Ion Acceleration and the Development of a Power-law Energy Spectrum in Magnetic Reconnection

Abstract

How charged particles are accelerated efficiently and form a power-law energy spectrum in magnetic reconnection is a problem that is not well understood. In a previous paper, it was shown that the electron Kelvin–Helmholtz instability (EKHI) in force-free magnetic reconnection generates fast-expanding vortices that can accelerate electrons in a few tens of ion gyroperiods (less than 1 ms in the solar corona) to form a power-law energy distribution. In this paper, we present a particle-in-cell (PIC) simulation study of ion acceleration in force-free magnetic reconnection in the presence of the EKHI-induced turbulence. We find that ions are not significantly accelerated by the EKHI-induced stochastic electric field until the magnetic vortices expand to sizes comparable to the ion gyroradius. The Alfvén waves generated by the EKHI couple with the magnetic vortices, leading to resonance between the ions inside the magnetic vortices and Alfvén waves and enhanced ion heating. The induced Alfvén wave resonance results in a broken power-law energy spectrum with a breakpoint at ∼ m i v A 2 , where v A is the Alfvén velocity. We show that the process that forms the nonthermal tail is a second-order Fermi mechanism and the mean spectral index is α = (1 + 4 a 2 D / R )/2, where D is the spatial scale of the inductive electric field, R is that of vortices, and a = B g / B 0 , with ratio of guide field B g and asymptotic B 0 .