Quasi-wave trains in a cold collisionless plasma

Abstract

Non-linear hydromagnetic waves in a cold collisionless plasma are investigated by numerical and analytic methods. For this problem, Saffman has already implied that there may exist a non-periodic wave different from the well-known solitary wave (or wave train). His analysis is based on the assumption that the quasi-ergodic theorem can be applied to the present problem. However, the propriety of the assumption has not been discussed.It is seen from the computer calculations that in general the waves do not have periodicity, as Saffman pointed out. Furthermore, some concrete examples show the behaviour of these ergodic waves more clearly. The width of the waves is of the order of ion Larmor radius. These waves are here called quasi-wave trains. In some special cases, the waves reduce to wave trains (with periodicity). Some of them have a length scale of the geometric mean between the Larmor radii of the electron and of the ion.