b2x := 0.0 ; +acbv13.l2b2s := -0.0 ; +acbh13.r4b2x := 0.0 ; +acbh13.r4b2s := 0.0 ; +acbh15.r4b2x := 7.77892736475e-08 ; +acbh15.r4b2s := 1.57799146059e-06 ; +acbh15.l5b2x := -1.05335934009e-11 ; +acbh15.l5b2s := 3.85745585979e-10 ; +acbh13.l5b2x := -7.77460689653e-08 ; +acbh13.l5b2s := -1.57718168219e-06 ; +acbh12.r5b2x := -4.79886283372e-08 ; +acbh12.r5b2s := 1.79261294456e-07 ; +acbh14.r5b2x := 3.62342438539e-10 ; +acbh14.r5b2s := -1.64917344322e-09 ; +acbh16.l6b2x := 4.82873723788e-08 ; +acbh16.l6b2s := -1.80653214379e-07 ; +acbh14.l6b2x := 0.0 ; +acbh14.l6b2s := 0.0 ; +acbv14.r4b2x := 0.0 ; +acbv14.r4b2s := 0.0 ; +acbv16.r4b2x := -5.79872853642e-08 ; +acbv16.r4b2s := 3.55277845225e-07 ; +acbv14.l5b2x := 1.4920017182e-10 ; +acbv14.l5b2s := -7.37010130222e-10 ; +acbv12.l5b2x := 5.79242552072e-08 ; +acbv12.l5b2s := -3.54947058945e-07 ; +acbv13.r5b2x := 9.7814414783e-08 ; +acbv13.r5b2s := 2.0609972915e-06 ; +acbv15.r5b2x := -1.97182827442e-10 ; +acbv15.r5b2s := -4.96646958719e-09 ; +acbv15.l6b2x := -9.7807466221e-08 ; +acbv15.l6b2s := -2.0611017098e-06 ; +acbv13.l6b2x := 0.0 ; +acbv13.l6b2s := 0.0 ; +on_afp := 0.0 ; +acbxv1.l1_afp := -2.761792544e-06 ; +acbxv2.l1_afp := -2.761792544e-06 ; +acbxv3.l1_afp := -2.761792544e-06 ; +acbxv1.r1_afp := 2.837557237e-06 ; +acbxv2.r1_afp := 2.837557237e-06 ; +acbxv3.r1_afp := 2.837557237e-06 ; +acbyvs4.r1b1_afp := -5.552323793e-06 ; +acbcv6.r1b1_afp := -1.792589991e-05 ; +acbcv8.r1b1_afp := 6.80009834e-06 ; +acbcv10.r1b1_afp := 0.0 ; +acbyvs4.l1b1_afp := 1.926e-05 ; +acbcv5.l1b1_afp := -5.012094668e-06 ; +acbcv7.l1b1_afp := -6.186216108e-06 ; +acbyvs4.l1b2_afp := -4.942158777e-06 ; +acbcv6.l1b2_afp := -2.032384469e-05 ; +acbcv8.l1b2_afp := 7.629068216e-06 ; +acbcv10.l1b2_afp := 0.0 ; +acbyvs4.r1b2_afp := 1.926e-05 ; +acbcv5.r1b2_afp := -4.85283998e-06 ; +acbcv7.r1b2_afp := -7.625067806e-06 ; +on_x2 := 0.0 ; +on_x8 := 0.0 ; +on_s_x1h := 0.0 ; +on_s_x5v := 0.0 ; +on_xx1_v := 0.0 ; +on_xx1_h := 0.0 ; +on_xx5_h := 0.0 ; +on_xx5_v := 0.0 ; +on_xx2v := 0.0 ; +on_xx8v := 0.0 ; +on_sep2 := 0.0 ; +on_sep8 := 0.0 ; +on_s_sep1v := 0.0 ; +on_s_sep5h := 0.0 ; +on_ssep1_h := 0.0 ; +on_ssep5_v := 0.0 ; +on_o1 := 0.0 ; +on_o5 := 0.0 ; +on_o1h := 0.0 ; +on_a1 := 0.0 ; +on_a5 := 0.0 ; +on_a1v := 0.0 ; +on_oe2 := 0.0 ; +on_xip1b1 := 0.0 ; +on_yip1b1 := 0.0 ; +on_xip1b2 := 0.0 ; +on_yip1b2 := 0.0 ; +on_xip2b1 := 0.0 ; +on_yip2b1 := 0.0 ; +on_xip2b2 := 0.0 ; +on_yip2b2 := 0.0 ; +on_xip5b1 := 0.0 ; +on_yip5b1 := 0.0 ; +on_xip5b2 := 0.0 ; +on_yip5b2 := 0.0 ; +on_xip8b1 := 0.0 ; +on_yip8b1 := 0.0 ; +on_xip8b2 := 0.0 ; +on_yip8b2 := 0.0 ; +on_alice := 1.0294117647058822 ; +on_lhcb := 1.0294117647058822 ; +on_sol_atlas := 1.0294117647058822 ; +on_sol_alice := 1.0294117647058822 ; +on_sol_cms := 1.0294117647058822 ; +phase_change.b1 := 0.0 ; +phase_change.b2 := 0.0 ; +on_xip1b1_acbch6.l1b1 := -4.219585044032242e-05 ; +on_xip1b1_acbyh4.l1b1 := 5.674427937997501e-05 ; +on_xip1b1_acbyhs4.r1b1 := 0.0001253782377336029 ; +on_xip1b1_acbch5.r1b1 := -8.144398681169772e-05 ; +tar := 6.321733691215325e-08 ; +tar_on_xip1b1 := 5.480216589868758e-34 ; +on_xip1b2_acbch5.l1b2 := -6.81401888672696e-05 ; +on_xip1b2_acbyhs4.l1b2 := 0.00011038067306096388 ; +on_xip1b2_acbyh4.r1b2 := 6.12199726960084e-05 ; +on_xip1b2_acbch6.r1b2 := -4.749314151616001e-05 ; +tar_on_xip1b2 := 6.77942809525387e-33 ; +on_yip1b1_acbcv5.l1b1 := -6.841909563070299e-05 ; +on_yip1b1_acbyvs4.l1b1 := 0.00011102288225691566 ; +on_yip1b1_acbyv4.r1b1 := 6.0191392698800446e-05 ; +on_yip1b1_acbcv6.r1b1 := -4.744162522844933e-05 ; +tar_on_yip1b1 := 7.565012031452367e-34 ; +on_yip1b2_acbcv6.l1b2 := -4.334914692798376e-05 ; +on_yip1b2_acbyv4.l1b2 := 5.6426482359689895e-05 ; +on_yip1b2_acbyvs4.r1b2 := 0.00012472851882719963 ; +on_yip1b2_acbcv5.r1b2 := -8.154606540635933e-05 ; +tar_on_yip1b2 := 5.011686057986609e-35 ; +akmsib.l2b1 := 0.0 ; +akmsia.l2b1 := 0.0 ; +on_xip2b1_acbyh5.l2b1 := -4.2098472662399755e-05 ; +akmki := 0.0 ; +on_xip2b1_acbyhs4.l2b1 := 8.828010510159435e-05 ; +on_xip2b1_acbyh4.r2b1 := 6.829854755266193e-05 ; +on_xip2b1_acbchs5.r2b1 := -7.339997820052372e-05 ; +tar_on_xip2b1 := 3.7812689500527024e-34 ; +akmsib.l2b2 := 0.0 ; +akmsia.l2b2 := 0.0 ; +on_xip2b2_acbyhs5.l2b2 := -4.848494883604539e-05 ; +on_xip2b2_acbyh4.l2b2 := 4.27238549257652e-05 ; +on_xip2b2_acbyhs4.r2b2 := 0.00010118258693497292 ; +on_xip2b2_acbch5.r2b2 := -4.7772582456640444e-05 ; +tar_on_xip2b2 := 2.586034618632138e-34 ; +on_yip2b1_acbyvs5.l2b1 := -4.725344055181878e-05 ; +on_yip2b1_acbyv4.l2b1 := 4.784375154299932e-05 ; +on_yip2b1_acbyvs4.r2b1 := 9.837660995146651e-05 ; +on_yip2b1_acbcv5.r2b1 := -4.832978268547589e-05 ; +tar_on_yip2b1 := 1.6975741581220035e-34 ; +on_yip2b2_acbyv5.l2b2 := -4.102531176444281e-05 ; +on_yip2b2_acbyvs4.l2b2 := 9.14012148532379e-05 ; +on_yip2b2_acbyv4.r2b2 := 6.376776563219623e-05 ; +on_yip2b2_acbcvs5.r2b2 := -7.416659716721753e-05 ; +tar_on_yip2b2 := 2.481721702531495e-34 ; +on_xip5b1_acbch6.l5b1 := -3.487324591016468e-05 ; +on_xip5b1_acbyh4.l5b1 := 6.433999649202314e-05 ; +on_xip5b1_acbyhs4.r5b1 := 0.00013495578303533872 ; +on_xip5b1_acbch5.r5b1 := -0.00010150372027732581 ; +tar_on_xip5b1 := 3.85660071230109e-33 ; +on_xip5b2_acbch5.l5b2 := -0.00012154830472235692 ; +on_xip5b2_acbyhs4.l5b2 := 0.00015706013885953302 ; +on_xip5b2_acbyh4.r5b2 := 6.1344652930332e-05 ; +on_xip5b2_acbch6.r5b2 := -3.191191555927055e-05 ; +tar_on_xip5b2 := 9.115979295532216e-34 ; +on_yip5b1_acbcv5.l5b1 := -0.00012154819624977798 ; +on_yip5b1_acbyvs4.l5b1 := 0.00015705961107618954 ; +on_yip5b1_acbyv4.r5b1 := 6.117293976996428e-05 ; +on_yip5b1_acbcv6.r5b1 := -3.206452183027358e-05 ; +tar_on_yip5b1 := 2.0762263356042148e-34 ; +on_yip5b2_acbcv6.l5b2 := -3.494938767655902e-05 ; +on_yip5b2_acbyv4.l5b2 := 6.426461507613413e-05 ; +on_yip5b2_acbyvs4.r5b2 := 0.00013494459761300115 ; +on_yip5b2_acbcv5.r5b2 := -0.00010159132359789973 ; +tar_on_yip5b2 := 2.2502599243371774e-33 ; +on_xip8b1_acbch5.l8b1 := -4.1529035018089314e-05 ; +on_xip8b1_acbyhs4.l8b1 := 8.657150508662218e-05 ; +on_xip8b1_acbyh4.r8b1 := 2.6831015102944304e-05 ; +akmsia.r8b1 := 0.0 ; +akmsib.r8b1 := 0.0 ; +on_xip8b1_acbch6.r8b1 := -1.4454633795177191e-05 ; +tar_on_xip8b1 := 4.780285229601347e-36 ; +on_xip8b2_acbchs5.l8b2 := -4.9089476220300435e-05 ; +on_xip8b2_acbyh4.l8b2 := 4.96436405093638e-05 ; +on_xip8b2_acbyhs4.r8b2 := 8.711654052308774e-05 ; +on_xip8b2_acbyh5.r8b2 := -4.074680536249977e-05 ; +akmsia.r8b2 := 0.0 ; +akmsib.r8b2 := 0.0 ; +tar_on_xip8b2 := 5.820994069805249e-34 ; +on_yip8b1_acbcvs5.l8b1 := -4.804453821602786e-05 ; +on_yip8b1_acbyv4.l8b1 := 5.0568413128917355e-05 ; +on_yip8b1_acbyvs4.r8b1 := 8.669056083488854e-05 ; +on_yip8b1_acbyv5.r8b1 := -4.058325411919836e-05 ; +tar_on_yip8b1 := 1.1563817901014355e-33 ; +on_yip8b2_acbcv5.l8b2 := -4.0718330343021376e-05 ; +on_yip8b2_acbyvs4.l8b2 := 8.713532101318999e-05 ; +on_yip8b2_acbyv4.r8b2 := 4.9632915307332384e-05 ; +on_yip8b2_acbyvs5.r8b2 := -4.901120062836297e-05 ; +tar_on_yip8b2 := 6.971702975585732e-35 ; +tar_lumiknob := 1.8227787472719014e-32 ; +dp_trim.b1 := 0.0 ; +on_xx2h := 0.0 ; +on_ssep5_h := 0.0 ; +on_xx8h := 0.0 ; +dqpx.b1_op := 0.0 ; +dqpy.b1_op := 0.0 ; +dqx.b1_op := 0.0 ; +dqy.b1_op := 0.0 ; +cmrs.b1_op := 0.0 ; +cmis.b1_op := 0.0 ; +vrf400 := 0.0 ; +lagrf400.b1 := 0.0 ; +on_ssep1_v := 0.0 ; +akbqkv.l4b1 := 0.0 ; +khmkqa.l4b1 := 0.0 ; +kvmkqa.l4b1 := 0.0 ; +akbqkh.l4b1 := 0.0 ; +akadtkh.l4b1 := 0.0 ; +akadtkv.r4b1 := 0.0 ; +kmu.r4b1 := 0.0 ; +akmkd := 0.0 ; +__0__ := 0.0 ; +len := 13373.0 ; +i := 13373.0 ; +s_betx := 2546.406441599483 ; +s_bety := -2542.509437344329 ; +s := 26658.883199998916 ; +betx := 0.5099999999149608 ; +alfx := -4.623965289143816e-10 ; +mux := 62.30999999891203 ; +bety := 0.1530000000345655 ; +alfy := 1.730364715300466e-10 ; +muy := 60.32000000149761 ; +x := 0.0 ; +px := 0.0 ; +y := 0.0 ; +py := 0.0 ; +t := 0.0 ; +pt := 0.0 ; +dx := -1.2762700990662323e-11 ; +dpx := -1.1428456899905896e-12 ; +dy := 0.0 ; +dpy := 0.0 ; +wx := 0.0 ; +phix := 0.0 ; +dmux := 0.0 ; +wy := 0.0 ; +phiy := 0.0 ; +dmuy := 0.0 ; +ddx := 0.0 ; +ddpx := 0.0 ; +ddy := 0.0 ; +ddpy := 0.0 ; +r11 := -0.0 ; +r12 := -0.0 ; +r21 := -0.0 ; +r22 := -0.0 ; +energy := 6800.0 ; +l := 0.0 ; +angle := -0.0 ; +k0l := -0.0 ; +k0sl := -0.0 ; +k1l := -0.0 ; +k1sl := -0.0 ; +k2l := -0.0 ; +k2sl := -0.0 ; +k3l := -0.0 ; +k3sl := -0.0 ; +k4l := -0.0 ; +k4sl := -0.0 ; +k5l := -0.0 ; +k5sl := -0.0 ; +k6l := -0.0 ; +k6sl := -0.0 ; +k7l := -0.0 ; +k7sl := -0.0 ; +k8l := -0.0 ; +k8sl := -0.0 ; +k9l := -0.0 ; +k9sl := -0.0 ; +k10l := -0.0 ; +k10sl := -0.0 ; +k11l := -0.0 ; +k11sl := -0.0 ; +k12l := -0.0 ; +k12sl := -0.0 ; +k13l := -0.0 ; +k13sl := -0.0 ; +k14l := -0.0 ; +k14sl := -0.0 ; +k15l := -0.0 ; +k15sl := -0.0 ; +k16l := -0.0 ; +k16sl := -0.0 ; +k17l := -0.0 ; +k17sl := -0.0 ; +k18l := -0.0 ; +k18sl := -0.0 ; +k19l := -0.0 ; +k19sl := -0.0 ; +k20l := -0.0 ; +k20sl := -0.0 ; +ksi := -0.0 ; +hkick := -0.0 ; +vkick := -0.0 ; +tilt := 0.0 ; +e1 := 0.0 ; +e2 := 0.0 ; +h1 := 0.0 ; +h2 := 0.0 ; +hgap := 0.0 ; +fint := 0.0 ; +fintx := 0.0 ; +volt := -0.0 ; +lag := 0.0 ; +freq := 0.0 ; +harmon := 0.0 ; +mech_sep := 0.0 ; +v_pos := 0.0 ; +bbcharge := 0.0 ; +xma := 0.0 ; +yma := 0.0 ; +sigx := 0.0 ; +sigy := 0.0 ; +lrad := 0.0 ; +re11 := 0.0 ; +re12 := 0.0 ; +re13 := 0.0 ; +re14 := 0.0 ; +re15 := 0.0 ; +re16 := 0.0 ; +re21 := 0.0 ; +re22 := 0.0 ; +re23 := 0.0 ; +re24 := 0.0 ; +re25 := 0.0 ; +re26 := 0.0 ; +re31 := 0.0 ; +re32 := 0.0 ; +re33 := 0.0 ; +re34 := 0.0 ; +re35 := 0.0 ; +re36 := 0.0 ; +re41 := 0.0 ; +re42 := 0.0 ; +re43 := 0.0 ; +re44 := 0.0 ; +re45 := 0.0 ; +re46 := 0.0 ; +re51 := 0.0 ; +re52 := 0.0 ; +re53 := 0.0 ; +re54 := 0.0 ; +re55 := 0.0 ; +re56 := 0.0 ; +re61 := 0.0 ; +re62 := 0.0 ; +re63 := 0.0 ; +re64 := 0.0 ; +re65 := 0.0 ; +re66 := 0.0 ; +kmax := 0.0 ; +kmin := 0.0 ; +calib := 0.0 ; +polarity := 0.0 ; +alfa := 0.0003473919198234345 ; +beta11 := 0.0 ; +beta12 := 0.0 ; +beta13 := 0.0 ; +beta21 := 0.0 ; +beta22 := 0.0 ; +beta23 := 0.0 ; +beta31 := 0.0 ; +beta32 := 0.0 ; +beta33 := 0.0 ; +alfa11 := 0.0 ; +alfa12 := 0.0 ; +alfa13 := 0.0 ; +alfa21 := 0.0 ; +alfa22 := 0.0 ; +alfa23 := 0.0 ; +alfa31 := 0.0 ; +alfa32 := 0.0 ; +alfa33 := 0.0 ; +gama11 := 0.0 ; +gama12 := 0.0 ; +gama13 := 0.0 ; +gama21 := 0.0 ; +gama22 := 0.0 ; +gama23 := 0.0 ; +gama31 := 0.0 ; +gama32 := 0.0 ; +gama33 := 0.0 ; +beta11p := 0.0 ; +beta12p := 0.0 ; +beta13p := 0.0 ; +beta21p := 0.0 ; +beta22p := 0.0 ; +beta23p := 0.0 ; +beta31p := 0.0 ; +beta32p := 0.0 ; +beta33p := 0.0 ; +alfa11p := 0.0 ; +alfa12p := 0.0 ; +alfa13p := 0.0 ; +alfa21p := 0.0 ; +alfa22p := 0.0 ; +alfa23p := 0.0 ; +alfa31p := 0.0 ; +alfa32p := 0.0 ; +alfa33p := 0.0 ; +gama11p := 0.0 ; +gama12p := 0.0 ; +gama13p := 0.0 ; +gama21p := 0.0 ; +gama22p := 0.0 ; +gama23p := 0.0 ; +gama31p := 0.0 ; +gama32p := 0.0 ; +gama33p := 0.0 ; +disp1 := 0.0 ; +disp2 := 0.0 ; +disp3 := 0.0 ; +disp4 := 0.0 ; +disp1p := 0.0 ; +disp2p := 0.0 ; +disp3p := 0.0 ; +disp4p := 0.0 ; +disp1p2 := 0.0 ; +disp2p2 := 0.0 ; +disp3p2 := 0.0 ; +disp4p2 := 0.0 ; +disp1p3 := 0.0 ; +disp2p3 := 0.0 ; +disp3p3 := 0.0 ; +disp4p3 := 0.0 ; +mu1 := 0.0 ; +mu2 := 0.0 ; +mu3 := 0.0 ; +sig11 := 0.509999999925224 ; +sig12 := 5.326299401531287e-10 ; +sig13 := 0.0 ; +sig14 := 0.0 ; +sig15 := 1.2662779247130593e-11 ; +sig16 := 0.0 ; +sig21 := 5.328359975464991e-10 ; +sig22 := 1.9607843146025878 ; +sig23 := 0.0 ; +sig24 := 0.0 ; +sig25 := -3.315342677047401e-11 ; +sig26 := 0.0 ; +sig31 := 0.0 ; +sig32 := 0.0 ; +sig33 := 0.15299999998407188 ; +sig34 := -1.651834224958293e-10 ; +sig35 := 0.0 ; +sig36 := 0.0 ; +sig41 := 0.0 ; +sig42 := 0.0 ; +sig43 := -1.6506973565810767e-10 ; +sig44 := 6.535947711030101 ; +sig45 := 0.0 ; +sig46 := 0.0 ; +sig51 := 1.2661369958882752e-11 ; +sig52 := -3.314461357874065e-11 ; +sig53 := 0.0 ; +sig54 := 0.0 ; +sig55 := -2.6608408829988057e-15 ; +sig56 := 0.0 ; +sig61 := 0.0 ; +sig62 := 0.0 ; +sig63 := 0.0 ; +sig64 := 0.0 ; +sig65 := 0.0 ; +sig66 := 0.0 ; +n1 := 0.0 ; +natural_x := 0.18135974460496665 ; +natural_y := 0.23510336093527437 ; +dp_trim.b2 := 0.0 ; +dqpx.b2_op := 0.0 ; +dqpy.b2_op := 0.0 ; +dqx.b2_op := 0.0 ; +dqy.b2_op := 0.0 ; +cmrs.b2_op := 0.0 ; +cmis.b2_op := 0.0 ; +lagrf400.b2 := 0.0 ; +kcs.a78b2 := 0.0 ; +khmkqa.l4b2 := 0.0 ; +kvmkqa.l4b2 := 0.0 ; +kmu.l4b2 := 0.0 ; +akadtkv.l4b2 := 0.0 ; +akadtkh.r4b2 := 0.0 ; +akbqkh.r4b2 := 0.0 ; +akbqkv.r4b2 := 0.0 ; +__1__ := 0.0 ; +slicefactor := 8.0 ; +nparasitic := 45.0 ; +b_t_dist := 25.0 ; +b_h_dist := 3.740022895622896 ; +where := 168.30103030303033 ; +n := 46.0 ; diff --git a/test_data/lhc_2024/pytrain/pytrain_collision.json b/test_data/lhc_2024/pytrain/pytrain_collision.json new file mode 100644 index 000000000..7806a44b0 --- /dev/null +++ b/test_data/lhc_2024/pytrain/pytrain_collision.json @@ -0,0 +1 @@ +{"scenario": "collision", "description": "pytrain (thin sf8) reference, LHC collision 6.8 TeV R2025aRP 15 cm flat optics with end-of-levelling knobs (head-on IP1/5 + BBLR, 45 LR/side at IP1/2/5/8), 1.1e11 p/bunch, 2.3 um, full 2460-bunch scheme, 6 solver iterations. Same column conventions as injection.", "solver_iterations": 6, "generated_by": "test_data/lhc_2024/pytrain/regenerate_collision.py", "b1": {"slots": [20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 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Orbits x/y at MKIP1 (physical frame), dx/dy = deviation from bunch average; qx/qy fractional tunes, dqx/dqy = shift vs bare thin lattice.", "solver_iterations": 3, "generated_by": "test_data/lhc_2024/pytrain/regenerate_injection.py", "b1": {"slots": [20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 259, 260, 261, 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IP2/8), tunes/chroma matched to 62.316/60.322, Q'=10, +1.1e11 p/bunch, 2.3 um, full 2460-bunch scheme, 6 solver iterations. Same +scenario as the xsuite example +``xtrack/examples/lhc_multibunch_bb/002_multibunch_sectormaps_collisions.py`` +and the test ``test_lhc_multibunch_train.py``. + +The squeezed optics generate their knobs via MAD-X matching, which xsuite +cannot execute -- therefore this script also dumps the complete numeric +MAD-X global-variable state (after optics + knobs + matching) as the +flattened optics file used by the xsuite example. The acc-models-lhc optics +repository (public, tag pinned below) is fetched into a temporary directory +-- no local checkout is needed. + +Requires pytrain + cpymad (NOT installable in the xsuite environment), e.g.: + cd /opt/mihostet/python/pytrain && venv39/bin/python /regenerate_collision.py +""" +import os, json, time +import tempfile +import urllib.request +import zipfile +import numpy as np +from cpymad import madx as cpymadx +from pytrain.cpymad import (cpymad_lhc_makethin, cpymad_lhc_install_bb_markers, + cpymad_lhc_cycle, cpymad_generate_train_maps, + cpymad_lhc_match_tune_chroma) +from pytrain.machine import FillingScheme +from pytrain.solver import solve_train +from pytrain.twiss import oneturn_map, closed_orbit, tune + +HERE = os.path.dirname(os.path.abspath(__file__)) +DATA = os.path.dirname(HERE) # test_data/lhc_2024 +ACC_MODELS_ZIP = ('https://gitlab.cern.ch/acc-models/acc-models-lhc/-/' + 'archive/v2026.6/acc-models-lhc-v2026.6.zip') +INT, EMIT, N_ITER = 1.1e11, 2.3e-6, 6 +t0 = time.time() + +# Fetch the optics model into a temporary directory (as in the notebook +# examples); the archive extracts to acc-models-lhc-/, renamed to +# acc-models-lhc/ so the relative paths inside the optics files resolve. +modeldir = tempfile.TemporaryDirectory(prefix='acc-models-lhc-') +print(f'fetching {ACC_MODELS_ZIP} ...', flush=True) +zpath = os.path.join(modeldir.name, 'acc-models-lhc.zip') +urllib.request.urlretrieve(ACC_MODELS_ZIP, zpath) +with zipfile.ZipFile(zpath) as zf: + zf.extractall(modeldir.name) +os.remove(zpath) +extracted, = [d for d in os.listdir(modeldir.name) + if d.startswith('acc-models-lhc')] +os.rename(os.path.join(modeldir.name, extracted), + os.path.join(modeldir.name, 'acc-models-lhc')) +print(f'model ready in {modeldir.name} ({time.time()-t0:.0f}s)', flush=True) + +madx = cpymadx.Madx(stdout=False) +madx.chdir(modeldir.name) +madx.options.echo = madx.options.info = madx.options.warn = False +madx.call('acc-models-lhc/lhc.seq') +madx.input(''' +beam, sequence=lhcb1, bv= 1, particle=proton, charge=1, mass=0.938272046, + energy=6800, npart=1.2e11, kbunch=2400; +beam, sequence=lhcb2, bv=-1, particle=proton, charge=1, mass=0.938272046, + energy=6800, npart=1.2e11, kbunch=2400; +''') +madx.call('acc-models-lhc/operation/optics/' + 'R2025aRP_A15cmC15cmA10mL200cm_Flat.madx') + +# knobs (end-of-levelling scenario) +madx.globals.on_x1_v = 0 +madx.globals.on_x5_h = 0 +madx.globals.on_x1_h = 120 +madx.globals.on_x5_v = -120 +madx.globals.on_sep1_h = 0 +madx.globals.on_sep5_v = 0 +madx.globals.on_sep2h = -0.1 +madx.globals.on_sep2v = 0 +madx.globals.on_x2v = 200 +madx.globals.on_sep8h = -0.02 +madx.globals.on_sep8v = 0.01 +madx.globals.on_x8h = 0 +madx.globals.on_x8v = 200 +madx.globals.on_a2 = 0 +madx.globals.on_a8 = 0 +madx.globals.on_disp = 1 +madx.globals.on_alice = '7000/nrj' +madx.globals.on_lhcb = '7000/nrj' +madx.globals.on_sol_atlas = '7000/nrj' +madx.globals.on_sol_cms = '7000/nrj' +madx.globals.on_sol_alice = '7000/nrj' +madx.globals['KOF.B1'] = -12 +madx.globals['KOD.B1'] = -12 +madx.globals['KOF.B2'] = -12 +madx.globals['KOD.B2'] = -12 +print(f'optics + knobs {time.time()-t0:.0f}s', flush=True) + +cpymad_lhc_makethin(madx, slicefactor=8) +cpymad_lhc_cycle(madx, start='IP3') +cpymad_lhc_install_bb_markers(madx, nparasitic=45) +cpymad_lhc_match_tune_chroma(madx, qx_b1=62.316, qy_b1=60.322, + qx_b2=62.316, qy_b2=60.322, + qpx_b1=10.0, qpy_b1=10.0, + qpx_b2=10.0, qpy_b2=10.0, tolerance=1e-4) +print(f'thin + markers + matched {time.time()-t0:.0f}s', flush=True) + +# dump the full numeric global-variable state as a flattened optics file +knobs = {} +for name in madx.globals: + if name == 'version': + continue + try: + knobs[name] = float(madx.globals[name]) + except (TypeError, ValueError): + pass +with open(os.path.join(DATA, 'collision_optics_15cm_flat_2026.madx'), + 'w') as fid: + fid.write( + "! Flattened LHC collision optics, 6.8 TeV, " + "R2025aRP_A15cmC15cmA10mL200cm_Flat\n" + "! (acc-models-lhc branch 2026) with end-of-levelling knobs and " + "tunes/chroma\n! matched to 62.316/60.322, Q'=10. Generated by\n" + "! test_data/lhc_2024/pytrain/regenerate_collision.py\n\n") + for kk, vv in knobs.items(): + fid.write(f'{kk} := {vv!r} ;\n') +print(f'dumped {len(knobs)} globals to ' + f'collision_optics_15cm_flat_2026.madx', flush=True) + +machine, tw1, tw2, maps1, maps2 = cpymad_generate_train_maps(madx, + num_slots=3564) +z1 = closed_orbit(oneturn_map(maps1)); qx0_1, qy0_1 = tune(oneturn_map(maps1), z1) +z2 = closed_orbit(oneturn_map(maps2)); qx0_2, qy0_2 = tune(oneturn_map(maps2), z2) +print(f'bare thin tunes B1 {qx0_1:.5f}/{qy0_1:.5f} ' + f'B2 {qx0_2:.5f}/{qy0_2:.5f}', flush=True) + +sc = json.load(open(os.path.join( + DATA, '25ns_2460b_2448_2092_2239_144bpi_20inj.json'))) +sb1 = np.array(sc['schemebeam1'], float) +sb2 = np.array(sc['schemebeam2'], float) +fs = FillingScheme(sb1*INT, sb2*INT, sb1*EMIT, sb1*EMIT, sb2*EMIT, sb2*EMIT) +res = solve_train(machine, fs, tw1, maps1, tw2, maps2, + tolerance=1e-9, max_iter=N_ITER) + + +def beam_dict(qx, qy, qx0, qy0, cox, coy): + m = np.isfinite(qx) + slots = np.where(m)[0] + x, y = cox[m], coy[m] + return {'slots': [int(v) for v in slots], + 'qx': list(qx[m]), 'qy': list(qy[m]), + 'dqx': list(qx[m] - qx0), 'dqy': list(qy[m] - qy0), + 'x': list(x), 'y': list(y), + 'dx': list(x - x.mean()), 'dy': list(y - y.mean())} + + +qx1, qy1 = res.bunch_tunes_b1(); qx2, qy2 = res.bunch_tunes_b2() +cox1, coy1 = res.bunch_positions_b1('MKIP1') +cox2, coy2 = res.bunch_positions_b2('MKIP1') +out = { + 'scenario': 'collision', + 'description': ( + 'pytrain (thin sf8) reference, LHC collision 6.8 TeV R2025aRP 15 cm ' + 'flat optics with end-of-levelling knobs (head-on IP1/5 + BBLR, ' + '45 LR/side at IP1/2/5/8), 1.1e11 p/bunch, 2.3 um, full 2460-bunch ' + 'scheme, 6 solver iterations. Same column conventions as injection.'), + 'solver_iterations': N_ITER, + 'generated_by': 'test_data/lhc_2024/pytrain/regenerate_collision.py', + 'b1': beam_dict(qx1, qy1, qx0_1, qy0_1, cox1, coy1), + 'b2': beam_dict(qx2, qy2, qx0_2, qy0_2, cox2, coy2), +} +with open(os.path.join(HERE, 'pytrain_collision.json'), 'w') as fid: + json.dump(out, fid) +print(f'DONE {time.time()-t0:.0f}s -> pytrain_collision.json', flush=True) diff --git a/test_data/lhc_2024/pytrain/regenerate_injection.py b/test_data/lhc_2024/pytrain/regenerate_injection.py new file mode 100644 index 000000000..f3015deeb --- /dev/null +++ b/test_data/lhc_2024/pytrain/regenerate_injection.py @@ -0,0 +1,79 @@ +"""Regenerate ``pytrain_injection.json``: pytrain (TRAIN) reference for the +LHC injection multi-bunch beam-beam scenario (BBLR only, 45 LR/side at +IP1/2/5/8, 450 GeV, 1.8e11 p/bunch, 1.5 um, full 2460-bunch scheme, 3 solver +iterations) -- the same scenario as the xsuite example +``xtrack/examples/lhc_multibunch_bb/001_multibunch_sectormaps_injection.py`` +and the test ``test_lhc_multibunch_train.py``. + +Requires pytrain + cpymad (NOT installable in the xsuite environment), e.g.: + cd /opt/mihostet/python/pytrain && venv39/bin/python /regenerate_injection.py +""" +import os, json, time +import numpy as np +from cpymad import madx as cpymadx +from pytrain.cpymad import (cpymad_lhc_makethin, cpymad_lhc_install_bb_markers, + cpymad_lhc_cycle, cpymad_generate_train_maps) +from pytrain.machine import FillingScheme +from pytrain.solver import solve_train +from pytrain.twiss import oneturn_map, closed_orbit, tune + +HERE = os.path.dirname(os.path.abspath(__file__)) +DATA = os.path.dirname(HERE) # test_data/lhc_2024 +INT, EMIT, N_ITER = 1.8e11, 1.5e-6, 3 +t0 = time.time() + +madx = cpymadx.Madx(stdout=False) +madx.options.echo = madx.options.info = madx.options.warn = False +madx.call(os.path.join(DATA, 'lhc.seq')) +madx.call(os.path.join(DATA, 'injection_optics.madx')) +madx.input('beam,sequence=lhcb1,particle=proton,energy=NRJ;' + 'beam,sequence=lhcb2,particle=proton,energy=NRJ,bv=-1;') +cpymad_lhc_makethin(madx, slicefactor=8) +cpymad_lhc_install_bb_markers(madx, nparasitic=45) +cpymad_lhc_cycle(madx, start='IP3') +machine, tw1, tw2, maps1, maps2 = cpymad_generate_train_maps(madx, + num_slots=3564) +z1 = closed_orbit(oneturn_map(maps1)); qx0_1, qy0_1 = tune(oneturn_map(maps1), z1) +z2 = closed_orbit(oneturn_map(maps2)); qx0_2, qy0_2 = tune(oneturn_map(maps2), z2) +print(f'model ready {time.time()-t0:.0f}s bare thin tunes ' + f'B1 {qx0_1:.5f}/{qy0_1:.5f} B2 {qx0_2:.5f}/{qy0_2:.5f}', flush=True) + +sc = json.load(open(os.path.join( + DATA, '25ns_2460b_2448_2092_2239_144bpi_20inj.json'))) +sb1 = np.array(sc['schemebeam1'], float) +sb2 = np.array(sc['schemebeam2'], float) +fs = FillingScheme(sb1*INT, sb2*INT, sb1*EMIT, sb1*EMIT, sb2*EMIT, sb2*EMIT) +res = solve_train(machine, fs, tw1, maps1, tw2, maps2, + tolerance=1e-9, max_iter=N_ITER) + + +def beam_dict(qx, qy, qx0, qy0, cox, coy): + m = np.isfinite(qx) + slots = np.where(m)[0] + x, y = cox[m], coy[m] + return {'slots': [int(v) for v in slots], + 'qx': list(qx[m]), 'qy': list(qy[m]), + 'dqx': list(qx[m] - qx0), 'dqy': list(qy[m] - qy0), + 'x': list(x), 'y': list(y), + 'dx': list(x - x.mean()), 'dy': list(y - y.mean())} + + +qx1, qy1 = res.bunch_tunes_b1(); qx2, qy2 = res.bunch_tunes_b2() +cox1, coy1 = res.bunch_positions_b1('MKIP1') +cox2, coy2 = res.bunch_positions_b2('MKIP1') +out = { + 'scenario': 'injection', + 'description': ( + 'pytrain (thin sf8) reference, LHC injection 450 GeV, BBLR only ' + '(45 LR/side at IP1/2/5/8), 1.8e11 p/bunch, 1.5 um, full 2460-bunch ' + 'scheme, 3 solver iterations. Orbits x/y at MKIP1 (physical frame), ' + 'dx/dy = deviation from bunch average; qx/qy fractional tunes, ' + 'dqx/dqy = shift vs bare thin lattice.'), + 'solver_iterations': N_ITER, + 'generated_by': 'test_data/lhc_2024/pytrain/regenerate_injection.py', + 'b1': beam_dict(qx1, qy1, qx0_1, qy0_1, cox1, coy1), + 'b2': beam_dict(qx2, qy2, qx0_2, qy0_2, cox2, coy2), +} +with open(os.path.join(HERE, 'pytrain_injection.json'), 'w') as fid: + json.dump(out, fid) +print(f'DONE {time.time()-t0:.0f}s -> pytrain_injection.json', flush=True) diff --git a/tests/test_lhc_multibunch_train.py b/tests/test_lhc_multibunch_train.py new file mode 100644 index 000000000..f63190755 --- /dev/null +++ b/tests/test_lhc_multibunch_train.py @@ -0,0 +1,305 @@ +# copyright ############################### # +# This file is part of the Xtrack Package. # +# Copyright (c) CERN, 2024. # +# ######################################### # + +"""Cross-check of the LHC multi-bunch beam-beam machinery against pytrain +(TRAIN): builds the sector-map model (as in ``examples/lhc_multibunch_bb``, +minimal logic duplicated below so the test is self-contained) for both the +injection (BBLR only) and the collision (6.8 TeV squeezed, head-on + BBLR) +scenarios -- all 2460+2460 bunches -- and compares the per-bunch closed-orbit +deviations and tune shifts at IP1 with the stored pytrain references +(``test_data/lhc_2024/pytrain/pytrain_{injection,collision}.json``, +regenerated with the scripts in the same directory). + +Model (following pytrain / TRAIN): long-range encounter ``n`` sits at +``n * b_h_dist`` from the IP (``b_h_dist`` = half a 25 ns slot); beam-1 bunch +``b1`` meets beam-2 bunch ``b1 + offset`` with ``offset = round(2 * (s - +s_IP1) / slot_len) mod N_SLOTS``; the coherent (rigid-bunch) kick uses the +convolved pair size (``coherent=True`` elements convolve each beam's own +``sigma = sqrt(beta * nemitt / gamma0)``); the beam separation is the +closed-orbit difference plus the SIGNED geometric survey separation of the +two rings. Bunches are labelled by ``zeta = slot * ZETA_PER_SLOT`` and the +elements pair them via ``zeta_offset``/``zeta_period``. + +NOTE: slow (several minutes per scenario, dominated by building the +second-order maps of both beams). +""" + +import json +import pathlib + +import numpy as np +import pytest +from scipy.constants import c as clight + +import xobjects as xo +import xtrack as xt +import xfields as xf + +test_data_folder = pathlib.Path( + __file__).parent.joinpath('../test_data').absolute() +lhc_data = test_data_folder / 'lhc_2024' + +N_SLOTS = 3564 +ZETA_PER_SLOT = 25e-9 * clight # per-bunch zeta label spacing [m] +IPS = (1, 2, 5, 8) +NPARASITIC = 45 # long-range encounters per IP side + +SCENARIOS = { + 'injection': dict(p0c=450e9, bunch_intensity=1.8e11, nemitt=1.5e-6, + optics='injection_optics.madx', n_iter=3), + 'collision': dict(p0c=6800e9, bunch_intensity=1.1e11, nemitt=2.3e-6, + optics='collision_optics_15cm_flat_2026.madx', + n_iter=4), +} + +# pytrain is a thin (slicefactor 8) model solved with second-order beam-beam +# maps, xsuite an exact-kick model built from a thick lattice, so the two +# never agree to machine precision: +# - orbits: sub-nm to few-nm agreement in collision; at injection a few +# pytrain bunches show um-level slicing artifacts (measured max 2.5e-5). +# - tune shifts: at injection the pytrain per-bunch tunes are not converging +# well; in collision the second-order map truncation of the head-on kick +# gives a ~2% shift (max 5.1e-4). +TOLERANCES = { + # orbit atol tune atol tune rms + 'injection': dict(orbit=5e-5, tune=1e-1, tune_rms=1e-2), + 'collision': dict(orbit=2e-7, tune=2e-3, tune_rms=1e-3), +} + + +def _wrap_frac_tune(v): + """Tune difference on the fractional-tune circle, wrapped to + (-0.5, 0.5].""" + return (np.asarray(v) + 0.5) % 1.0 - 0.5 + + +def _encounter_specs(): + """Yield (name, ip, signed_n); signed_n == 0 is the head-on encounter.""" + for ip in IPS: + yield f'bb_ip{ip}_ho', ip, 0 + for n in range(1, NPARASITIC + 1): + yield f'bb_ip{ip}_r{n:02d}', ip, +n + yield f'bb_ip{ip}_l{n:02d}', ip, -n + + +def _marker_name(name, mirror): + return name + ('_b2' if mirror else '_b1') + + +ENC_NAMES = [n for n, _, _ in _encounter_specs()] +MARKER_NAMES = {False: [_marker_name(n, False) for n in ENC_NAMES], + True: [_marker_name(n, True) for n in ENC_NAMES]} + + +def _load_lines(p0c, optics): + env = xt.load(str(lhc_data / 'lhc.seq'), format='madx', + reverse_lines=['lhcb2']) + for ln in (env.lhcb1, env.lhcb2): + ln.particle_ref = xt.Particles(mass0=xt.PROTON_MASS_EV, p0c=p0c) + env.vars.load(str(lhc_data / optics)) + for ln in (env.lhcb1, env.lhcb2): + ln.twiss_default['method'] = '4d' + ln.cycle(name_first_element='ip3', inplace=True) # no IP at s=0 + return env.lhcb1, env.lhcb2 + + +def _install_markers(line, mirror, b_h_dist): + # the reversed beam-2 line mirrors left/right so a marker name is the + # same physical point in both beams + env = line.env + places = [] + for name, ip, sn in _encounter_specs(): + at = (-sn if mirror else sn) * b_h_dist + 1e-6 + places.append(env.place( + env.new(_marker_name(name, mirror), xt.Marker), + at=at, from_=f'ip{ip}')) + line.insert(places) + + +def _compute_geometry(line_b1, line_b2, slot_len): + """Per-encounter slot offset, convolved betas and SIGNED survey + separation (TRAIN convention: sign from the direction of the separation + vector relative to the ring azimuth; flips between IP1/5 and IP2/8).""" + tw1 = line_b1.twiss() + tw2 = line_b2.twiss() + sv1 = line_b1.survey() + sv2 = line_b2.survey() + + s_ip1 = tw1['s', 'ip1'] + ip_pos = {} + for ip in IPS: + ip_pos[ip] = ( + np.array([sv1['X', f'ip{ip}'], sv1['Y', f'ip{ip}'], + sv1['Z', f'ip{ip}']]), + np.array([sv2['X', f'ip{ip}'], sv2['Y', f'ip{ip}'], + sv2['Z', f'ip{ip}']])) + r1 = sv1.rows[MARKER_NAMES[False]] + r2 = sv2.rows[MARKER_NAMES[True]] + m1 = np.stack([r1.X, r1.Y, r1.Z], axis=1) + m2 = np.stack([r2.X, r2.Y, r2.Z], axis=1) + + length = line_b1.get_length() + geom = {} + for j, (name, ip, sn) in enumerate(_encounter_specs()): + n1, n2 = MARKER_NAMES[False][j], MARKER_NAMES[True][j] + s_marker = tw1['s', n1] + offset = int(round(2 * (s_marker - s_ip1) / slot_len)) % N_SLOTS + s1 = m1[j] - ip_pos[ip][0] + s2 = m2[j] - ip_pos[ip][1] + s2 = np.array([-s2[0], s2[1], -s2[2]]) # B2 survey rotated 180 deg + d = s1 - s2 + ang = np.arctan2(d[2], d[0]) - 2 * np.pi * s_marker / length + ang = (ang + np.pi) % (2 * np.pi) - np.pi + xsign = 1.0 if abs(ang) <= np.pi / 2 else -1.0 + geom[name] = dict( + offset=offset, + betx_b1=float(tw1['betx', n1]), + bety_b1=float(tw1['bety', n1]), + betx_b2=float(tw2['betx', n2]), + bety_b2=float(tw2['bety', n2]), + sep_x=float(np.hypot(d[0], d[2]) * xsign), + sep_y=float(d[1]), + ) + return geom + + +def _install_bb(line, mirror, geom, n_other, nemitt, gamma0, beta0): + env = line.env + places = [] + names = [] + for name, ip, sn in _encounter_specs(): + e = geom[name] + # beam1 pairs b2 = b1 + offset; beam2 pairs b1 = b2 - offset + zoff = (-e['offset'] if mirror else e['offset']) * ZETA_PER_SLOT + # coherent rigid-bunch kick: the element convolves this beam's own + # size with each opposing bunch's size + own, oth = ('b2', 'b1') if mirror else ('b1', 'b2') + bb = xf.BeamBeamBiGaussianMultibunch2D( + num_bunches=n_other, + zeta_offset=zoff, zeta_match_tol=0.4 * ZETA_PER_SLOT, + zeta_period=N_SLOTS * ZETA_PER_SLOT, # pairing wraps the ring + other_beam_q0=1.0, other_beam_beta0=beta0, + coherent=True, + sigma_x=np.sqrt(e[f'betx_{own}'] * nemitt / gamma0), + sigma_y=np.sqrt(e[f'bety_{own}'] * nemitt / gamma0), + other_beam_sigma_x=np.sqrt(e[f'betx_{oth}'] * nemitt / gamma0), + other_beam_sigma_y=np.sqrt(e[f'bety_{oth}'] * nemitt / gamma0), + _context=line._context) + elname = _marker_name(name, mirror) + '_bb' + places.append(env.place(elname, bb, at=_marker_name(name, mirror))) + names.append((name, elname)) + line.insert(places) + return {name: line[elname] for name, elname in names} + + +def _update_opposing(bb_dict, mbtw_other, zeta_other, marker_names_other, + geom, p0c, bunch_intensity): + """Write the opposing beam's per-bunch orbit + survey separation into the + beam-beam elements. Between the two (opposite-parity) beam lines x flips""" + # mbtw['x', names] resolves the marker rows once and slices the numpy + # columns of all bunch tables (fast multi-element access) + xs = -mbtw_other['x', marker_names_other] + ys = mbtw_other['y', marker_names_other] + p = xt.Particles(p0c=p0c, mass0=xt.PROTON_MASS_EV, q0=1.0, + x=np.zeros(len(zeta_other)), y=np.zeros(len(zeta_other)), + zeta=zeta_other, weight=bunch_intensity) + for j, name in enumerate(ENC_NAMES): + p.x[:] = xs[:, j] - geom[name]['sep_x'] + p.y[:] = ys[:, j] - geom[name]['sep_y'] + bb_dict[name].update_from_other_beam(p) + + +def _run_xsuite_scenario(scenario): + par = SCENARIOS[scenario] + line_b1, line_b2 = _load_lines(par['p0c'], par['optics']) + slot_len = line_b1.get_length() / N_SLOTS + b_h_dist = slot_len / 2.0 + gamma0 = line_b1.particle_ref.gamma0[0] + beta0 = line_b1.particle_ref.beta0[0] + + _install_markers(line_b1, mirror=False, b_h_dist=b_h_dist) + _install_markers(line_b2, mirror=True, b_h_dist=b_h_dist) + geom = _compute_geometry(line_b1, line_b2, slot_len) + + red_b1 = line_b1.get_line_with_second_order_maps( + split_at=MARKER_NAMES[False]) + red_b2 = line_b2.get_line_with_second_order_maps( + split_at=MARKER_NAMES[True]) + for rl in (red_b1, red_b2): + rl.twiss_default['method'] = '4d' + tw_red = red_b1.twiss() + tw_red2 = red_b2.twiss() + + with open(lhc_data / '25ns_2460b_2448_2092_2239_144bpi_20inj.json') as f: + scheme = json.load(f) + slots_b1 = np.where(np.array(scheme['schemebeam1']) > 0)[0] + slots_b2 = np.where(np.array(scheme['schemebeam2']) > 0)[0] + zeta_b1 = slots_b1 * ZETA_PER_SLOT + zeta_b2 = slots_b2 * ZETA_PER_SLOT + + bb_b1 = _install_bb(red_b1, False, geom, len(slots_b2), par['nemitt'], + gamma0, beta0) + bb_b2 = _install_bb(red_b2, True, geom, len(slots_b1), par['nemitt'], + gamma0, beta0) + + # self-consistent solve: iterate the fast multibunch twiss on both + # beams, feeding each beam's orbits into the other beam's elements + for _ in range(par['n_iter']): + mbtw_b1 = red_b1.twiss_multibunch(zeta_bunches=zeta_b1, + mode='fast_orbit', + show_progress=False) + mbtw_b2 = red_b2.twiss_multibunch(zeta_bunches=zeta_b2, + mode='fast_orbit', + show_progress=False) + _update_opposing(bb_b1, mbtw_b2, zeta_b2, MARKER_NAMES[True], geom, + p0c=par['p0c'], bunch_intensity=par['bunch_intensity']) + _update_opposing(bb_b2, mbtw_b1, zeta_b1, MARKER_NAMES[False], geom, + p0c=par['p0c'], bunch_intensity=par['bunch_intensity']) + + def extract(mbtw, slots, bare_qx, bare_qy, mirror): + marker = _marker_name('bb_ip1_ho', mirror) + x = mbtw['x', marker] + if mirror: + x = -x # reversed beam-2 line -> physical frame + y = mbtw['y', marker] + return dict(slots=slots, + dx=x - x.mean(), dy=y - y.mean(), + dqx=_wrap_frac_tune(mbtw.qx - bare_qx), + dqy=_wrap_frac_tune(mbtw.qy - bare_qy)) + + return (extract(mbtw_b1, slots_b1, tw_red.qx, tw_red.qy, mirror=False), + extract(mbtw_b2, slots_b2, tw_red2.qx, tw_red2.qy, mirror=True)) + + +@pytest.mark.parametrize('scenario', ['injection', 'collision']) +def test_lhc_multibunch_train(scenario): + with open(test_data_folder / 'lhc_2024' / 'pytrain' + / f'pytrain_{scenario}.json') as fid: + ref = json.load(fid) + tol = TOLERANCES[scenario] + + res_b1, res_b2 = _run_xsuite_scenario(scenario) + + for beam, res in (('b1', res_b1), ('b2', res_b2)): + rr = ref[beam] + assert np.array_equal(res['slots'], np.asarray(rr['slots'])) + + # per-bunch closed-orbit deviation (from the bunch average) at IP1 + xo.assert_allclose(res['dx'], np.asarray(rr['dx']), + rtol=0, atol=tol['orbit']) + xo.assert_allclose(res['dy'], np.asarray(rr['dy']), + rtol=0, atol=tol['orbit']) + + # per-bunch beam-beam tune shifts (fractional-tune circle), larger + # tolerance: pytrain tunes carry thin-slicing / map-truncation errors + for col in ('dqx', 'dqy'): + dq_xs = res[col] + dq_pt = _wrap_frac_tune(np.asarray(rr[col])) + xo.assert_allclose(dq_xs, dq_pt, rtol=0, atol=tol['tune']) + rms = float(np.sqrt(np.mean( + _wrap_frac_tune(dq_xs - dq_pt) ** 2))) + assert rms < tol['tune_rms'], ( + f'{scenario} {beam} {col}: RMS tune-shift difference ' + f'{rms:.2e} exceeds {tol["tune_rms"]:.0e}') diff --git a/tests/test_second_order_taylor_map.py b/tests/test_second_order_taylor_map.py index 34a8fbf48..56fbed3a7 100644 --- a/tests/test_second_order_taylor_map.py +++ b/tests/test_second_order_taylor_map.py @@ -6,6 +6,7 @@ import pathlib import numpy as np +import pytest from cpymad.madx import Madx import xobjects as xo @@ -59,6 +60,271 @@ def test_line_with_second_order_maps(test_context): xo.assert_allclose(tw_map.line_length, tw.line_length, rtol=0, atol=5e-9) +@for_all_test_contexts +def test_line_with_second_order_maps_split_at_octupoles(test_context): + + line = xt.load(test_data_folder / + 'hllhc15_thick/lhc_thick_with_knobs.json') + line.build_tracker(_context=test_context) + line.vars['vrf400'] = 16 + line.vars['lagrf400.b1'] = 0.5 + + # power the Landau octupoles (strong amplitude detuning) + for vv in line.vars.keys(): + if vv.startswith('kof.') or vv.startswith('kod.'): + line.vars[vv] = 40. + + mo_names = [nn for nn in line.element_names if nn.startswith('mo.')] + assert len(mo_names) == 168 + + ele_cut = ['ip1', 'ip2', 'ip3', 'ip4', 'ip5', 'ip6', 'ip7'] + + # splitting also at the octupoles keeps them as exact elements between + # the maps (split elements are excluded from the maps) + line_maps_keep = line.get_line_with_second_order_maps( + split_at=ele_cut + mo_names) + line_maps = line.get_line_with_second_order_maps(split_at=ele_cut) + for lm in (line_maps_keep, line_maps): + lm.build_tracker(_context=test_context) + + # the kept octupoles are present as exact elements + assert isinstance(line_maps_keep[mo_names[0]], xt.Octupole) + assert mo_names[0] not in line_maps.element_names + + tw = line.twiss() + tw_map = line_maps_keep.twiss() + + xo.assert_allclose(tw_map.rows[ele_cut].s, tw.rows[ele_cut].s, rtol=0, atol=1e-12) + xo.assert_allclose(tw_map.rows[ele_cut].x, tw.rows[ele_cut].x, rtol=0, atol=1e-12) + xo.assert_allclose(tw_map.rows[ele_cut].px, tw.rows[ele_cut].px, rtol=0, atol=1e-12) + xo.assert_allclose(tw_map.rows[ele_cut].y, tw.rows[ele_cut].y, rtol=0, atol=1e-12) + xo.assert_allclose(tw_map.rows[ele_cut].py, tw.rows[ele_cut].py, rtol=0, atol=1e-12) + xo.assert_allclose(tw_map.rows[ele_cut].betx, tw.rows[ele_cut].betx, rtol=1e-5, atol=0) + xo.assert_allclose(tw_map.rows[ele_cut].bety, tw.rows[ele_cut].bety, rtol=1e-5, atol=0) + xo.assert_allclose(np.mod(tw_map.qx, 1), np.mod(tw.qx, 1), rtol=0, atol=1e-7) + xo.assert_allclose(np.mod(tw_map.qy, 1), np.mod(tw.qy, 1), rtol=0, atol=1e-7) + xo.assert_allclose(tw_map.dqx, tw.dqx, rtol=0, atol=5e-2) + xo.assert_allclose(tw_map.dqy, tw.dqy, rtol=0, atol=5e-2) + + # amplitude detuning is preserved by the kept octupoles (the small + # residual difference is the sextupole-driven detuning, which second + # order maps cannot carry), while it is absent from the plain map line: + # launch test particles at small and high amplitude and measure their + # tunes from the turn-by-turn data + def _tune_fft(xs): + """Fractional tune from turn-by-turn data (Hann window + parabolic + interpolation of the FFT peak).""" + xs = xs - np.mean(xs) + ff = np.abs(np.fft.rfft(xs * np.hanning(len(xs)))) + ii = np.argmax(ff[1:-1]) + 1 + dd = 0.5 * (ff[ii - 1] - ff[ii + 1]) / (ff[ii - 1] - 2 * ff[ii] + ff[ii + 1]) + return (ii + dd) / len(xs) + + dq = {} + for label, ll in (('ref', line), ('keep', line_maps_keep), + ('maps', line_maps)): + pp = ll.build_particles(x_norm=[0.5, 5., 0.5], y_norm=[0.5, 0.5, 5.], + nemitt_x=2.5e-6, nemitt_y=2.5e-6) + ll.track(pp, num_turns=512, turn_by_turn_monitor=True, + freeze_longitudinal=True) + mon = ll.record_last_track + ctx2np = test_context.nparray_from_context_array + qx = [_tune_fft(ctx2np(mon.x)[jj, :]) for jj in range(3)] + qy = [_tune_fft(ctx2np(mon.y)[jj, :]) for jj in range(3)] + dq[label] = (qx[1] - qx[0], qy[2] - qy[0]) # amplitude detuning + + assert dq['ref'][0] > 5e-3 # measured: ~1e-2 + assert dq['ref'][1] > 5e-3 + xo.assert_allclose(dq['keep'], dq['ref'], rtol=0, atol=1e-3) + xo.assert_allclose(dq['maps'], (0, 0), rtol=0, atol=5e-4) + + +@for_all_test_contexts +def test_second_order_maps_split_at_thick_elements(test_context): + + # FODO ring made only of exactly-linear elements (quadrupoles and + # expanded drifts) plus two thick octupoles kept exact in the map line + # by splitting at them: tracking through the map line must reproduce + # the full line exactly. + env = xt.Environment() + env.particle_ref = xt.Particles(p0c=10e9) + components = [] + for cc in range(8): + components += [ + env.new(f'qf{cc}', xt.Quadrupole, k1=0.12, length=0.5), + env.new(f'd1{cc}', xt.Drift, length=2.), + env.new(f'qd{cc}', xt.Quadrupole, k1=-0.12, length=0.5), + env.new(f'd2{cc}', xt.Drift, length=2.), + ] + # two octupoles back to back (empty span between kept elements) and a + # marker directly downstream (empty span between keep and split_at) + components[8:8] = [env.new('mo1', xt.Octupole, k3=3000., length=0.3), + env.new('mo2', xt.Octupole, k3=-2000., length=0.3), + env.new('m1', xt.Marker)] + line = env.new_line(components=components) + line.twiss_default['method'] = '4d' + line.build_tracker(_context=test_context) + + line_maps_keep = line.get_line_with_second_order_maps( + split_at=['m1', 'mo1', 'mo2']) + line_maps = line.get_line_with_second_order_maps(split_at=['m1']) + + # no maps are generated for the empty spans between adjacent cuts + names = list(line_maps_keep.element_names) + assert names[names.index('mo1') + 1] == 'mo2' + assert names[names.index('mo2') + 1] == 'm1' + + for lm in (line_maps_keep, line_maps): + lm.twiss_default['method'] = '4d' + lm.build_tracker(_context=test_context) + + tw = line.twiss() + tw_keep = line_maps_keep.twiss() + xo.assert_allclose(tw_keep.qx, tw.qx, rtol=0, atol=1e-8) + xo.assert_allclose(tw_keep.qy, tw.qy, rtol=0, atol=1e-8) + + p_test = dict(x=2e-3, px=1e-5, y=-1.5e-3, py=2e-5) + res = {} + for label, ll in (('keep', line_maps_keep), ('maps', line_maps), + ('ref', line)): + pp = ll.build_particles(**p_test) + ll.track(pp, num_turns=50) + res[label] = np.array([getattr(pp, cc)[0] for cc in ['x', 'px', 'y', 'py']]) + + # kept octupoles -> exact (everything else is linear) + xo.assert_allclose(res['keep'], res['ref'], rtol=0, atol=1e-12) + # octupoles inside the maps -> their nonlinearity is lost + assert np.max(np.abs(res['maps'] - res['ref'])) > 1e-5 + + # the original line is not affected by the map lines (shared elements + # must not be moved out of its buffer) + pp = line.build_particles(**p_test) + line.track(pp, num_turns=1) + + with pytest.raises(ValueError, match='not present in the line'): + line.get_line_with_second_order_maps(split_at=['does_not_exist']) + + +@for_all_test_contexts +def test_second_order_maps_split_at_repeated_names(test_context): + + # ring with REPEATED element names (same elements placed several times, + # as it happens e.g. for the drift pieces generated by element + # insertions): element handling refers to the disambiguated names + # 'name::N' used in the line/twiss tables. As above, all elements are + # exactly linear except one thick octupole, so the map line with the + # octupole split at must reproduce the full line exactly. + elements = { + 'qf': xt.Quadrupole(k1=0.12, length=0.5), + 'qd': xt.Quadrupole(k1=-0.12, length=0.5), + 'dd': xt.Drift(length=2.), + 'mo': xt.Octupole(k3=3000., length=0.3), + 'm1': xt.Marker(), + } + element_names = [] + for cc in range(8): + element_names += ['qf', 'dd', 'qd', 'dd'] + # octupole surrounded by repeated-name drifts (the map following it + # starts at a repeated element), marker in the second cell + element_names[2:2] = ['mo'] + element_names[8:8] = ['m1'] + line = xt.Line(elements=elements, element_names=element_names) + line.particle_ref = xt.Particles(p0c=10e9) + line.twiss_default['method'] = '4d' + line.build_tracker(_context=test_context) + + # split at the octupole (unique name) and at one particular occurrence + # of the repeated drift (disambiguated name) + line_maps_keep = line.get_line_with_second_order_maps( + split_at=['m1', 'mo', 'dd::5']) + line_maps = line.get_line_with_second_order_maps(split_at=['m1']) + + # the split elements appear in the new line under the same names, + # including the repeated first element of the line + for nn in ('qf::0', 'mo', 'm1', 'dd::5'): + assert nn in line_maps_keep.element_names + assert isinstance(line_maps_keep['dd::5'], xt.Drift) + + for lm in (line_maps_keep, line_maps): + lm.twiss_default['method'] = '4d' + lm.build_tracker(_context=test_context) + + tw = line.twiss() + tw_keep = line_maps_keep.twiss() + xo.assert_allclose(tw_keep.qx, tw.qx, rtol=0, atol=1e-8) + xo.assert_allclose(tw_keep.qy, tw.qy, rtol=0, atol=1e-8) + + p_test = dict(x=2e-3, px=1e-5, y=-1.5e-3, py=2e-5) + res = {} + for label, ll in (('keep', line_maps_keep), ('maps', line_maps), + ('ref', line)): + pp = ll.build_particles(**p_test) + ll.track(pp, num_turns=50) + res[label] = np.array([getattr(pp, cc)[0] for cc in ['x', 'px', 'y', 'py']]) + + # split octupole -> exact (everything else is linear) + xo.assert_allclose(res['keep'], res['ref'], rtol=0, atol=1e-12) + # octupole inside the maps -> its nonlinearity is lost + assert np.max(np.abs(res['maps'] - res['ref'])) > 1e-5 + + # a repeated plain name is ambiguous and not accepted + with pytest.raises(ValueError, match='not present in the line'): + line.get_line_with_second_order_maps(split_at=['dd']) + + +@for_all_test_contexts +def test_second_order_maps_split_at_sliced_line(test_context): + + # sliced lattice (thin slices and slice drifts, with parent/replica + # bookkeeping): the map line built on it must reproduce the sliced line + # exactly when the only nonlinear element (a thick octupole, excluded + # from the slicing) is split at. + env = xt.Environment() + env.particle_ref = xt.Particles(p0c=10e9) + components = [] + for cc in range(8): + components += [ + env.new(f'qf{cc}', xt.Quadrupole, k1=0.12, length=0.5), + env.new(f'd1{cc}', xt.Drift, length=2.), + env.new(f'qd{cc}', xt.Quadrupole, k1=-0.12, length=0.5), + env.new(f'd2{cc}', xt.Drift, length=2.), + ] + components[8:8] = [env.new('mo1', xt.Octupole, k3=3000., length=0.3), + env.new('m1', xt.Marker)] + line = env.new_line(components=components) + line.twiss_default['method'] = '4d' + line.slice_thick_elements(slicing_strategies=[ + xt.Strategy(slicing=None), # default: don't slice + xt.Strategy(slicing=xt.Teapot(4), element_type=xt.Quadrupole), + ]) + line.build_tracker(_context=test_context) + + line_maps_keep = line.get_line_with_second_order_maps( + split_at=['m1', 'mo1']) + line_maps = line.get_line_with_second_order_maps(split_at=['m1']) + for lm in (line_maps_keep, line_maps): + lm.twiss_default['method'] = '4d' + lm.build_tracker(_context=test_context) + + tw = line.twiss() + tw_keep = line_maps_keep.twiss() + xo.assert_allclose(tw_keep.qx, tw.qx, rtol=0, atol=1e-8) + xo.assert_allclose(tw_keep.qy, tw.qy, rtol=0, atol=1e-8) + + p_test = dict(x=2e-3, px=1e-5, y=-1.5e-3, py=2e-5) + res = {} + for label, ll in (('keep', line_maps_keep), ('maps', line_maps), + ('ref', line)): + pp = ll.build_particles(**p_test) + ll.track(pp, num_turns=50) + res[label] = np.array([getattr(pp, cc)[0] for cc in ['x', 'px', 'y', 'py']]) + + # split octupole -> exact (thin quad slices and drifts are linear) + xo.assert_allclose(res['keep'], res['ref'], rtol=0, atol=1e-12) + # octupole inside the maps -> its nonlinearity is lost + assert np.max(np.abs(res['maps'] - res['ref'])) > 1e-5 + + @for_all_test_contexts def test_second_order_maps_against_madx(test_context, sandbox_cwd): diff --git a/xtrack/__init__.py b/xtrack/__init__.py index 12fb46df1..f3b80d683 100644 --- a/xtrack/__init__.py +++ b/xtrack/__init__.py @@ -21,6 +21,7 @@ from .targets import (TargetLuminosity, TargetSeparationOrthogonalToCrossing, TargetSeparation) from .twiss import TwissInit, TwissTable +from .twiss import twiss_line_multibunch, MultiBunchTwiss from .aperture import Aperture, ApertureBuilder from .rdt import rdt_first_order_perturbation from .loss_location_refinement import LossLocationRefinement diff --git a/xtrack/line.py b/xtrack/line.py index de6e14e4c..027db3e52 100644 --- a/xtrack/line.py +++ b/xtrack/line.py @@ -24,7 +24,8 @@ DEFAULT_MATRIX_STABILITY_TOL, get_R_matrix, get_T_matrix_line, find_closed_orbit_line, - get_non_linear_chromaticity, twiss_line) + get_non_linear_chromaticity, twiss_line, + twiss_line_multibunch) from .api_categorization import GroupedAPICollector, doc_group, property_with_doc_group from . import beam_elements @@ -2212,6 +2213,18 @@ def twiss(self, particle_ref=None, method=None, twiss.__doc__ = twiss_line.__doc__ + def twiss_multibunch(self, zeta_bunches=None, particles=None, + method='4d', bunch_names=None, + show_progress=True, mode='fast', **kwargs): + if not self._has_valid_tracker(): + self.build_tracker() + return twiss_line_multibunch( + self, zeta_bunches=zeta_bunches, particles=particles, + method=method, bunch_names=bunch_names, + show_progress=show_progress, mode=mode, **kwargs) + + twiss_multibunch.__doc__ = twiss_line_multibunch.__doc__ + @doc_group("Tracking and Analysis") def twiss4d(self, **kwargs): @@ -5368,13 +5381,21 @@ def merge_consecutive_multipoles(self, inplace=True, keep=None): def get_line_with_second_order_maps(self, split_at): ''' - Return a new lines with segments definded by the elements in `split_at` + Return a new line with segments defined by the elements in `split_at` replaced by second order maps. Parameters ---------- split_at : list of str - Names of elements at which to split the line. + Names of elements at which to split the line. These elements are + kept as they are in the new line and are excluded from the maps: + each map spans from the exit of one split element to the + entrance of the next. Hence also thick and/or nonlinear elements + can be preserved exactly by splitting at them (e.g. octupoles, + to retain their amplitude detuning). Repeated elements are + referred to by their disambiguated name 'name::N' (as shown in + the line table and in the twiss table); the same names are used + in the returned line. Returns ------- @@ -5383,15 +5404,30 @@ def get_line_with_second_order_maps(self, split_at): ''' self._method_incompatible_with_compose() + if not self._has_valid_tracker(): + self.build_tracker() + + # element names disambiguated for repeated elements ('name::N', as + # in the line table and in the twiss table); for non-repeated + # elements they coincide with the plain element names + ele_names = self._element_names_unique + + missing = set(split_at) - set(ele_names) + if missing: + raise ValueError(f'Elements {sorted(missing)} are not present in the line') + + ele_idx = {nn: ii for ii, nn in enumerate(ele_names)} + ele_cut_ext = split_at.copy() - if self.element_names[0] not in ele_cut_ext: - ele_cut_ext.insert(0, self.element_names[0]) - if self.element_names[-1] not in ele_cut_ext: - ele_cut_ext.append(self.element_names[-1]) + if ele_names[0] not in ele_cut_ext: + ele_cut_ext.insert(0, ele_names[0]) + if ele_names[-1] not in ele_cut_ext: + ele_cut_ext.append(ele_names[-1]) + ele_cut_set = set(ele_cut_ext) ele_cut_sorted = [] - for ee in self.element_names: - if ee in ele_cut_ext: + for ee in ele_names: + if ee in ele_cut_set: ele_cut_sorted.append(ee) elements_map_line = [] @@ -5400,10 +5436,21 @@ def get_line_with_second_order_maps(self, split_at): for ii in range(len(ele_cut_sorted)-1): names_map_line.append(ele_cut_sorted[ii]) - elements_map_line.append(self.get(ele_cut_sorted[ii])) + # element object by its unique name: `element_names` and + # `self.element_names` are index-aligned (all occurrences of a + # repeated element share the same object) + elements_map_line.append(self.get(self.element_names[ele_idx[ele_cut_sorted[ii]]])) + + # the split element is placed in the new line as it is, hence it + # is excluded from the map: the map starts at its exit, i.e. at + # the entrance of the following element (relevant for thick + # split elements) + map_start = ele_names[ele_idx[ele_cut_sorted[ii]] + 1] + if map_start == ele_cut_sorted[ii+1]: + continue # nothing between this element and the next cut smap = xt.SecondOrderTaylorMap.from_line( - self, start=ele_cut_sorted[ii], + self, start=map_start, end=ele_cut_sorted[ii+1], twiss_table=tw, _buffer=self._buffer) @@ -5411,7 +5458,7 @@ def get_line_with_second_order_maps(self, split_at): elements_map_line.append(smap) names_map_line.append(ele_cut_sorted[-1]) - elements_map_line.append(self.get(ele_cut_sorted[-1])) + elements_map_line.append(self.get(self.element_names[ele_idx[ele_cut_sorted[-1]]])) line_maps = Line(elements=elements_map_line, element_names=names_map_line) line_maps.particle_ref = self.particle_ref.copy() diff --git a/xtrack/twiss.py b/xtrack/twiss.py index 89d81bc91..d40a2d2ca 100644 --- a/xtrack/twiss.py +++ b/xtrack/twiss.py @@ -6081,3 +6081,519 @@ def _6d_w_matrix(betx, bety, alfx, alfy, bets, dx, dpx, dy, dpy): out[2, 5] = dy out[3, 5] = dpy return out + + +class MultiBunchTwiss: + + """ + Container for the per-bunch Twiss results of a multi-bunch beam, as returned + by :func:`twiss_line_multibunch`. + + Each bunch of the beam sits at a distinct longitudinal position ``zeta`` and, + through a multi-bunch beam-beam element, experiences a different force. As a + consequence its closed orbit and linear optics (in particular the tunes) + differ from bunch to bunch. This object holds one :class:`TwissTable` per + bunch and offers convenient per-bunch access to scalar quantities. + + - ``mbtw[i]`` returns the :class:`TwissTable` of bunch ``i``. + - ``mbtw['qx']`` (or any scalar Twiss quantity) returns a numpy array with + the value for each bunch; for a column quantity (e.g. ``mbtw['x']``) + the full per-bunch columns are stacked into an (n_bunches, n_rows) + array. + - ``mbtw['x', 'ip1']`` / ``mbtw['x', list_of_names]`` return the column + values at the given element(s) for every bunch, shape (n_bunches,) / + (n_bunches, n_names). The row positions are resolved once (all bunch + tables share the same row order), so this is the FAST way to extract + per-bunch values at many elements. + - Scalar quantities are also available as attributes, e.g. ``mbtw.qx``. + - ``mbtw.zeta_bunches`` is the array of the bunch longitudinal positions. + """ + + def __init__(self, bunch_twiss, zeta_bunches, bunch_names=None): + self.bunch_twiss = list(bunch_twiss) + self.zeta_bunches = np.atleast_1d(np.asarray(zeta_bunches, dtype=float)) + self.num_bunches = len(self.bunch_twiss) + if bunch_names is None: + bunch_names = [f'bunch_{i}' for i in range(self.num_bunches)] + self.bunch_names = list(bunch_names) + self._name_pos = None # lazy {element name: row index} + + def __len__(self): + return self.num_bunches + + def __iter__(self): + return iter(self.bunch_twiss) + + def rows_index(self, names): + """Row index (or index array) of the given element name(s), shared by + all bunch tables.""" + if self._name_pos is None: + self._name_pos = {nn: ii for ii, nn in + enumerate(self.bunch_twiss[0].name)} + if isinstance(names, str): + return self._name_pos[names] + return np.array([self._name_pos[nn] for nn in names]) + + def __getitem__(self, key): + if isinstance(key, (int, np.integer, slice)): + return self.bunch_twiss[key] + if isinstance(key, tuple): + col, names = key + idx = self.rows_index(names) + return np.array([tw[col][idx] for tw in self.bunch_twiss]) + return np.array([tw[key] for tw in self.bunch_twiss]) + + def __getattr__(self, name): + if name.startswith('_'): + raise AttributeError(name) + try: + values = [tw[name] for tw in self.bunch_twiss] + except (KeyError, NameError): # Table evals unknown string keys + raise AttributeError(name) + if np.isscalar(values[0]): + return np.array(values) + raise AttributeError( + f"'{name}' is not a per-bunch scalar quantity; use " + f"mbtw['{name}'] or mbtw['{name}', element_names]") + + def bunch(self, name): + """Return the TwissTable of the bunch with the given name.""" + return self.bunch_twiss[self.bunch_names.index(name)] + + def __repr__(self): + return (f'MultiBunchTwiss({self.num_bunches} bunches, ' + f'zeta={np.array2string(self.zeta_bunches, precision=3)})') + + +def _mb_co_search(line, zeta_t, delta_t, Z_init, hs, co_tol, max_iter_co): + + """Batched Newton closed-orbit search: for every target (a bunch at fixed + ``zeta`` and ``delta``) track the closed-orbit candidate plus 8 transverse + central-difference probes, all targets in ONE tracking call per iteration. + Returns ``(Z, J, dzeta_turn)``: converged 4D closed orbits, one-turn 4x4 + Jacobians, and the one-turn zeta slippage of each closed orbit.""" + + ctx2np = line._context.nparray_from_context_array + n_t = len(zeta_t) + ZZ = Z_init.copy() + converged = False + for _ in range(max_iter_co): + XX = np.repeat(ZZ[:, None, :], 9, axis=1) + for kk in range(4): + XX[:, 1 + 2 * kk, kk] += hs[kk] + XX[:, 2 + 2 * kk, kk] -= hs[kk] + pp = line.build_particles( + x=XX[..., 0].ravel(), px=XX[..., 1].ravel(), + y=XX[..., 2].ravel(), py=XX[..., 3].ravel(), + zeta=np.repeat(zeta_t[:, None], 9, axis=1).ravel(), + delta=np.repeat(delta_t[:, None], 9, axis=1).ravel()) + line.track(pp, num_turns=1) + if not np.all(ctx2np(pp.state) > 0): + raise ClosedOrbitSearchError( + 'Particles lost while tracking the multibunch finite-' + 'difference probes') + order = np.argsort(ctx2np(pp.particle_id)) + out = np.stack([ctx2np(pp.x), ctx2np(pp.px), + ctx2np(pp.y), ctx2np(pp.py)], axis=-1)[order] + out = out.reshape(n_t, 9, 4) + zeta_out = ctx2np(pp.zeta)[order].reshape(n_t, 9)[:, 0] + + FF = out[:, 0, :] - ZZ # one-turn residual + JJ = np.empty((n_t, 4, 4)) + for kk in range(4): + JJ[:, :, kk] = (out[:, 1 + 2 * kk, :] + - out[:, 2 + 2 * kk, :]) / (2 * hs[kk]) + if np.max(np.abs(FF)) < co_tol: + converged = True + break + dZZ = np.linalg.solve(JJ - np.eye(4)[None, :, :], -FF[:, :, None]) + ZZ += dZZ[:, :, 0] + if not converged: + raise ClosedOrbitSearchError( + f'Multibunch closed-orbit search did not converge in ' + f'{max_iter_co} iterations (residual {np.max(np.abs(FF)):.2e})') + return ZZ, JJ, zeta_out - zeta_t + + +def _mb_fractional_tunes(JJ): + + """Per-target fractional tunes from the 4x4 one-turn Jacobians + (eigenvalues; modes classified by eigenvector dominance; the sign of + R12/R34 resolves the q <-> 1-q mirror ambiguity).""" + + n_t = len(JJ) + qx = np.full(n_t, np.nan) + qy = np.full(n_t, np.nan) + eigvals, eigvecs = np.linalg.eig(JJ) + for nn in range(n_t): + for ii in np.where(np.imag(eigvals[nn]) > 0)[0]: + vv = eigvecs[nn][:, ii] + is_x = (abs(vv[0])**2 + abs(vv[1])**2 + >= abs(vv[2])**2 + abs(vv[3])**2) + qq = np.angle(eigvals[nn][ii]) / (2 * np.pi) # in (0, 0.5) + if is_x: + qx[nn] = qq if JJ[nn][0, 1] >= 0 else 1 - qq + else: + qy[nn] = qq if JJ[nn][2, 3] >= 0 else 1 - qq + return qx, qy + + +def _twiss_multibunch_fast(line, zeta_bunches, steps_R_matrix=None, + co_tol=1e-11, max_iter_co=20, + compute_optics=False, delta_chrom=5e-5): + + """Batched per-bunch 4D closed solution (closed orbit + tunes + element-by- + element orbit, optionally linear optics and global quantities) for a + multi-bunch beam. + + Instead of one full twiss per bunch (each with its own closed-orbit search + and finite-difference R-matrix probes), the finite-difference probes of ALL + bunches are tracked together: per Newton iteration one single tracking call + with ``n_bunches x 9`` particles (closed-orbit candidate + central- + difference probes in x, px, y, py, each at its own fixed ``zeta``). The + per-bunch 4x4 one-turn Jacobian from the probes drives a batched Newton + update of all closed orbits simultaneously; the same Jacobians give the + per-bunch fractional tunes. A final single tracking call with an element- + by-element monitor records each bunch's closed orbit at every element. + + With ``compute_optics=False`` (mode='fast_orbit') the per-bunch + :class:`TwissTable` has columns ``name, s, x, px, y, py`` and scalars + ``qx``/``qy`` == ``qx_frac``/``qy_frac`` (only the FRACTIONAL tunes are + available without the optics pass) and ``zeta0``. + + With ``compute_optics=True`` (mode='fast') the final monitored pass tracks + the probes (plus two dispersion probes in delta) instead of only the + closed orbits. The per-element transfer Jacobians propagate the Courant- + Snyder normal form W (from :mod:`xtrack.linear_normal_form`, same + conventions as standard twiss), adding columns ``betx, alfx, bety, alfy, + mux, muy, dx, dpx, dy, dpy``. Global scalars follow the standard twiss + naming: ``qx``/``qy`` are the ACCUMULATED tunes (integer part included, + from mux/muy -- meaningful only if no single element advances the phase by + more than one turn), ``qx_frac``/``qy_frac`` the exact fractional tunes, + ``dqx``/``dqy`` the chromaticities (from two additional off-momentum + closed-orbit searches at delta = +/- ``delta_chrom``), ``c_minus`` the + closest-tune-approach coupling coefficient, and ``slip_factor``/ + ``slip_factor_dzeta_ddelta``/``momentum_compaction_factor`` the + longitudinal slippage quantities of the off-momentum closed orbits. + """ + + ctx = line._context + ctx2np = ctx.nparray_from_context_array + zeta_bunches = np.atleast_1d(np.asarray(zeta_bunches, dtype=float)) + n_bunches = len(zeta_bunches) + + steps = _complete_steps_r_matrix_with_default(steps_R_matrix) + hs = np.array([steps['dx'], steps['dpx'], steps['dy'], steps['dpy']]) + + # Batched Newton search for the per-bunch 4D closed orbit (zeta fixed, + # delta = 0), layout per bunch: [co, x+, x-, px+, px-, y+, y-, py+, py-] + ZZ, JJ, _ = _mb_co_search(line, zeta_bunches, np.zeros(n_bunches), + np.zeros((n_bunches, 4)), hs, co_tol, + max_iter_co) + + # Per-bunch fractional tunes from the 4x4 one-turn Jacobians + qx_frac, qy_frac = _mb_fractional_tunes(JJ) + + ltab = line.get_table() # includes '_end_point', matching the monitor + names = np.asarray(ltab.name) + s_all = np.asarray(ltab.s) + n_pts = len(names) + + if not compute_optics: + # Element-by-element closed orbit of all bunches in one tracking call + pp = line.build_particles( + x=ZZ[:, 0], px=ZZ[:, 1], y=ZZ[:, 2], py=ZZ[:, 3], + zeta=zeta_bunches, delta=0.) + line.track(pp, num_turns=1, turn_by_turn_monitor='ONE_TURN_EBE') + rec = line.record_last_track + x_ebe = ctx2np(rec.x); px_ebe = ctx2np(rec.px) + y_ebe = ctx2np(rec.y); py_ebe = ctx2np(rec.py) + + bunch_twiss = [] + for nn in range(n_bunches): + tab = TwissTable(dict(name=names, s=s_all, + x=x_ebe[nn].copy(), px=px_ebe[nn].copy(), + y=y_ebe[nn].copy(), py=py_ebe[nn].copy()), + periodic=True) + # without the optics pass only the fractional tunes are available + tab._data['qx'] = float(qx_frac[nn]) + tab._data['qy'] = float(qy_frac[nn]) + tab._data['qx_frac'] = float(qx_frac[nn]) + tab._data['qy_frac'] = float(qy_frac[nn]) + tab._data['zeta0'] = float(zeta_bunches[nn]) + bunch_twiss.append(tab) + return bunch_twiss + + # ------------------------------------------------------------------ + # Optics: per-bunch Courant-Snyder normal form W0 from the converged + # one-turn Jacobians (same conventions as standard twiss), then one + # monitored pass with the FD probes to propagate it element by element. + # ------------------------------------------------------------------ + dd = steps['ddelta'] + W0 = np.empty((n_bunches, 4, 4)) + for nn in range(n_bunches): + M6 = np.eye(6) + M6[:4, :4] = JJ[nn] + WW, _, _, _ = lnf.get_linear_normal_form(M6, only_4d_block=True) + W0[nn] = WW[:4, :4] + + # Chromaticity and longitudinal slippage: two additional batched + # closed-orbit searches at delta = +/- delta_chrom (both delta families + # stacked in one search; seeded with the on-momentum orbits, the Newton + # reconverges in a couple of iterations). + zeta2 = np.concatenate([zeta_bunches, zeta_bunches]) + delta2 = np.concatenate([np.full(n_bunches, +delta_chrom), + np.full(n_bunches, -delta_chrom)]) + _, J2, dzeta2 = _mb_co_search(line, zeta2, delta2, + np.concatenate([ZZ, ZZ]), hs, co_tol, + max_iter_co) + qxp, qyp = _mb_fractional_tunes(J2[:n_bunches]) + qxm, qym = _mb_fractional_tunes(J2[n_bunches:]) + + def _wrap_half(v): + return (v + 0.5) % 1.0 - 0.5 + + dqx = _wrap_half(qxp - qxm) / (2 * delta_chrom) + dqy = _wrap_half(qyp - qym) / (2 * delta_chrom) + # one-turn zeta slippage of the off-momentum closed orbits (the slippage + # of the on-momentum orbit cancels in the difference) + slip_dzeta_ddelta = (dzeta2[:n_bunches] + - dzeta2[n_bunches:]) / (2 * delta_chrom) + line_length = line.get_length() + gamma0 = float(ctx2np(line.particle_ref.gamma0)[0]) + if line_length > 0: + slip_factor = -slip_dzeta_ddelta / line_length + momentum_compaction = slip_factor + 1 / gamma0**2 + else: + slip_factor = np.full(n_bunches, np.nan) + momentum_compaction = np.full(n_bunches, np.nan) + + out_cols = {kk: np.empty((n_bunches, n_pts)) for kk in + ['x', 'px', 'y', 'py', 'betx', 'alfx', 'bety', 'alfy', + 'mux', 'muy', 'dx', 'dpx', 'dy', 'dpy']} + cmin_pts = np.empty((n_bunches, n_pts)) + + # probes per bunch: [co, x+-, px+-, y+-, py+- (transverse), delta+-] + n_probes = 11 + # chunk the monitored pass to bound the monitor memory + chunk = max(1, int(4e6 // (n_probes * n_pts))) + for c0 in range(0, n_bunches, chunk): + c1 = min(c0 + chunk, n_bunches) + nb = c1 - c0 + XX = np.repeat(ZZ[c0:c1, None, :], n_probes, axis=1) + for kk in range(4): + XX[:, 1 + 2 * kk, kk] += hs[kk] + XX[:, 2 + 2 * kk, kk] -= hs[kk] + delta = np.zeros((nb, n_probes)) + delta[:, 9] = +dd + delta[:, 10] = -dd + zz = np.repeat(zeta_bunches[c0:c1, None], n_probes, axis=1) + pp = line.build_particles( + x=XX[..., 0].ravel(), px=XX[..., 1].ravel(), + y=XX[..., 2].ravel(), py=XX[..., 3].ravel(), + zeta=zz.ravel(), delta=delta.ravel()) + line.track(pp, num_turns=1, turn_by_turn_monitor='ONE_TURN_EBE') + if not np.all(ctx2np(pp.state) > 0): + raise ClosedOrbitSearchError( + 'Particles lost while tracking the multibunch optics probes') + rec = line.record_last_track + traj = np.stack([ctx2np(rec.x), ctx2np(rec.px), + ctx2np(rec.y), ctx2np(rec.py)], axis=-1) + traj = traj.reshape(nb, n_probes, n_pts, 4) + + for kk, key in enumerate(['x', 'px', 'y', 'py']): + out_cols[key][c0:c1] = traj[:, 0, :, kk] + + # per-element transfer Jacobians M(0->s), shape (nb, n_pts, 4, 4) + MM = np.empty((nb, n_pts, 4, 4)) + for kk in range(4): + MM[:, :, :, kk] = (traj[:, 1 + 2 * kk] - traj[:, 2 + 2 * kk]) \ + / (2 * hs[kk]) + + # periodic dispersion: D(s) = M(0->s) D0 + dtraj/ddelta(s), with + # D0 = (I - J)^-1 dtraj/ddelta(one turn) + Tdelta = (traj[:, 9] - traj[:, 10]) / (2 * dd) # (nb, n_pts, 4) + D0 = np.linalg.solve(np.eye(4)[None, :, :] - JJ[c0:c1], + Tdelta[:, -1, :, None])[:, :, 0] + DD = np.einsum('bpij,bj->bpi', MM, D0) + Tdelta + for kk, key in enumerate(['dx', 'dpx', 'dy', 'dpy']): + out_cols[key][c0:c1] = DD[:, :, kk] + + # propagate the normal form: W(s) R(mu) = M(0->s) W0. beta/alpha are + # invariant under the in-block rotation R; the rotation angle is the + # phase advance (zero at s=0 by the Courant-Snyder phase fixing). + Ws = np.einsum('bpij,bjk->bpik', MM, W0[c0:c1]) + out_cols['betx'][c0:c1] = Ws[..., 0, 0]**2 + Ws[..., 0, 1]**2 + out_cols['alfx'][c0:c1] = -(Ws[..., 0, 0] * Ws[..., 1, 0] + + Ws[..., 0, 1] * Ws[..., 1, 1]) + out_cols['bety'][c0:c1] = Ws[..., 2, 2]**2 + Ws[..., 2, 3]**2 + out_cols['alfy'][c0:c1] = -(Ws[..., 2, 2] * Ws[..., 3, 2] + + Ws[..., 2, 3] * Ws[..., 3, 3]) + for th_key, (r0, r1) in [('mux', (0, 1)), ('muy', (2, 3))]: + th = np.arctan2(Ws[..., r0, r1], Ws[..., r0, r0]) + dth = np.diff(th, axis=1) % (2 * np.pi) # increments in [0, 2pi) + mu = np.concatenate( + [np.zeros((nb, 1)), np.cumsum(dth, axis=1)], axis=1) + out_cols[th_key][c0:c1] = mu / (2 * np.pi) + + # local coupling coefficient (Y. Luo et al., C-A/AP/#174 and R. Jones, + # CAS 2018 -- same formula as standard twiss). Standard twiss stores + # the W matrix re-phased to Courant-Snyder form at every element + # (w12 = 0, w11 = sqrt(betx) > 0); the numerators are invariant under + # that in-block rotation, the denominators are sqrt(betx)/sqrt(bety). + c_r1 = (np.sqrt(Ws[..., 2, 0]**2 + Ws[..., 2, 1]**2) + / np.sqrt(out_cols['betx'][c0:c1])) + c_r2 = (np.sqrt(Ws[..., 0, 2]**2 + Ws[..., 0, 3]**2) + / np.sqrt(out_cols['bety'][c0:c1])) + dq_frac = np.abs(np.mod(out_cols['mux'][c0:c1, -1], 1) + - np.mod(out_cols['muy'][c0:c1, -1], 1))[:, None] + cmin_pts[c0:c1] = (2 * np.sqrt(c_r1 * c_r2) * dq_frac + / (1 + c_r1 * c_r2)) + + if line_length > 0: + c_minus = trapz(cmin_pts, s_all, axis=1) / line_length + else: + c_minus = np.mean(cmin_pts, axis=1) + + bunch_twiss = [] + for nn in range(n_bunches): + data = dict(name=names, s=s_all) + for key, arr in out_cols.items(): + data[key] = arr[nn].copy() + tab = TwissTable(data, periodic=True) + # standard twiss naming: qx/qy are the accumulated (full) tunes + tab._data['qx'] = float(out_cols['mux'][nn][-1]) + tab._data['qy'] = float(out_cols['muy'][nn][-1]) + tab._data['qx_frac'] = float(qx_frac[nn]) + tab._data['qy_frac'] = float(qy_frac[nn]) + tab._data['dqx'] = float(dqx[nn]) + tab._data['dqy'] = float(dqy[nn]) + tab._data['c_minus'] = float(c_minus[nn]) + tab._data['slip_factor'] = float(slip_factor[nn]) + tab._data['slip_factor_dzeta_ddelta'] = float(slip_dzeta_ddelta[nn]) + tab._data['momentum_compaction_factor'] = float( + momentum_compaction[nn]) + tab._data['line_length'] = float(line_length) + tab._data['zeta0'] = float(zeta_bunches[nn]) + bunch_twiss.append(tab) + return bunch_twiss + + +def twiss_line_multibunch(line, zeta_bunches=None, particles=None, + method='4d', bunch_names=None, + show_progress=True, mode='fast', **kwargs): + + """ + Compute a closed (periodic) Twiss solution for each bunch of a multi-bunch + beam. + + In a multi-bunch beam every bunch occupies a distinct longitudinal position + ``zeta`` and, through a multi-bunch beam-beam element (e.g. + :class:`xfields.BeamBeamBiGaussianMultibunch2D`), sees a different force. + This function fixes ``zeta`` to each bunch position in turn and computes the + corresponding periodic solution, so that the per-bunch closed orbit and + optics (including the coherent beam-beam tune shift) are obtained. + + The opposing beam is assumed frozen during the computation (as stored in the + beam-beam element). For a self-consistent solution of two colliding beams, + call this function alternately on each beam, updating the opposing-beam + state from the freshly computed per-bunch closed orbits and iterating until + convergence. + + Parameters + ---------- + line : Line + The beam line (containing the multi-bunch beam-beam element(s)). + zeta_bunches : array_like, optional + Longitudinal positions of the bunches. Mutually exclusive with + ``particles``. + particles : xpart.Particles, optional + Particles object of the beam in which each active macroparticle is one + bunch; the bunch positions are read from its ``zeta``. Mutually + exclusive with ``zeta_bunches``. + method : {'4d', '6d'}, optional + Twiss method. Defaults to ``'4d'`` (``zeta`` is held fixed at each bunch + position, which is the relevant regime for the coherent multi-bunch + problem). + bunch_names : list of str, optional + Names for the bunches (used for labelling). Defaults to + ``['bunch_0', 'bunch_1', ...]``. + show_progress : bool, optional + If True (default), display a ``tqdm`` progress bar over the bunches + (``mode='full'`` only). + mode : {'fast', 'fast_orbit', 'full'}, optional + ``'fast'`` (default): the finite-difference probes of ALL bunches are + tracked together (one tracking call per Newton iteration of the + batched closed-orbit search, plus one monitored element-by-element + call and two off-momentum closed-orbit searches), which is orders of + magnitude faster than one twiss per bunch. The per-bunch result is a + :class:`TwissTable` with the element-by-element closed orbit and + linear optics (``name, s, x, px, y, py, betx, alfx, bety, alfy, mux, + muy, dx, dpx, dy, dpy``) and global quantities following the standard + twiss naming: ``qx``/``qy`` (tunes including integer), ``qx_frac``/``qy_frac`` + (fractional tunes), ``dqx``/``dqy`` (chromaticities), + ``c_minus``, ``slip_factor``, ``momentum_compaction_factor``. + Requires ``method='4d'``. + ``'fast_orbit'``: as ``'fast'`` but the optics pass and the global + quantities are skipped; the per-bunch :class:`TwissTable` contains + only the closed orbit (``name, s, x, px, y, py``) and the fractional + tunes (``qx`` == ``qx_frac``: the integer part is not available + without the optics pass). About a third of the cost of ``'fast'`` -- + useful in iteration loops that only feed back orbits. + ``'full'``: one full :func:`twiss_line` per bunch (complete + :class:`TwissTable`); slow. + **kwargs : + Additional keyword arguments forwarded to :func:`twiss_line` / + :meth:`Line.twiss` (e.g. ``nemitt_x``, ``chrom``, ...) in + ``mode='full'``. ``zeta0`` must not be given (it is set internally to + each bunch position). In ``mode='fast'`` only ``chrom`` is accepted + (and ignored); other kwargs raise. + + Returns + ------- + MultiBunchTwiss + Container with one table per bunch (a full :class:`TwissTable` in + ``mode='full'``, a lightweight orbit/tunes table in ``mode='fast'``). + See :class:`MultiBunchTwiss`. + """ + + if 'zeta0' in kwargs: + raise ValueError( + '`zeta0` cannot be provided to twiss_line_multibunch; it is set ' + 'internally to each bunch position.') + + if (zeta_bunches is None) == (particles is None): + raise ValueError('Provide exactly one of `zeta_bunches` or `particles`.') + + if particles is not None: + state = particles._context.nparray_from_context_array(particles.state) + mask = state > 0 + zeta_bunches = particles._context.nparray_from_context_array(particles.zeta)[mask] + + zeta_bunches = np.atleast_1d(np.asarray(zeta_bunches, dtype=float)) + num_bunches = len(zeta_bunches) + + if num_bunches == 0: + raise ValueError('No bunches to twiss.') + + if mode in ('fast', 'fast_orbit'): + if method != '4d': + raise ValueError(f"mode='{mode}' requires method='4d'") + unsupported = set(kwargs) - {'chrom'} + if unsupported: + raise ValueError( + f'kwargs {sorted(unsupported)} are not supported in ' + f"mode='{mode}'; use mode='full'") + bunch_twiss = _twiss_multibunch_fast(line, zeta_bunches, compute_optics=(mode == 'fast')) + elif mode == 'full': + from tqdm.auto import tqdm + bunch_twiss = [] + iterator = tqdm(zeta_bunches, desc='twiss_multibunch', + unit='bunch', disable=not show_progress) + for zb in iterator: + tw = twiss_line(line, method=method, zeta0=float(zb), **kwargs) + bunch_twiss.append(tw) + else: + raise ValueError(f'Unknown mode {mode!r} (use "fast", "fast_orbit" or "full")') + + return MultiBunchTwiss(bunch_twiss, zeta_bunches, bunch_names=bunch_names)