Eigen-frequencies and shapes of the non-local magnetic kink-modes m=1, n>1 in a field reversal pinch are obtainedudin cylindrical force-free approximation by shooting method. The mode profile and the resistive layer containing theudresonant surface of the internal kinks are calculated numerically. Instability is revealed, both for external and internaludmodes, which is not effected by resistive layer in plasmas with high conductivity, it is determined by the currentudgradient due to the high paramagnetic parameter in the pinch core.
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