Dissipative trapped-electron instability in quasihelically symmetric stellarators

Abstract

The linear electrostatic dissipative trapped-electron mode is investigated in a quasihelically symmetric (QHS) stellarator and a configuration whose symmetry is spoiled by the addition of a mirror contribution to the magnetic spectrum. The effect of the trapped electrons is accounted for using the drift kinetic equation with an energy-dependent Krook collision operator and an effective collision frequency giving the rate of detrapping. The ballooning mode formalism and Wentzel-Kramers-Brillouin type boundary conditions are used to solve an eigenvalue problem for a drift wave equation with nearly adiabatic electrons in a fully three-dimensional magnetohydrodynamic equilibria. The trapped-electron growth rate is calulated using a perturbative approach. Multiple classes of helically localized and toroidally localized eigenfunctions in the ballooning space are calculated. The results of the QHS configuration is compared and contrasted with the results of the mirror configuration. The helically trapped modes are found to be most destabilizing. In both configurations the magnitude of the linear growth rates are comparable, crudely indicating the same level of anomalous flux as has also been observed in the edge region of experiments.