Weak Nonlinear Magneto-Acoustic Waves in a Cold Plasma in the Presence of Effective Electron-Ion Collisions

Abstract

Nonlinear perturbation method is applied to describe the behaviour of unsteaby magneto-acoustic waves of small but finite amplitude propagating in a cold plasma in the presence of effective electron-ion collisions.
It is shown under an assumption of small effective collision frequency that the original system of equations can be reduced to a single nonlinear equation which has a combined form of the Korteweg-de Vries and the Burgers equations. The dispersion term is just the same as that of collisionless case, whereas the dissipation term is found to be proportional to the magnetic viscosity. A qualitative discussion is given concerning the steady solutions of this equation.