def test_SPS_RL(self):
PL_gain = 1000 # gain of phase loop
rtol = 1e-4 # relative tolerance
atol = 0 # absolute tolerance
# Phase loop setup
phase_loop = BeamFeedback(self.ring, self.rf_station, self.profile,
{'machine': 'SPS_RL', 'PL_gain': PL_gain})
# Tracker setup
section_tracker = RingAndRFTracker(
self.rf_station, self.beam, Profile=self.profile,
BeamFeedback=phase_loop, interpolation=False)
tracker = FullRingAndRF([section_tracker])
# average beam position
beamAvgPos = np.zeros(self.ring.n_turns)
n_turns = self.ring.n_turns
for turn in range(n_turns):
beamAvgPos[turn] = np.mean(self.beam.dt)
self.profile.track()
tracker.track()
# difference between beam position and synchronuous position
# (assuming no beam loading)
delta_tau = beamAvgPos - (np.pi - self.rf_station.phi_rf[0, :-1])\
/ self.rf_station.omega_rf[0, :-1]
# initial position for analytic solution
init_pos = self.time_offset
omega_eff = cmath.sqrt(-PL_gain**2 + 4*self.rf_station.omega_s0[0]**2)
time = np.arange(n_turns) * self.ring.t_rev[0]
# initial derivative for analytic solution;
# defined such that analytical solution at turn 1 agrees with numerical
# solution
init_slope = 0.5 * (delta_tau[1] * omega_eff * np.exp(0.5*PL_gain*time[1])
/ np.sin(0.5*omega_eff*time[1]) - delta_tau[0]
* (PL_gain+omega_eff/np.tan(0.5*omega_eff*time[1]))).real
delta_tau_analytic = init_pos * np.exp(-0.5*PL_gain*time)
delta_tau_analytic *= np.cos(0.5*time*omega_eff).real\
+ (PL_gain+2*init_slope/init_pos)\
* (np.sin(0.5*time*omega_eff)/omega_eff).real
difference = delta_tau - delta_tau_analytic
# normalize result
difference = difference / np.max(difference)
# expected difference
difference_exp = np.array([
-1.56306635e-05, -1.55605315e-05, -2.10224435e-05, -3.18525050e-05,
-4.74014489e-05, -6.70584402e-05, -9.01307422e-05, -1.15823959e-04,
-1.43290487e-04, -1.71572162e-04, -1.99820151e-04, -2.27071730e-04,
-2.52331681e-04, -2.74668126e-04, -2.93165304e-04, -3.06972913e-04,
-3.15442474e-04, -3.17857324e-04, -3.13794970e-04, -3.02786089e-04,
-2.84680298e-04, -2.59322215e-04, -2.26874004e-04, -1.87452375e-04,
-1.41293604e-04, -8.89863575e-05, -3.08865701e-05, 3.22411495e-05,
9.97408029e-05, 1.70914181e-04, 2.44766912e-04, 3.20596833e-04,
3.97403451e-04, 4.74233283e-04, 5.50189125e-04, 6.24368453e-04,
6.95836553e-04, 7.63737143e-04, 8.27069057e-04, 8.84995559e-04,
9.36770723e-04, 9.81561780e-04, 1.01869959e-03, 1.04738842e-03,
1.06711062e-03, 1.07736961e-03, 1.07778386e-03, 1.06805613e-03,
1.04797776e-03, 1.01747638e-03, 9.76519221e-04, 9.25420191e-04,
8.64415092e-04, 7.93844624e-04, 7.14396030e-04, 6.26549187e-04,
5.31154439e-04, 4.28985322e-04, 3.21198916e-04, 2.08550190e-04,
9.21607082e-05, -2.68249728e-05, -1.47278123e-04, -2.67890543e-04,
-3.87642210e-04, -5.05244473e-04, -6.19660328e-04, -7.29670300e-04,
-8.34272846e-04, -9.32388033e-04, -1.02301036e-03, -1.10520861e-03,
-1.17824066e-03, -1.24119243e-03, -1.29350096e-03, -1.33458128e-03,
-1.36388379e-03, -1.38105465e-03, -1.38595634e-03, -1.37832214e-03,
-1.35829791e-03, -1.32588558e-03, -1.28146000e-03, -1.22518721e-03,
-1.15769141e-03, -1.07943574e-03, -9.91143310e-04, -8.93671637e-04,
-7.87961546e-04, -6.74866999e-04, -5.55444011e-04, -4.30919368e-04,
-3.02270469e-04, -1.70824836e-04, -3.77396109e-05, 9.56816273e-05,
2.28299979e-04, 3.58842001e-04, 4.86074690e-04, 6.08875045e-04,
7.26090501e-04, 8.36677390e-04, 9.39639556e-04, 1.03407702e-03,
1.11906014e-03, 1.19386315e-03, 1.25779004e-03, 1.31037519e-03,
1.35108872e-03, 1.37958003e-03, 1.39570542e-03, 1.39927441e-03,
1.39033118e-03, 1.36892681e-03, 1.33533475e-03, 1.28987173e-03,
1.23311389e-03, 1.16551418e-03, 1.08773037e-03, 1.00059786e-03,
9.04879918e-04, 8.01551710e-04, 6.91575582e-04, 5.75952750e-04,
4.55756793e-04, 3.32302985e-04, 2.06487043e-04, 7.95882588e-05,
-4.72208138e-05, -1.72823958e-04, -2.96101535e-04, -4.15925168e-04,
-5.31250383e-04, -6.41017819e-04, -7.44349685e-04, -8.40276057e-04,
-9.28032591e-04, -1.00688055e-03, -1.07610640e-03, -1.13518206e-03,
-1.18370702e-03, -1.22129557e-03, -1.24764964e-03, -1.26264035e-03,
-1.26627364e-03, -1.25857717e-03, -1.23964021e-03,
-1.20980891e-03, -1.16944284e-03, -1.11887385e-03,
-1.05870668e-03, -9.89617769e-04, -9.12311681e-04,
-8.27560752e-04, -7.36170045e-04, -6.39042153e-04,
-5.37114997e-04, -4.31247869e-04, -3.22637131e-04,
-2.12194968e-04, -1.00869243e-04, 1.03136916e-05,
1.20241207e-04, 2.27979265e-04, 3.32675130e-04,
4.33323979e-04, 5.29105666e-04, 6.19142445e-04,
7.02728753e-04, 7.79114404e-04, 8.47787258e-04,
9.08216047e-04, 9.59821724e-04, 1.00228122e-03,
1.03538392e-03, 1.05880009e-03, 1.07260841e-03,
1.07662550e-03, 1.07093155e-03, 1.05577003e-03,
1.03129797e-03, 9.97904596e-04, 9.55975595e-04,
9.05955028e-04, 8.48396342e-04, 7.83925297e-04,
7.13242537e-04, 6.36896396e-04, 5.55809454e-04,
4.70697276e-04, 3.82464668e-04, 2.91766220e-04,
1.99564879e-04, 1.06707654e-04, 1.40463177e-05,
-7.76333806e-05, -1.67470574e-04, -2.54708122e-04,
-3.38623857e-04, -4.18484684e-04])
difference_exp = difference_exp/np.max(difference_exp)
np.testing.assert_allclose(difference_exp, difference,
rtol=rtol, atol=atol,
err_msg='In TestBeamFeedback test_SPS_RL: difference between simulated and analytic result different than expected')
my_beam = Beam(general_params, n_macroparticles, n_particles)
cut_options = CutOptions(cut_left=0, cut_right=2.0 * 0.9e-6, n_slices=200)
slices_ring = Profile(my_beam, cut_options)
#Phase loop
#configuration = {'machine': 'PSB', 'PL_gain': 0., 'RL_gain': [34.8,16391],
# 'PL_period': 10.e-6, 'RL_period': 7}
configuration = {
'machine': 'PSB',
'PL_gain': 0,
'RL_gain': [1.e7, 1.e11],
'period': 10.e-6
}
phase_loop = BeamFeedback(general_params, rf_params, slices_ring,
configuration)
#Long tracker
long_tracker = RingAndRFTracker(rf_params, my_beam, BeamFeedback=phase_loop)
full_ring = FullRingAndRF([long_tracker])
distribution_type = 'gaussian'
bunch_length = 200.0e-9
distribution_variable = 'Action'
matched_from_distribution_function(my_beam,
full_ring,
bunch_length=bunch_length,
distribution_type=distribution_type,
distribution_variable=distribution_variable,
profile = Profile(beam, CutOptions(n_slices=n_slices, cut_left=-0.5e-9,
cut_right=(cutRange-0.5e-9)))
mpiprint("Beam generated, profile set...")
mpiprint("Using %d slices" % n_slices)
# Define emittance BUP feedback
noiseFB = LHCNoiseFB(rf, profile, bl_target)
mpiprint("Phase noise feedback set...")
# Define phase loop and frequency loop gain
PL_gain = 1./(5.*ring.t_rev[0])
SL_gain = PL_gain/10.
# Noise injected in the PL delayed by one turn and opposite sign
config = {'machine': 'LHC', 'PL_gain': PL_gain, 'SL_gain': SL_gain}
PL = BeamFeedback(ring, rf, profile, config, PhaseNoise=LHCnoise,
LHCNoiseFB=noiseFB)
mpiprint(" PL gain is %.4e 1/s for initial turn T0 = %.4e s" % (PL.gain,
ring.t_rev[0]))
mpiprint(" SL gain is %.4e turns" % PL.gain2)
mpiprint(" Omega_s0 = %.4e s at flat bottom, %.4e s at flat top"
% (rf.omega_s0[0], rf.omega_s0[n_turns]))
mpiprint(" SL a_i = %.4f a_f = %.4f" % (PL.lhc_a[0], PL.lhc_a[n_turns]))
mpiprint(" SL t_i = %.4f t_f = %.4f" % (PL.lhc_t[0], PL.lhc_t[n_turns]))
# Injecting noise in the cavity, PL on
# Define machine impedance from http://impedance.web.cern.ch/impedance/
ZTot = np.loadtxt(os.path.join(inputDir, 'Zlong_Allthemachine_450GeV_B1_LHC_inj_450GeV_B1.dat'),
skiprows=1)
ZTable = InputTable(ZTot[:, 0], ZTot[:, 1], ZTot[:, 2])
indVoltage = InducedVoltageFreq(
PLoffset = None
PLdict = {
'time_offset': PLoffset,
'PL_gain': PLgain,
'window_coefficient': PLalpha
}
PL_save_turns = 50
if PL_2ndLoop == 'R_Loop':
gain2nd = 5e9
PLdict['machine'] = 'SPS_RL'
PLdict['RL_gain'] = gain2nd
elif PL_2ndLoop == 'F_Loop':
gain2nd = 0.9e-1
PLdict['machine'] = 'SPS_F'
PLdict['FL_gain'] = gain2nd
phaseLoop = BeamFeedback(ring, rf_station, profile, PLdict)
beamPosPrev = t_batch_begin + 0.5 * t_rf
# SPS --- Tracker Setup ----------------------------------------
mpiprint('Setting up tracker')
tracker = RingAndRFTracker(rf_station,
beam,
Profile=profile,
TotalInducedVoltage=inducedVoltage,
interpolation=True)
fulltracker = FullRingAndRF([tracker])
mpiprint('Creating SPS bunch from PS bunch')
# create 72 bunches from PS bunch
def setUp(self, negativeEta=True, acceleration=True, singleRF=True):
# Defining parameters -------------------------------------------------
# Bunch parameters
N_b = 1.e9 # Intensity
N_p = 100000 # Macro-particles
tau_0 = 50.e-9 # Initial bunch length, 4 sigma [s]
# Machine parameters
C = 1567.5 # Machine circumference [m]
p_1i = 3.e9 # Synchronous momentum [eV/c]
p_1f = 30.0e9 # Synchronous momentum, final
p_2f = 40.e9 # Synchronous momentum [eV/c]
p_2i = 60.e9 # Synchronous momentum, final
gamma_t = 31.6 # Transition gamma
alpha_1 = -1. / gamma_t / gamma_t # First order mom. comp. factor
alpha_2 = 1. / gamma_t / gamma_t # First order mom. comp. factor
# RF parameters
h = [9, 18] # Harmonic number
V = [1800.e3, 110.e3] # RF voltage [V]
phi_1 = [np.pi + 1., np.pi / 6 + 2.] # Phase modulation/offset
phi_2 = [1., np.pi / 6 + 2.] # Phase modulation/offset
N_t = 43857
# Defining classes ----------------------------------------------------
# Define general parameters
if (negativeEta == True):
if acceleration == True:
# eta < 0, acceleration
general_params = Ring(C, alpha_1,
np.linspace(p_1i, p_1f, N_t + 1),
Proton(), N_t)
elif acceleration == False:
# eta < 0, deceleration
general_params = Ring(C, alpha_1,
np.linspace(p_1f, p_1i, N_t + 1),
Proton(), N_t)
if singleRF == True:
rf_params = RFStation(general_params,
9,
1.8e6,
np.pi + 1.,
n_rf=1)
elif singleRF == False:
rf_params = RFStation(general_params, h, V, phi_1, n_rf=2)
rf_params.phi_s = calculate_phi_s(
rf_params,
Particle=general_params.Particle,
accelerating_systems='all')
elif (negativeEta == False):
if acceleration == True:
# eta > 0, acceleration
general_params = Ring(C, alpha_2,
np.linspace(p_2i, p_2f, N_t + 1),
Proton(), N_t)
elif acceleration == False:
# eta > 0, deceleration
general_params = Ring(C, alpha_2,
np.linspace(p_2f, p_2i, N_t + 1),
Proton(), N_t)
if singleRF == True:
rf_params = RFStation(general_params, 9, 1.8e6, 1., n_rf=1)
elif singleRF == False:
rf_params = RFStation(general_params, h, V, phi_2, n_rf=2)
rf_params.phi_s = calculate_phi_s(
rf_params,
Particle=general_params.Particle,
accelerating_systems='all')
# Define beam and distribution
beam = Beam(general_params, N_p, N_b)
bigaussian(general_params, rf_params, beam, tau_0 / 4, seed=1234)
#print(np.mean(beam.dt))
slices = Profile(
beam, CutOptions(cut_left=0.e-9, cut_right=600.e-9, n_slices=1000))
slices.track()
configuration = {
'machine': 'LHC',
'PL_gain': 0.1 * general_params.t_rev[0]
}
PL = BeamFeedback(general_params, rf_params, slices, configuration)
PL.beam_phase()
# Quantities to be compared
self.phi_s = rf_params.phi_s[0]
self.phi_b = PL.phi_beam
self.phi_rf = rf_params.phi_rf[0, 0]
self.dE_sep = separatrix(general_params, rf_params,
[-5.e-7, -3.e-7, 1.e-7, 3.e-7, 7.e-7, 9.e-7])