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rfbucket.py 7.09 KiB
# -*- coding: utf-8 -*-
"""
Created on Wed Mar 16 17:54:36 2022
@author: foosang
"""
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import fsolve
class RFBucket:
"""
Calculate the RF bucket for a given synchronous phase. Valid for both
sine and cosine RF convention, but limited to the following intervals:
sine convention : [0,180°],
cosine convention : [-90°,90°].
Parameters
----------
phi_s : float
Synchronous phase in [rad].
convention : {"cos", "sin"}, optional
RF convention corresponding to input phi_s. Use "cos" or "sin" for a
cosine or sine convention, respectively. The default is "cos".
Attributes
----------
phi_s : float
Synchronous phase in [rad].
convention : str
RF convention.
above_transition : bool
Depending on phi_s and convention, above_transition is True when the
system is above the transition energy and is False if the system is
below the transition energy.
"""
def __init__(self, phi_s, convention="cos"):
if convention == "sin":
if phi_s<0 or phi_s>np.pi:
raise ValueError("The synchronous phase is outside the valid range.")
else:
if phi_s>=0 and phi_s<=np.pi/2:
self.above_transition = False
else:
self.above_transition = True
elif convention == "cos":
if phi_s<-np.pi/2 or phi_s>np.pi/2:
raise ValueError("The synchronous phase is outside the valid range.")
else:
if phi_s>=-np.pi/2 and phi_s<=0:
self.above_transition = False
else:
self.above_transition = True
else:
raise ValueError("Invalid RF convention.")
self.phi_s = phi_s
self.convention = convention
if self.convention == "cos":
if self.above_transition is True:
self._phi_s = np.pi - (np.pi/2 - phi_s)
else:
self._phi_s = np.pi/2 - phi_s
elif self.convention == "sin":
if self.above_transition is True:
self._phi_s = np.pi - phi_s
else:
self._phi_s = phi_s
def separatrix(self, phi):
"""
Calculate the separatrix in longitudinal phase space.
Parameters
----------
phi : array of float
Phase interval on which the separatrix will be calculated in [rad]
Returns
-------
y1 : array
The positive half of the separatrix in the unit of (dphi/dt)/Omega_s,
where dphi/dt is phase velocity and Omega_s is synchrotron
oscillation frequency.
y2 : array
The negative half of the separatrix in the same unit as y1.
"""
y1 = np.sqrt(2/np.cos(self._phi_s)*(np.cos(phi)+phi*np.sin(self._phi_s)-
np.cos(np.pi-self._phi_s)-(np.pi-self._phi_s)*np.sin(self._phi_s)))
y2 = -1*y1
return y1, y2
def separatrix_root(self, x):
"""
Function used for determining the root of the separatrix equation.
"""
value = np.cos(x) + x*np.sin(self._phi_s) - \
np.cos(np.pi-self._phi_s) - (np.pi-self._phi_s)*np.sin(self._phi_s)
return value
def plot_separatrix(self, phi, unit="deg"):
"""
Plot separatrix
Parameters
----------
phi : array of float
Phase interval on which the separatrix will be calculated in [rad]
unit : {"deg", "rad"}, optional
Unit of horizontal axis. Use "deg" for degree or "rad" for radian.
The default is "deg".
Returns
-------
fig : Figure
Figure object with the separatrix plotted on it.
"""
y1, y2 = self.separatrix(phi)
if self.convention == "cos":
if self.above_transition is True:
phi = phi - np.pi/2
else:
phi = -1*(phi - np.pi/2)
elif self.convention == "sin":
if self.above_transition is True:
phi = np.pi - phi
fig, ax = plt.subplots()
if unit == "deg":
phi = phi/np.pi * 180
xlabel = "$\\phi$ (deg)"
elif unit == "rad":
xlabel = "$\\phi$ (rad)"
ax.plot(phi, y1, color="tab:blue")
ax.plot(phi, y2, color="tab:blue")
ax.set_xlabel(xlabel)
ax.set_ylabel('$\\dot{\\phi} / \\Omega_s$')
return fig
def bucket_height(self, ring, Vrf, E0, plane):
"""
Calculate the height of the RF bucket which corresponds to the maximum
energy deviation.
Parameters
----------
ring : Synchrotron object
Vrf : float
RF voltage in [V].
E0 : float
Beam energy in [eV].
plane : {"x", "y"}
The considered plane of motion of the beam. Use "x" for the
horizontal plane or "y" for the vertical plane.
Returns
-------
delta_max : float
Maximum energy deviation.
"""
G = np.sqrt(0.5* abs(2*np.cos(self._phi_s)-(np.pi-2*self._phi_s)*
np.sin(self._phi_s)))
plane_dict = {'x':0, 'y':1}
index = plane_dict[plane]
beta = ring.optics.local_beta[index]
h = ring.h
eta = ring.eta
delta_max = G * np.sqrt(2*beta**2*E0*Vrf/(np.pi*h*abs(eta))) / E0
return delta_max
def extreme_phases(self):
"""
Calculate the two extreme phases on the separatrix.
Returns
-------
phi_min : float
The minimum phase in [rad].
phi_max : float
The maximum phase in [rad].
"""
if self._phi_s > np.pi/2 and self._phi_s <= np.pi:
x0 = 270 / 180 * np.pi # Iinitial estimate of the root
phi_min0 = np.pi - self._phi_s
phi_max0 = fsolve(self.separatrix_root, x0=x0)[0]
elif self._phi_s >= 0 and self._phi_s <= np.pi/2:
x0 = -90 / 180 * np.pi # Initial estimate of the root
phi_max0 = np.pi - self._phi_s
phi_min0 = fsolve(self.separatrix_root, x0=x0)[0]
if self.convention == "cos":
if self.above_transition is True:
phi_min = phi_min0 - np.pi/2
phi_max = phi_max0 - np.pi/2
else:
phi_min = -1*(phi_max0 - np.pi/2)
phi_max = -1*(phi_min0 - np.pi/2)
elif self.convention == "sin":
if self.above_transition is True:
phi_min = np.pi - phi_max0
phi_max = np.pi - phi_min0
else:
phi_min = phi_min0
phi_max = phi_max0
return phi_min, phi_max