Fluid models for kinetic effects on coherent nonlinear Alfvacute en waves. I. Fundamental theory

Collisionless regime kinetic models for coherent nonlinear Alfvacute en wave dynamics are studied using fluid moment equations with an approximate closure anzatz. Resonant particle effects are modeled 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 Schroedinger equation thus has a spatially nonlocal nonlinear term describing the long-time evolution of the envelope of parallel-propagating Alfvacute en waves, as well. Coefficients in the nonlinear terms are free of the (1-β)-1 singularity usually encountered in previous analyses, and have a very simple form that clarifies the physical processes governing the large-amplitude Alfvacute enic nonlinear dynamics. The nonlinearity appears via coupling of an Alfvacute enic mode to a kinetic ion-acoustic mode. Damping of the nonlinear Alfvacute en 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. copyright 1996 American Institute of Physics