Three-dimensional quasistatic model for high brightness beam dynamics simulation

In this paper, we present a three-dimensional quasistatic model for high brightness beam dynamics simulation in rf/dc photoinjectors, rf linacs, and similar devices on parallel computers. In this model, electrostatic space-charge forces within a charged particle beam are calculated self-consistently at each time step by solving the three-dimensional Poisson equation in the beam frame and then transforming back to the laboratory frame. When the beam has a large energy spread, it is divided into a number of energy bins or slices so that the space-charge forces are calculated from the contribution of each bin and summed together. Image-charge effects from conducting photocathode are also included efficiently using a shifted-Green function method. For a beam with large aspect ratio, e.g., during emission, an integrated Green function method is used to solve the three-dimensional Poisson equation. Using this model, we studied beam transport in one Linac Coherent Light Sources photoinjector design through the first traveling wave linac with initial misalignment with respect to the accelerating axis.

Figure 1

A schematic plot of an electron bunch in front of the conducting photocathode together with its image charge.

Figure 2

Image-charge electric potential on the axis for a round beam from the shifted-Green function solution together with the analytical solution.

Figure 3

Transverse (left) and longitudinal (right) rms sizes as a function of distance with and without the image-charge effects from photocathode.

Figure 4

Electric fields along $x$ axis (left) and along $z$ axis (right) of a beam with aspect ratio one from solutions of the integrated Green function method, the standard Green function method, and the analytical method.

Figure 5

Electric fields along $x$ axis (left) and along $z$ axis (right) of an uniform ellipsoidal beam with aspect ratio 30 from solutions of the integrated Green function method, the standard Green function method, and the analytical method.

Figure 6

Electric fields along $z$ axis of a Gaussian beam with aspect ratio 30 from solutions of the integrated Green function method and the standard Green function method.

Figure 7

Transverse (left) and longitudinal (right) rms sizes as a function of distance from the simulation using the standard and integrated Green function method.

Figure 8

Computing time of solving the 3D Poisson equation as a function of number of grid points using the FFT based integrated Green function method.

Figure 9

Transverse (left) and longitudinal (right) rms sizes as a function of distance using one, two and four slices in the simulation.

Figure 10

Speedup of the parallel implementation as a function of processor number on an IBM SP3 supercomputer.

Figure 11

Transverse normalized rms emittance as a function of distance using one slice, two slice, four slice, and eight slice model of the beam.

Figure 12

Emittance growth at the end of the injector as a function of initial misalignment of the beam.