A kinetic theory for toroidal systems which includes the effects of collisions as well as instabilities is constructed. This yields a pair of evolution equations; one for the spectrum and one for the distribution function. In addition, this theory yields a toroidal generalization of the usual collision operator which is shown to have many similar properties, conservation laws, and H theorem, to the usual collision operator.
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Hitchcock et al. (1983) studied this question.
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