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Wiki source code of Partial Coherence Simulation

Version 9.1 by sndueste on 2020/07/07 16:55
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1 In order to simulate the temporal and spectral distribution of SASE pulses there is an easy way based random fluctuations filtered spectrally and temporally.
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3 The only input parameters are the center wavelength, spectral bandwidth and the pulse duration.
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5 Here you can find a small python script (by (% class="twikiNewLink" %)MartinB(%%)) implementing the partial coherence method as described in:
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7 * **Thomas Pfeifer et al. //Partial-coherence method to model experimental free-electron laser pulse statistics,// Opt. Lett. 35, 3441-3443 (2010);** [[link to the paper>>url:http://dx.doi.org/10.1364/OL.35.003441||shape="rect"]]
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11 The pulse shapes in time AND corresponding spectral distribution can be easily created with:
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13 * (((
14 a python script
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16 {{expand title="Click here to expand the script ..."}}
17 import numpy as np
18 import matplotlib.pyplot as plt
19
20 def GetSASE(CentralEnergy, dE_FWHM, dt_FWHM, samples=0, Axis=True):
21 h=4.135667662 #in eV*fs
22 dE=dE_FWHM/2.355 #in eV, converts to sigma
23 dt=dt_FWHM/2.355 #in fs, converts to sigma
24 if samples == 0:
25 samples=int(400.*dt*CentralEnergy/h)
26 else:
27 if (samples < 400.*dt*CentralEnergy/h):
28 print("Number of samples is a little small, proceeding anyway. Got", samples, "prefer more than",400.*dt*CentralEnergy/h)
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30 EnAxis=np.linspace(0.,20.*CentralEnergy,num=samples)
31 EnInput=np.zeros(samples, dtype=np.complex64)
32 EnInput=np.exp(-(EnAxis-CentralEnergy)~*~*2/2./dE~*~*2+2*np.pi*1j*np.random.random(size=samples))
33 En_FFT=np.fft.fft(EnInput)
34 TAxis=np.fft.fftfreq(samples,d=(20.*CentralEnergy)/samples)*h
35 TOutput=np.exp(-TAxis~*~*2/2./dt~*~*2)*En_FFT
36 EnOutput=np.fft.ifft(TOutput)
37 if (Axis):
38 return EnAxis, EnOutput, TAxis, TOutput
39 else:
40 return EnOutput, TOutput
41
42 \\
43
44 # set the main parameters here:
45 CentralEnergy=80. # in eV
46 bandwidth=0.5 # bandwidth in %
47 dt_FWHM=30. # FWHM of the temporal duration on average
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49 dE_FWHM=CentralEnergy/100 *bandwidth # calculate bandwidth of the spectrum in eV
50
51 # calculate 3 SASE pulses
52 EnAxis, EnOutput, TAxis, TOutput = GetSASE(CentralEnergy=CentralEnergy, dE_FWHM=dE_FWHM, dt_FWHM=dt_FWHM)
53 EnAxis2, EnOutput2, TAxis2, TOutput2 = GetSASE(CentralEnergy=CentralEnergy, dE_FWHM=dE_FWHM, dt_FWHM=dt_FWHM)
54 EnAxis3, EnOutput3, TAxis3, TOutput3 = GetSASE(CentralEnergy=CentralEnergy, dE_FWHM=dE_FWHM, dt_FWHM=dt_FWHM)
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56
57 # plot spectrum
58 ax1 = plt.subplot(1, 2, 1)
59 plt.plot(EnAxis,np.absolute(EnOutput),EnAxis2,np.absolute(EnOutput2),EnAxis3,np.absolute(EnOutput3) )
60 plt.xlim(CentralEnergy-2.*dE_FWHM,CentralEnergy+2.*dE_FWHM)
61 plt.title('Average pulse duration: %.1f fs' % dt_FWHM )
62 ax1.set_xlabel('Photon energy in eV')
63 ax1.set_ylabel('spectral intensity')
64
65 # plot time structure
66 ax1 =plt.subplot(1, 2, 2)
67 plt.plot(TAxis,np.absolute(TOutput),TAxis2,np.absolute(TOutput2), TAxis3,np.absolute(TOutput3))
68 plt.xlim(-2.*dt_FWHM,+2.*dt_FWHM)
69 ax1.set_xlabel('time in fs')
70 ax1.set_ylabel('pulse amplitude')
71
72 plt.show()
73 {{/expand}}
74 )))
75 * or the same as a Jupyter Notebook** [[attach:GenerateSASE.ipynb]] **
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77 ==
78 Some examples: ==
79
80 //CentralEnergy=80 # in eV//
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82 //bandwidth=0.5 # bandwidth in %//
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84 //dt_FWHM=10, 30., 70  # FWHM of the temporal duration on average//
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89 [[image:attach:2020-07-07 16_51_14-Window.png||height="250"]]
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93 [[image:attach:2020-07-07 16_53_22-Window.png||height="250"]]
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95 [[image:attach:2020-07-07 16_52_27-Window.png||height="250"]]
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