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Stabilization of the trapped-electron mode by a collisionally broadened Landau resonance

The non-local theory of the dissipative trapped-electron instability, including magnetic shear, is extended to higher electron collisionality. In regions sufficiently close to a rational magnetic surface the trapped-electron mode becomes a ‘collisionless’ drift mode, which is Landau-damped (where η ≡ ∂ ln Te/∂ ln ne > 0). The collisional broadening of the untrapped electron Landau resonance makes this an effective stabilization mechanism, even when the parallel phase velocity lies in the trapped-particle region of parallel velocities. For the normal temperature gradient (η > 0) and for large aspect ratio (ϵ−1 > 1) a sufficient condition for stability is obtained that is independent of shear: ϵ½ η1/3 < 1. For the inverted gradient case (η < 0) a shear stabilization criterion is derived.