Stability Property of Numerical Cherenkov Radiation and its Application to Relativistic Shock Simulations

We studied the stability property of numerical Cherenkov radiation in relativistic plasma flows employing particle-in-cell simulations. Using the implicit finite-difference time-domain method to solve Maxwell equations, we found that nonphysical instability was greatly inhibited with a Courant-Friedrichs-Lewy (CFL) number of 1.0. The present result contrasts with recently reported results (Vay, J. L., et al. 2011, J. Comp. Phys, 230, 5908; Godfrey. B., & Vay, J. L. 2013, J. Comp. Phys, 243, 260; Xu, X., et al. 2013, Comput. Phys. Commun, 184, 2503) in which magical CFL numbers in the range 0.5-0.7 were obtained with explicit field solvers. In addition, we found employing higher-order shape functions and an optimal implicitness factor further suppressed long-wavelength modes of the instability. The findings allowed the examination of the long-term evolution of a relativistic collisionless shock without the generation of nonphysical wave excitations in the upstream. This achievement will allow us to investigate particle accelerations in relativistic shocks associated with, for example, gamma-ray bursts.