Steady non-linear waves in a warm collision-free plasma

We describe the speed and structure of steady non-linear waves moving with uniform velocity in an oblique direction across a magnetic field in a collision-free plasma with temperature. This is a self-consistent formulation in which the plasma motion is governed by the Vlasov equation for ions and electrons coupled to the Poisson-Maxwell equations. This difficult problem can be solved in the Iimiting case of small-amplitude non-linear waves if we assume that the same scaling laws hold for the warm plasma as those for a cold plasma. This work was done under the auspices of the U.S. Atomic Energy Commission