Finite Amplitude Compression Waves in a Collision-Free Plasma

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Abstract
One-dimensional compression waves in a collision-free plasma are studied using the adiabatic two-fluid model. It is supposed that an initial magnetic field makes an arbitrary angle θ with the direction of wave propagation and ε2 denotes the electron-ion mass ratio. An extensive study of the steady flows is carried out which is particularly full in the limiting cases ε = 0 or 1; the effect of introducing a friction term in the equations is also considered. Then an asymptotic treatment is found to provide a simple but qualitatively correct picture of the dependence of small amplitude waves on ε and θ between these extremes. Finally the picture is filled in by solving the piston problem numerically. It is found that two types of wave occur: roughly when tan θ > ε−1 − ε, the usual flow consists of a main wavefront followed by an oscillatory wave train; while, in the contrary case, the wave front is preceded by an oscillatory precursor. This precursor is on the scale of the ion gyromagnetic radius while the wave train scales like the geometric mean of this and the electron gyro-radius.