Fluid Models for Kinetic Effects on Coherent Nonlinear Alfvén Waves I: Fundamental Theory

Collisionless regime kinetic models for coherent nonlinear Alfvén wave dynamics are studied using fluid moment equations with an approximate closure anzatz. Resonant particle effects are modelled by incorporating an additional term representing dissipation akin to parallel heat conduction. Unlike collisional dissipation, parallel heat conduction is presented by an integral operator. The modified derivative nonlinear Schrödinger equation thus has a spatially nonlocal nonlinear term describing the long-time evolution of the envelope of parallel-propagating Alfvén waves, as well. Coefficients in the nonlinear terms are free of the (1− β) singularity usually encountered in previous analyses, and have very a simple form which clarifies the physical processes governing the large amplitude Alfvénic nonlinear dynamics. The nonlinearity appears via coupling of an Alfvénic mode to a kinetic ion-acoustic mode. Damping of the nonlinear Alfvén wave appears via strong Landau damping of the ion-acoustic wave when the electron-to-ion temperature ratio is close to unity. For a (slightly) obliquely propagating wave, there are finite Larmor radius corrections in the dynamical equation. This effect depends on the angle of wave propagation relative to B0 and vanishes for the limit of strictly parallel propagation. Explicit magnetic perturbation envelope equations amenable to further analysis and numerical solution are obtained. Implications of these models for collisionless shock dynamics are discussed. PACS numbers: 52.35.Mw, 52.30.-q, 96.50.Ek † Also: Russian Research Centre “Kurchatov Institute”, Institute for Nuclear Fusion, Moscow 123182, RUSSIA. ‡ Also: General Atomics, San Diego, California 92122.