2. Basic equations
where the current density, , and the charge density, s, have to be calculated using a suitable mathematical model of the plasma. The most popular models are based on the ideal MHD equations, the two-fluid MHD equations, and kinetic Vlasov equations.
As discussed in the Introduction, we use the mathematical model of two-fluid MHD in order to take into account some important linear and nonlinear effects in the low-frequency short-scale AWs. In two-fluid MHD the electron and ion fluids are allowed to move in separate ways, but are coupled by collective electromagnetic fields and by the electron-ion friction force. The equations of motion for the electrons and ions are:
where is the ion/electron pressure, (but we do not require ). The parallel friction force, , responsible for the (parallel) resistivity along , is
where is the electron collision frequency.
Note that we have dropped the perpendicular friction force, responsible for the perpendicular resistivity, because its contribution in the wave dissipation is times smaller than contribution of the parallel resistivity ( and are the parallel and perpendicular wavelengths).
where the subscript s denotes particles species, .
© European Southern Observatory (ESO) 2000
Online publication: June 5, 2000