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The localized displacements of the second kind in a non-axisymmetric toroidal plasma with a sheared magnetic field is investigated. One is led to the study of a second order linear differential equation. The usual criterion of the first kind is obtained as a limiting case. The second part of the paper is devoted to the evaluation of the growth rate of these instabilities. In the last part, the numerical results of some special cases in axisymmetric are given.
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C. Mercier (1979) studied this question.
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