def generate_6D_Gaussian_bunch_matched(
self, n_macroparticles, intensity, epsn_x, epsn_y,
sigma_z=None, epsn_z=None):
'''Generate a 6D Gaussian distribution of particles which is
transversely as well as longitudinally matched.
The distribution is found iteratively to exactly yield the
given bunch length while at the same time being stationary in
the non-linear bucket. Thus, the bunch length should amount
to the one specificed and should not change significantly
during the synchrotron motion.
Requires self.longitudinal_mode == 'non-linear'
for the bucket.
'''
assert self.longitudinal_mode == 'non-linear'
epsx_geo = epsn_x/self.betagamma
epsy_geo = epsn_y/self.betagamma
injection_optics = self.transverse_map.get_injection_optics()
bunch = gen.ParticleGenerator(macroparticlenumber=n_macroparticles,
intensity=intensity, charge=self.charge, mass=self.mass,
circumference=self.circumference, gamma=self.gamma,
distribution_x = gen.gaussian2D(epsx_geo), alpha_x=injection_optics['alpha_x'], beta_x=injection_optics['beta_x'], D_x=injection_optics['D_x'],
distribution_y = gen.gaussian2D(epsy_geo), alpha_y=injection_optics['alpha_y'], beta_y=injection_optics['beta_y'], D_y=injection_optics['D_y'],
distribution_z = gen.RF_bucket_distribution(self.longitudinal_map.get_bucket(gamma=self.gamma), sigma_z=sigma_z, epsn_z=epsn_z),
).generate()
return bunch
def generate_6D_Gaussian_bunch_matched(
self, n_macroparticles, intensity, epsn_x, epsn_y,
sigma_z=None, epsn_z=None, margin=0):
'''Generate a 6D Gaussian distribution of particles which is
transversely as well as longitudinally matched.
The distribution is found iteratively to exactly yield the
given bunch length while at the same time being stationary in
the non-linear bucket. Thus, the bunch length should amount
to the one specificed and should not change significantly
during the synchrotron motion.
Requires self.longitudinal_focusing == 'non-linear'
for the bucket.
'''
assert self.longitudinal_focusing == 'non-linear'
epsx_geo = epsn_x/self.betagamma
epsy_geo = epsn_y/self.betagamma
bunch = gen.ParticleGenerator(macroparticlenumber=n_macroparticles,
intensity=intensity, charge=self.charge, mass=self.mass,
circumference=self.circumference, gamma=self.gamma,
distribution_x=gen.gaussian2D(epsx_geo),
alpha_x=self.alpha_x[0], beta_x=self.beta_x[0], D_x=self.D_x[0],
distribution_y=gen.gaussian2D(epsy_geo),
alpha_y=self.alpha_y[0], beta_y=self.beta_y[0], D_y=self.D_y[0],
distribution_z=gen.RF_bucket_distribution(
rfbucket=self.longitudinal_map.get_bucket(gamma=self.gamma),
sigma_z=sigma_z, epsn_z=epsn_z, margin=margin,
printer=self._printer)
).generate()
return bunch
def generate_6D_Gaussian_bunch(self, n_macroparticles, intensity,
epsn_x, epsn_y, sigma_z):
'''Generate a 6D Gaussian distribution of particles which is
transversely matched to the Synchrotron. Longitudinally, the
distribution is matched only in terms of linear focusing.
For a non-linear bucket, the Gaussian distribution is cut along
the separatrix (with some margin). It will gradually filament
into the bucket. This will change the specified bunch length.
'''
if self.longitudinal_mode == 'linear':
check_inside_bucket = lambda z,dp : np.array(len(z)*[True])
elif self.longitudinal_mode == 'non-linear':
check_inside_bucket = self.longitudinal_map.get_bucket(
gamma=self.gamma).make_is_accepted(margin=0.05)
else:
raise NotImplementedError(
'Something wrong with self.longitudinal_mode')
eta = self.longitudinal_map.alpha_array[0] - self.gamma**-2
beta_z = np.abs(eta)*self.circumference/2./np.pi/self.longitudinal_map.Qs
sigma_dp = sigma_z/beta_z
epsx_geo = epsn_x/self.betagamma
epsy_geo = epsn_y/self.betagamma
injection_optics = self.transverse_map.get_injection_optics()
bunch = gen.ParticleGenerator(macroparticlenumber=n_macroparticles,
intensity=intensity, charge=self.charge, mass=self.mass,
circumference=self.circumference, gamma=self.gamma,
distribution_x = gen.gaussian2D(epsx_geo), alpha_x=injection_optics['alpha_x'], beta_x=injection_optics['beta_x'], D_x=injection_optics['D_x'],
distribution_y = gen.gaussian2D(epsy_geo), alpha_y=injection_optics['alpha_y'], beta_y=injection_optics['beta_y'], D_y=injection_optics['D_y'],
distribution_z = gen.cut_distribution(gen.gaussian2D_asymmetrical(sigma_u=sigma_z, sigma_up=sigma_dp),is_accepted=check_inside_bucket),
).generate()
return bunch
def generate_6D_Gaussian_bunch(
self, n_macroparticles, intensity, epsn_x, epsn_y, sigma_z
):
"""Generate a 6D Gaussian distribution of particles which is
transversely matched to the Synchrotron. Longitudinally, the
distribution is matched only in terms of linear focusing.
For a non-linear bucket, the Gaussian distribution is cut along
the separatrix (with some margin). It will gradually filament
into the bucket. This will change the specified bunch length.
"""
if self.longitudinal_mode == "linear":
check_inside_bucket = lambda z, dp: np.array(len(z) * [True])
Q_s = self.longitudinal_map.Q_s
elif self.longitudinal_mode == "non-linear":
bucket = self.longitudinal_map.get_bucket(
gamma=self.gamma, mass=self.mass, charge=self.charge
)
check_inside_bucket = bucket.make_is_accepted(margin=0.05)
Q_s = bucket.Q_s
else:
raise NotImplementedError("Something wrong with self.longitudinal_mode")
eta = self.longitudinal_map.alpha_array[0] - self.gamma ** -2
beta_z = np.abs(eta) * self.circumference / 2.0 / np.pi / Q_s
sigma_dp = sigma_z / beta_z
epsx_geo = epsn_x / self.betagamma
epsy_geo = epsn_y / self.betagamma
injection_optics = self.transverse_map.get_injection_optics()
bunch = generators.ParticleGenerator(
macroparticlenumber=n_macroparticles,
intensity=intensity,
charge=self.charge,
mass=self.mass,
circumference=self.circumference,
gamma=self.gamma,
distribution_x=generators.gaussian2D(epsx_geo),
alpha_x=injection_optics["alpha_x"],
beta_x=injection_optics["beta_x"],
D_x=injection_optics["D_x"],
distribution_y=generators.gaussian2D(epsy_geo),
alpha_y=injection_optics["alpha_y"],
beta_y=injection_optics["beta_y"],
D_y=injection_optics["D_y"],
distribution_z=generators.cut_distribution(
generators.gaussian2D_asymmetrical(sigma_u=sigma_z, sigma_up=sigma_dp),
is_accepted=check_inside_bucket,
),
).generate()
return bunch
def generate_6D_Gaussian_bunch_matched(
self, n_macroparticles, intensity, epsn_x, epsn_y, sigma_z=None, epsn_z=None
):
"""Generate a 6D Gaussian distribution of particles which is
transversely as well as longitudinally matched.
The distribution is found iteratively to exactly yield the
given bunch length while at the same time being stationary in
the non-linear bucket. Thus, the bunch length should amount
to the one specificed and should not change significantly
during the synchrotron motion.
Requires self.longitudinal_mode == 'non-linear'
for the bucket.
"""
if self.longitudinal_mode == 'linear':
assert(sigma_z is not None)
bunch = self.generate_6D_Gaussian_bunch(n_macroparticles, intensity,
epsn_x, epsn_y, sigma_z)
elif self.longitudinal_mode == "non-linear":
epsx_geo = epsn_x / self.betagamma
epsy_geo = epsn_y / self.betagamma
injection_optics = self.transverse_map.get_injection_optics()
bunch = generators.ParticleGenerator(
macroparticlenumber=n_macroparticles,
intensity=intensity,
charge=self.charge,
mass=self.mass,
circumference=self.circumference,
gamma=self.gamma,
distribution_x=generators.gaussian2D(epsx_geo),
alpha_x=injection_optics["alpha_x"],
beta_x=injection_optics["beta_x"],
D_x=injection_optics["D_x"],
distribution_y=generators.gaussian2D(epsy_geo),
alpha_y=injection_optics["alpha_y"],
beta_y=injection_optics["beta_y"],
D_y=injection_optics["D_y"],
distribution_z=generators.RF_bucket_distribution(
self.longitudinal_map.get_bucket(gamma=self.gamma),
sigma_z=sigma_z,
epsn_z=epsn_z,
),
).generate()
else:
raise ValueError('Unknown longitudinal mode!')
return bunch
def setUp(self):
np.random.seed(0)
self.nparticles = 1000
self.epsx = 0.5
self.intensity = 1e11
self.charge = constants.e
self.mass = constants.m_p
self.circumference = 99
self.gamma = 27.1
self.generator = gf.ParticleGenerator(
self.nparticles, self.intensity,
self.charge, self.mass, self.circumference, self.gamma,
distribution_x=gf.gaussian2D(0.5),alpha_x=-0.7, beta_x=4, D_x=0,
distribution_z=gf.gaussian2D(3.0),
printer=SilentPrinter())
self.beam = self.generator.generate()
def test_cut_bucket_distribution(self):
'''Tests functionality of the cut-bucket matchor '''
nparticles = 100
h1 = 4620
h2 = 4*4620
V1 = 10e6
V2 = 1e6
dphi1 = 0
dphi2 = 0
alpha = 0.00308
p_increment = 0
long_map = RFSystems(self.circumference, [h1, h2], [V1, V2],
[dphi1, dphi2], [alpha], self.gamma, p_increment, charge=self.charge, mass=self.mass)
bucket = long_map.get_bucket(gamma=self.gamma)
is_accepted_fn = bucket.make_is_accepted(margin=0.)
bunch = gf.ParticleGenerator(
nparticles, 11, constants.e, constants.m_p,
self.circumference, self.gamma,
distribution_z=gf.cut_distribution(
is_accepted=is_accepted_fn,
distribution=gf.gaussian2D(0.01))).generate()
self.assertEqual(nparticles, len(bunch.z),
'bucket_cut_distribution loses particles')
self.assertTrue(np.sum(is_accepted_fn(bunch.z, bunch.dp)) == nparticles,
'not all particles generated with the cut RF matcher' +
' lie inside the specified separatrix')
def generate_6D_Gaussian_bunch(self, n_macroparticles, intensity, epsn_x,
epsn_y, sigma_z):
'''Generate a 6D Gaussian distribution of particles which is
transversely matched to the Synchrotron. Longitudinally, the
distribution is matched only in terms of linear focusing.
For a non-linear bucket, the Gaussian distribution is cut along
the separatrix (with some margin). It will gradually filament
into the bucket. This will change the specified bunch length.
'''
if self.longitudinal_focusing == 'linear':
check_inside_bucket = lambda z, dp: np.array(len(z) * [True])
elif self.longitudinal_focusing == 'non-linear':
check_inside_bucket = self.longitudinal_map.get_bucket(
gamma=self.gamma).make_is_accepted(margin=0.05)
else:
raise NotImplementedError(
'Something wrong with self.longitudinal_focusing')
beta_z = np.abs(self.eta) * self.circumference / 2. / np.pi / self.Q_s
sigma_dp = sigma_z / beta_z
epsx_geo = epsn_x / self.betagamma
epsy_geo = epsn_y / self.betagamma
bunch = gen.ParticleGenerator(
macroparticlenumber=n_macroparticles,
intensity=intensity,
charge=self.charge,
mass=self.mass,
circumference=self.circumference,
gamma=self.gamma,
distribution_x=gen.gaussian2D(epsx_geo),
alpha_x=self.alpha_x[0],
beta_x=self.beta_x[0],
D_x=self.D_x[0],
distribution_y=gen.gaussian2D(epsy_geo),
alpha_y=self.alpha_y[0],
beta_y=self.beta_y[0],
D_y=self.D_y[0],
distribution_z=gen.cut_distribution(
gen.gaussian2D_asymmetrical(sigma_u=sigma_z,
sigma_up=sigma_dp),
is_accepted=check_inside_bucket)).generate()
return bunch
def generate_6D_Gaussian_bunch_matched_parabolic(self,
n_macroparticles,
intensity,
epsn_x,
epsn_y,
sigma_z=None,
epsn_z=None,
margin=0):
'''
Modified version to use parabolic longitudinal profile
instead of the gaussian one
Added 06.04.2018
'''
assert self.longitudinal_focusing == 'non-linear'
epsx_geo = epsn_x / self.betagamma
epsy_geo = epsn_y / self.betagamma
bunch = gen.ParticleGenerator(
macroparticlenumber=n_macroparticles,
intensity=intensity,
charge=self.charge,
mass=self.mass,
circumference=self.circumference,
gamma=self.gamma,
distribution_x=gen.gaussian2D(epsx_geo),
alpha_x=self.alpha_x[0],
beta_x=self.beta_x[0],
D_x=self.D_x[0],
distribution_y=gen.gaussian2D(epsy_geo),
alpha_y=self.alpha_y[0],
beta_y=self.beta_y[0],
D_y=self.D_y[0],
distribution_z=gen.RF_bucket_distribution(
rfbucket=self.longitudinal_map.get_bucket(gamma=self.gamma),
distribution_type=ParabolicDistribution,
sigma_z=sigma_z,
epsn_z=epsn_z,
margin=margin,
printer=self._printer)).generate()
return bunch
def test_distributions(self):
'''Tests whether the specified distributions return the coords
in the correct format (dimensions). If new distributions are added,
add them to the test here!
'''
# Gaussian
dist = gf.gaussian2D(0.1)
self.distribution_testing_implementation(dist)
# Uniform
dist = gf.uniform2D(-2., 3.)
self.distribution_testing_implementation(dist)
def test_update_beam_with_new_coords(self):
'''Tests whether adding new coordinates to the beam
works as expected
'''
x_copy = self.beam.x.copy()
longitudinal_generator = gf.ParticleGenerator(
self.nparticles, self.intensity, self.charge,
self.mass, self.circumference, self.gamma,
distribution_z=gf.gaussian2D(3.0))
longitudinal_generator.update(self.beam)
self.assertEqual(self.beam.dp.size, self.nparticles,
'Updating the beam with new coordinates leads to' +
'faulty coordinates')
for n in range(self.nparticles):
self.assertAlmostEqual(x_copy[n], self.beam.x[n],
msg='Updating the beam with new coordinates invalidates' +
'existing coordinates')
def prepareDis(self, twiss, closed_orbit):
if closed_orbit is not None:
x_co = twiss[0]['x']
y_co = twiss[0]['y']
else:
x_co = 0
y_co = 0
np.random.seed(0)
D_x_0 = twiss[0]['dx'] * self.beta
D_y_0 = twiss[0]['dy'] * self.beta
Dp_x_0 = twiss[0]['dpx'] * self.beta
Dp_y_0 = twiss[0]['dpy'] * self.beta
bx_0 = twiss[0]['betx']
by_0 = twiss[0]['bety']
s0 = twiss[-1]['s']
circumference = s0
alfx_0 = twiss[0]['alfx']
alfy_0 = twiss[0]['alfy']
pyht_beam = generators.generate_Gaussian6DTwiss(
self.npart,
1,
self.charge,
self.mass,
s0,
self.gamma,
alfx_0,
alfy_0,
bx_0,
by_0,
1,
self.epsn_x,
self.epsn_y,
1,
dispersion_x=None,
dispersion_y=None,
limit_n_rms_x=self.limit_n_rms_x**2,
limit_n_rms_y=self.limit_n_rms_y**2,
limit_n_rms_z=self.limit_n_rms_z**2,
)
distribution_z_uncut = generators.gaussian2D(self.sig_z**2)
is_accepted = generators.make_is_accepted_within_n_sigma(
epsn_rms=self.sig_z,
limit_n_rms=2.5,
)
distribution_z_cut = generators.cut_distribution(
distribution_z_uncut, is_accepted)
z, dp = distribution_z_cut(self.npart)
pyht_beam.z, pyht_beam.dp = z, dp / self.beta_z
# recentre on 0 to avoid dipolar motion:
pyht_beam.x -= pyht_beam.mean_x()
pyht_beam.xp -= pyht_beam.mean_xp()
pyht_beam.y -= pyht_beam.mean_y()
pyht_beam.yp -= pyht_beam.mean_yp()
pyht_beam.z -= pyht_beam.mean_z()
pyht_beam.dp -= pyht_beam.mean_dp()
# PyHT generates around 0, need to offset with closed orbit:
pyht_beam.x += x_co
pyht_beam.y += y_co
# add dispersive contribution to coordinates:
pyht_beam.x += D_x_0 * pyht_beam.dp
pyht_beam.y += D_y_0 * pyht_beam.dp
# also need to add D'_{x,y} to momenta:
pyht_beam.xp += Dp_x_0 * pyht_beam.dp
pyht_beam.yp += Dp_y_0 * pyht_beam.dp
return pyht_beam
def characterize_impedances(wake_dipolar_element, wake_quadrupolar_element,
n_samples_hh_kk, test_amplitude, intensity,
sigma_z, circumference, particle_charge,
particle_mass, particle_gamma, z_cut, n_tail_cut,
detuning_fit_order):
# Build response matrix for dipolar impedance
slicer_for_harmonicresponse = UniformBinSlicer(n_samples_hh_kk,
z_cuts=(-z_cut, z_cut))
# Make a test bunch (I need only longitudinal profile and energy to be correct)
bunch = generators.ParticleGenerator(
macroparticlenumber=n_samples_hh_kk * 1000,
intensity=intensity,
charge=particle_charge,
mass=particle_mass,
circumference=circumference,
gamma=particle_gamma,
distribution_x=generators.gaussian2D(1e-9), # Dummy not really used
alpha_x=0,
beta_x=100,
D_x=0.,
distribution_y=generators.gaussian2D(1e-9),
alpha_y=0.,
beta_y=100.,
D_y=0.,
distribution_z=generators.cut_distribution(
generators.gaussian2D_asymmetrical(sigma_u=sigma_z, sigma_up=1e-4),
is_accepted=(lambda z, dp: np.array(len(z) * [True]))),
).generate()
bunch.x *= 0
bunch.xp *= 0
bunch.y *= 0
bunch.yp *= 0
# Generate configurations
assert (n_samples_hh_kk % 2 == 0)
cos_ampl_list = []
sin_ampl_list = []
n_osc_list = []
for ii in range(n_samples_hh_kk // 2):
cos_ampl_list.append(test_amplitude)
sin_ampl_list.append(0.)
n_osc_list.append(ii)
cos_ampl_list.append(0.)
sin_ampl_list.append(test_amplitude)
n_osc_list.append(ii + 1)
# cos_ampl_list = [100*1e-4]
# sin_ampl_list = [0]
# n_osc_list = [3]
# Measure responses
x_meas_mat = []
x_mat = []
dpx_mat = []
y_meas_mat = []
y_mat = []
dpy_mat = []
for itest in range(len(cos_ampl_list)):
N_oscillations = n_osc_list[itest]
sin_amplitude = sin_ampl_list[itest]
cos_amplitude = cos_ampl_list[itest]
# Recenter all slices
slices_set = bunch.get_slices(slicer_for_harmonicresponse,
statistics=True)
for ii in range(slices_set.n_slices):
ix = slices_set.particle_indices_of_slice(ii)
if len(ix) > 0:
bunch.x[ix] -= np.mean(bunch.x[ix])
bunch.xp[ix] -= np.mean(bunch.xp[ix])
bunch.y[ix] -= np.mean(bunch.y[ix])
bunch.yp[ix] -= np.mean(bunch.yp[ix])
# Get slice centers
z_slices = slices_set.z_centers
N_slices = len(z_slices)
# Get z_step beween slices and define z_range
z_step = z_slices[1] - z_slices[0]
z_range = z_slices[-1] - z_slices[0] + z_step # Last term is to make
# sinusoids numerically
# orthogonal
# Generate ideal sinusoidal distortion
x_y_ideal = (sin_amplitude *
np.sin(2 * np.pi * N_oscillations * z_slices / z_range) +
cos_amplitude *
np.cos(2 * np.pi * N_oscillations * z_slices / z_range))
# Add sinusoidal distortion to particles
bunch.x += sin_amplitude * np.sin(
2 * np.pi * N_oscillations * bunch.z / z_range)
bunch.x += cos_amplitude * np.cos(
2 * np.pi * N_oscillations * bunch.z / z_range)
bunch.y += sin_amplitude * np.sin(
2 * np.pi * N_oscillations * bunch.z / z_range)
bunch.y += cos_amplitude * np.cos(
2 * np.pi * N_oscillations * bunch.z / z_range)
# Measure
bunch.clean_slices()
slices_set = bunch.get_slices(slicer_for_harmonicresponse,
statistics=True)
x_slices = slices_set.mean_x
y_slices = slices_set.mean_y
int_slices = slices_set.lambda_bins() / qe
bunch.clean_slices()
# Apply impedance
wake_dipolar_element.track(bunch)
# Measure kicks
bunch.clean_slices()
slices_set = bunch.get_slices(slicer_for_harmonicresponse,
statistics=True)
dpx_slices = slices_set.mean_xp
dpy_slices = slices_set.mean_yp
# Store results
x_mat.append(x_y_ideal.copy())
x_meas_mat.append(x_slices.copy())
dpx_mat.append(dpx_slices.copy())
y_mat.append(x_y_ideal.copy())
y_meas_mat.append(y_slices.copy())
dpy_mat.append(dpy_slices.copy())
x_mat = np.array(x_mat)
x_meas_mat = np.array(x_meas_mat)
dpx_mat = np.array(dpx_mat)
y_mat = np.array(y_mat)
y_meas_mat = np.array(y_meas_mat)
dpy_mat = np.array(dpy_mat)
HH_x = x_mat
KK_x = dpx_mat
HH_y = y_mat
KK_y = dpy_mat
if n_tail_cut > 0:
KK_x[:, :n_tail_cut] = 0.
KK_x[:, -n_tail_cut:] = 0.
KK_y[:, :n_tail_cut] = 0.
KK_y[:, -n_tail_cut:] = 0.
#############################
# Detuning characterization #
#############################
if wake_quadrupolar_element is not None:
bunch.x *= 0
bunch.xp *= 0
bunch.y *= 0
bunch.yp *= 0
bunch.x += test_amplitude
bunch.y += test_amplitude
bunch.clean_slices()
wake_quadrupolar_element.track(bunch)
bunch.clean_slices()
slices_set = bunch.get_slices(slicer_for_harmonicresponse,
statistics=True)
dpx_slices = slices_set.mean_xp
dpy_slices = slices_set.mean_yp
k_quadx = slices_set.mean_xp / test_amplitude
k_quady = slices_set.mean_yp / test_amplitude
px = np.polyfit(z_slices, k_quadx, deg=detuning_fit_order)
py = np.polyfit(z_slices, k_quady, deg=detuning_fit_order)
alpha_Nx = px[::-1]
alpha_Ny = py[::-1]
wake_characterization = {
'HH_x': HH_x,
'KK_x': KK_x,
'HH_y': HH_y,
'KK_y': KK_y,
'z_slices': z_slices,
'alpha_Nx': alpha_Nx,
'alpha_Ny': alpha_Ny
}
return wake_characterization
