Plasmoid instability in the semi-collisional regime

TL;DR

This paper analytically and numerically studies the semi-collisional plasmoid instability regime, predicting its existence at lower Lundquist numbers and validating it through gyrokinetic simulations, with implications for experimental observation.

Contribution

It introduces and validates the semi-collisional regime of plasmoid instability, showing it occurs at lower Lundquist numbers than previously thought, using reduced gyrokinetic simulations.

Findings

Plasmoid instability occurs at Lundquist numbers as low as ~250.

The semi-collisional regime exists within specific bounds of S related to L and ρ_S.

Self-consistent formation of current sheets during nonlinear evolution was demonstrated.

Abstract

We investigate analytically and numerically the semi-collisional regime of the plasmoid instability, defined by the inequality $\delta_{SP} \gg \rho_s \gg \delta_{in}$, where $\delta_{SP}$ is the width of a Sweet-Parker current sheet, $\rho_S$ is the ion sound Larmor radius, and $\delta_{in}$ 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 $(L/\rho_S)^{14/9} < S <(L/\rho_S)^2$ (for a sinusoidal-like magnetic configuration; for a Harris-type sheet the lower bound is replaced with $(L/\rho_S)^{8/5}$). These bounds are validated numerically by means of simulations using a reduced gyrokinetic model (Zocco & Schekochihin, $\it{Physics~of~Plasmas}$, ${\bf 18}$, 2011) conducted with the code $\tt{Viriato}$. Importantly, this regime is conjectured 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 $\sim 250$. The simulations do not prescribe a Sweet-Parker sheet; rather, one is formed self-consistenly during the nonlinear evolution of the initial tearing mode configuration. This proves that this regime of the plasmoid instability is realizable, at least at the relatively low values of the Lundquist number that are accessible to current dedicated experiments.