Symplectic multiparticle tracking model for self-consistent space-charge simulation

Symplectic tracking is important in accelerator beam dynamics simulation. So far, to the best of our knowledge, there is no self-consistent symplectic space-charge tracking model available in the accelerator community. In this paper, we present a two-dimensional and a three-dimensional symplectic multiparticle spectral model for space-charge tracking simulation. This model includes both the effect from external fields and the effect of self-consistent space-charge fields using a split-operator method. Such a model preserves the phase space structure and shows much less numerical emittance growth than the particle-in-cell model in the illustrative examples.

Figure 1

Charge density distribution along the $x$ axis.

Figure 2

Electric field on $x$ axis from the above direct spectral solver (red) and from the 2nd order finite difference solver (green) (left), and the normalized relative field difference (right).

Figure 3

RMS envelope evolution of the beam.

Figure 4

Stroboscopic plot (every 10 periods) of phase space evolution of a test particle from the symplectic-spectral model (top) and from the PIC-finite difference model (bottom).

Figure 5

Four dimensional emittance growth evolution from the symplectic multiparticle spectral model (red) and from the PIC finite difference model(green).

Figure 6

The transverse (left) and longitudinal (right) density profiles of a 3D bunched beam.

Figure 7

Relative transverse electric field difference along x-axis (left) and longitudinal electric field difference along z-axis (right) from the gridless spectral method and the spectral-finite difference solver.

Figure 8

Transverse (left) and longitudinal (right) RMS envelope evolution of the bunched beam inside a periodic focusing channel.

Figure 9

Six-dimensional rms emittance growth evolution in the periodic channel from the symplectic spectral model (red) and from the PIC (green).

Figure 10

Parallel speedup of the 2D and the 3D symplectic tracking models on a Cray XC30 computer.