Plasmoid instability in the semi-collisional regime*

Theoretical and numerical investigations were performed to validate the existence of the semi-collisional regime, which is unstable to plasmoids, in the magnetic reconnection phase space; governed by Lundquist number S and system size L in units of ion (sound) Larmor radius, ρ_s/L. The semi-collisional regime of the plasmoid instability is defined by the inequality δ_SP  >> ρ_s >> δ_in, where δ_SP is the width of a Sweet-Parker current sheet, and δ_in is the width of the boundary layer that arises in the plasmoid instability analysis. This inequality translates to theoretically predicted bounds, given by (L/ρ_s)^14/9 < S < (L/ρ_s)² (for a sinusoidal-like magnetic configuration; for a Harris-type sheet the lower bound is replaced with (L/ρ_s)^8/5). 
These bounds are validated numerically using a reduced gyrokinetic model (Zocco & Schekochihin, Physics of Plasmas, 18, 2011) conducted with the code Viriato. Importantly, this regime is shown to allow for plasmoid formation at relatively low, experimentally accessible, values of the Lundquist number.  Our simulations obtain plasmoid instability at values of S as low as ∼250.