Two-fluid equations for low-n singular modes in the low-frequency regime

Abstract

Braginskii’s two-fluid equations are employed to obtain the eigenmode equations governing low-n singular modes in toroidal geometry. Collisional effects are neglected. The equilibrium electric field is taken into account. The frequency of the modes is assumed to be lower than that of the ion acoustic wave along the magnetic field lines. In this low-frequency regime it is shown that the pressure of the ion fluid tends to be constant along the magnetic field lines, as also does that of the electron fluid, and the parallel electric field tends to vanish. The finite-gyroradius (FGR) effect is recovered by taking into consideration the diamagnetic drift velocity and the gyroviscosity of the ion fluid. The results show that the toroidal effect gives rise not only to the so-called apparent mass effect, but also to an enhancement of the FGR and equilibrium electric field effects. The toroidicity-induced FGR and equilibrium electric field effects are shown to be even more important than those exhibited in the cylindrical equilibrium model.