Negative-energy modes in a magnetically confined plasma in the framework of Maxwell-drift kinetic theory

For the cases of tokamaklike and shearless stellaratorlike equilibria, which are described on the basis of, respectively, a slightly modified Maxwellian and a Maxwellian distribution function, the existence of perpendicular negative-energy modes is related to the threshold value 2/3 of the quantity ην=∂ lnTν/∂ lnNν, where Tν is the temperature and Nν the density of some particle species. This is lower than the critical ην value for the onset of linear temperature-gradient-driven modes. For various tokamaklike and stellaratorlike, analytic cold-ion equilibria with non-negative and negative values of ηe, for which the criterion above is not necessary, a substantial fraction of thermal electrons is associated with negative-energy modes (active particles). In particular, for linearly (marginally) stable equilibria with ηe=1, nearly one-third of the electrons are active. For all equilibria considered, the phase space occupied by active electrons increases as one proceeds from the center to the plasma edge region. Consequently, negative-energy modes, relating to nonlinear instabilities that could cause anomalous transport, exist equally well in both confinement systems