Kinetic treatment of nonlinear magnetized plasma motions - General geometry and parallel waves

The expansion of kinetic equations in the limit of a strong magnetic field is presented. This gives a natural description of the motions of magnetized plasmas, which are slow compared to the particle gyroperiods and gyroradii. Although the approach is 3D, this very general result is used only to focus on the parallel propagation of nonlinear Alfven waves. The derivative nonlinear Schroedinger-like equation is obtained. Two new terms occur compared to earlier treatments, a nonlinear term proportional to the heat flux along the magnetic field line and a higher-order dispersive term. It is shown that kinetic description avoids the singularities occurring in magnetohydrodynamic or multifluid approaches, which correspond to the degenerate case of sound speeds equal to the Alfven speed, and that parallel heat fluxes cannot be neglected, not even in the case of low parallel plasma beta. A truly stationary soliton solution is derived.