Two-fluid code

As a third alternative besides the full particle mode and the hybrid mode the code can be run as a two-fluid code. The electrons are described by the same set of equations as in the hybrid code whereas the particle ions are replaced by an additional set of fluid equations. As in the hybrid case the Helmholtz equation is solved with a multigrid algorithm.

Equations

As in the hybrid model the dynamics of the electron fluid and the magnetic field is given by (compare M. A. Shay, J. F. Drake, B. N. Rogers, Journal of Geophys. Res. 106, 3759, 2001)

with the electron skin depth d_e. The ion fluid equations are

with an isotropic pressure as in the electron case.

Numerical algorithms

All quantities in the two-fluid model are advanced with the trapezoidal leapfrog algorithm. The inversion of the Helmholtz equation is performed with the multigrid algorithm described in the full particle code.