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Wiki source code of Partial Coherence Simulation

Version 8.1 by sndueste on 2020/07/06 16:59
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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 spectraly and temporally.
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3 The only input parameters are the 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 methode as described in 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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7 The pulse shapes in time AND corresponding spectral dstribution can be easily created with:
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9 * (((
10 a python script
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12 {{expand title="Click here to expand the script ..."}}
13 import numpy as np
14 import matplotlib.pyplot as plt
15
16 def GetSASE(CentralEnergy, dE_FWHM, dt_FWHM, samples=0, Axis=True):
17 h=4.135667662 #in eV*fs
18 dE=dE_FWHM/2.355 #in eV, converts to sigma
19 dt=dt_FWHM/2.355 #in fs, converts to sigma
20 if samples == 0:
21 samples=int(400.*dt*CentralEnergy/h)
22 else:
23 if (samples < 400.*dt*CentralEnergy/h):
24 print("Number of samples is a little small, proceeding anyway. Got", samples, "prefer more than",400.*dt*CentralEnergy/h)
25
26 EnAxis=np.linspace(0.,20.*CentralEnergy,num=samples)
27 EnInput=np.zeros(samples, dtype=np.complex64)
28 EnInput=np.exp(-(EnAxis-CentralEnergy)~*~*2/2./dE~*~*2+2*np.pi*1j*np.random.random(size=samples))
29 En_FFT=np.fft.fft(EnInput)
30 TAxis=np.fft.fftfreq(samples,d=(20.*CentralEnergy)/samples)*h
31 TOutput=np.exp(-TAxis~*~*2/2./dt~*~*2)*En_FFT
32 EnOutput=np.fft.ifft(TOutput)
33 if (Axis):
34 return EnAxis, EnOutput, TAxis, TOutput
35 else:
36 return EnOutput, TOutput
37
38 \\
39
40 # set the main parameters here:
41 CentralEnergy=80. # in eV
42 bandwidth=0.5 # bandwidth in %
43 dt_FWHM=30. # FWHM of the temporal duration on average
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45 dE_FWHM=CentralEnergy/100 *bandwidth # calculate bandwidth of the spectrum in eV
46
47 # calculate 3 SASE pulses
48 EnAxis, EnOutput, TAxis, TOutput = GetSASE(CentralEnergy=CentralEnergy, dE_FWHM=dE_FWHM, dt_FWHM=dt_FWHM)
49 EnAxis2, EnOutput2, TAxis2, TOutput2 = GetSASE(CentralEnergy=CentralEnergy, dE_FWHM=dE_FWHM, dt_FWHM=dt_FWHM)
50 EnAxis3, EnOutput3, TAxis3, TOutput3 = GetSASE(CentralEnergy=CentralEnergy, dE_FWHM=dE_FWHM, dt_FWHM=dt_FWHM)
51
52
53 # plot spectrum
54 ax1 = plt.subplot(1, 2, 1)
55 plt.plot(EnAxis,np.absolute(EnOutput),EnAxis2,np.absolute(EnOutput2),EnAxis3,np.absolute(EnOutput3) )
56 plt.xlim(CentralEnergy-2.*dE_FWHM,CentralEnergy+2.*dE_FWHM)
57 plt.title('Average pulse duration: %.1f fs' % dt_FWHM )
58 ax1.set_xlabel('Photon energy in eV')
59 ax1.set_ylabel('spectral intensity')
60
61 # plot time structure
62 ax1 =plt.subplot(1, 2, 2)
63 plt.plot(TAxis,np.absolute(TOutput),TAxis2,np.absolute(TOutput2), TAxis3,np.absolute(TOutput3))
64 plt.xlim(-2.*dt_FWHM,+2.*dt_FWHM)
65 ax1.set_xlabel('time in fs')
66 ax1.set_ylabel('pulse amplitude')
67
68 plt.show()
69 {{/expand}}
70 )))
71 * a Jupyter Notebook** [[attach:GenerateSASE.ipynb]] **
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74 Some examples of results:
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78 [[image:attach:partia__coherence2.png]] or: [[image:attach:image2020-2-5_15-14-4.png||width="480"]]
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