Bunching Factors¶

Import packages¶

In [1]:

%load_ext autoreload
%autoreload 2

%load_ext autoreload %autoreload 2

In [2]:

import numpy as np
from numpy import genfromtxt
import scipy
from scipy import special
from zfel.particles import general_load_bucket
import matplotlib.pyplot as plt

import numpy as np from numpy import genfromtxt import scipy from scipy import special from zfel.particles import general_load_bucket import matplotlib.pyplot as plt

Input parameters¶

In [3]:

npart   = 512                       # n-macro-particles per bucket 
s_steps = 200#31                    # n-sample points along bunch length
z_steps = 200#20                    # n-sample points along undulator
energy  = 4313.34*1E6               # electron energy [eV]
eSpread = 0#1.0e-4                  # relative rms energy spread [ ]
emitN   = 1.2e-6                    # normalized transverse emittance [m-rad]
currentMax = 3900                   # peak current [Ampere]
beta = 26                           # mean beta [meter]
unduPeriod = 0.03                   # undulator period [meter]
unduK = 3.5                         # undulator parameter, K [ ]
unduL = 70#30                       # length of undulator [meter]
radWavelength = 1.5e-9              # seed wavelength? [meter], used only in single-freuqency runs
dEdz = 0                            # rate of relative energy gain or taper [keV/m], optimal~130
iopt = 5                            # 5=SASE, 4=seeded
P0 = 10000*0.0                      # small seed input power [W]
constseed = 1                       # whether we want to use constant random seed for reproducibility, 1 Yes, 0 No
particle_position=genfromtxt('./data/weird_particle_position.csv', delimiter=',') # or None  
# particle information with positions in meter and eta,\
# if we want to load random particle positions and energy, then set None
hist_rule='square-root'             # 'square-root' or 'sturges' or 'rice-rule' or 'self-design', number \
                                    #  of intervals to generate the histogram of eta value in a bucket

npart = 512 # n-macro-particles per bucket s_steps = 200#31 # n-sample points along bunch length z_steps = 200#20 # n-sample points along undulator energy = 4313.34*1E6 # electron energy [eV] eSpread = 0#1.0e-4 # relative rms energy spread [ ] emitN = 1.2e-6 # normalized transverse emittance [m-rad] currentMax = 3900 # peak current [Ampere] beta = 26 # mean beta [meter] unduPeriod = 0.03 # undulator period [meter] unduK = 3.5 # undulator parameter, K [ ] unduL = 70#30 # length of undulator [meter] radWavelength = 1.5e-9 # seed wavelength? [meter], used only in single-freuqency runs dEdz = 0 # rate of relative energy gain or taper [keV/m], optimal~130 iopt = 5 # 5=SASE, 4=seeded P0 = 10000*0.0 # small seed input power [W] constseed = 1 # whether we want to use constant random seed for reproducibility, 1 Yes, 0 No particle_position=genfromtxt('./data/weird_particle_position.csv', delimiter=',') # or None # particle information with positions in meter and eta,\ # if we want to load random particle positions and energy, then set None hist_rule='square-root' # 'square-root' or 'sturges' or 'rice-rule' or 'self-design', number \ # of intervals to generate the histogram of eta value in a bucket

In [4]:

particle_position[:,1]

particle_position[:,1]

Out[4]:

array([ 0.005,  0.005,  0.005, ..., -0.005, -0.005, -0.005])

Calculating intermediate parameters and bunching factor¶

In [5]:

# whether to use constant random seed for reproducibility
if constseed==1:
    np.random.seed(22)

# Some constant values
mc2 = 0.51099906E6#510.99906E-3      # Electron rest mass in eV
c = 2.99792458E8        # light speed in meter
e = 1.60217733E-19      # electron charge in Coulomb

gamma0  = energy/mc2                                    # central energy of the beam in unit of mc2

resWavelength = unduPeriod*(1+unduK**2/2.0)\
                /(2*gamma0**2)                          # resonant wavelength
coopLength = resWavelength/unduPeriod                # cooperation length
gainLength = 1                                      # rough gain length
#cs0  = bunchLength/coopLength                           # bunch length in units of cooperation length     
z0    = unduL/gainLength                                # wiggler length in units of gain length
delt  = z0/z_steps                                      # integration step in z0 ~ 0.1 gain length
dels  = delt                                            # integration step in s0 must be same as in z0 
gbar  = (resWavelength-radWavelength)\
        /(radWavelength)                                # scaled detune parameter
delg  = eSpread                                         # Gaussian energy spread in units of rho 
Ns    = currentMax*unduL/unduPeriod/z_steps\
        *resWavelength/c/e                              # N electrons per s-slice [ ]
#load buckets
#[thet_init,eta_init]=general_load_bucket(npart,gbar,delg,iopt\
#    ,Ns,coopLength,resWavelength,particle_position,s_steps,dels,hist_rule)

#load buckets                 
data = general_load_bucket(npart,Ns,coopLength,s_steps,dels,
                           particle_position=particle_position,
                           hist_rule=hist_rule,gbar=0,delg=None,iopt=None)  
thet_init = data['thet_init']
eta_init = data['eta_init']

bunching=np.mean(np.real(np.exp(-1j*thet_init)),axis=1)\
  +np.mean(np.imag(np.exp(-1j*thet_init)),axis=1)*1j            #bunching factor calculation   
bunching.shape

# whether to use constant random seed for reproducibility if constseed==1: np.random.seed(22) # Some constant values mc2 = 0.51099906E6#510.99906E-3 # Electron rest mass in eV c = 2.99792458E8 # light speed in meter e = 1.60217733E-19 # electron charge in Coulomb gamma0 = energy/mc2 # central energy of the beam in unit of mc2 resWavelength = unduPeriod*(1+unduK**2/2.0)\ /(2*gamma0**2) # resonant wavelength coopLength = resWavelength/unduPeriod # cooperation length gainLength = 1 # rough gain length #cs0 = bunchLength/coopLength # bunch length in units of cooperation length z0 = unduL/gainLength # wiggler length in units of gain length delt = z0/z_steps # integration step in z0 ~ 0.1 gain length dels = delt # integration step in s0 must be same as in z0 gbar = (resWavelength-radWavelength)\ /(radWavelength) # scaled detune parameter delg = eSpread # Gaussian energy spread in units of rho Ns = currentMax*unduL/unduPeriod/z_steps\ *resWavelength/c/e # N electrons per s-slice [ ] #load buckets #[thet_init,eta_init]=general_load_bucket(npart,gbar,delg,iopt\ # ,Ns,coopLength,resWavelength,particle_position,s_steps,dels,hist_rule) #load buckets data = general_load_bucket(npart,Ns,coopLength,s_steps,dels, particle_position=particle_position, hist_rule=hist_rule,gbar=0,delg=None,iopt=None) thet_init = data['thet_init'] eta_init = data['eta_init'] bunching=np.mean(np.real(np.exp(-1j*thet_init)),axis=1)\ +np.mean(np.imag(np.exp(-1j*thet_init)),axis=1)*1j #bunching factor calculation bunching.shape

Out[5]:

(200,)

Verify whether the initial bunching level is reasonable¶

In [6]:

print(np.sqrt(np.mean(np.absolute(bunching)**2)))
print(1/np.sqrt(Ns))

print(np.sqrt(np.mean(np.absolute(bunching)**2))) print(1/np.sqrt(Ns))

0.0008998043866928952
0.0008389101946493842