A numerical study of tearing instability growth rate as a function of current sheet thickness in the kinetic regime

In this study, we use fully kinetic Particle In Cell (PIC) simulations to investigate numerically the dispersion relation of the tearing instability in the kinetic regime, which is at the moment rather poorly explored by theoretical investigations. To reduce the computational cost of the simulations, we use the the semi-implicit, energy conserving ECsim code (Lapenta et al, 2017), that allows us to step over the smaller scales and fastest frequencies and focus on characteristic scales of interest, with excellent energy conservation.

We run several simulations with current sheets of fixed length. The current sheet half-thickness is progressively increased from $\delta \sim d_i$ to significantly larger. The other simulation parameters are kept identical.

In our simulations, the tearing instability grows without external perturbation from the particle noise of PIC simulations. Later onset times are (predictably) observed when the number of particles per cell is increased.

Several modes grow unstable in each simulation. We plot the growth rates of the unstable modes as a function of the current sheet thickness. We obtain a spread around a curve decreasing with increasing current sheet thickness.