diff --git a/collective_effects/__init__.py b/collective_effects/__init__.py
index 67c3d4f6011d9fc22f490119b06933d996d50655..d14360ffa3ea6025eeba8dd2a0b1cead9fb592f3 100644
--- a/collective_effects/__init__.py
+++ b/collective_effects/__init__.py
@@ -7,9 +7,10 @@ Created on Tue Jan 14 12:25:30 2020
from mbtrack2.collective_effects.instabilities import mbi_threshold, cbi_threshold
from mbtrack2.collective_effects.resistive_wall import skin_depth, CircularResistiveWall
+from mbtrack2.collective_effects.resonator import Resonator
from mbtrack2.collective_effects.tapers import StupakovRectangularTaper, StupakovCircularTaper
-from mbtrack2.collective_effects.wakefield import ComplexData, Impedance, WakeFunction, ImpedanceModel, Wakefield
-from mbtrack2.collective_effects.wakefield import read_CST, read_IW2D, spectral_density
-from mbtrack2.collective_effects.wakefield import gaussian_bunch_spectrum, beam_spectrum, effective_impedance
-from mbtrack2.collective_effects.wakefield import yokoya_elliptic, beam_loss_factor
-from mbtrack2.collective_effects.wakefield import double_sided_impedance
\ No newline at end of file
+from mbtrack2.collective_effects.wakefield import ComplexData, Impedance, WakeFunction, ImpedanceModel, WakeField
+from mbtrack2.collective_effects.utilities import read_CST, read_IW2D, spectral_density
+from mbtrack2.collective_effects.utilities import gaussian_bunch_spectrum, beam_spectrum, effective_impedance
+from mbtrack2.collective_effects.utilities import yokoya_elliptic, beam_loss_factor
+from mbtrack2.collective_effects.utilities import double_sided_impedance
\ No newline at end of file
diff --git a/collective_effects/resistive_wall.py b/collective_effects/resistive_wall.py
index 240e30e268dfa956dd1a2dbc005e88cfe6897dca..2df32f47833f7caba38c24dc733523e1097e44be 100644
--- a/collective_effects/resistive_wall.py
+++ b/collective_effects/resistive_wall.py
@@ -1,6 +1,6 @@
# -*- coding: utf-8 -*-
"""
-Define resistive wall elements based on the Wakefield class.
+Define resistive wall elements based on the WakeField class.
@author: Alexis Gamelin
@date: 14/01/2020
@@ -8,7 +8,7 @@ Define resistive wall elements based on the Wakefield class.
import numpy as np
from scipy.constants import mu_0, epsilon_0, c
-from mbtrack2.collective_effects.wakefield import Wakefield, Impedance
+from mbtrack2.collective_effects.wakefield import WakeField, Impedance
def skin_depth(omega, rho, mu_r = 1, epsilon_r = 1):
""" General formula for the skin depth
@@ -32,9 +32,9 @@ def skin_depth(omega, rho, mu_r = 1, epsilon_r = 1):
return delta
-class CircularResistiveWall(Wakefield):
+class CircularResistiveWall(WakeField):
"""
- Resistive wall Wakefield element for a circular beam pipe, approximated
+ Resistive wall WakeField element for a circular beam pipe, approximated
formulas from Eq. (2.77) of Chao book [1].
Parameters
diff --git a/collective_effects/resonator.py b/collective_effects/resonator.py
index 410a287a18d3a526b05b477429e9fbf385f73049..c6a083d86542067dd1e8916ab7bcfb3ee6592d79 100644
--- a/collective_effects/resonator.py
+++ b/collective_effects/resonator.py
@@ -1,20 +1,20 @@
# -*- coding: utf-8 -*-
"""
This module defines the impedances and wake functions from the resonator model
-based on the Wakefield class.
+based on the WakeField class.
@author: Alexis Gamelin, Watanyu Foosang
@date: 25/09/2020
"""
import numpy as np
-from mbtrack2.collective_effects.wakefield import (Wakefield, Impedance,
+from mbtrack2.collective_effects.wakefield import (WakeField, Impedance,
WakeFunction)
-class Resonator(Wakefield):
+class Resonator(WakeField):
def __init__(self, Rs, fr, Q, plane, n_wake=1e4, n_imp=1e4, imp_freq_lim=50e9):
"""
- Resonator model Wakefield element which computes the impedance and the
+ Resonator model WakeField element which computes the impedance and the
wake function in both longitudinal and transverse case.
Parameters
diff --git a/collective_effects/tapers.py b/collective_effects/tapers.py
index 34dde1855a4ab3b3b2fcb0f220da80010286ab3b..8d944e2b84c772ceb99823fc57783c41daabf209 100644
--- a/collective_effects/tapers.py
+++ b/collective_effects/tapers.py
@@ -8,11 +8,11 @@ Created on Tue Mar 31 13:15:36 2020
from scipy.constants import mu_0, epsilon_0, c, pi
import numpy as np
from scipy.integrate import trapz
-from mbtrack2.collective_effects.wakefield import Wakefield, Impedance
+from mbtrack2.collective_effects.wakefield import WakeField, Impedance
-class StupakovRectangularTaper(Wakefield):
+class StupakovRectangularTaper(WakeField):
"""
- Rectangular vertical taper Wakefield element, using the low frequency
+ Rectangular vertical taper WakeField element, using the low frequency
approxmiation. Assume constant taper angle. Formulas from [1].
! Valid for low w
@@ -136,9 +136,9 @@ class StupakovRectangularTaper(Wakefield):
return -1j*pi*self.Z0/4*integral
-class StupakovCircularTaper(Wakefield):
+class StupakovCircularTaper(WakeField):
"""
- Circular taper Wakefield element, using the low frequency
+ Circular taper WakeField element, using the low frequency
approxmiation. Assume constant taper angle. Formulas from [1].
! Valid for low w
diff --git a/collective_effects/utilities.py b/collective_effects/utilities.py
new file mode 100644
index 0000000000000000000000000000000000000000..8f792b2ce17194998a0aea4c524dbcf6135b7d91
--- /dev/null
+++ b/collective_effects/utilities.py
@@ -0,0 +1,393 @@
+# -*- coding: utf-8 -*-
+"""
+This module defines utilities functions, helping to deals with the
+collective_effects module.
+
+@author: Alexis Gamelin
+@date: 28/09/2020
+"""
+
+import pandas as pd
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.interpolate import interp1d
+from mbtrack2.collective_effects.wakefield import Impedance
+
+def read_CST(file, impedance_type='long', divide_by=None):
+ """
+ Read CST file format into an Impedance object.
+
+ Parameters
+ ----------
+ file : str
+ Path to the file to read.
+ impedance_type : str, optional
+ Type of the Impedance object.
+ divide_by : float, optional
+ Divide the impedance by a value. Mainly used to normalize transverse
+ impedance by displacement.
+
+ Returns
+ -------
+ result : Impedance object
+ Data from file.
+ """
+ df = pd.read_csv(file, comment="#", header = None, sep = "\t",
+ names = ["Frequency","Real","Imaginary"])
+ df["Frequency"] = df["Frequency"]*1e9
+ if divide_by is not None:
+ df["Real"] = df["Real"]/divide_by
+ df["Imaginary"] = df["Imaginary"]/divide_by
+ if impedance_type == "long":
+ df["Real"] = np.abs(df["Real"])
+ df.set_index("Frequency", inplace = True)
+ result = Impedance(variable = df.index,
+ function = df["Real"] + 1j*df["Imaginary"],
+ impedance_type=impedance_type)
+ return result
+
+def read_IW2D(file, impedance_type='long'):
+ """
+ Read IW2D file format into an Impedance object.
+
+ Parameters
+ ----------
+ file : str
+ Path to the file to read.
+ impedance_type : str, optional
+ Type of the Impedance object.
+
+ Returns
+ -------
+ result : Impedance object
+ Data from file.
+ """
+ df = pd.read_csv(file, sep = ' ', header = None,
+ names = ["Frequency","Real","Imaginary"], skiprows=1)
+ df.set_index("Frequency", inplace = True)
+ result = Impedance(variable = df.index,
+ function = df["Real"] + 1j*df["Imaginary"],
+ impedance_type=impedance_type)
+ return result
+
+def spectral_density(frequency, sigma, m = 1, mode="Hermite"):
+ """
+ Compute the spectral density of different modes for various values of the
+ head-tail mode number, based on Table 1 p238 of [1].
+
+ Parameters
+ ----------
+ frequency : list or numpy array
+ sample points of the spectral density in [Hz]
+ sigma : float
+ RMS bunch length in [s]
+ m : int, optional
+ head-tail (or azimutal/synchrotron) mode number
+ mode: str, optional
+ type of the mode taken into account for the computation:
+ -"Hermite" modes for Gaussian bunches
+
+ Returns
+ -------
+ numpy array
+
+ References
+ ----------
+ [1] : Handbook of accelerator physics and engineering, 3rd printing.
+ """
+
+ if mode == "Hermite":
+ return (2*np.pi*frequency*sigma)**(2*m)*np.exp(
+ -1*(2*np.pi*frequency*sigma)**2)
+ else:
+ raise NotImplementedError("Not implemanted yet.")
+
+def gaussian_bunch_spectrum(frequency, sigma):
+ """
+ Compute a Gaussian bunch spectrum [1].
+
+ Parameters
+ ----------
+ frequency : array
+ sample points of the beam spectrum in [Hz].
+ sigma : float
+ RMS bunch length in [s].
+
+ Returns
+ -------
+ bunch_spectrum : array
+ Bunch spectrum sampled at points given in frequency.
+
+ References
+ ----------
+ [1] : Gamelin, A. (2018). Collective effects in a transient microbunching
+ regime and ion cloud mitigation in ThomX. p86, Eq. 4.19
+ """
+ return np.exp(-1/2*(2*np.pi*frequency)**2*sigma**2)
+
+
+def beam_spectrum(frequency, M, bunch_spacing, sigma=None,
+ bunch_spectrum=None):
+ """
+ Compute the beam spectrum assuming constant spacing between bunches [1].
+
+ Parameters
+ ----------
+ frequency : list or numpy array
+ sample points of the beam spectrum in [Hz].
+ M : int
+ Number of bunches.
+ bunch_spacing : float
+ Time between two bunches in [s].
+ sigma : float, optional
+ If bunch_spectrum is None then a Gaussian bunch with sigma RMS bunch
+ length in [s] is assumed.
+ bunch_spectrum : array, optional
+ Bunch spectrum sampled at points given in frequency.
+
+ Returns
+ -------
+ beam_spectrum : array
+
+ References
+ ----------
+ [1] Rumolo, G - Beam Instabilities - CAS - CERN Accelerator School:
+ Advanced Accelerator Physics Course - 2014, Eq. 9
+ """
+
+ if bunch_spectrum is None:
+ bunch_spectrum = gaussian_bunch_spectrum(frequency, sigma)
+
+ beam_spectrum = (bunch_spectrum * np.exp(1j*np.pi*frequency *
+ bunch_spacing*(M-1)) *
+ np.sin(M*np.pi*frequency*bunch_spacing) /
+ np.sin(np.pi*frequency*bunch_spacing))
+
+ return beam_spectrum
+
+
+def effective_impedance(ring, imp, m, mu, sigma, M, tuneS, xi=None,
+ mode="Hermite"):
+ """
+ Compute the effective (longitudinal or transverse) impedance.
+ Formulas from Eq. (1) and (2) p238 of [1].
+
+ Parameters
+ ----------
+ ring : Synchrotron object
+ imp : Impedance object
+ mu : int
+ coupled bunch mode number, goes from 0 to (M-1) where M is the
+ number of bunches
+ m : int
+ head-tail (or azimutal/synchrotron) mode number
+ sigma : float
+ RMS bunch length in [s]
+ M : int
+ Number of bunches.
+ tuneS : float
+ Synchrotron tune.
+ xi : float, optional
+ (non-normalized) chromaticity
+ mode: str, optional
+ type of the mode taken into account for the computation:
+ -"Hermite" modes for Gaussian bunches
+
+ Returns
+ -------
+ Zeff : float
+ effective impedance in [ohm] or in [ohm/m] depanding on the impedance
+ type.
+
+ References
+ ----------
+ [1] : Handbook of accelerator physics and engineering, 3rd printing.
+ """
+
+ if not isinstance(imp, Impedance):
+ raise TypeError("{} should be an Impedance object.".format(imp))
+
+ fmin = imp.data.index.min()
+ fmax = imp.data.index.max()
+ if fmin > 0:
+ double_sided_impedance(imp)
+
+ if mode == "Hermite":
+ def h(f):
+ return spectral_density(frequency=f, sigma=sigma, m=m,
+ mode="Hermite")
+ else:
+ raise NotImplementedError("Not implemanted yet.")
+
+ pmax = fmax/(ring.f0 * M) - 1
+ pmin = fmin/(ring.f0 * M) + 1
+
+ p = np.arange(pmin,pmax+1)
+
+ if imp.impedance_type == "long":
+ fp = ring.f0*(p*M + mu + m*tuneS)
+ fp = fp[np.nonzero(fp)] # Avoid division by 0
+ num = np.sum( imp(fp) * h(fp) / (fp*2*np.pi) )
+ den = np.sum( h(fp) )
+ Zeff = num/den
+
+ elif imp.impedance_type == "xdip" or imp.impedance_type == "ydip":
+ if imp.impedance_type == "xdip":
+ tuneXY = ring.tune[0]
+ if xi is None :
+ xi = ring.chro[0]
+ elif imp.impedance_type == "ydip":
+ tuneXY = ring.tune[1]
+ if xi is None:
+ xi = ring.chro[1]
+ fp = ring.f0*(p*M + mu + tuneXY + m*tuneS)
+ f_xi = xi/ring.eta*ring.f0
+ num = np.sum( imp(fp) * h(fp - f_xi) )
+ den = np.sum( h(fp - f_xi) )
+ Zeff = num/den
+ else:
+ raise TypeError("Effective impedance is only defined for long, xdip"
+ " and ydip impedance type.")
+
+ return Zeff
+
+
+def yokoya_elliptic(x_radius , y_radius):
+ """
+ Compute Yokoya factors for an elliptic beam pipe.
+ Function adapted from N. Mounet IW2D.
+
+ Parameters
+ ----------
+ x_radius : float
+ Horizontal semi-axis of the ellipse in [m].
+ y_radius : float
+ Vertical semi-axis of the ellipse in [m].
+
+ Returns
+ -------
+ yoklong : float
+ Yokoya factor for the longitudinal impedance.
+ yokxdip : float
+ Yokoya factor for the dipolar horizontal impedance.
+ yokydip : float
+ Yokoya factor for the dipolar vertical impedance.
+ yokxquad : float
+ Yokoya factor for the quadrupolar horizontal impedance.
+ yokyquad : float
+ Yokoya factor for the quadrupolar vertical impedance.
+ """
+ if y_radius < x_radius:
+ small_semiaxis = y_radius
+ large_semiaxis = x_radius
+ else:
+ small_semiaxis = x_radius
+ large_semiaxis = y_radius
+
+ # read Yokoya factors interpolation file
+ # BEWARE: columns are ratio, dipy, dipx, quady, quadx
+ yokoya_file = pd.read_csv("collective_effects/data/" +
+ "Yokoya_elliptic_from_Elias_USPAS.csv")
+ ratio_col = yokoya_file["x"]
+ # compute semi-axes ratio (first column of this file)
+ ratio = (large_semiaxis - small_semiaxis)/(large_semiaxis + small_semiaxis)
+
+ # interpolate Yokoya file at the correct ratio
+ yoklong = 1
+
+ if y_radius < x_radius:
+ yokydip = np.interp(ratio, ratio_col, yokoya_file["dipy"])
+ yokxdip = np.interp(ratio, ratio_col, yokoya_file["dipx"])
+ yokyquad = np.interp(ratio, ratio_col, yokoya_file["quady"])
+ yokxquad = np.interp(ratio, ratio_col, yokoya_file["quadx"])
+ else:
+ yokxdip = np.interp(ratio, ratio_col, yokoya_file["dipy"])
+ yokydip = np.interp(ratio, ratio_col, yokoya_file["dipx"])
+ yokxquad = np.interp(ratio, ratio_col, yokoya_file["quady"])
+ yokyquad = np.interp(ratio, ratio_col, yokoya_file["quadx"])
+
+ return (yoklong, yokxdip, yokydip, yokxquad, yokyquad)
+
+def beam_loss_factor(impedance, frequency, spectrum, ring):
+ """
+ Compute "beam" loss factor using the beam spectrum, uses a sum instead of
+ integral compared to loss_factor [1].
+
+ Parameters
+ ----------
+ impedance : Impedance of type "long"
+ frequency : array
+ Sample points of spectrum.
+ spectrum : array
+ Beam spectrum to consider.
+ ring : Synchrotron object
+
+ Returns
+ -------
+ kloss_beam : float
+ Beam loss factor in [V/C].
+
+ References
+ ----------
+ [1] : Handbook of accelerator physics and engineering, 3rd printing.
+ Eq (3) p239.
+ """
+ pmax = np.floor(impedance.data.index.max()/ring.f0)
+ pmin = np.floor(impedance.data.index.min()/ring.f0)
+
+ if pmin >= 0:
+ double_sided_impedance(impedance)
+ pmin = -1*pmax
+
+ p = np.arange(pmin+1,pmax)
+ pf0 = p*ring.f0
+ ReZ = np.real(impedance(pf0))
+ spectral_density = np.abs(spectrum)**2
+ # interpolation of the spectrum is needed to avoid problems liked to
+ # division by 0
+ # computing the spectrum directly to the frequency points gives
+ # wrong results
+ spect = interp1d(frequency, spectral_density)
+ kloss_beam = ring.f0 * np.sum(ReZ*spect(pf0))
+
+ return kloss_beam
+
+def double_sided_impedance(impedance):
+ """
+ Add negative frequency points to single sided impedance spectrum following
+ symetries depending on impedance type.
+
+ Parameters
+ ----------
+ impedance : Impedance object
+ Single sided impedance.
+ """
+ fmin = impedance.data.index.min()
+
+ if fmin >= 0:
+ negative_index = impedance.data.index*-1
+ negative_data = impedance.data.set_index(negative_index)
+
+ imp_type = impedance.impedance_type
+
+ if imp_type == "long":
+ negative_data["imag"] = -1*negative_data["imag"]
+
+ elif (imp_type == "xdip") or (imp_type == "ydip"):
+ negative_data["real"] = -1*negative_data["real"]
+
+ elif (imp_type == "xquad") or (imp_type == "yquad"):
+ negative_data["real"] = -1*negative_data["real"]
+
+ else:
+ raise ValueError("Wrong impedance type")
+
+ try:
+ negative_data = negative_data.drop(0)
+ except KeyError:
+ pass
+
+ all_data = impedance.data.append(negative_data)
+ all_data = all_data.sort_index()
+ impedance.data = all_data
+
diff --git a/collective_effects/wakefield.py b/collective_effects/wakefield.py
index 7854a48b66a4d130476650d607763c1ff2b1d4af..13515477a3bb0db8ae77bb29b73f241efe7c4680 100644
--- a/collective_effects/wakefield.py
+++ b/collective_effects/wakefield.py
@@ -19,6 +19,7 @@ from scipy.integrate import trapz
from scipy.constants import c
from mpl_toolkits.axes_grid1.inset_locator import inset_axes
from mbtrack2.tracking.element import Element
+from mbtrack2.collective_effects.utilities import beam_spectrum, gaussian_bunch_spectrum, beam_loss_factor
class ComplexData:
"""
@@ -564,16 +565,16 @@ class Impedance(ComplexData):
super().__init__(variable=freq_trun, function=imp)
self.data.index.name = "frequency [Hz]"
-class Wakefield:
+class WakeField:
"""
- Defines a Wakefield which corresponds to a single physical element which
+ Defines a WakeField which corresponds to a single physical element which
produces different types of wakes, represented by their Impedance or
WakeFunction objects.
Parameters
----------
structure_list : list, optional
- list of Impedance/WakeFunction objects to add to the Wakefield.
+ list of Impedance/WakeFunction objects to add to the WakeField.
name : str, optional
Attributes
@@ -584,13 +585,13 @@ class Wakefield:
Methods
-------
append_to_model(structure_to_add)
- Add Impedance/WakeFunction to Wakefield.
+ Add Impedance/WakeFunction to WakeField.
list_to_attr(structure_list)
- Add list of Impedance/WakeFunction to Wakefield.
+ Add list of Impedance/WakeFunction to WakeField.
add_wakefields(wake1, beta1, wake2, beta2)
- Add two Wakefields taking into account beta functions.
+ Add two WakeFields taking into account beta functions.
add_several_wakefields(wakefields, beta)
- Add a list of Wakefields taking into account beta functions.
+ Add a list of WakeFields taking into account beta functions.
"""
def __init__(self, structure_list=None, name=None):
@@ -599,7 +600,7 @@ class Wakefield:
def append_to_model(self, structure_to_add):
"""
- Add Impedance/WakeFunction component to Wakefield.
+ Add Impedance/WakeFunction component to WakeField.
Parameters
----------
@@ -625,7 +626,7 @@ class Wakefield:
def list_to_attr(self, structure_list):
"""
- Add list of Impedance/WakeFunction components to Wakefield.
+ Add list of Impedance/WakeFunction components to WakeField.
Parameters
----------
@@ -652,23 +653,23 @@ class Wakefield:
@staticmethod
def add_wakefields(wake1, beta1, wake2, beta2):
"""
- Add two Wakefields taking into account beta functions.
+ Add two WakeFields taking into account beta functions.
Parameters
----------
- wake1 : Wakefield
- Wakefield to add.
+ wake1 : WakeField
+ WakeField to add.
beta1 : array of shape (2,)
Beta functions at wake1 postion.
- wake2 : Wakefield
- Wakefield to add.
+ wake2 : WakeField
+ WakeField to add.
beta2 : array of shape (2,)
Beta functions at wake2 postion.
Returns
-------
- wake_sum : Wakefield
- Wakefield with summed components.
+ wake_sum : WakeField
+ WakeField with summed components.
"""
wake_sum = deepcopy(wake1)
@@ -694,28 +695,28 @@ class Wakefield:
@staticmethod
def add_several_wakefields(wakefields, beta):
"""
- Add a list of Wakefields taking into account beta functions.
+ Add a list of WakeFields taking into account beta functions.
Parameters
----------
- wakefields : list of Wakefield
- Wakefields to add.
+ wakefields : list of WakeField
+ WakeFields to add.
beta : array of shape (len(wakefields), 2)
- Beta functions at the Wakefield postions.
+ Beta functions at the WakeField postions.
Returns
-------
- wake_sum : Wakefield
- Wakefield with summed components..
+ wake_sum : WakeField
+ WakeField with summed components..
"""
if len(wakefields) == 1:
return wakefields[0]
elif len(wakefields) > 1:
- wake_sum = Wakefield.add_wakefields(wakefields[0], beta[:,0],
+ wake_sum = WakeField.add_wakefields(wakefields[0], beta[:,0],
wakefields[1], beta[:,1])
for i in range(len(wakefields) - 2):
- wake_sum = Wakefield.add_wakefields(wake_sum, [1 ,1],
+ wake_sum = WakeField.add_wakefields(wake_sum, [1 ,1],
wakefields[i+2], beta[:,i+2])
return wake_sum
else:
@@ -728,25 +729,25 @@ class ImpedanceModel(Element):
Parameters
----------
ring : Synchrotron object
- wakefield_list : list of Wakefield objects
- Wakefields to add to the model.
+ wakefield_list : list of WakeField objects
+ WakeFields to add to the model.
wakefiled_postions : list
Longitudinal positions corresponding to the added Wakfields.
Attributes
----------
- wakefields : list of Wakefield objects
- Wakefields in the model.
+ wakefields : list of WakeField objects
+ WakeFields in the model.
positions : array
- Wakefields positions.
+ WakeFields positions.
names : array
- Names of (unique) Wakefield objects.
- sum : Wakefield
- Sum of every Wakefield in the model.
- sum_"name" : Wakefield
+ Names of (unique) WakeField objects.
+ sum : WakeField
+ Sum of every WakeField in the model.
+ sum_"name" : WakeField
Sum of every Wakefield with the same "name".
sum_names : array
- Names of attributes where the wakefields are summed by name.
+ Names of attributes where the WakeFields are summed by name.
Methods
-------
@@ -755,17 +756,17 @@ class ImpedanceModel(Element):
add_multiple_elements(wakefield, wakefiled_postions)
Add the same element at different locations to the model.
sum_elements()
- Sum all wakefields into self.sum.
+ Sum all WakeFields into self.sum.
update_name_list()
Update self.names with uniques names of self.wakefields.
find_wakefield(name)
- Return indexes of wakefields with the same name in self.wakefields.
+ Return indexes of WakeFields with the same name in self.wakefields.
sum_by_name(name)
Sum the elements with the same name in the model into sum_name.
sum_by_name_all(name)
Sum all the elements with the same name in the model into sum_name.
plot_area(Z_type="Zlong", component="real", sigma=None, attr_list=None)
- Plot the contributions of different kind of wakefields.
+ Plot the contributions of different kind of WakeFields.
"""
def __init__(self, ring, wakefield_list=None, wakefiled_postions=None):
@@ -788,9 +789,9 @@ class ImpedanceModel(Element):
raise NotImplementedError
def sum_elements(self):
- """Sum all wakefields into self.sum"""
+ """Sum all WakeFields into self.sum"""
beta = self.optics.beta(self.positions)
- self.sum = Wakefield.add_several_wakefields(self.wakefields, beta)
+ self.sum = WakeField.add_several_wakefields(self.wakefields, beta)
if "sum" not in self.sum_names:
self.sum_names = np.append(self.sum_names, "sum")
@@ -803,7 +804,7 @@ class ImpedanceModel(Element):
self.names = np.append(self.names, wakefield.name)
def count_elements(self):
- """Count number of each type of wakefield in the model."""
+ """Count number of each type of WakeField in the model."""
self.count = np.zeros(len(self.names))
for wakefield in self.wakefields:
if wakefield.name is not None:
@@ -811,12 +812,12 @@ class ImpedanceModel(Element):
def find_wakefield(self, name):
"""
- Return indexes of wakefields with the same name in self.wakefields.
+ Return indexes of WakeFields with the same name in self.wakefields.
Parameters
----------
name : str
- Wakefield name.
+ WakeField name.
Returns
-------
@@ -837,7 +838,7 @@ class ImpedanceModel(Element):
Parameters
----------
name : str
- Name of the wakefield to sum.
+ Name of the WakeField to sum.
"""
attribute_name = "sum_" + name
index = self.find_wakefield(name)
@@ -845,7 +846,7 @@ class ImpedanceModel(Element):
wakes = []
for i in index:
wakes.append(self.wakefields[i])
- wake_sum = Wakefield.add_several_wakefields(wakes, beta)
+ wake_sum = WakeField.add_several_wakefields(wakes, beta)
setattr(self, attribute_name, wake_sum)
if attribute_name not in self.sum_names:
self.sum_names = np.append(self.sum_names, attribute_name)
@@ -863,8 +864,8 @@ class ImpedanceModel(Element):
Parameters
----------
- wakefield_list : list of Wakefield objects
- Wakefields to add to the model.
+ wakefield_list : list of WakeField objects
+ WakeFields to add to the model.
wakefiled_postions : list
Longitudinal positions corresponding to the added Wakfields.
"""
@@ -883,8 +884,8 @@ class ImpedanceModel(Element):
Parameters
----------
- wakefield : Wakefield object
- Wakefield to add to the model.
+ WakeField : WakeField object
+ WakeField to add to the model.
wakefiled_postions : list
Longitudinal positions corresponding to the added Wakfield.
"""
@@ -897,7 +898,7 @@ class ImpedanceModel(Element):
def plot_area(self, Z_type="Zlong", component="real", sigma=None,
attr_list=None, zoom=False):
"""
- Plot the contributions of different kind of wakefields.
+ Plot the contributions of different kind of WakeFields.
Parameters
----------
@@ -1128,395 +1129,3 @@ class ImpedanceModel(Element):
summary["P (bunch) [W]"] = summary["loss factor (bunch) [V/pC]"]*1e12*Q**2/(self.ring.T0)*M
return summary
-
-
-def read_CST(file, impedance_type='long', divide_by=None):
- """
- Read CST file format into an Impedance object.
-
- Parameters
- ----------
- file : str
- Path to the file to read.
- impedance_type : str, optional
- Type of the Impedance object.
- divide_by : float, optional
- Divide the impedance by a value. Mainly used to normalize transverse
- impedance by displacement.
-
- Returns
- -------
- result : Impedance object
- Data from file.
- """
- df = pd.read_csv(file, comment="#", header = None, sep = "\t",
- names = ["Frequency","Real","Imaginary"])
- df["Frequency"] = df["Frequency"]*1e9
- if divide_by is not None:
- df["Real"] = df["Real"]/divide_by
- df["Imaginary"] = df["Imaginary"]/divide_by
- if impedance_type == "long":
- df["Real"] = np.abs(df["Real"])
- df.set_index("Frequency", inplace = True)
- result = Impedance(variable = df.index,
- function = df["Real"] + 1j*df["Imaginary"],
- impedance_type=impedance_type)
- return result
-
-def read_IW2D(file, impedance_type='long'):
- """
- Read IW2D file format into an Impedance object.
-
- Parameters
- ----------
- file : str
- Path to the file to read.
- impedance_type : str, optional
- Type of the Impedance object.
-
- Returns
- -------
- result : Impedance object
- Data from file.
- """
- df = pd.read_csv(file, sep = ' ', header = None,
- names = ["Frequency","Real","Imaginary"], skiprows=1)
- df.set_index("Frequency", inplace = True)
- result = Impedance(variable = df.index,
- function = df["Real"] + 1j*df["Imaginary"],
- impedance_type=impedance_type)
- return result
-
-def spectral_density(frequency, sigma, m = 1, mode="Hermite"):
- """
- Compute the spectral density of different modes for various values of the
- head-tail mode number, based on Table 1 p238 of [1].
-
- Parameters
- ----------
- frequency : list or numpy array
- sample points of the spectral density in [Hz]
- sigma : float
- RMS bunch length in [s]
- m : int, optional
- head-tail (or azimutal/synchrotron) mode number
- mode: str, optional
- type of the mode taken into account for the computation:
- -"Hermite" modes for Gaussian bunches
-
- Returns
- -------
- numpy array
-
- References
- ----------
- [1] : Handbook of accelerator physics and engineering, 3rd printing.
- """
-
- if mode == "Hermite":
- return (2*np.pi*frequency*sigma)**(2*m)*np.exp(
- -1*(2*np.pi*frequency*sigma)**2)
- else:
- raise NotImplementedError("Not implemanted yet.")
-
-def gaussian_bunch_spectrum(frequency, sigma):
- """
- Compute a Gaussian bunch spectrum [1].
-
- Parameters
- ----------
- frequency : array
- sample points of the beam spectrum in [Hz].
- sigma : float
- RMS bunch length in [s].
-
- Returns
- -------
- bunch_spectrum : array
- Bunch spectrum sampled at points given in frequency.
-
- References
- ----------
- [1] : Gamelin, A. (2018). Collective effects in a transient microbunching
- regime and ion cloud mitigation in ThomX. p86, Eq. 4.19
- """
- return np.exp(-1/2*(2*np.pi*frequency)**2*sigma**2)
-
-
-def beam_spectrum(frequency, M, bunch_spacing, sigma=None,
- bunch_spectrum=None):
- """
- Compute the beam spectrum assuming constant spacing between bunches [1].
-
- Parameters
- ----------
- frequency : list or numpy array
- sample points of the beam spectrum in [Hz].
- M : int
- Number of bunches.
- bunch_spacing : float
- Time between two bunches in [s].
- sigma : float, optional
- If bunch_spectrum is None then a Gaussian bunch with sigma RMS bunch
- length in [s] is assumed.
- bunch_spectrum : array, optional
- Bunch spectrum sampled at points given in frequency.
-
- Returns
- -------
- beam_spectrum : array
-
- References
- ----------
- [1] Rumolo, G - Beam Instabilities - CAS - CERN Accelerator School:
- Advanced Accelerator Physics Course - 2014, Eq. 9
- """
-
- if bunch_spectrum is None:
- bunch_spectrum = gaussian_bunch_spectrum(frequency, sigma)
-
- beam_spectrum = (bunch_spectrum * np.exp(1j*np.pi*frequency *
- bunch_spacing*(M-1)) *
- np.sin(M*np.pi*frequency*bunch_spacing) /
- np.sin(np.pi*frequency*bunch_spacing))
-
- return beam_spectrum
-
-
-def effective_impedance(ring, imp, m, mu, sigma, M, tuneS, xi=None,
- mode="Hermite"):
- """
- Compute the effective (longitudinal or transverse) impedance.
- Formulas from Eq. (1) and (2) p238 of [1].
-
- Parameters
- ----------
- ring : Synchrotron object
- imp : Impedance object
- mu : int
- coupled bunch mode number, goes from 0 to (M-1) where M is the
- number of bunches
- m : int
- head-tail (or azimutal/synchrotron) mode number
- sigma : float
- RMS bunch length in [s]
- M : int
- Number of bunches.
- tuneS : float
- Synchrotron tune.
- xi : float, optional
- (non-normalized) chromaticity
- mode: str, optional
- type of the mode taken into account for the computation:
- -"Hermite" modes for Gaussian bunches
-
- Returns
- -------
- Zeff : float
- effective impedance in [ohm] or in [ohm/m] depanding on the impedance
- type.
-
- References
- ----------
- [1] : Handbook of accelerator physics and engineering, 3rd printing.
- """
-
- if not isinstance(imp, Impedance):
- raise TypeError("{} should be an Impedance object.".format(imp))
-
- fmin = imp.data.index.min()
- fmax = imp.data.index.max()
- if fmin > 0:
- double_sided_impedance(imp)
-
- if mode == "Hermite":
- def h(f):
- return spectral_density(frequency=f, sigma=sigma, m=m,
- mode="Hermite")
- else:
- raise NotImplementedError("Not implemanted yet.")
-
- pmax = fmax/(ring.f0 * M) - 1
- pmin = fmin/(ring.f0 * M) + 1
-
- p = np.arange(pmin,pmax+1)
-
- if imp.impedance_type == "long":
- fp = ring.f0*(p*M + mu + m*tuneS)
- fp = fp[np.nonzero(fp)] # Avoid division by 0
- num = np.sum( imp(fp) * h(fp) / (fp*2*np.pi) )
- den = np.sum( h(fp) )
- Zeff = num/den
-
- elif imp.impedance_type == "xdip" or imp.impedance_type == "ydip":
- if imp.impedance_type == "xdip":
- tuneXY = ring.tune[0]
- if xi is None :
- xi = ring.chro[0]
- elif imp.impedance_type == "ydip":
- tuneXY = ring.tune[1]
- if xi is None:
- xi = ring.chro[1]
- fp = ring.f0*(p*M + mu + tuneXY + m*tuneS)
- f_xi = xi/ring.eta*ring.f0
- num = np.sum( imp(fp) * h(fp - f_xi) )
- den = np.sum( h(fp - f_xi) )
- Zeff = num/den
- else:
- raise TypeError("Effective impedance is only defined for long, xdip"
- " and ydip impedance type.")
-
- return Zeff
-
-
-def yokoya_elliptic(x_radius , y_radius):
- """
- Compute Yokoya factors for an elliptic beam pipe.
- Function adapted from N. Mounet IW2D.
-
- Parameters
- ----------
- x_radius : float
- Horizontal semi-axis of the ellipse in [m].
- y_radius : float
- Vertical semi-axis of the ellipse in [m].
-
- Returns
- -------
- yoklong : float
- Yokoya factor for the longitudinal impedance.
- yokxdip : float
- Yokoya factor for the dipolar horizontal impedance.
- yokydip : float
- Yokoya factor for the dipolar vertical impedance.
- yokxquad : float
- Yokoya factor for the quadrupolar horizontal impedance.
- yokyquad : float
- Yokoya factor for the quadrupolar vertical impedance.
- """
- if y_radius < x_radius:
- small_semiaxis = y_radius
- large_semiaxis = x_radius
- else:
- small_semiaxis = x_radius
- large_semiaxis = y_radius
-
- # read Yokoya factors interpolation file
- # BEWARE: columns are ratio, dipy, dipx, quady, quadx
- yokoya_file = pd.read_csv("collective_effects/data/" +
- "Yokoya_elliptic_from_Elias_USPAS.csv")
- ratio_col = yokoya_file["x"]
- # compute semi-axes ratio (first column of this file)
- ratio = (large_semiaxis - small_semiaxis)/(large_semiaxis + small_semiaxis)
-
- # interpolate Yokoya file at the correct ratio
- yoklong = 1
-
- if y_radius < x_radius:
- yokydip = np.interp(ratio, ratio_col, yokoya_file["dipy"])
- yokxdip = np.interp(ratio, ratio_col, yokoya_file["dipx"])
- yokyquad = np.interp(ratio, ratio_col, yokoya_file["quady"])
- yokxquad = np.interp(ratio, ratio_col, yokoya_file["quadx"])
- else:
- yokxdip = np.interp(ratio, ratio_col, yokoya_file["dipy"])
- yokydip = np.interp(ratio, ratio_col, yokoya_file["dipx"])
- yokxquad = np.interp(ratio, ratio_col, yokoya_file["quady"])
- yokyquad = np.interp(ratio, ratio_col, yokoya_file["quadx"])
-
- return (yoklong, yokxdip, yokydip, yokxquad, yokyquad)
-
-def beam_loss_factor(impedance, frequency, spectrum, ring):
- """
- Compute "beam" loss factor using the beam spectrum, uses a sum instead of
- integral compared to loss_factor [1].
-
- Parameters
- ----------
- impedance : Impedance of type "long"
- frequency : array
- Sample points of spectrum.
- spectrum : array
- Beam spectrum to consider.
- ring : Synchrotron object
-
- Returns
- -------
- kloss_beam : float
- Beam loss factor in [V/C].
-
- References
- ----------
- [1] : Handbook of accelerator physics and engineering, 3rd printing.
- Eq (3) p239.
- """
- pmax = np.floor(impedance.data.index.max()/ring.f0)
- pmin = np.floor(impedance.data.index.min()/ring.f0)
-
- if pmin >= 0:
- double_sided_impedance(impedance)
- pmin = -1*pmax
-
- p = np.arange(pmin+1,pmax)
- pf0 = p*ring.f0
- ReZ = np.real(impedance(pf0))
- spectral_density = np.abs(spectrum)**2
- # interpolation of the spectrum is needed to avoid problems liked to
- # division by 0
- # computing the spectrum directly to the frequency points gives
- # wrong results
- spect = interp1d(frequency, spectral_density)
- kloss_beam = ring.f0 * np.sum(ReZ*spect(pf0))
-
- return kloss_beam
-
-def double_sided_impedance(impedance):
- """
- Add negative frequency points to single sided impedance spectrum following
- symetries depending on impedance type.
-
- Parameters
- ----------
- impedance : Impedance object
- Single sided impedance.
- """
- fmin = impedance.data.index.min()
-
- if fmin >= 0:
- negative_index = impedance.data.index*-1
- negative_data = impedance.data.set_index(negative_index)
-
- imp_type = impedance.impedance_type
-
- if imp_type == "long":
- negative_data["imag"] = -1*negative_data["imag"]
-
- elif (imp_type == "xdip") or (imp_type == "ydip"):
- negative_data["real"] = -1*negative_data["real"]
-
- elif (imp_type == "xquad") or (imp_type == "yquad"):
- negative_data["real"] = -1*negative_data["real"]
-
- else:
- raise ValueError("Wrong impedance type")
-
- try:
- negative_data = negative_data.drop(0)
- except KeyError:
- pass
-
- all_data = impedance.data.append(negative_data)
- all_data = all_data.sort_index()
- impedance.data = all_data
-
-
-
-
-
-
-
-
-
-
-
-
-