Extending the collisional fluid equations into the long mean-free-path regime in toroidal plasmas. II. Frequency dependence

Abstract

In Part I [K. C. Shaing and D. A. Spong, Phys. Fluids B 2, 1190 (1990)], an expression for the pressure anisotropy that is valid in the plateau regime is derived from the linear drift kinetic equation that is driven by the plasma flows. To apply this expression to investigate the magnetohydrodynamic instabilities, a more general frequency-dependent pressure anisotropy is calculated here for both the plateau regime and the collisional fluid regime for toroidal plasmas with arbitrary symmetry property. It is found that when the growth rate of the mode is larger than the typical particle transit frequency and the collision frequency, the pressure anisotropy scales inversely with the mode growth rate instead of the collision frequency. It is also shown that when νk in Eqs. (6) and (7) of a previous paper [K. C. Shaing, Phys. Fluids B 5, 3841 (1993)] is replaced by (νk+γ), equilibrium time-dependent plasma viscosities for toroidal plasmas are obtained. Here, νk is the Coulomb collision frequency and γ is the plasma flow damping rate.