Particle-In-Cell Simulations of a Nonlinear Transverse Electromagnetic Wave in a Pulsar Wind Termination Shock

A 2.5-dimensional particle-in-cell code is used to investigate the propagation of a large-amplitude, superluminal, nearly transverse electromagnetic (TEM) wave in a relativistically streaming electron-positron plasma with and without a shock. In the freestreaming, unshocked case, the analytic TEM dispersion relation is verified, and the streaming is shown to stabilize the wave against parametric instabilities. In the confined, shocked case, the wave induces strong, coherent particle oscillations, heats the plasma, and modifies the shock density profile via ponderomotive effects. The wave decays over $\gtrsim 10^2$ skin depths; the decay length scale depends primarily on the ratio between the wave frequency and the effective plasma frequency, and on the wave amplitude. The results are applied to the termination shock of the Crab pulsar wind, where the decay length-scale (at least 0.05") might be comparable to the thickness of filamentary, variable substructure observed in the optical and X-ray wisps and knots.