A PIC Simulation Method for Ultra-Long-Range Transport of High-Energy Charged Particle Beams

In some situation where precise simulation of phase space or radius of beam are necessary during the propagation of charged particle beams, we must include the effects of space charge forces on the beam. However, for the commonly used particle-in-cell(PIC) algorithm in those situation, directly solving the static electromagnetic field based on particle distribution and current distribution will lead to a poor accuracy of simulation results because retarded potential was not considered. While calculating retarded potential directly in the laboratory frame will result in a very high computing cost. Here we propose a simulation method based on relativistic coordinate system transformation for high-energy particle beam propagation. In this method, the particles and external electromagnetic fields are transformed to the beam rest frame where the PIC method are carried out, and the results are transformed back to the laboratory frame finally. Because of coordinate transformation, the influence of retarded potential can be reduced, and the simulation will require shorter propagation time and smaller modeling domain with a ratio of nearly one in relativity factor γ. Therefore, using this simulation method will greatly reduce the computational cost of beam transmission and achieve higher computational accuracy for simulation of propagation.