Kinetic simulations of the lowest-order unstable mode of relativistic magnetostatic equilibria

Abstract

We present the results of particle-in-cell numerical pair plasma simulations of relativistic 2D magnetostatic equilibria known as the 'ABC' fields. In particular, we focus on the lowest-order unstable configuration consisting of two minima and two maxima of the magnetic vector potential. Breaking of the initial symmetry leads to exponential growth of the electric energy and to the formation of two current layers, which is consistent with the picture of 'X-point collapse' first described by Syrovatskii. Magnetic reconnection within the layers heats a fraction of particles to very high energies. After the saturation of the linear instability, the current layers are disrupted and the system evolves chaotically, diffusing the particle energies in a stochastic second-order Fermi process leading to the formation of power-law energy distributions. The power-law slopes harden with the increasing mean magnetization, but they are significantly softer than those produced in simulations initiated from Harris-type layers. The maximum particle energy is proportional to the mean magnetization, which is attributed partly to the increase of the effective electric field and partly to the increase of the acceleration time scale. We describe in detail the evolving structure of the dynamical current layers, and report on the conservation of magnetic helicity. These results can be applied to highly magnetized astrophysical environments, where ideal plasma instabilities trigger rapid magnetic dissipation with efficient particle acceleration and flares of high-energy radiation.