Finite Larmor radius magnetohydrodynamics of the Rayleigh–Taylor instability

Abstract

The evolution of the Rayleigh–Taylor instability is studied using finite Larmor radius (FLR) magnetohydrodynamic (MHD) theory. Finite Larmor radius effects are introduced in the momentum equation through an anisotropic ion stress tensor. Roberts and Taylor [Phys. Rev. Lett. 3, 197 (1962)], using fluid theory, demonstrated that FLR effects can stabilize the Rayleigh–Taylor instability in the short-wavelength limit (kLn≫1, where k is the wave number and Ln is the density gradient scale length). In this paper a linear mode equation is derived that is valid for arbitrary kLn. Analytic solutions are presented in both the short-wavelength (kLn≫1) and long-wavelength (kLn≪1) regimes, and numerical solutions are presented for the intermediate regime (kLn∼1). The long-wavelength modes are shown to be the most difficult to stabilize. More important, the nonlinear evolution of the Rayleigh–Taylor instability is studied using a newly developed two-dimensional (2-D) FLR MHD code. The FLR effects are shown to be a stabilizing influence on the Rayleigh–Taylor instability; the short-wavelength modes are the easiest to stabilize, consistent with linear theory. In the nonlinear regime, the FLR effects cause the ‘‘bubbles and spikes’’ that develop because of the Rayleigh–Taylor instability to convect along the density gradient and to tilt. Applications of this model to space and laboratory plasma phenomena are discussed.