Multifluid equations for MHD

The derivation proceeds to explicitly calculate the Lorentz force resulting from the small ion drift velocities. The net effect is that in this limit all the ions move perpendicular to the magnetic field with the same speed, but are free‐streaming relative to one another in the parallel direction.

The ions couple one to another in the parallel direction from changes in the magnetic field direction, leading to a collision‐like term that, however, maintains a constant total kinetic energy. The equations governing parallel (centrifugal) acceleration, which may be an important process for ionospheric outflow, are then derived. The dispersion relation for a two‐species, isotropic fluid with arbitrary mass and charge fractions, as well as electron pressure, is derived and the resulting wave modes are analyzed.