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A cylindrical pinch is treated in the approximation that plasma and field are separated by a thin surface. The external B field is taken to be completely longitudinal as in linear θ-pinches. Particles move in straight lines inside of the surface and bounce off of it specularly. Anisotropies in the velocity distribution are shown to result in instabilities of the ``mirror'' and ``fire hose'' types as well as flute instabilities of a type which have no analog in small gyroradius theory. Growth rates are obtained and a region of positive stability is found for a particular class of unperturbed distribution functions. The effect of a small net angular momentum is considered.
R. L. Morse (1967) studied this question.