Particle Hall-MHD simulation of collisionless reconnection: Ion gyro-radius correction

Fluid-ion dynamics from a Hall-MHD calculation and test ions that are advanced in Hall-MHD fields are compared to particle-ion dynamics from a hybrid simulation of two-dimensional reconnection in a thin current sheet. These comparisons demonstrate that off-diagonal terms of the ion pressure tenser are important to correctly model the ion out-of-plane momentum transport from the X point. These effects can be efficiently modeled in Hall-MHD simulations by advancing test ions in the Hall-MHD fields, accumulating the pressure tenser onto the spatial grid, and modifying the ion momentum equation. With ion gyro-radius corrections, the "particle Hall-MHD" simulation is shown to model accurately the ion out-of-plane momentum transport from the X point and the reconnection rate comparison with the hybrid simulation is improved.