Time Integration of the Field and Electron Pressure Equations

Abstract

The integration in time of the electromagnetic field equations is an important part of the hybrid simulation The induction equation contains four main terms which describe the following processes First of all a convection of the magnetic field is conditioned by a macroscopic flux of plasma The so-called Hall term may generate the low-frequency waves, namely, Alfvén waves, helicons, and a whistler, and the formation of so-called magnetic barriers, the magnetopause, overshoots at the shock fronts etc The term with the anomalous resistivity may cause dissipation effects: heating of electrons at the shocks and widening of the shock fronts The anomalous resistivity may also play a crucial role in the magnetic field reconnection The electron pressure gradient term plays an important role at the plasma discontinuities Our discrete model must describe all of the processes as well as the initial differential induction equation So we have to make a good finite-difference approximation for the main terms: the convection term, the dispersion (Hall) term, the resistance term, and the electron pressure gradient term The hybrid model also includes the electron inertia term, so we have to make a good approximation for this term as well The approximation of the convective term, the diffusion term, and the electron pressure gradient has been discussed widely in the papers and books on computational hydrodynamics.