Abstract
In order to determine the character of an instability, different criteria can be applied. The paper presents an application of the frequency-loop criterion of Fainberg et al. (1961), the pole-pinching criterion of Bers and Briggs (1964) and the frequency-cusp criterion of Derfler (1970) to determine the type of the helical instability of the positive column in a diffusion dominated low pressure discharge and its dependence on the applied axial magnetic field strength. The conformal mapping of the wave number plane into the frequency plane, which is given by the dispersion relation D( omega ,k)=0, is studied numerically especially in the area of saddle points in the k plane and in branch points of the omega plane. For the numerical calculations the plasma parameters of a helium discharge and of a neon discharge are used. The results of the different criteria are compared.
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