Simulation of synchrotron radiation from electron beams affected by vibrations and drifts

This paper presents results of simulations of synchrotron radiation from electron beams affected by instabilities in position and angle at the source point. The goal of this work is to develop and test instrumentation for studies of the effects of the electron beam’s vibrations and drifts on beamline performance at synchrotron light sources. To perform these simulations, numerical methods were developed and implemented in the Python version of the Synchrotron Radiation Workshop (srw) code. The simulation results were compared against analytical formulas and experimental results obtained from an x-ray pinhole-camera diagnostics beamline at NSLS-II. We compared the measured data with the prediction by our code for amplitudes of orbit oscillation from $6–60\mu \mathrm{m}$ and frequencies between 1 and 40 Hz, also taking into account the effects of misalignment of the pinhole. The simulation results are in good agreement with both analytical estimates and experimental data.

Figure 1

A diagram showing the electron’s trajectory and introducing variables for the SR calculation in Eq. (1).

Figure 2

A diagram introducing variables for the SR propagation in Eq. (2).

Figure 3

Simulated intensity of SR (at 2.39 keV, critical energy) from a filament electron beam for (a) no noise and (b) a harmonic noise with amplitude $a=0.2\mathrm{mrad}$.

Figure 4

Simulation and analytical results for vertical cuts of the average intensity distributions at 2.39 keV photon energy for (a) a harmonic noise in the vertical angle (one period of oscillation) with amplitudes of 0,0.2,0.4 mrad; (b) a Gaussian noise with the standard deviations of 0,0.2,0.4 mrad; and (c) comparison of the simulation results from 10,000 and 50,000 initial conditions with the analytical result of the Gaussian noise with $\sigma =0.4\mathrm{mrad}$. The magnetic field and beam parameters are the same as those used in the calculations illustrated in Fig. 3.

Figure 5

A simplified diagram of the x-ray pinhole-camera diagnostic beamline at NSLS-II.

Figure 6

Simulated normalized intensity (vertical profiles) from the x-ray pinhole-camera diagnostic beamline for polychromatic x-rays (dashed lines) and monochromatic x-rays (solid lines) for (a) the PSF and (b) the convolution of the PSF with the particle density distribution in the electron beam.

Figure 7

Images of the pinhole camera from the experiment (top) and simulation (bottom) for (a) no excitation and (b) an excitation with an amplitude of $60\mu \mathrm{m}$, while the beam size was about $20\mu \mathrm{m}$.

Figure 8

Integrated intensity (vertical profiles) from the experiment (blue lines) and simulation (black lines) with (a) no excitation and excited with amplitudes (b) $6\mu \mathrm{m}$, (c) $30\mu \mathrm{m}$, and (d) $60\mu \mathrm{m}$.

Figure 9

Integrated intensity (vertical profiles) from the experiment (blue lines) and simulation (black lines). The beam was excited with amplitudes and frequencies of (a) $6\mu \mathrm{m}$, 1 Hz, (b) $60\mu \mathrm{m}$, 1 Hz, (c) $60\mu \mathrm{m}$, 5 Hz, and (d) $60\mu \mathrm{m}$, 30 Hz.

Figure 10

Images of the pinhole camera from the experiment (top) and the simulation (bottom) with a vertical pinhole misalignment of (a) $-100\mu \mathrm{m}$ and (b) $100\mu \mathrm{m}$. The beam was excited with an amplitude of $60\mu \mathrm{m}$.

Figure 11

Integrated intensity (vertical) with a pinhole misalignment of $100\mu \mathrm{m}$ from the experiment (blue lines) and simulation (black lines). The beam was excited with an amplitude of $60\mu \mathrm{m}$ and frequencies of (a) 1 Hz, (b) 5 Hz, (c) 20 Hz, and (d) 40 Hz.