The dispersion equation for longitudinal oscillations in an infinite collisionless anisotropic plasma in a uniform magnetic field is investigated. It is shown that nonoscillating, exponentially growing modes cannot exist in a plasma whose equilibrium distribution function is a two-temperature Maxwellian. This is demonstrated by showing that the dispersion equation has no solution under these conditions. The Nyquist criterion for plasma instability is also invoked to prove that all longitudinal modes propagating along the magnetic field in such a plasma are stable.
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Kammash et al. (1964) studied this question.
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