Plasmoid instability in the semi-collisional regime

We investigate analytically and numerically the semi-collisional regime of the plasmoid instability, defined by the inequality $δ_{SP} \gg ρ_s \gg δ_{in}$, where $δ_{SP}$ is the width of a Sweet-Parker current sheet, $ρ_S$ is the ion sound Larmor radius, and $δ_{in}$ is width of boundary layer that arises in the plasmoid instability analysis. Theoretically, this regime is predicted to exist if the Lundquist number $S$ and the length of the current sheet $L$ are such that $(L/ρ_S)^{14/9} < S