Anomalous viscosity due to drift wave turbulence

The transport matrix, due to low-frequency microturbulence, is obtained for a cylindrical plasma including anomalous ion and electron viscosities. Quasilinear theory is used in the electrostatic limit. Particle, momentum, and energy fluxes are represented in terms of three thermodynamical forces, which are generated by the density gradient, the gradient of the parallel flow, the temperature gradient, radial electric field, and the convection of the wave. The characteristics of the matrix are examined. The 3x3 transport matrices for electrons and ions are symmetric but contain off-diagonal elements. In the drift wave approximation, the ion flux decouples from the thermodynamical force on the electrons, and vice versa. The ion anomalous viscosity, the heat conductivity, and the off-diagonal elements are found to be comparable. The anomalous electron viscosity due to the drift wave is calculated to be small. The transport equations of ions show that pure heat conductivity, which is the value when the net particle flux is zero, is small compared to the heat conductivity [i.e., (3,3) component of the transport matrix]. The anomalous viscosity gives rise to an additional heating on the ions because of viscous damping. The condition for a particle pinch to occur is also examined. If the convection of the wave is neglected, an inward pinch of ions against the density gradient is caused by the electric field, while that of the electrons is due to the electron temperature gradient.