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transfer_functions.py
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transfer_functions.py
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# -*- coding: utf-8 -*-
"""
Created on Sun May 5 12:15:26 2019
@author: rvroerm
"""
import os
import math as math
import numpy as np
from math import sin, cos, tan, sinh, cosh, tanh, exp, log, log10, sqrt, pi
from numpy import sign
from scipy.optimize import curve_fit
import warnings
#import matplotlib.pyplot as plt
def transport_count_lines(transport_file, N_segments = 10, print_elements=False):
"""
counts the number of relevant lines in file
N_segments is the number of points displayed by element
print_elements = boolean to print lines read in file
"""
it_z = 0
filepath = transport_file
with open(filepath) as fp:
line = fp.readline()
cnt = 1
while line:
data = line.split()
if data: # string is not empty
if data[0][0:2] == "4." or data[0][0:2] == "5." or data[0][0:3] == "50." or data[0][0:3] == "18.":
it_z = it_z + N_segments
if print_elements: print(data)
elif data[0][0:2] == "3." or data[0][0:2] == "2.":
it_z = it_z + 1
if print_elements: print(data)
elif data[0][0:5] == '(slit':
it_z = it_z + N_segments - 1
if print_elements: print(data)
line = fp.readline()
cnt += 1
if print_elements: print('----')
return it_z+1
def split_transport_file(transport_file):
"""
split file between different beamline sections
saves the output files in the current folder
"""
initial_beam_found = False
gantry_found = False
ISO_found = False
with open(transport_file) as infile, open('transport_file_ESS.txt', 'w') as outfile:
copy = False
for line in infile:
if line.strip().replace(" ","") == "/*Initialbeam*/":
initial_beam_found = True
copy = True
elif line.strip().replace(" ","") == "/*Gantry*/":
gantry_found = True
copy = False
elif copy:
outfile.write(line)
outfile.close()
with open(transport_file) as infile, open('transport_file_GTR.txt', 'w') as outfile:
copy = False
for line in infile:
if line.strip().replace(" ","") == "/*Gantry*/":
copy = True
elif line.strip().replace(" ","") == "/*ISO*/":
ISO_found = True
copy = False
elif copy:
outfile.write(line)
if not initial_beam_found:
warnings.warn(" /*Initialbeam*/ label not defined in Transport file, plots might not correspond to the desired location")
if not gantry_found:
warnings.warn(" /*Gantry*/ label not defined in Transport file, plots might not correspond to the desired location")
if not ISO_found:
warnings.warn(" /*ISO*/ label not defined in Transport file, plots might not correspond to the desired location")
outfile.close()
def Brho_scale_transport(transport_file,newE,new_file_path="D:/temp/",rest_mass=938):
"""
B rho scaling from a transport file
code will fail if no line "1.xxxx" is found before other elements (which should never happen)
"""
filename = os.path.basename(transport_file)
filename_noext = os.path.splitext(filename)[0] + "_" + str(newE) + "MeV" + ".txt"
with open(transport_file) as infile, open(new_file_path + filename_noext, 'w') as outfile:
line = infile.readline()
cnt = 1
while line:
#print("Line {}: {}".format(cnt, line.strip()))
data = line.split()
if data: # string is not empty
if data[0][0:2] == "1.":
oldE = PtoE(float(data[7].replace(";","") ))
scaling_ratio = Brho_scaling(oldE,newE,rest_mass)
data[7] = EtoP(newE)
outfile.write("".join(str(data)).replace(","," ").replace('[',"").replace(']',"").replace("'","") + '\n')
elif data[0][0:2] == "4.":
data[2] = float(data[2].replace(";","") )*scaling_ratio
outfile.write("".join(str(data)).replace(","," ").replace('[',"").replace(']',"").replace("'","") + '\n')
elif data[0][0:2] == "5.":
data[2] = float(data[2].replace(";","") )*scaling_ratio
outfile.write("".join(str(data)).replace(","," ").replace('[',"").replace(']',"").replace("'","") + '\n')
elif data[0][0:2] == "18.":
data[2] = float(data[2].replace(";","") )*scaling_ratio
outfile.write("".join(str(data)).replace(","," ").replace('[',"").replace(']',"").replace("'","") + '\n')
else:
outfile.write(line)
else:
outfile.write(line)
line = infile.readline()
cnt += 1
def transport_input(transport_file,beam,refE,it_p,N_segments,gap,k1,k2,z,it_z,scaling_ratio = 1,kill_lost_particles=True,gap_X=1,paraxial_correction = False,dpz_tolerance=10**-6):
"""
opens a transport file and computes beam through magnets for one particle
scaling_ratio can be used to make a Brho scaling of the transport file
"""
# default settings
B = 0
filepath = transport_file
with open(filepath) as fp:
line = fp.readline()
prev_line = fp.readline()
cnt = 1
while line:
#print("Line {}: {}".format(cnt, line.strip()))
data = line.split()
data_prev = prev_line.split()
if data: # string is not empty
if data[0][0:2] == "2.":
if data_prev :
if data_prev[0] == "4.":
# exit pole face (entrance managed within 4.0)
angle = float(data[1].replace(";","") )
[beam[:,:,it_p],it_z] = pole_face(angle,B,gap,k1,k2,beam[:,:,it_p],refE,it_z, paraxial_correction = paraxial_correction)
if data[0][0:2] == "3.":
# drift
L = float(data[1].replace(";","") )
z = z + L
[beam[:,:,it_p],it_z] = drift(L,beam[:,:,it_p],refE,it_z,1)
if data[0][0:2] == "4.":
# sector bending
L = float(data[1].replace(";","") )
B = float(data[2].replace(";","") )*scaling_ratio
n = float(data[3].replace(";","") )
if data_prev :
if data_prev[0] == "2.": # entrance pole face
angle = float(data_prev[1].replace(";","") )
[beam[:,:,it_p],it_z] = pole_face(angle,B,gap,k1,k2,beam[:,:,it_p],refE,it_z, paraxial_correction = paraxial_correction)
[beam[:,:,it_p],it_z] = sec_bend(L,B,n,gap,beam[:,:,it_p],refE,it_z,N_segments=N_segments, \
kill_lost_particles=kill_lost_particles,gap_X=gap_X,paraxial_correction = paraxial_correction, dpz_tolerance=dpz_tolerance)
if data[0][0:2] == "5.":
# quad
L = float(data[1].replace(";","") )
B = float(data[2].replace(";","") )*scaling_ratio
a = float(data[3].replace(";","") )/1000 # aperture converted to meters
#[beam[:,:,it_p],it_z] = quad(L,B,a,beam[:,:,it_p],it_z,refE,N_segments,kill_lost_particles)
[beam[:,:,it_p],it_z] = quad(L,B,a,beam[:,:,it_p],it_z,refE,N_segments=N_segments, \
kill_lost_particles=kill_lost_particles,paraxial_correction=paraxial_correction,dpz_tolerance=dpz_tolerance)
if data[0][0:3] == "18.":
# sextupole
L = float(data[1].replace(";","") )
B = float(data[2].replace(";","") )*scaling_ratio
a = float(data[3].replace(";","") )/1000 # aperture converted to meters
angle = float(data[4].replace(";","") ) # not used in original transport
[beam[:,:,it_p],it_z] = sextupole(L,B,a,angle,beam[:,:,it_p],it_z,refE,N_segments,kill_lost_particles)
if data[0][0:3] == '50.':
# linear wedge
L = float(data[1].replace(";","") )
width = float(data[2].replace(";","") )
mat = data[3].replace(";","")
[beam[:,:,it_p],it_z] = wedge_X(L,width,mat,beam[:,:,it_p],it_z,refE,N_segments)
if data[0][0:5] == '(slit':
# slit
L = float(data[1].replace(";","") )
leftX = float(data[2].replace(";","") )
rightX = float(data[3].replace(";","") )
mat = data[4].replace(";","")
[beam[:,:,it_p],it_z] = slitX(L,leftX,rightX,mat,beam[:,:,it_p],it_z,refE,N_segments)
line = fp.readline() # skip next drift
cnt +=1
prev_line = line
line = fp.readline()
cnt += 1
return [beam, it_z]
def drift(L,beam,refE,it_z,N_segments=1):
L_segment = L/N_segments
ref_p = EtoP(refE)
p = ref_p + beam[it_z,6]*ref_p
gamma = PtoGamma(p,938)
drift_mat = np.array([[1,L_segment,0,0,0,0],[0,1,0,0,0,0],[0,0,1,L_segment,0,0],[0,0,0,1,0,0],[0,0,0,0,1,L_segment/gamma**2],[0,0,0,0,0,1]])
for i in range(0,N_segments):
it_z = it_z + 1
beam[it_z,0] = beam[it_z-1,0] + L_segment
beam[it_z,1:7] = np.matmul(drift_mat,np.transpose(beam[it_z-1,1:7]))
L_eff = abs(L_segment/cos(sqrt(beam[it_z,2]**2+beam[it_z,4]**2))) # effective length travelled by particle (negliect change in direction)
beam[it_z,5] = (L_segment - L_eff) + beam[it_z,5] #higher order correction related to beam angle
return [beam, it_z]
def drift_core(L,beam,refE):
ref_p = EtoP(refE)
p = ref_p + beam[5]*ref_p
gamma = PtoGamma(p,938)
drift_mat = np.array([[1,L,0,0,0,0],[0,1,0,0,0,0],[0,0,1,L,0,0],[0,0,0,1,0,0],[0,0,0,0,1,L/gamma**2],[0,0,0,0,0,1]])
beam = np.matmul(drift_mat,np.transpose(beam))
return beam
def drift_matrix(L,p,rest_mass=938):
gamma = PtoGamma(p,938)
drift_mat = np.array([[1,L,0,0,0,0],[0,1,0,0,0,0],[0,0,1,L,0,0],[0,0,0,1,0,0],[0,0,0,0,1,L/gamma**2],[0,0,0,0,0,1]])
return drift_mat
def RF_cavity(delta_E,cav_length,freq,phi,beam,refE,it_z,N_segments = 10):
# simplified version, neglects defocusing effects
omega = 2*math.pi*freq
ref_p = EtoP(refE)
for i in range(0,N_segments):
p = ref_p + beam[it_z,6]*ref_p
speed_ref = PtoV(ref_p,938)
E_i = PtoE(p)
z_eff = beam[it_z,0] + beam[it_z,5]
t = z_eff/speed_ref # divide by speed_ref because speed difference is included in z_eff
E_f = E_i + delta_E/N_segments*cos(omega*t+phi)
p_f = EtoP(E_f)
[beam,it_z] = drift(cav_length/N_segments,beam,refE,it_z,1)
beam[it_z,6] = (p_f - ref_p)/ref_p
return [beam, it_z]
def RF_cavity_old(delta_E,freq,phi,beam,refE,it_z):
# simplified version, neglects defocusing effects
ref_p = EtoP(refE)
p = ref_p + beam[it_z,6]*ref_p
speed_ref = PtoV(ref_p,938)
E_i = PtoE(p)
z_eff = beam[it_z,0] + beam[it_z,5]
t = z_eff/speed_ref
omega = 2*math.pi*freq
E_f = E_i + delta_E*cos(omega*t+phi)
p_f = EtoP(E_f)
#print('E_i = ',E_i,', E_f = ',E_f,', t = ',t)
#print(beam[it_z,:])
it_z += 1
beam[it_z,0:5] = beam[it_z-1,0:5]
beam[it_z,6] = (p_f - ref_p)/ref_p
return [beam, it_z]
def quad_matrix(L,B,a,p,rest_mass=938):
"""
returns the transfer matrix for a particle of momentum p
L =length, B=field, a=aperture
"""
if B==0:
return drift_matrix(L, p, rest_mass=rest_mass)
gamma = PtoGamma(p,rest_mass)
Brho = PtoBrho(p)
#Brho = 1/300*sqrt(refE**2+2*938*refE)
k_q = sqrt(abs(B)/a*(1/Brho))
if B>0:
# X focusing
quad_mat = np.array([[cos(k_q*L),1/k_q*sin(k_q*L),0,0,0,0],
[-k_q*sin(k_q*L),cos(k_q*L),0,0,0,0],
[0,0,cosh(k_q*L),1/k_q*sinh(k_q*L),0,0],
[0,0,k_q*sinh(k_q*L),cosh(k_q*L),0,0],
[0,0,0,0,1,L/gamma**2],
[0,0,0,0,0,1]])
else:
# Y focusing
quad_mat = np.array([[cosh(k_q*L),1/k_q*sinh(k_q*L),0,0,0,0],
[k_q*sinh(k_q*L),cosh(k_q*L),0,0,0,0],
[0,0,cos(k_q*L),1/k_q*sin(k_q*L),0,0],
[0,0,-k_q*sin(k_q*L),cos(k_q*L),0,0],
[0,0,0,0,1,L/gamma**2],
[0,0,0,0,0,1]])
return quad_mat
def sextupole(L,B,a,alpha,beam,it_z,refE,N_segments = 10):
"""
sextupole: L =length, B=field, a=aperture, alpha = angle
"""
alpha = math.radians(alpha)
L_segment = L/N_segments
ref_p = EtoP(refE)
p = ref_p + beam[it_z,6]*ref_p
E = PtoE(p)
Brho = 1/300*sqrt(E**2+2*938*E)
#Brho = 1/300*sqrt(refE**2+2*938*refE)
k_s = sqrt(abs(B)/a**2*(1/Brho))
R11 = 1
R12 = L_segment
T111 = -1/2 * k_s**2 * L_segment**2
T112 = -1/3 * k_s**2 * L_segment**3
T122 = -1/12 * k_s**2 * L_segment**4
T133 = - T111
T134 = - T112
T144 = - T122
R22 = 1
T211 = - k_s**2 * L_segment
T212 = - k_s**2 * L_segment**2
T222 = -1/3 * k_s**2 * L_segment**3
T233 = - T211
T234 = - T212
T244 = - T222
R33 = 1
R34 = L_segment
T313 = k_s**2 * L_segment**2
T314 = 1/3 * k_s**2 * L_segment**3
T323 = 1/3 * k_s**2 * L_segment**3
T324 = 1/6 * k_s**2 * L_segment**4
R44 = 1
T413 = 2 * k_s**2 * L_segment
T414 = k_s**2 * L_segment**2
T423 = T414
T424 = 2/3 * k_s**2 * L_segment**3
beam_rot_out = np.empty((6,1))
for i in range(0,N_segments):
it_z = it_z + 1
beam[it_z,0] = beam[it_z-1,0] + L_segment
beam_rot_in = rot_beam(beam[it_z-1,1:7],alpha)
beam_rot_out[0] = R11*beam_rot_in[0] + R12*beam_rot_in[1] + T111*beam_rot_in[0]**2 + T112*beam_rot_in[0]*beam_rot_in[1] + T122*beam_rot_in[1]**2 + T133*beam_rot_in[2]**2 + T134*beam_rot_in[2]*beam_rot_in[3] + T144*beam_rot_in[3]**2
beam_rot_out[1] = R22*beam_rot_in[1] + T211*beam_rot_in[0]**2 + T212*beam_rot_in[0]*beam_rot_in[1] + T222*beam_rot_in[1]**2 + T233*beam_rot_in[2]**2 + T234*beam_rot_in[2]*beam_rot_in[3] + T244*beam_rot_in[3]**2
beam_rot_out[2] = R33*beam_rot_in[2] + R34*beam_rot_in[3] + T313*beam_rot_in[0]*beam_rot_in[2] + T314*beam_rot_in[0]*beam_rot_in[3] + T323*beam_rot_in[1]*beam_rot_in[2] + T324*beam_rot_in[1]*beam_rot_in[3]
beam_rot_out[3] = R44*beam_rot_in[3] + T413*beam_rot_in[0]*beam_rot_in[2] + T414*beam_rot_in[0]*beam_rot_in[3] + T423*beam_rot_in[1]*beam_rot_in[2] + T424*beam_rot_in[1]*beam_rot_in[3]
beam_rot_out[4] = beam_rot_in[4]
beam_rot_out[5] = beam_rot_in[5]
beam_rot_out = rot_beam(beam_rot_out,-alpha)
beam[it_z,1:7] = np.transpose(beam_rot_out)
return [beam, it_z]
def sec_bend_matrix(L,B,n,p,rest_mass=938):
if B==0:
return drift_matrix(L, p, rest_mass=rest_mass)
Brho = PtoBrho(p)
h = B/Brho
if n>0 and n<1:
kx = sqrt((1-n)*h**2)
ky = sqrt(n*h**2)
bend_mat = np.array([[cos(kx*L),1/kx*sin(kx*L),0,0,0,h/kx**2*(1-cos(kx*L))],
[-kx*sin(kx*L),cos(kx*L),0,0,0,h/kx*sin(kx*L)],
[0,0,cos(ky*L),1/ky*sin(ky*L),0,0],
[0,0,-ky*sin(ky*L),cos(ky*L),0,0],
[-h/kx*sin(kx*L),-h/kx**2*(1-cos(kx*L)),0,0,1,-h**2/kx**3*(kx*L-sin(kx*L))],
[0,0,0,0,0,1]])
elif n>1:
kx = sqrt(-(1-n)*h**2) #complex value --> change sign and forumulas
ky = sqrt(n*h**2)
bend_mat = np.array([[cosh(kx*L),1/kx*sinh(kx*L),0,0,0,-h/kx**2*(1-cosh(kx*L))],
[kx*sinh(kx*L),cosh(kx*L),0,0,0,h/kx*sinh(kx*L)],
[0,0,cos(ky*L),1/ky*sin(ky*L),0,0],
[0,0,-ky*sin(ky*L),cos(ky*L),0,0],
[-h/kx*sinh(kx*L),h/kx**2*(1-cosh(kx*L)),0,0,1,h**2/kx**3*(kx*L-sinh(kx*L))],
[0,0,0,0,0,1]])
elif n<0:
kx = sqrt((1-n)*h**2)
ky = sqrt(-n*h**2) #complex value --> change sign and forumulas
bend_mat = np.array([[cos(kx*L),1/kx*sin(kx*L),0,0,0,h/kx**2*(1-cos(kx*L))],
[-kx*sin(kx*L),cos(kx*L),0,0,0,h/kx*sin(kx*L)],
[0,0,cosh(ky*L),1/ky*sinh(ky*L),0,0],
[0,0,ky*sinh(ky*L),cosh(ky*L),0,0],
[-h/kx*sin(kx*L),-h/kx**2*(1-cos(kx*L)),0,0,1,-h**2/kx**3*(kx*L-sin(kx*L))],
[0,0,0,0,0,1]])
elif n==1: #kx=0
ky = sqrt(n*h**2)
bend_mat = np.array([[1,L,0,0,0,0],
[0,1,0,0,0,0],
[0,0,cos(ky*L),1/ky*sin(ky*L),0,0],
[0,0,-ky*sin(ky*L),cos(ky*L),0,0],
[-h*L,-h*L**2/2,0,0,1,-h**2*L**3/6],
[0,0,0,0,0,1]])
elif n==0:
kx = sqrt((1-n)*h**2) #ky=0
bend_mat = np.array([[cos(kx*L),1/kx*sin(kx*L),0,0,0,h/kx**2*(1-cos(kx*L))],
[-kx*sin(kx*L),cos(kx*L),0,0,0,h/kx*sin(kx*L)],
[0,0,1,L,0,0],
[0,0,0,1,0,0],
[-h/kx*sin(kx*L),-h/kx**2*(1-cos(kx*L)),0,0,1,-h**2/kx**3*(kx*L-sin(kx*L))],
[0,0,0,0,0,1]])
return bend_mat
def pole_face_mat(angle,B,gap,p,k1=0.5,k2=0,paraxial_correction = False):
"""
k1 and k2 related to frindge field properties; default k1=0.5, k2=0
see SLAC transport manual
"""
if B==0 :
return np.identity(6)
Brho = PtoBrho(p)
radius = Brho/B
beta = math.radians(angle)
psi = k1*(gap/radius)*((1+sin(beta)**2)/cos(beta))*(1-k1*k2*gap/radius*tan(beta))
pole_mat = np.array([[1,0,0,0,0,0],
[tan(beta)/radius,1,0,0,0,0],
[0,0,1,0,0,0],
[0,0,-tan(beta-psi)/radius,1,0,0],
[0,0,0,0,1,0],
[0,0,0,0,0,1]])
return pole_mat
def solenoid_mat(L, B, a, p, refE, N_segments=20):
"""
Transfer function for a solenoid
"""
Brho = PtoBrho(p)
K = 1/2 * B/Brho
entrance_mat = np.array([[1,0,0,0,0,0],
[0,1,K,0,0,0],
[0,0,1,0,0,0],
[-K,0,0,1,0,0],
[0,0,0,0,1,0],
[0,0,0,0,0,1]])
exit_mat = np.array([[1,0,0,0,0,0],
[0,1,-K,0,0,0],
[0,0,1,0,0,0],
[K,0,0,1,0,0],
[0,0,0,0,1,0],
[0,0,0,0,0,1]])
C = cos(K*L)
S = sin(K*L)
segment_mat = np.array([[1,S*C/K,0,S*S/K,0,0],
[0,2*C*C-1,0,2*S*C,0,0],
[0,-S*S/K,1,S*C/K,0,0],
[0,-2*S*C,0,2*C*C-1,0,0],
[0,0,0,0,1,L/gamma**2],
[0,0,0,0,0,1]])
solenoid_mat = exit_mat @ segment_mat @ entrance_mat
return solenoid_mat
def wedge_X(thickness_max,width,mat,beam,it_z,refE,N_segments=10):
x = beam[it_z,1]
a = thickness_max/width
b = thickness_max/2
thickness = max(a*x+b,0)
for i in range(0,N_segments):
it_z = it_z + 1
beam[it_z,0] = beam[it_z-1,0] + thickness/N_segments
[beam[it_z,1:7],sigma] = Highland(thickness/N_segments,mat,beam[it_z-1,1:7],refE)
return [beam, it_z]
def wedge_circular(L_min,a_min,L_max,a_max,mat,N_steps,beam,it_z,refE):
# wedge made of stack of N_steps collimators, with a min thickness L_min for an aperture a_min and a max thickness L_max at an aperture a_max
#entrance edge
if abs(L_max-L_min) > 0 :
for i in range(0,N_steps):
a = (a_max*(N_steps-i) + a_min*i)/N_steps
L = (L_max - L_min)/(N_steps)/2
#print("i = ",i,"a = ",a,", L = ",L)
[beam, it_z] = collimator(L,a,mat,beam,it_z,1,refE)
#central part
if L_min > 0 :
[beam, it_z] = collimator(L_min,a,mat,beam,it_z,1,refE)
#exit edge
if abs(L_max-L_min) > 0 :
for i in range(N_steps-1,-1,-1):
a = (a_max*(N_steps-i) + a_min*i)/N_steps
L = (L_max - L_min)/(N_steps)/2
#print("i = ",i,"a = ",a,", L = ",L)
[beam, it_z] = collimator(L,a,mat,beam,it_z,1,refE)
return beam
def slit(orientation,L_m,left,right,mat,beam,it_z,refE,N_segments=10):
"""
slit with 2 blades (left and right)
"""
L_segment = L_m/N_segments
if orientation == 'X':
for i in range(0,N_segments):
if (beam[it_z,1] <= left or beam[it_z,1] >= right):
it_z = it_z + 1
beam[it_z,0] = beam[it_z-1,0] + L_segment
[beam[it_z,1:7],sigma] = Highland(L_segment,mat,beam[it_z-1,1:7],refE)
else:
[beam,it_z] = drift(L_segment,beam,refE,it_z,1)
elif orientation == 'Y':
for i in range(0,N_segments):
if (beam[it_z,3] <= left or beam[it_z,3] >= right):
it_z = it_z + 1
beam[it_z,0] = beam[it_z-1,0] + L_segment
[beam[it_z,1:7],sigma] = Highland(L_segment,mat,beam[it_z-1,1:7],refE)
else:
[beam,it_z] = drift(L_segment,beam,refE,it_z,1)
return [beam, it_z]
def slitX(L_m,leftX,rightX,mat,beam,it_z,refE,N_segments=10):
"""
slit along X axis, with 2 blades (left and right)
"""
L_segment = L_m/N_segments
for i in range(0,N_segments):
if (beam[it_z,1] <= leftX or beam[it_z,1] >= rightX):
it_z = it_z + 1
beam[it_z,0] = beam[it_z-1,0] + L_segment
[beam[it_z,1:7],sigma] = Highland(L_segment,mat,beam[it_z-1,1:7],refE)
else:
[beam,it_z] = drift(L_segment,beam,refE,it_z,1)
return [beam, it_z]
def collimator(L_m,a,mat,beam,it_z,refE,N_segments):
"""
L_m=collimator thickness, a=aperture radius, mat=material
"""
L_segment = L_m/N_segments
for i in range(0,N_segments):
if sqrt(beam[it_z,1]**2 + beam[it_z,3]**2) >= a:
it_z = it_z + 1
beam[it_z,0] = beam[it_z-1,0] + L_segment
[beam[it_z,1:7],sigma] = Highland(L_segment,mat,beam[it_z-1,1:7],refE)
else:
[beam,it_z] = drift(L_segment,beam,refE,it_z,1) # drift only
# if sqrt(beam[it_z,1]**2 + beam[it_z,3]**2) >= a:
# L_segment = L_m/N_segments
# for i in range(0,N_segments):
# it_z = it_z + 1
# beam[it_z,0] = beam[it_z-1,0] + L_segment
# [beam[it_z,1:7],sigma] = Highland(L_segment,mat,beam[it_z-1,1:7])
#
# else:
# [beam,it_z] = drift2(L_m,beam,it_z,N_segments) # drift only
return [beam, it_z]
def rot_mat(angle):
""" rotation matrix for the beam coordinates by some angle in the X-Y plane"""
rot_mat = np.array([[cos(angle),0,sin(angle),0,0,0],
[0,cos(angle),0,sin(angle),0,0],
[-sin(angle),0,cos(angle),0,0,0],
[0,-sin(angle),0,cos(angle),0,0],
[0,0,0,0,1,0],
[0,0,0,0,0,1]])
return rot_mat
def rot_beam(beam, angle):
""" rotate the beam coordinates by some angle in the X-Y plane"""
beam = np.matmul(rot_mat(angle), beam)
return beam
def Highland(L_m,mat,beam_in,refE):
"""computes scattering angle"""
ref_p = EtoP(refE)
p = ref_p + beam_in[5]*ref_p
E = PtoE(p)
if math.isnan(E):
beam_out = beam_in
sigma = float('nan')
elif L_m <= 0 :
beam_out = beam_in
sigma = 0
else:
p = sqrt(2*938*E+E**2)
gamma = (938+E)/938
beta = sqrt(1-1/gamma**2)
if mat == 'water':
Lrad = 36.08
density = 1
cWET = 1
elif mat == 'tantalum':
Lrad = 6.82
density = 16.69
cWET = 0.5057
elif mat == 'lexan':
Lrad = 41.72
density = 1.2
cWET = 0.95237
elif mat == 'carbon':
Lrad = 42.7
density = 2
cWET = 0.894
elif mat == 'iron':
Lrad = 13.84
density = 7.874
cWET = 0.4349
elif mat == 'lead':
Lrad = 7.39
density = 8.3
cWET = 0.675
elif mat == 'aluminum' or mat == 'aluminium ':
Lrad = 24.01
density = 2.7
cWET = 0.778
else:
raise Exception('material not found')
# modify energy
p_range = EtoR(E)
WET = L_m*100*cWET*density/cos(sqrt(beam_in[1]**2+beam_in[3]**2))
new_p_range = p_range - WET
if new_p_range>0:
# assume drift is independent of the scattering (i.e. impact on angle only)
beam_out = drift_core(L_m,beam_in,refE)
L_gcm2 = abs(L_m*100*density/cos(sqrt(beam_in[1]**2+beam_in[3]**2)))
sigma = 14.1/p/beta*sqrt(L_gcm2/Lrad)*(1+1/9*log10(L_gcm2/Lrad))
angleX = np.random.normal(0,sigma)
angleY = np.random.normal(0,sigma)
beam_out[1] = beam_in[1] + angleX
beam_out[3] = beam_in[3] + angleY
new_E = RtoE(new_p_range)
new_p = EtoP(new_E)
# make the same calculations for the initial energy to avoid rounding errors
old_E = RtoE(p_range)
old_p = EtoP(old_E)
beam_out[5] = beam_out[5] + (new_p-old_p)/ref_p
else:
beam_out = np.empty(6)
beam_out[:] = np.nan
sigma = 0
return [beam_out, sigma]
def PtoGamma(p,rest_mass=938):
"""impulsion (in Mev/c) to gamma factor"""
beta = PtoBeta(p,rest_mass)
gamma = BetatoGamma(beta)
return gamma
def PtoV(p,rest_mass=938):
"""impulsion (in Mev/c) to speed (in m/s)"""
light_speed = 2.998*10**8
speed = PtoBeta(p,rest_mass)*light_speed
return speed
def PtoBeta(p,rest_mass=938):
""" impulsion (in Mev/c) to speed (in 1/c)"""
beta = p/sqrt(rest_mass**2 + p**2)
return beta
def VtoGamma(v):
return 1/sqrt(1-v**2/(2.998*10**8)**2)
def GammatoV(gamma):
return 2.998*10**8 * sqrt(1 - 1/gamma**2)
def BetatoGamma(beta):
return 1/sqrt(1-beta**2)
def GammatoBeta(gamma):
return sqrt(1 - 1/gamma**2)
def BetatoP(beta,rest_mass=938):
""" returns p in [MeV/c]"""
gamma = BetatoGamma(beta)
return beta*gamma*rest_mass
def EtoP(E,rest_mass=938):
"""energy to impulsion"""
p = sqrt(E**2 + 2*rest_mass*E)
return p
def PtoE(p,rest_mass=938):
"""energy to impulsion"""
E = sqrt(p**2 + rest_mass**2) - rest_mass
return E
def EtoR(E):
R=exp(-0.013296*log(E)**3 + 0.15248*log(E)**2 + 1.2193*log(E) - 5.5064)
return R
def RtoE(R):
E=exp(0.0015739*log(R)**3 - 0.0040274*log(R)**2 + 0.55919*log(R) + 3.4658)
return E
def EtoBrho(E,rest_mass=938):
Brho = 1/300*sqrt(E**2+2*rest_mass*E)
return Brho
def PtoBrho(p):
Brho = 1/300*p
return Brho
def Brho_scaling(refE,newE,rest_mass=938):
refBrho = 1/rest_mass*sqrt(refE**2+2*rest_mass*refE)
newBrho = 1/rest_mass*sqrt(newE**2+2*rest_mass*newE)
return newBrho/refBrho
def Gaussian_fit(data,p0):
"""
p0 is the initial guess for the fitting coefficients (A, mu and sigma above)# p0 is the initial guess for the fitting coefficients (A, mu and sigma below)
"""
# Define model function to be used to fit to the data above:
def gauss(x, *p):
A, mu, sigma = p
return A*np.exp(-(x-mu)**2/(2.*sigma**2))
mask = ~np.isnan(data)
hist, bin_edges = np.histogram(data[mask], density=True)
bin_centres = (bin_edges[:-1] + bin_edges[1:])/2
coeff, var_matrix = curve_fit(gauss, bin_centres, hist, p0=p0)
print('Fitted amplitude = ', coeff[0])
print('Fitted mean = ', coeff[1])
print('Fitted standard deviation = ', coeff[2])
return coeff
def EOM_particle_in_Bfield(Delta_z,beam,p_ref,Bx,By,Bz=0,part_mass=1.67*10**-27,rest_mass=938):
#beam = np.array([z,sizeX,divX,sizeY,divY,0,dponp])
light_speed = 2.998*10**8
p_tot0 = p_ref * (beam[6] + 1)
beta0 = PtoBeta(p_tot0,rest_mass)
betaZ0 = beta0 / sqrt(1 + beam[2]**2 + beam[4]**2)
betaX0 = betaZ0 * beam[2]
betaY0 = betaZ0 * beam[4]
px0 = BetatoP(betaX0,rest_mass)
py0 = BetatoP(betaY0,rest_mass)
pz0 = BetatoP(betaZ0,rest_mass)
Delta_t = Delta_z/betaZ0/light_speed
# betaX0 = PtoBeta(px0,rest_mass)
# betaY0 = PtoBeta(py0,rest_mass)
# betaZ0 = PtoBeta(pz0,rest_mass)
fact = 10**-6 * Delta_t * light_speed**2
px = px0 + fact * (betaY0*Bz - betaZ0*By)
py = py0 + fact * (betaZ0*Bx - betaX0*Bz)
pz = pz0 + fact * (betaX0*By - betaY0*Bx)
# normalize to prevent propagation of rounding errors from linearization
p_tot = sqrt(px**2 + py**2 + pz**2)
px = px * p_tot0/p_tot
py = py * p_tot0/p_tot
pz = pz * p_tot0/p_tot
# compute speeds
vx = PtoV(px,rest_mass)
vy = PtoV(py,rest_mass)
vz = PtoV(pz,rest_mass)
vx0 = betaX0*light_speed
vy0 = betaY0*light_speed