Anisotropic dissipative effects on the buoyancy instability with background heat flux

Abstract

The linear buoyancy instability in magnetized plasmas is investigated in the presence of anisotropic resistivity and viscosity by taking into account the background heat flux. The magnetic field is assumed to be homogeneous and has both horizontal and vertical components. The heat is primarily transported along the magnetic force lines when the gyro radius is much less than the mean collision free path. The Hall term is examined first and shows a damping effect on the magnetothermal instability. The heat-flux-driven buoyancy instability (HBI) is then investigated by taking into account the parallel resistivity (PR), cross-field resistivity (CR), and the anisotropic viscosity. The general dispersion relation (DR) is derived and discussed in several special cases. We show that only the CR and viscosity exert effects on the DR in the first case. The critical condition for the occurrence of HBI is modified by the CR coupled with the viscosity and the value of the instability growth rate is diminished by them. The effects due to the PR (resp. viscosity) on the HBI are examined next. The PR (resp. viscosity) is shown to alter not only the growth rate but also the instability criterion. There exists an unstable mode when the temperature decreases in the direction of gravity while this case is proven to be magnetothermally stable in the ideal magnetohydrodynamic limit. A new unstable mode is solely induced by the presence of PR (resp. viscosity). When the PR and CR are both taken into account, the resistivity is shown to induce a damping mode rather than an instability. Finally, considering the PR and viscosity simultaneously, it is found that a new unstable mode is excited when the PR is not equal to the viscosity, or else, dissipation effects do not alter the instability criterion and just cut down the growth rate.