The stability theory of electrostatic modes is formulated for a general axisymmetric magnetic mirror trap. For a low-β plasma with a small average gyroradius, the integral wave equation is derived for general variations in the perturbation and the equilibrium. The single-particle orbits used in the theory are calculated correct to the second order in the gyroradius expansion parameter. In special wave-frequency ranges additional expansions give previously studied forms of the mode equation. Criteria for the occurrence of flutelike modes and localized modes are given and the stability conditions discussed.
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Horton et al. (1971) studied this question.
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