High resolution simulation of beam dynamics in electron linacs for x-ray free electron lasers

In this paper we report on large-scale high resolution simulations of beam dynamics in electron linacs for the next-generation x-ray free electron lasers (FELs). We describe key features of a parallel macroparticle simulation code including three-dimensional (3D) space-charge effects, short-range structure wakefields, coherent synchrotron radiation (CSR) wakefields, and treatment of radio-frequency (rf) accelerating cavities using maps obtained from axial field profiles. We present a study of the microbunching instability causing severe electron beam fragmentation in the longitudinal phase space which is a critical issue for future FELs. Using parameters for a proposed FEL linac at Lawrence Berkeley National Laboratory (LBNL), we show that a large number of macroparticles (beyond 100 million) is generally needed to control the numerical macroparticle shot noise and avoid overestimating the microbunching instability. We explore the effect of the longitudinal grid on simulation results. We also study the effect of initial uncorrelated energy spread on the final uncorrelated energy spread of the beam for the FEL linac.

Figure 1

Horizontal and longitudinal trajectories through an rf cavity from the linear transfer map and from direct numerical integration.

Figure 2

Amplitude of energy modulations as a function of distance induced by space charge starting from initial 5% current sinusoidal modulations with wavelengths $\lambda =15\mu \mathrm{m}$, $30\mu \mathrm{m}$, and $50\mu \mathrm{m}$ for a beam drifting in free space with initial uniform transverse density, circular cross section, and vanishing emittance. The results from IMPACT simulations (dots) are compared to the longitudinal space-charge impedance models of Eq. (19), dashed lines, and Eq. (21), solid lines.

Figure 3

The transfer function of the filter in frequency domain.

Figure 4

Longitudinal phase-space distribution after a bending magnet for an initial sinusoidal density modulation. Numerical result (red), analytical prediction (blue), and the initial distribution (green) are shown.

Figure 5

Slice (or uncorrelated) energy spread at the exit of the linac as a function of the number of macroparticles used in the simulations. The reported slice energy spread is averaged over all the slices in the beam core. Two examples with 5 and 2 keV initial uncorrelated energy spread are compared.

Figure 6

The rms energy fluctuation at the exit of the linac as a function of the number of macroparticles used in the simulations. Two examples of beams with 5 and 2 keV initial uncorrelated energy spread are compared.

Figure 7

The gain curve for the microbunching instability through a portion of beam line considered in our studies for an FEL linac at LBNL (see text). Linear theory (solid line) is compared to results from macroparticle simulations (dots). The reported value of $\lambda$ is for the modulation wavelength before compression.

Figure 8

Final energy spread from simulations using 2048 and 4096 grid points.

Figure 9

A schematic plot of a proposed FEL linac at Berkeley.

Figure 10

Final uncorrelated energy spread distribution resulting from an initial square root parabolic current profile with initial 2, 5, 7.5, 10, and 15 keV uncorrelated energy.

Figure 11

Longitudinal phase space at the end of the linac using one billion (left) and five billion macroparticles (right) with an initial 5 keV rms uncorrelated energy spread.

Figure 12

Current profile at the end of the linac with initial 5 keV rms uncorrelated energy spread.

Figure 13

Initial current profile fluctuation of a Gaussian distribution from two million particle direct sampling, from one billion particle up-sampling with $20\mu \mathrm{m}$ longitudinal box size, with $300\mu \mathrm{m}$ longitudinal box size, with $500\mu \mathrm{m}$ longitudinal box size, and from one billion particle direct sampling.