On hydromagnetic waves of finite amplitude in a cold plasma

Abstract

The existence of steady, one-dimensional, finite-amplitude waves in a cold collison-free plasma is investigated for the case in which the plasma and the magnetic field are uniform far ahead of the wave. It is supposed that the magnetic field at infinity is inclined at an angle β to the direction normal to the plane of the waves (0 ≤ β ≤ ½π). It is shown that the problem is equivalent to determining the orbits of a particle in a uniformly rotating field of force. Two types of waves are found to exist for β ≠ 0: solitary waves and quasishocks. In a quasi-shock, the plasma and magnetic field oscillate irregularly behind the wave front about mean values, which are different from the values ahead of the wave. The width of the wave front is of the order of the ion gyroradius. The quasi-shocks resemble oblique magnetohydrodynamic shock-waves. For the case β = 0, only solitary waves exist, which have already been described (Saffman 1961). The stability of the waves is considered, and it is concluded that the quasishocks are stable but that the solitary waves for β ≠ 0 are unstable.