For two-dimensional reconnection in a thin Harris current sheet, fluid–ion dynamics from a Hall-magnetohydrodynamics (Hall-MHD) calculation using a scalar ion pressure are compared to the particle–ion dynamics obtained from a hybrid simulation and from test ions that are advanced in Hall-MHD fields. Skewed ion velocity distributions from the particle calculations are shown to produce off-diagonal elements of the ion pressure tensor. These comparisons demonstrate that the inclusion of off-diagonal terms in the ion pressure tensor is important to correctly model the ion out-of-plane momentum transport from the X point. It is shown that these effects can be modeled efficiently in Hall-MHD simulations in a predictor–corrector manner that uses particle ions to implement the ion gyro-radius corrections. By advancing test ions in the Hall-MHD fields at every time step, accumulating the ion pressure tensor onto the spatial grid, and adding its divergence to the ion momentum equation, this particle Hall-MHD simulation models well the ion out-of-plane momentum transport from the X point.

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