From 42cd27aa91bcd778ef7dcead7dbb55149b881c5a Mon Sep 17 00:00:00 2001
From: Gamelin Alexis <gamelin@synchrotron-soleil.fr>
Date: Fri, 3 Apr 2020 12:19:22 +0200
Subject: [PATCH] Add taper Wakefield elements
Circular and rectangular tapers
Correct module name in tools.py
Add kick factor calculation for quadrupolar wakes (similar to dipolar ones)
---
collective_effects/tapers.py | 212 +++++++++++++++++++++++++++++++++++
collective_effects/tools.py | 6 +-
2 files changed, 217 insertions(+), 1 deletion(-)
create mode 100644 collective_effects/tapers.py
diff --git a/collective_effects/tapers.py b/collective_effects/tapers.py
new file mode 100644
index 0000000..0e09b36
--- /dev/null
+++ b/collective_effects/tapers.py
@@ -0,0 +1,212 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Tue Mar 31 13:15:36 2020
+
+@author: gamelina
+"""
+
+from scipy.constants import mu_0, epsilon_0, c, pi
+import numpy as np
+from scipy.integrate import trapz
+from collective_effects.wakefield import Wakefield, Impedance
+
+class StupakovRectangularTaper(Wakefield):
+ """
+ Rectangular vertical taper Wakefield element, using the low frequency
+ approxmiation. Assume constant taper angle. Formulas from [1].
+
+ ! Valid for low w
+
+ Parameters
+ ----------
+ frequency: frequency points where the impedance will be evaluated in [Hz]
+ gap_entrance : full vertical gap at taper entrance in [m]
+ gap_exit: full vertical gap at taper exit in [m]
+ length: taper length in [m]
+ width : full horizontal width of the taper in [m]
+ """
+
+ def __init__(self, frequency, gap_entrance, gap_exit, length, width,
+ m_max=100, n_points=int(1e4)):
+ super().__init__()
+
+ self.frequency = frequency
+ self.gap_entrance = gap_entrance
+ self.gap_exit = gap_exit
+ self.length = length
+ self.width = width
+ self.m_max = m_max
+ self.n_points = n_points
+
+ Zlong = Impedance(variable = frequency, function = self.long(), impedance_type='long')
+ Zxdip = Impedance(variable = frequency, function = self.xdip(), impedance_type='xdip')
+ Zydip = Impedance(variable = frequency, function = self.ydip(), impedance_type='ydip')
+ Zxquad = Impedance(variable = frequency, function = -1*self.quad(), impedance_type='xquad')
+ Zyquad = Impedance(variable = frequency, function = self.quad(), impedance_type='yquad')
+
+ super().append_to_model(Zlong)
+ super().append_to_model(Zxdip)
+ super().append_to_model(Zydip)
+ super().append_to_model(Zxquad)
+ super().append_to_model(Zyquad)
+
+ @property
+ def gap_prime(self):
+ return (self.gap_entrance-self.gap_exit)/self.length
+
+ @property
+ def angle(self):
+ return np.arctan((self.gap_entrance/2 - self.gap_exit/2)/self.length)
+
+ @property
+ def Z0(self):
+ return mu_0*c
+
+ def long(self, frequency=None):
+
+ if frequency is None:
+ frequency = self.frequency
+
+ def F(x, m_max):
+ m = np.arange(0, m_max)
+ phi = np.outer(pi*x/2, 2*m+1)
+ val = 1/(2*m+1)/(np.cosh(phi)**2)*np.tanh(phi)
+ return val.sum(1)
+
+ z = np.linspace(0, self.length, self.n_points)
+ g = np.linspace(self.gap_entrance, self.gap_exit, self.n_points)
+
+ to_integrate = self.gap_prime**2*F(g/self.width, self.m_max)
+ integral = trapz(to_integrate,x=z)
+
+ return -1j*frequency*self.Z0/(2*c)*integral
+
+ def Z_over_n(self, f0):
+ return np.imag(self.long(1))*f0
+
+ def ydip(self):
+
+ def G1(x, m_max):
+ m = np.arange(0, m_max)
+ phi = np.outer(pi*x/2, 2*m+1)
+ val = (2*m+1)/(np.sinh(phi)**2)/np.tanh(phi)
+ val = x[:,None]**3*val
+ return val.sum(1)
+
+ z = np.linspace(0, self.length, self.n_points)
+ g = np.linspace(self.gap_entrance, self.gap_exit, self.n_points)
+
+ to_integrate = self.gap_prime**2/(g**3)*G1(g/self.width, self.m_max)
+ integral = trapz(to_integrate, x=z)
+
+ return -1j*pi*self.width*self.Z0/4*integral
+
+ def xdip(self):
+
+ def G3(x, m_max):
+ m = np.arange(0,m_max)
+ phi = np.outer(pi*x, m)
+ val = 2*m/(np.cosh(phi)**2)*np.tanh(phi)
+ val = x[:,None]**2*val
+ return val.sum(1)
+
+ z = np.linspace(0, self.length, self.n_points)
+ g = np.linspace(self.gap_entrance, self.gap_exit, self.n_points)
+
+ to_integrate = self.gap_prime**2/(g**2)*G3(g/self.width, self.m_max)
+ integral = trapz(to_integrate, x=z)
+
+ return -1j*pi*self.Z0/4*integral
+
+
+ def quad(self):
+
+ def G2(x, m_max):
+ m = np.arange(0, m_max)
+ phi = np.outer(pi*x/2, 2*m+1)
+ val = (2*m+1)/(np.cosh(phi)**2)*np.tanh(phi)
+ val = x[:,None]**2*val
+ return val.sum(1)
+
+ z = np.linspace(0, self.length, self.n_points)
+ g = np.linspace(self.gap_entrance, self.gap_exit, self.n_points)
+
+ to_integrate = self.gap_prime**2/(g**2)*G2(g/self.width, self.m_max)
+ integral = trapz(to_integrate, x=z)
+
+ return -1j*pi*self.Z0/4*integral
+
+class StupakovCircularTaper(Wakefield):
+ """
+ Circular taper Wakefield element, using the low frequency
+ approxmiation. Assume constant taper angle. Formulas from [1].
+
+ ! Valid for low w
+
+ Parameters
+ ----------
+ frequency: frequency points where the impedance will be evaluated in [Hz]
+ radius_entrance : radius at taper entrance in [m]
+ radius_exit : radius at taper exit in [m]
+ length : taper length in [m]
+ """
+
+ def __init__(self, frequency, radius_entrance, radius_exit, length,
+ m_max=100, n_points=int(1e4)):
+ super().__init__()
+
+ self.frequency = frequency
+ self.radius_entrance = radius_entrance
+ self.radius_exit = radius_exit
+ self.length = length
+ self.m_max = m_max
+ self.n_points = n_points
+
+ Zlong = Impedance(variable = frequency, function = self.long(), impedance_type='long')
+ Zxdip = Impedance(variable = frequency, function = self.dip(), impedance_type='xdip')
+ Zydip = Impedance(variable = frequency, function = self.dip(), impedance_type='ydip')
+
+ super().append_to_model(Zlong)
+ super().append_to_model(Zxdip)
+ super().append_to_model(Zydip)
+
+ @property
+ def angle(self):
+ return np.arctan((self.radius_entrance-self.radius_exit)/self.length)
+
+ @property
+ def radius_prime(self):
+ return (self.radius_entrance-self.radius_exit)/self.length
+
+ @property
+ def Z0(self):
+ return mu_0*c
+
+ def long(self, frequency=None):
+
+ if frequency is None:
+ frequency = self.frequency
+
+ return (self.Z0/(2*pi)*np.log(self.radius_entrance/self.radius_exit)
+ - 1j*self.Z0*frequency/(2*c)*self.radius_prime**2*self.length)
+
+ def Z_over_n(self, f0):
+ return np.imag(self.long(1))*f0
+
+ def dip(self, frequency=None):
+
+ if frequency is None:
+ frequency = self.frequency
+
+ z = np.linspace(0, self.length, self.n_points)
+ r = np.linspace(self.radius_entrance, self.radius_exit, self.n_points)
+
+ to_integrate = self.radius_prime**2/(r**2)
+ integral = trapz(to_integrate, x=z)
+
+ return (self.Z0*c/(4*pi**2*frequency)*(1/(self.radius_exit**2) -
+ 1/(self.radius_entrance**2)) - 1j*self.Z0/(2*pi)*integral)
+
+
+
+
diff --git a/collective_effects/tools.py b/collective_effects/tools.py
index 3f3f633..7209a4b 100644
--- a/collective_effects/tools.py
+++ b/collective_effects/tools.py
@@ -9,7 +9,7 @@ Tools and utilities functions for the Wakefield and impedances classes.
import pandas as pd
import numpy as np
from scipy.integrate import trapz
-from CollectiveEffect.wakefield import Wakefield, Impedance, WakeFunction
+from collective_effects.wakefield import Wakefield, Impedance, WakeFunction
#from ..Tracking.synchrotron import Synchrotron
def read_CST(file, impedance_type='long'):
@@ -64,6 +64,10 @@ def loss_factor(wake, sigma):
if(wake.impedance_type == "xdip" or wake.impedance_type == "ydip"):
kloss = trapz(x = omega,
y = 1/np.pi*wake.data["imag"][positive_index]*gaussian_spectrum)
+ if(wake.impedance_type == "xquad" or wake.impedance_type == "yquad"):
+ kloss = trapz(x = omega,
+ y = 1/np.pi*wake.data["imag"][positive_index]*gaussian_spectrum)
+
if isinstance(wake, WakeFunction):
# To be implemented.
pass
--
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