# -*- coding: utf-8 -*- __author__ = "Konstantin Klementiev" __date__ = "1 Nov 2019" import os, sys; sys.path.append(os.path.join('..', '..')) # analysis:ignore import numpy as np import matplotlib.pyplot as plt from matplotlib.legend_handler import HandlerBase import xrt.backends.raycing.sources as rs from xrt.backends.raycing.physconsts import CH withXrtSampling = True withCoisson = True thetaMax, psiMax = 60e-6, 30e-6 # rad if withCoisson: coissonD = np.linspace(-0.4, 1.2, 17) coissonA = np.array([0.45, 0.47, 0.50, 0.54, 0.58, 0.63, 0.69, 0.75, 0.82, 0.90, 0.98, 1.06, 1.14, 1.22, 1.30, 1.37, 1.44]) coissonS = np.array([4.51, 3.82, 3.31, 2.96, 2.67, 2.46, 2.29, 2.15, 2.04, 1.95, 1.88, 1.84, 1.82, 1.82, 1.87, 1.97, 2.16]) def coisson(Ec, L, N, n): E = Ec * (1 - coissonD/N/n) # in eV lambdaC = CH / Ec * 1e-7 # in mm div2 = coissonA**2 div2 *= (lambdaC / L) lin2 = coissonS**2 lin2 *= (lambdaC * L) / (4*np.pi)**2 return E, div2, lin2 class TwoLineObjectsHandler(HandlerBase): def create_artists(self, legend, orig_handle, x0, y0, width, height, fontsize, trans): l1 = plt.Line2D([x0, x0+width], [0.7*height, 0.7*height], linestyle=orig_handle[0].get_linestyle(), color=orig_handle[0].get_color()) l2 = plt.Line2D([x0, x0+width], [0.3*height, 0.3*height], linestyle=orig_handle[1].get_linestyle(), color=orig_handle[1].get_color()) return [l1, l2] class TwoScatterObjectsHandler(HandlerBase): def create_artists(self, legend, orig_handle, x0, y0, width, height, fontsize, trans): l1 = plt.Line2D([x0+0.2*width], [0.5*height], marker=orig_handle[0].get_paths()[0], color=orig_handle[0].get_edgecolors()[0], markerfacecolor='none') l2 = plt.Line2D([x0+0.8*width], [0.5*height], marker=orig_handle[1].get_paths()[0], color=orig_handle[1].get_edgecolors()[0], markerfacecolor='none') return [l1, l2] def main(): und = rs.Undulator( name='MAX IV U19', eE=3.0, eI=0.5, eEpsilonX=0.263, eEpsilonZ=0.008, betaX=9., betaZ=2., # """Compare with # Harry Westfahl Jr et al. J. Synchrotron Rad. (2017). 24, 566–575. # But notice their non-equidistant (in energy) harmonics.""" # name='Sirius U19', eE=3.0, eI=0.35, # eEpsilonX=0.245, eEpsilonZ=0.0024, # betaX=1.5, betaZ=1.5, period=19, n=105, targetE=(10000, 7), xPrimeMax=thetaMax*1e3, zPrimeMax=psiMax*1e3, xPrimeMaxAutoReduce=False, zPrimeMaxAutoReduce=False, eEspread=1e-3, targetOpenCL='CPU', precisionOpenCL='float32') print(u"Electron beam linear sizes = {0:.3f} µm × {1:.3f} µm".format( und.dx*1e3, und.dz*1e3)) print(u"Electron beam angular sizes = {0:.3f} µrad × {1:.3f} µrad".format( und.dxprime*1e6, und.dzprime*1e6)) E = np.linspace(1400., 16000., 1460+1) sx0, sz0 = und.get_SIGMA(E, with0eSpread=True) sPx0, sPz0 = und.get_SIGMAP(E, with0eSpread=True) sx, sz = und.get_SIGMA(E) sPx, sPz = und.get_SIGMAP(E) fig1 = plt.figure(1) ax1 = fig1.add_subplot(111) ax1.set_title("{0} undulator: linear source size".format(und.name)) ax1.set_xlabel(u'energy (keV)') ax1.set_ylabel(u'rms linear source size (µm)') l1, = ax1.plot(E*1e-3, sx0*1e3, '--C0') l2, = ax1.plot(E*1e-3, sz0*1e3, '--C1') l3, = ax1.plot(E*1e-3, sx*1e3, '-C0') l4, = ax1.plot(E*1e-3, sz*1e3, '-C1') ax1.set_ylim(0, None) leg1 = ax1.legend([(l1, l3), (l2, l4)], [r"$\sigma_x$", r"$\sigma_y$"], handler_map={tuple: TwoLineObjectsHandler()}, loc=(0.86, 0.73)) leg2 = ax1.legend([(l1, l2), (l3, l4)], [r'$\sigma_E$ = 0', r'$\sigma_E$ = 0.1%'], handler_map={tuple: TwoLineObjectsHandler()}, title='at energy spread', loc=(0.73, 0.5)) ax1.add_artist(leg1) ax1.add_artist(leg2) fig2 = plt.figure(2) ax2 = fig2.add_subplot(111) ax2.set_title("{0} undulator: angular source size".format(und.name)) ax2.set_xlabel(u'energy (keV)') ax2.set_ylabel(u'rms angular source size (µrad)') ax2.plot(E*1e-3, sPx0*1e6, '--C0') ax2.plot(E*1e-3, sPz0*1e6, '--C1') ax2.plot(E*1e-3, sPx*1e6, '-C0') ax2.plot(E*1e-3, sPz*1e6, '-C1') ax2.set_ylim(0, None) leg1 = ax2.legend([(l1, l3), (l2, l4)], [r"$\sigma'_x$", r"$\sigma'_y$"], handler_map={tuple: TwoLineObjectsHandler()}, loc=(0.56, 0.83)) leg2 = ax2.legend([(l1, l2), (l3, l4)], [r'$\sigma_E$ = 0', r'$\sigma_E$ = 0.1%'], handler_map={tuple: TwoLineObjectsHandler()}, title='at energy spread', loc='upper right') ax2.add_artist(leg1) ax2.add_artist(leg2) if withXrtSampling: theta = np.linspace(-1, 1, 401) * thetaMax * 2 psi = np.linspace(-1, 1, 201) * psiMax * 2 Eh = (np.arange(1, 12, 2) * und.E1 + np.linspace(-14, 10, 13)[:, np.newaxis]) sh = Eh.shape Efine = np.linspace(10000-14., 10000+10., 1400+1) sx0fine, sz0fine = und.get_SIGMA(Efine, with0eSpread=True) sxfine, szfine = und.get_SIGMA(Efine) sPxfine, sPzfine = und.get_SIGMAP(Efine) und.eEspread = 0. print('please wait...') flux, sigma2theta, sigma2psi, dx2, dz2 = und.real_photon_source_sizes( Eh.ravel(), theta, psi, method=0.39) sigma2theta += und.dxprime**2 sigma2psi += und.dzprime**2 dx2 += und.dx**2 dz2 += und.dz**2 fluxsh = flux.reshape(sh) fluxMax = fluxsh.max(axis=0) l5 = ax2.scatter(Eh*1e-3, sigma2theta**0.5*1e6, s=fluxsh/fluxMax[np.newaxis, :]*50, facecolors='none', edgecolors='C0') l6 = ax2.scatter(Eh*1e-3, sigma2psi**0.5*1e6, s=fluxsh/fluxMax*50, facecolors='none', edgecolors='C1') l7 = ax1.scatter(Eh*1e-3, dx2**0.5*1e3, s=fluxsh/fluxMax[np.newaxis, :]*50, facecolors='none', edgecolors='C0') l8 = ax1.scatter(Eh*1e-3, dz2**0.5*1e3, s=fluxsh/fluxMax*50, facecolors='none', edgecolors='C1') if withCoisson: cE, cA2, cS2 = coisson(und.E1*7, und.L0*und.Np, und.Np, 7) cXP = (und.dxprime**2 + cA2)**0.5 cZP = (und.dzprime**2 + cA2)**0.5 cX = (und.dx**2 + cS2)**0.5 cZ = (und.dz**2 + cS2)**0.5 # inset2 axS2 = fig2.add_axes([0.17, 0.17, 0.22, 0.3]) axS2.plot(Efine, sPxfine*1e6, '-C0') axS2.plot(Efine, sPzfine*1e6, '-C1') if withCoisson: l9 = axS2.scatter(cE, cXP*1e6, marker='+', s=40, facecolors='C0', edgecolors='C0') l10 = axS2.scatter(cE, cZP*1e6, marker='+', s=40, facecolors='C1', edgecolors='C1') axS2.scatter(Eh, sigma2theta**0.5*1e6, s=fluxsh/fluxMax[np.newaxis, :]*50, facecolors='none', edgecolors='C0') axS2.scatter(Eh, sigma2psi**0.5*1e6, s=fluxsh/fluxMax*50, facecolors='none', edgecolors='C1') axS2.set_xlim(10000-14, 10000+10) axS2.set_xticklabels( ['', '-10 eV', r'$E_{\rm harm}$', '+10 eV'], minor=False) axS2.set_ylim(6, 14) ax2.arrow(6.3, 6.5, 3.0, 2.8, head_width=0.3, head_length=0.75) # inset1 axS1 = fig1.add_axes([0.35, 0.36, 0.22, 0.3]) axS1.plot(Efine, sz0fine*1e3, '--C1') axS1.plot(Efine, szfine*1e3, '-C1') if withCoisson: l11 = axS1.scatter(cE, cX*1e3, marker='+', s=40, facecolors='C0', edgecolors='C0') l12 = axS1.scatter(cE, cZ*1e3, marker='+', s=40, facecolors='C1', edgecolors='C1') axS1.scatter(Eh, dx2**0.5*1e3, s=fluxsh/fluxMax[np.newaxis, :]*50, facecolors='none', edgecolors='C0') axS1.scatter(Eh, dz2**0.5*1e3, s=fluxsh/fluxMax*50, facecolors='none', edgecolors='C1') axS1.set_xlim(10000-14, 10000+10) axS1.set_xticklabels( ['', '-10 eV', r'$E_{\rm harm}$', '+10 eV'], minor=False) axS1.set_ylim(4.5, 6) ax1.arrow(8.5, 16., 1.1, -7.5, head_width=0.3, head_length=2.) lCur, lLab = [(l5, l6)], [r'xrt'] if withCoisson: lCur.append((l9, l10)) lLab.append('Coïsson, SPIE 88') leg3 = ax2.legend(lCur, lLab, title=r'sampled at $\sigma_E$ = 0 by:', handler_map={tuple: TwoScatterObjectsHandler()}, loc=(0.37, 0.03)) lCur, lLab = [(l7, l8)], [r'xrt'] if withCoisson: lCur.append((l11, l12)) lLab.append('Coïsson, SPIE 88') leg4 = ax1.legend(lCur, lLab, title=r'sampled at $\sigma_E$ = 0 by:', handler_map={tuple: TwoScatterObjectsHandler()}, loc=(0.66, 0.25)) fig1.savefig("undulatorLinearSize.png") fig2.savefig("undulatorAngularSize.png") if __name__ == '__main__': main() plt.show() print("Done")