Nonlinear Landau damping of nonlocal MHD waves: Exact solutions and particle acceleration

¹ Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, 44780 Bochum, Germany
² : Department of Geological Sciences, University of South Carolina, Columbia, SC 29208, USA e-mail: black@geol.sc.edu

Corresponding author: R. Schlickeiser, r.schlickeiser@tp4.ruhr-uni-bochum.de

Received: 16 July 2001
Accepted: 27 November 2001

Abstract

In order to describe correctly the heating rate of the interstellar medium by plasma wave energy losses, we investigate the influence of non-linear amplitude effects on wave characteristics, using the Rogister-Mjølhus-Wyller equation, which is the most complete plasma kinetic description for nonlinear magnetohydrodynamic (MHD) waves propagating parallel to an ambient magnetic field. It is demonstrated (1) that any energy change arises only as a consequence of the nonlocal term in this equation, and (2) that the energy transfer rate can be evaluated in terms of quadratures dependent on the initial and/or boundary conditions imposed on exact solutions to the derivative non-linear Schrödinger equation. Moreover, the Rogister-Mjølhus-Wyller equation implies the presence of oscillatory solutions, independent of the strength of the nonlocal term, indicating that such waves play a role in the long-term evolution of the interstellar medium. These waves propagate in both positive and negative senses (depending on their wavenumbers), suggesting a bifurcation of energy flux directions at large and small spatial scales. Such a division is of significance not only for the long term behavior of the interstellar medium, but also for particle energization.