A two-fluid interpretation of low frequency modes in Tokamaks

The linear stability of low frequency modes ( omega / omega ci<or=1) of a dissipationless two-fluid cylindrical analogue of Tokamak is investigated. The eigenvalue problem comprises a coupled first-order and second-order differential equation. Given certain plausible assumptions, the case of an internal resonant point is solved analytically. The resulting modes and frequencies are qualitatively similar to those observed. The analogue of the MHD uniform current model is solved exactly and the usual MHD marginal stability boundary is shown to be modified. More general considerations show, that even in the absence of dissipation, the magnetic field is not 'frozen' to the ions or the electrons. Furthermore, in general the MHD equations can only be recovered by a limiting process which is inappropriate to Tokamaks. For very low frequencies ( omega << omega *), however, single and two-fluid theories predict the same magnetic field structure but different electric fields. The present analysis which covers frequencies from zero to omega Alfven, including drift and acoustic frequencies predicts that both discrete and continuum modes can be unstable which is in contrast to ideal MHD.