Hybrid simulation of space plasmas: Models with massless fluid representation of electrons. II. Slow and intermediate shocks

Abstract

This is a second article in a series of reviews on hybrid simulation of low-frequency processes in space plasmas. A hybrid model is described with ions represented by particles and electrons by a massless fluid. The main numerical schemes for the implementation of this model are described: the generalized Ohm law scheme and the predictor-corrector scheme. The first part of the article provides basic background information: MHD models (ideal, resistive, and Hall model); the Rankine-Hugoniot relationship for MHD discontinuities; the Hoffman-Teller coordinate system; and a classification of discontinuities. The review part of the article surveys the literature on simulation of slow shocks (including switch-off shocks) and intermediate shocks. The survey of literature on hybrid simulation of intermediate shocks is concluded with a review of studies that use two different numerical codes (the hybrid model and the resistive Hall MHD model). The computation results produced by the two codes are compared. The concluding part presents some remarks concerning the existence of intermediate shocks and their relationship with rotational discontinuities in various numerical models (ideal MHD, resistive MHD, the hybrid model).

Simulation of Space Plasma Allowing for the Hall Effect: Magnetic Reconnection

“…The fields and the electron dynamics are modeled by the following equations: The first term in the right-hand side of (11.2) describes the Hall effect and introduces the length scale δ i , which appears implicitly through variable normalization in (2). Electron inertia enters Ohm's law (11.2) also implicitly (through the term proportional to δ e 2 in the definition of ′ B (11.3)).…”