From 8604b647e00075e77496f8144949e01686db2c5c Mon Sep 17 00:00:00 2001 From: SebastienJoly <56296618+SebastienJoly@users.noreply.github.com> Date: Thu, 19 Jan 2023 13:57:37 +0100 Subject: [PATCH 1/4] Updating wakes.py module New implementation for the WakeTable object. Can now integrate a wake table for each slicer bin instead of interpolating it. Leaving the previous WakeTable syntax will continue to use the default method (interpolation). --- PyHEADTAIL/impedances/wakes.py | 134 ++++++++++++++++++++++++++++----- 1 file changed, 114 insertions(+), 20 deletions(-) diff --git a/PyHEADTAIL/impedances/wakes.py b/PyHEADTAIL/impedances/wakes.py index 82c9a11b..aa8d3ffc 100644 --- a/PyHEADTAIL/impedances/wakes.py +++ b/PyHEADTAIL/impedances/wakes.py @@ -26,6 +26,7 @@ from collections import deque from scipy.constants import c, physical_constants from scipy.interpolate import interp1d +from scipy.integrate import quad from abc import ABCMeta, abstractmethod from PyHEADTAIL.impedances.wake_kicks import * @@ -169,7 +170,7 @@ class WakeTable(WakeSource): data from a table. """ def __init__(self, wake_file, wake_file_columns, n_turns_wake=1, - *args, **kwargs): + method='interpolated', *args, **kwargs): """ Load data from the wake_file and store them in a dictionary self.wake_table. Keys are the names specified by the user in wake_file_columns and describe the names of the wake field @@ -177,24 +178,20 @@ def __init__(self, wake_file, wake_file_columns, n_turns_wake=1, given by the corresponding data read from the table. The nomenclature of the wake components must be strictly obeyed. Valid names for wake components are: - 'constant_x', 'constant_y', 'dipole_x', 'dipole_y', 'dipole_xy', 'dipole_yx', 'quadrupole_x', 'quadrupole_y', 'quadrupole_xy', 'quadrupole_yx', 'longitudinal'. - The order of wake_file_columns is relevant and must correspond to the one in the wake_file. There is no way to check this here and it is in the responsibility of the user to ensure it is correct. Two checks made here are whether the length of wake_file_columns corresponds to the number of columns in the wake_file and whether a column 'time' is specified. - The units and signs of the wake table data are assumed to follow the HEADTAIL conventions, i.e. time: [ns] transverse wake components: [V/pC/mm] longitudinal wake component: [V/pC]. - The parameter 'n_turns_wake' defines how many turns are considered for the multiturn wakes. It is 1 by default, i.e. multiturn wakes are off. """ @@ -216,6 +213,78 @@ def __init__(self, wake_file, wake_file_columns, n_turns_wake=1, self.n_turns_wake = n_turns_wake + if 'beta' in kwargs.keys(): + self.beta = kwargs['beta'] + else: + self.beta = 1 + print("Relativistic beta not specified for integrated" + " wakefield method, assumed to be equal to 1" + if method == 'integrated' else '') + + if (method == 'integrated') & ('slicer' in kwargs.keys()): + self.method = method + self.slicer = kwargs['slicer'] + else: + self.method = 'interpolated' + print("Slicer not specified for integrated wakefield" + " method, switch to interpolated method" + if method == 'integrated' else '') + + + def integrate_wake_table_component(self, wake_component): + """ Integrate a wake table component over a + bin slicing defined by the slicer object. Integrated wake is + used by the "integrated wake" method. """ + convert_to_s = 1e-9 + convert_to_V_per_Cm = 1e15 + + z_bins = np.linspace(2*self.slicer.z_cuts[0], 2*self.slicer.z_cuts[1], + 2*self.slicer.n_slices+1, endpoint=True) + z_centers = z_bins[:-1] + np.diff(z_bins)/2 + dt_bins = z_bins / (self.beta*c) + dt_centers = z_centers / (self.beta*c) + + wake_time = convert_to_s * self.wake_table['time'] + wake_strength = -convert_to_V_per_Cm * self.wake_table[wake_component] + wake_table_function = interp1d(wake_time, wake_strength) + + if (wake_time[0] == 0) and (wake_strength[0] == 0): + def wake_table_function(dt): + dt = np.clip(dt, a_min=0, a_max=None) + return interp1d(wake_time, wake_strength)(dt) + + integrated_bins = [] + for i, time_bins in enumerate(dt_bins[:-1]): + integrated_bins.append(quad(wake_table_function, dt_bins[i], dt_bins[i+1], + limit=200)[0]/(dt_bins[i+1] - dt_bins[i])) + + interpolation_function = interp1d(dt_centers, integrated_bins) + def wake(dt, *args, **kwargs): + return interpolation_function(-dt) + self.prints(wake_component + + ' Assuming ultrarelativistic wake.') + + elif (wake_time[0] < 0): + def wake_table_function(dt): + return interp1d(wake_time, wake_strength)(dt) + + integrated_bins = [] + for i, time_bins in enumerate(dt_bins[:-1]): + integrated_bins.append(quad(wake_table_function, dt_bins[i], dt_bins[i+1], + limit=200)[0]/(dt_bins[i+1] - dt_bins[i])) + + interpolation_function = interp1d(dt_centers, integrated_bins) + def wake(dt, *args, **kwargs): + return interpolation_function(-dt) + self.prints(wake_component + ' Found low beta wake.') + + else: + raise ValueError(wake_component + + ' does not meet requirements.') + + return wake + + def get_wake_kicks(self, slicer): """ Factory method. Creates instances of the appropriate WakeKick objects for all the wake components provided by the @@ -227,57 +296,81 @@ def get_wake_kicks(self, slicer): if self._is_provided('constant_x'): wake_function = self.function_transverse('constant_x') wake_kicks.append(ConstantWakeKickX( - wake_function, slicer, self.n_turns_wake)) + wake_function, slicer, self.n_turns_wake, self.wake_table)) if self._is_provided('constant_y'): wake_function = self.function_transverse('constant_y') wake_kicks.append(ConstantWakeKickY( - wake_function, slicer, self.n_turns_wake)) + wake_function, slicer, self.n_turns_wake, self.wake_table)) if self._is_provided('longitudinal'): wake_function = self.function_longitudinal() wake_kicks.append(ConstantWakeKickZ( - wake_function, slicer, self.n_turns_wake)) + wake_function, slicer, self.n_turns_wake, self.wake_table)) # Dipolar wake kicks. if self._is_provided('dipole_x'): - wake_function = self.function_transverse('dipole_x') + if self.method == 'interpolated': + wake_function = self.function_transverse('dipole_x') + elif self.method == 'integrated': + wake_function = self.integrate_wake_table_component('dipole_x') wake_kicks.append(DipoleWakeKickX( - wake_function, slicer, self.n_turns_wake)) + wake_function, slicer, self.n_turns_wake, self.wake_table)) if self._is_provided('dipole_y'): - wake_function = self.function_transverse('dipole_y') + if self.method == 'interpolated': + wake_function = self.function_transverse('dipole_y') + elif self.method == 'integrated': + wake_function = self.integrate_wake_table_component('dipole_y') wake_kicks.append(DipoleWakeKickY( - wake_function, slicer, self.n_turns_wake)) + wake_function, slicer, self.n_turns_wake, self.wake_table)) if self._is_provided('dipole_xy'): - wake_function = self.function_transverse('dipole_xy') + if self.method == 'interpolated': + wake_function = self.function_transverse('dipole_xy') + elif self.method == 'integrated': + wake_function = self.integrate_wake_table_component('dipole_xy') wake_kicks.append(DipoleWakeKickXY( - wake_function, slicer, self.n_turns_wake)) + wake_function, slicer, self.n_turns_wake, self.wake_table)) if self._is_provided('dipole_yx'): - wake_function = self.function_transverse('dipole_yx') + if self.method == 'interpolated': + wake_function = self.function_transverse('dipole_yx') + elif self.method == 'integrated': + wake_function = self.integrate_wake_table_component('dipole_yx') wake_kicks.append(DipoleWakeKickYX( wake_function, slicer, self.n_turns_wake)) # Quadrupolar wake kicks. if self._is_provided('quadrupole_x'): - wake_function = self.function_transverse('quadrupole_x') + if self.method == 'interpolated': + wake_function = self.function_transverse('quadrupole_x') + elif self.method == 'integrated': + wake_function = self.integrate_wake_table_component('quadrupole_x') wake_kicks.append(QuadrupoleWakeKickX( wake_function, slicer, self.n_turns_wake)) if self._is_provided('quadrupole_y'): - wake_function = self.function_transverse('quadrupole_y') + if self.method == 'interpolated': + wake_function = self.function_transverse('quadrupole_y') + elif self.method == 'integrated': + wake_function = self.integrate_wake_table_component('quadrupole_y') wake_kicks.append(QuadrupoleWakeKickY( wake_function, slicer, self.n_turns_wake)) if self._is_provided('quadrupole_xy'): - wake_function = self.function_transverse('quadrupole_xy') - self.kicks.append(QuadrupoleWakeKickXY( + if self.method == 'interpolated': + wake_function = self.function_transverse('quadrupole_xy') + elif self.method == 'integrated': + wake_function = self.integrate_wake_table_component('quadrupole_xy') + wake_kicks.append(QuadrupoleWakeKickXY( wake_function, slicer, self.n_turns_wake)) if self._is_provided('quadrupole_yx'): - wake_function = self.function_transverse('quadrupole_yx') + if self.method == 'interpolated': + wake_function = self.function_transverse('quadrupole_yx') + elif self.method == 'integrated': + wake_function = self.integrate_wake_table_component('quadrupole_yx') wake_kicks.append(QuadrupoleWakeKickYX( wake_function, slicer, self.n_turns_wake)) @@ -336,6 +429,7 @@ def wake(dt, *args, **kwargs): else: raise ValueError(wake_component + ' does not meet requirements.') + return wake def function_longitudinal(self): From b2296484a7189ce8fdd0181a109e7b84b6f50960 Mon Sep 17 00:00:00 2001 From: SebastienJoly <56296618+SebastienJoly@users.noreply.github.com> Date: Mon, 23 Jan 2023 10:09:19 +0100 Subject: [PATCH 2/4] Adding PS wake Adding PS wake used in integrated wake field example. --- .../wakes/PS_wall_impedance_Ekin_2.0GeV.wake | 83037 ++++++++++++++++ 1 file changed, 83037 insertions(+) create mode 100644 examples/impedances/wakes/PS_wall_impedance_Ekin_2.0GeV.wake diff --git a/examples/impedances/wakes/PS_wall_impedance_Ekin_2.0GeV.wake b/examples/impedances/wakes/PS_wall_impedance_Ekin_2.0GeV.wake new file mode 100644 index 00000000..a20cd92b --- /dev/null +++ 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0.00020967071945165032 0.0003884493223963625 -0.00017877860850500364 0.00017877860054111726 +19952.62314968067 0.00020201379463567006 0.00037428437277622895 -0.0001722705787915127 0.0001722705778533785 +20892.961308531863 0.000194252980565318 0.0003599272193695936 -0.0001656742348964747 0.0001656742404901209 +21877.61623948657 0.00018639836511059998 0.00034539651389320066 -0.00015899815124052784 0.00015899814773144357 +22908.67652766833 0.00017846167866451517 0.000330713971040485 -0.00015225229278664832 0.00015225229219884638 +23988.32919018504 0.00017045623316844325 0.0003159042078044566 -0.00014544797363020374 0.0001454479750762883 +25118.864315085444 0.00016239697882402217 0.0003009948794510191 -0.00013859789840981357 0.0001385979015883816 +26302.679918942948 0.00015429995438715274 0.0002860156510063296 -0.0001317156976073354 0.00013171569618408347 +27542.287033370256 0.00014618128190510796 0.00027099635024916465 -0.00012481507036563993 0.0001248150674706935 +28840.315031254082 0.00013805632839763548 0.0002559654019853004 -0.00011790907518361586 0.00011790907289312429 +30199.517204007592 0.00012994103290077987 0.0002409522883579362 -0.00011101125663106938 0.00011101125494283415 From 9a3675bd9db9d445efce1c1f088a3b959e313190 Mon Sep 17 00:00:00 2001 From: SebastienJoly <56296618+SebastienJoly@users.noreply.github.com> Date: Mon, 23 Jan 2023 10:12:15 +0100 Subject: [PATCH 3/4] Adding new example file Example with new integrated wake field implementation. Method is compared with current interpolated implementation. --- ...04_integrated_vs_interpolated_wakefield.py | 151 ++++++++++++++++++ 1 file changed, 151 insertions(+) create mode 100644 examples/impedances/004_integrated_vs_interpolated_wakefield.py diff --git a/examples/impedances/004_integrated_vs_interpolated_wakefield.py b/examples/impedances/004_integrated_vs_interpolated_wakefield.py new file mode 100644 index 00000000..87ef0c95 --- /dev/null +++ b/examples/impedances/004_integrated_vs_interpolated_wakefield.py @@ -0,0 +1,151 @@ +#!/usr/bin/env python +# coding: utf-8 + +import numpy as np +import os,sys +import matplotlib.pyplot as plt +import time as time +from copy import deepcopy +from scipy.constants import m_p, c, e + +from PyHEADTAIL.machines.synchrotron import * +from PyHEADTAIL.impedances.wakes import WakeField, WakeSource, WakeTable +from PyHEADTAIL.particles.slicing import UniformBinSlicer +from PyHEADTAIL.general.printers import SilentPrinter + +def compute_wake_potential_with_convolution(n_slices_wake, method): + n_macroparticles = n_macroparticles_per_slice * n_slices_wake + slicer_uniform = UniformBinSlicer( + n_slices_wake, z_cuts=(-z_cut, z_cut)) + ww1 = WakeTable(wakefile1, wakefile_columns, n_turns_wake=n_turns_wake, + method=method, beta=machine.beta, slicer=slicer_uniform) + wake_field = WakeField(slicer_uniform, ww1) + + bunch = machine.generate_6D_Gaussian_bunch(n_macroparticles=n_macroparticles, + intensity=intensity, epsn_x=epsn_x, + epsn_y=epsn_y, sigma_z=sigma_z) + bunch.x += 1e-3 + bunch.y += 1e-3 + + slice_set = bunch.get_slices(slicer_uniform, statistics=['mean_xp', 'mean_yp']) + xp_before_kick = slice_set.mean_xp.copy() + + wake_field.track(bunch) + + slice_set2 = bunch.get_slices(slicer_uniform, statistics=['mean_xp', 'mean_yp']) + kick_xp = slice_set2.mean_xp - xp_before_kick + + window = slice_set2.z_centers.size//10 + z_convolution = slice_set2.z_centers[window//2:-window//2+1] + wake_potential_convolution = np.convolve(kick_xp, np.ones(window), "valid")/window + + return z_convolution, wake_potential_convolution + + + +R = 100 # PS radius +C = 2*R*np.pi + +# CREATE SYNCHROTRON (TRANSVERSE MAP + LONGITUDINAL MAP) +# ===================== +n_segments = 1 + +Q_x = 6.225 +Q_y = 6.24 +Q_s = 0.00126 # Used when longitudinal_mode = 'linear' + +Qp_x = 0. +Qp_y = 0. + +s = np.arange(0, n_segments + 1) * C / n_segments +alpha_x = 0 * np.ones(n_segments + 1) +beta_x = 16 * np.ones(n_segments) +D_x = 0 * np.ones(n_segments) +alpha_y = 0 * np.ones(n_segments) +beta_y = 16 * np.ones(n_segments) +D_y = 0 * np.ones(n_segments) + +charge = e +mass = m_p +alpha = 0.02687 +h = [7] +V = [50e3] +dphi = 0. + +gamma = 3.13 +p0 = np.sqrt(gamma**2 - 1) * m_p * c +p_increment = 0. + +# Machine with PS parameters +machine = Synchrotron(optics_mode = 'smooth', circumference = C, + n_segments = n_segments, alpha_x = alpha_x, + beta_x = beta_x, D_x = D_x, alpha_y = alpha_y, + beta_y = beta_y, D_y = D_y, accQ_x = Q_x, + accQ_y = Q_y, Qp_x = Qp_x, Qp_y = Qp_y, + alpha_mom_compaction = alpha, + longitudinal_mode = 'linear', Q_s = Q_s, h_RF = h, + dphi_RF = dphi, charge = e, mass = m_p, p0 = p0, + p_increment = p_increment) + +machine.gamma = gamma + +###############################################################################3 +# CREATE BEAM +# =========== +intensity = 1e11 + +epsn_x = 3.25e-6 # in [m rad] +epsn_y = 3.25e-6 # in [m rad] +sigma_z = 12.36 # in [m] +z_cut = 3 * sigma_z + + +# CREATE BEAM SLICERS +# =================== +n_macroparticles_per_slice = 700 + +# CREATE WAKES +# ============ + +# Wake Table +wakefile1 = ('/wakes/PS_wall_impedance_Ekin_2.0GeV.wake') +n_turns_wake = 1 + +wakefile_columns = ['time', 'dipole_x', 'nodipole_y', 'quadrupole_x', 'noquadrupole_y'] +ww1 = WakeTable(wakefile1, wakefile_columns, n_turns_wake=n_turns_wake, + method='interpolated', beta=machine.beta + ) + + +print('Plot wake table content') + +plt.figure(figsize=(8,6)) +plt.plot(ww1.wake_table['time'], ww1.wake_table['dipole_x'], label='dipole_x') +plt.plot(ww1.wake_table['time'], ww1.wake_table['quadrupole_x'], label='quadrupole_x') +plt.xlabel('Time [ns]') +plt.ylabel('W [V/pC/mm]') +plt.legend() +plt.xlim(-1, 2) +plt.show() + + +print('Methods comparison /n') +print('Integrated method might take up some time to integrate the wake file ' + 'as it contains many points.') +n_slices_integrated = 600 +n_slices_interpolated = 5000 +plt.figure() +plt.plot(*compute_wake_potential_with_convolution(n_slices_integrated, 'integrated'), + label=f'Integrated method, {n_slices_integrated:.0f} slices') +plt.plot(*compute_wake_potential_with_convolution(n_slices_interpolated, 'interpolated'), + ls='--', label=f'Integrated method, {n_slices_interpolated:.0f} slices') +plt.xlabel('z [m]') +plt.ylabel('Kick [a.u.]') +plt.grid() +plt.legend(bbox_to_anchor=(1,1)) +plt.show() + + +print('Results are exactly matching when both methods have converged. ' + 'Using the integrated method results in a factor ~5 reduction of ' + 'number of slices while giving the wake potential.') From 39f391963ba8450cd50cb221ad1f0253b3dfc5b1 Mon Sep 17 00:00:00 2001 From: SebastienJoly <56296618+SebastienJoly@users.noreply.github.com> Date: Thu, 11 Jan 2024 16:33:06 +0100 Subject: [PATCH 4/4] Multi turn wake integrated wakefield method Adding multi-turn wake capabilities to the integrated wakefield method. --- PyHEADTAIL/impedances/wakes.py | 30 ++++++++++++++++++++++++++---- 1 file changed, 26 insertions(+), 4 deletions(-) diff --git a/PyHEADTAIL/impedances/wakes.py b/PyHEADTAIL/impedances/wakes.py index aa8d3ffc..16ded37b 100644 --- a/PyHEADTAIL/impedances/wakes.py +++ b/PyHEADTAIL/impedances/wakes.py @@ -213,6 +213,7 @@ def __init__(self, wake_file, wake_file_columns, n_turns_wake=1, self.n_turns_wake = n_turns_wake + # beta check for non-relativistic case if 'beta' in kwargs.keys(): self.beta = kwargs['beta'] else: @@ -220,7 +221,16 @@ def __init__(self, wake_file, wake_file_columns, n_turns_wake=1, print("Relativistic beta not specified for integrated" " wakefield method, assumed to be equal to 1" if method == 'integrated' else '') - + + # circumference check for multiturns wake + if (method == 'integrated') & (n_turns_wake > 1) & ('circumference' in kwargs.keys()): + self.circumference = kwargs['circumference'] + elif (method == 'integrated') & (n_turns_wake > 1) & ('circumference' not in kwargs.keys()): + self.n_turns_wake = 1 + print("Machine circumference not specified for integrated wakefield" + " method with multiturns wake, assume one turn wake instead.") + + # slicer check for integrated method if (method == 'integrated') & ('slicer' in kwargs.keys()): self.method = method self.slicer = kwargs['slicer'] @@ -238,8 +248,21 @@ def integrate_wake_table_component(self, wake_component): convert_to_s = 1e-9 convert_to_V_per_Cm = 1e15 - z_bins = np.linspace(2*self.slicer.z_cuts[0], 2*self.slicer.z_cuts[1], - 2*self.slicer.n_slices+1, endpoint=True) + if self.n_turns_wake > 1: + """z_bins_single_turn = np.linspace(2*self.slicer.z_cuts[0], 2*self.slicer.z_cuts[1], + 2*self.slicer.n_slices+1, endpoint=True) + z_step = np.diff(z_bins_single_turn)[0] + z_bins = np.arange(2*self.slicer.z_cuts[0] - self.n_turns_wake * self.circumference, + 2*self.slicer.z_cuts[1] + self.n_turns_wake * self.circumference + z_step, + z_step)""" + z_bins = np.hstack([np.linspace(2*self.slicer.z_cuts[0], 2*self.slicer.z_cuts[1], + 2*self.slicer.n_slices+1, endpoint=True) + \ + n * self.circumference for n in range(self.n_turns_wake)]) + + else: + z_bins = np.linspace(2*self.slicer.z_cuts[0], 2*self.slicer.z_cuts[1], + 2*self.slicer.n_slices+1, endpoint=True) + z_centers = z_bins[:-1] + np.diff(z_bins)/2 dt_bins = z_bins / (self.beta*c) dt_centers = z_centers / (self.beta*c) @@ -465,7 +488,6 @@ def wake(dt, *args, **kwargs): ' requirements.') return wake - class Resonator(WakeSource): """ Class to describe the wake functions originating from a resonator impedance. Alex Chao's resonator model (Eq. 2.82) is used