Kinetic theory of tearing instability

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Abstract
The guiding‐center kinetic equation with Fokker‐Planck collision term is used to study, in cylindrical geometry, a class of dissipative instabilities of which the classical tearing mode is an archetype. Variational solution of the kinetic equation obviates the use of an approximate Ohm’s law or adiabatic assumption, as used in previous studies, and it provides a dispersive relation which is uniformly valid for any ratio of wave frequency to collision frequency. One result of using the rigorous collision operator is the prediction of a new instability. This instability, driven by the electron temperature gradient, is predicted to occur under the long mean‐free path conditions of present tokamak experiments, and has significant features in common with the kink‐like oscillations observed in such experiments.