Relativistic Plasmoid Instability in Pair Plasmas

Abstract

The problem of plasmoid instability in relativistic pair plasmas is investigated with a fluid model incorporating kinetic effects through thermal inertia, where both parallel modes and oblique modes are discussed. The dimensionless parameters, Lundquist number and electron skin depth, are found to determine the growth rate of the linear plasmoid instability as well as set the division among different parameter regimes. The onset and cascade of plasmoids are described, with two limits specified: plasmoid instability stemming from a Sweet–Parker-like steady-state current sheet, and the near-ideal limit where the current sheet breaks up on the way to a steady state. The tearing growth rate in evolving current sheets in the near-ideal regime well accounts for the sudden onset of the plasmoid instability. The regimes in between are characterized by modifications to the ideal limit, through which a continuous scaling law is established connecting the two limits. Scaling laws are obtained for the onset as well as the cascading process, and the cascade model in this paper predicts the critical parameters for the onset of plasmoid instability.