Self‐consistent Diffusive Lifetimes of Weibel Magnetic Fields in Gamma‐Ray Bursts

Abstract

Weibel filamentation in relativistic plasma shell collisions has been demonstrated as an efficient and fast mechanism for the generation of near-equipartition magnetic fields in self-consistent particle-in-cell (PIC) simulations. In generic γ-ray burst (GRB) models with kinetically dominated plasma outflow, sufficient strength and lifetime of magnetic fields are essential to validate synchrotron emission as the source of radiative outbursts. In this article we report on self-consistent PIC simulations of pair-plasma shell collisions in the highly relativistic regime with particle ensembles up to 5 × 108. Energy dependence of magnetic field generation in the Weibel process is discussed, and for the first time the diffusion-limited lifetime of magnetic fields is investigated self-consistently. In three different analyses the diffusion coefficient is determined self-consistently from the microphysical particle data. Cross-field diffusion is identified as Bohm-type by direct confirmation of the characteristic T/B-behavior. With the stability-limiting process pinned down, the lifetime of Weibel magnetic fields in plasma shell collisions subsumes to τωp0 ~ 109 (with ωp0 the plasma inertial timescale as characteristic of any system). In the context of typical synchrotron cooling times, we conclude that the Weibel fields are sufficiently long-lived for GRB prompt emission as well as afterglows, especially in view of the likely baryonic pollution of pair-plasma shells.