The system of equations appropriate of describing low-frequency modes (ω<Ωi) in general geometry for a three-species plasma is derived. The derivation employs an eikonal ansatz and for simplicity assumes Maxwellian unperturbed distribution functions, but permits arbitrary beta and asymmetry. The full system of equations includes ballooning, interchange and compressional Alfvén modes, and drift waves. As an example of the general forms, the stability of electron rings in bumpy tori and/or tandem mirrors is considered. Some simple estimates of the conditions necessary for stable operation are presented.
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Tsang et al. (1982) studied this question.
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