NONLINEAR ALFVEN-WAVE PROPAGATION IN NONHOMOGENEOUS COLLISIONLESS MEDIA

A collisionless model of nonlinear Alfven wave propagation in a nonhom ogeneous medium is formulated in terms of two amplitude equations for the slow plasma parameters, the only fast parameter being the transver se component of the unit vector along the local magnetic field. The mo del includes plasma pressure anisotropy and takes into account the rel ative motion of the plasma components along the magnetic field, effect s which have hitherto not been considered in a self-consistent manner. Exact one-dimensional solutions are found under the restriction that the magnetic field, bulk plasma velocity vectors, and propagation dire ction all remain in the same plane. It is shown that these solutions r educe exactly to the standard WKB approximate solution, i.e., it is sh own that the WKB solutions are, in fact, exact under the above stated restriction. The. restriction is not related to the limitations of the WKB approximation, but merely specifies the mode of the propagating w ave. This exact solution can be used as a zero-order approximation for the investigation of the stability of finite-amplitude Alfven waves. Thermal corrections to the wave amplitude solution are obtained as wel l as to the bulk plasma momentum equation. The wave amplitude solution shows that direct exchange of the Alfven wave energy with the kinetic energy of the particles is possible.