Hybrid codes (massless electron fluid)

Hybrid codes are widely used to model ion-scale phenomena in space plasmas. Hybrid codes differ from full particle (PIC) codes in that the electrons are modeled as a fluid that is usually assumed to be massless, while the electric field is not advanced in time, but instead calculated at the new time level from the advanced ion quantities and the magnetic field. In this chapter we concentrate on such hybrid models with massless electrons, beginning with a discussion of the basics of a simple hybrid code algorithm. We then show examples of recent use of hybrid codes for large-scale space plasma simulations of structures formed at planetary bow shock--foreshock systems, magnetic reconnection at the magnetopause, and complex phenomena in the magnetosheath due to the interaction of kinetic processes associated with the bow shock, magnetic reconnection, and turbulence. A discussion then follows of a number of other hybrid codes based on different algorithms that are presently in active use to investigate a variety of plasma processes in space as well as some recent work on the development of new models. We conclude with a few brief comments concerning the future development and use of hybrid codes.