Near-Steady Transition Waves of a Collisionless Plasma

Abstract

Plane waves of small amplitude ε in a cold plasma which propagate into an equilibrium state and the head of which approaches steadiness are studied on the basis of a one-fluid model with transverse magnetic field. Their asymptotic behavior is shown to depend on whether the limits are taken in the order ε → 0, t → ∞ or t → ∞, ε → 0. The latter, nonclassical limit is the physically relevant one, and an approach is developed which yields uniqueness results for it. It is shown that the wave must ultimately become nonlinear, and a steady solution can be approached only in a conditional sense. If the wave lowers the magnetic pressure, it must do so monotonely. If not, then it must begin with a near-periodic wave train approaching steady solutions locally, but different ones in different places.