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NASA NTRS1993

Collisionless parallel shocks

Consideration is given to a collisionless parallel shock based on solitary-type solutions of the modified derivative nonlinear Schroedinger equation (MDNLS) for parallel Alfven waves. The standard derivative nonlinear Schroedinger equation is generalized in order to include the possible anisotropy of the plasma distribution and higher-order Korteweg-de Vies-type dispersion. Stationary solutions of MDNLS are discussed. The anisotropic nature of 'adiabatic' reflections leads to the asymmetric particle distribution in the upstream as well as in the downstream regions of the shock. As a result, nonzero heat flux appears near the front of the shock. It is shown that this causes the stochastic behavior of the nonlinear waves, which can significantly contribute to the shock thermalization.

Khabibrakhmanov, I. KH.↗

NASA NTRS1992

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.

Khabibrakhmanov, I. KH.↗