Nonlinear viscosity and its role in drift-Alfvén modes

Abstract

The moment approach is used to analyze the part of the magnetized plasma viscosity related to the nonlinear character of the Landau collision integral in the Boltzmann kinetic equation (nonlinear viscosity), pointed out by Catto and Simakov [Phys. Plasmas 11, 90 (2004)]. It is shown that the results of these authors, who have used an alternative procedure based on a more detailed analysis of the kinetic equation, correspond to a 15-moment approach. In comparison with the 13-moment approach (density, temperature, velocity, heat flux, and the viscosity tensor) of Grad, the 15-moment approach takes into account two higher-order moments, one of which is the vector-type moment similar to the parallel heat flux and the second is the tensor-type moment similar to the parallel projection of the viscosity tensor. Both these higher-order moments enter into the Braginskii approximation. The nonlinear viscosity calculated in the scope of the 13-moment Grad approach is qualitatively the same as that found by Catto and Simakov. Its role is investigated for drift-Alfvén modes, driven by the combined effect of the dissipative part of perpendicular heat conductivity and the standard collisional viscosity, and it is shown to be essential for the radial transport of these modes. It is shown that the wave packet of drift-Alfvén modes, propagating in the diamagnetic drift direction and driven for reversed temperature gradient, is transported down the pressure gradient. In contrast to this, the wave packet propagating in the electron diamagnetic drift direction and driven for positive temperature gradient is transported up the pressure gradient.