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

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 CFL number of 1.0. The present result contrasts with recently reported results (Vay et al., 2011; Godfrey & Vay,2013) 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.

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N. Ikeya and Y. Matsumoto
Tue, 9 Dec 14

Comments: 12 pages, 8 figures