The stability of cylindersymmetric plasma configuration with volume currents is investigated by the method of small perturbations. The problem is reduced to only one eigen-value differential equation of second order. For
special current distribution with relativly strong concentration to the axis the eigen-values are computed numerically. For this current distribution specially for long wave lengths instability shows up. The rates of growth for different kinds of pertubations are given as a function of the wave length.
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