A fluid description for Landau damping of dispersive MHD waves

Abstract

Abstract. The dynamics of long oblique MHD waves in a collisionless plasma permeated by a uniform magnetic field is addressed using a Landau-fluid model that includes Hall effect and electron-pressure gradient in a generalized Ohm's law and retains ion finite Larmor radius (FLR) corrections to the gyrotropic pressure (Phys. Plasmas 10, 3906, 2003). This one-fluid model, built to reproduce the weakly nonlinear dynamics of long dispersive Alfvén waves propagating along an ambient field, is shown to correctly capture the Landau damping of oblique magnetosonic waves predicted by a kinetic theory based on the Vlasov-Maxwell system. For oblique and kinetic Alfvén waves (for which second order FLR corrections are to be retained), the linear character of waves with small but finite amplitudes is established, and the dispersion relation reproduced in the regime of adiabatic protons and isothermal electrons, associated with the condition m e /m p β T e /T p , where β is the squared ratio of the ion-acoustic to the Alfvén speeds. It is shown that in more general regimes, the heat fluxes are, to leading order, not gyrotropic and dependent on the Hall effect to leading order.

Landau-fluid simulations of Alfvén-wave instabilities in a warm collisionless plasma

“…This model was extended in Sulem (2003b, 2004b) by including dispersive effects, required to describe the formation of solitonic structures currently observed in the solar wind and the magnetosphere. This dispersive Landau fluid was demonstrated to accurately reproduce the dispersion relations and Landau damping rates of long-wavelength magnetosonic and Alfvén waves for any β larger than the electron to proton mass ratio m e /m p and any propagation angle α, including kinetic Alfvén waves with a transverse wavenumber not exceeding the inverse proton inertial length (Passot and Sulem, 2004a). This model also reproduces the weakly nonlinear dynamics of these waves.…”

Low-frequency linear waves and instabilities in uniform and stratified plasmas: the role of kinetic effects

“…With this closure, Passot and Sulem's (2003) model yields the same response functions as the more cumbersome 4+2 model of Snyder et al (1997). Moreover, although it was initially designed to accurately describe the weakly nonlinear dynamics of dispersive long parallel Alfvén waves, it is also able to correctly reproduce the Landau damping of long oblique magnetosonic waves, and it can be used to study oblique and kinetic Alfvén waves in the regime of adiabatic protons and isothermal electrons, subject to the additional condition that the Alfvén speed be much higher than the proton thermal speed and much lower than the electron thermal speed (see Passot and Sulem, 2004). …”

Landau fluid model for weakly nonlinear dispersive magnetohydrodynamics

“…This nonlinear wave equation correctly captures modulational instabilities, including transverse ones [27], but parametric instabilities are outside their scope. Performing the same asymptotic expansion on the dispersive Landau-fluid model, leads to the same KDNLS equation up to the replacement of the plasma response function by its two or four pole Padé approximants [23,28]. This shows that the Landau fluid model is also valid in the weakly nonlinear regime for modulational-type instabilities.…”