Kinetic theory of m=1 internal instabilities

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Abstract
The internal m=1 instability is investigated kinetically over the entire range of collisionality of the plasma using a pitch‐angle‐scattering collision operator to represent electron‐ion collisions. As a function of the ratio of plasma to magnetic pressure β, the ideal magnetohydrodynamic driving energy, and the collisionality, the m=1 mode falls into six basic categories. In the high β (typically βmi/me≳1), low collisionality regime of present tokamak discharges, the Doppler effects associated with electron thermal motion along B strongly modify the structure and growth rate of the instability. Electron thermal effects are found to be negligible, however, when the ideal magnetohydrodynamic driving energy is large. The effect of density and temperature gradients on the instability are also studied. When the electron diamagnetic frequency ω* is large, two distinct modes are typically found, one with ω≃ω* driven by the electron temperature gradient, and a second with ‖ω‖≪ω* driven by the magnetic energy. Simple descriptions of the mode in each of the regimes are presented.