Spontaneous decay of periodic magnetostatic equilibria

TL;DR

This paper investigates the stability of a class of periodic magnetostatic equilibria in relativistic plasmas, revealing their inherent instability and potential to produce energetic phenomena relevant to gamma-ray sources.

Contribution

It demonstrates the instability of uniform-alpha magnetostatic equilibria through numerical analysis and explores their nonlinear evolution, highlighting their relevance to cosmic gamma-ray sources.

Findings

Equilibria are unstable to ideal modes with exponential growth.

Unstable modes involve merging magnetic and current structures.

Solutions develop relativistic velocities and strong electric fields, releasing magnetic energy rapidly.

Abstract

In order to understand the conditions which lead a highly magnetized, relativistic plasma to become unstable, and in such cases how the plasma evolves, we study a prototypical class of magnetostatic equilibria where the magnetic field satisfies $\nabla \times\mathbf B = \alpha \mathbf B$, where $\alpha$ is spatially uniform, on a periodic domain. Using numerical solutions we show that generic examples of such equilibria are unstable to ideal modes (including incompressible ones) which are marked by exponential growth in the linear phase. We characterize the unstable mode, showing how it can be understood in terms of merging magnetic and current structures, and explicitly demonstrate its instability using the energy principle. Following the nonlinear evolution of these solutions, we find that they rapidly develop regions with relativistic velocities and electric fields of comparable magnitude to the magnetic field, liberating magnetic energy on dynamical timescales and eventually settling into a configuration with the largest allowable wavelength. These properties make such solutions a promising setting for exploring the mechanisms behind extreme cosmic sources of gamma rays.