Suppression of errors in simulated ultrarelativistic bunch propagation using the X-dispersionless Maxwell solver

Abstract

Because of the inherent value of high-energy particle beams for the study of quantum electrodynamics effects, it is of great importance to accurately model the physics in numerical simulations. Numerical effects may alter the dynamics of a simulation and may change the physics of energy losses on account of the radiation reaction (RR) force. In this work, the numerical Cherenkov effect in combination with the RR force are analyzed in the vacuum propagation of an ultrarelativistic electron bunch. It is revisited that the use of the standard Yee solver in the present setup triggers the numerical Cherenkov instability. With the instability at hand, the simulation results of the Yee solver are compared to data obtained by the X-dispersionless Maxwell solver, also known as the rhombi-in-plane (RIP) solver. There, the numerical instability is suppressed by several orders of magnitude. Afterward, the impact of radiation reaction on the dynamics is studied for both cases. It is shown that the combination of the Yee solver and the RR force enhances the error significantly and the electron bunch loses about 90% of its energy as a result. These huge energy losses can be observed only if both the Lorentz force and the RR force are enabled in the code. In contrast, the RIP Maxwell solver is not plagued by these issues and accurately calculates the dynamics of the electron bunch.