Effect of plasma-β on the onset of plasmoid instability in Sweet–Parker current sheets

Abstract

AbstractA numerical study of magnetic reconnection in two-dimensional resistive magnetohydrodynamics for Sweet–Parker current sheets that are subject to plasmoid instability is carried out. The effect of the initial upstream plasma-β on the critical Lundquist number Sc for the onset of plasmoid instability is studied. Our results indicate a weak dependence, with a value of Sc ≃ 1.5 × 104 in the limit of zero β, and a value of Sc ≃ 1 × 104 in the opposite high β regime (β ≫ 1). A similar dependence was previously obtained (Ni et al. 2012 Phys. Plasm. 19, 072902), but with a somewhat much larger variation, that can be largely attributed to the different configuration setup used in their study, and also to the definition of the Lundquist number. This conclusion does not depend significantly on the equilibrium used, i.e. both initial configurations with either plasma density or temperature spatial variations lead to very similar results. Finally, we show that the inner plasmoid structure appears as an under-dense hotted magnetic island, with a local temperature increase that is noticeably strengthened for low β cases.