Drift-ideal magnetohydrodynamics

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Abstract
The ideal magnetohydrodynamic equations are extended to include the frequency range ω≲ωd and ωci≲ω, where ω is the frequency of interest, ωd denotes any equilibrium drift frequency, and ωci is the ion cyclotron frequency. Such a frequency range is of interest in stability considerations for the ELMO Bumpy Torus and the tandem mirror fusion devices. Relative simplicity is attained by restricting the domain of validity of the equations to the collisional limit and the cold ion limit. The resulting equations are linearized and a normal mode analysis is performed to obtain the flute‐like modes of the system. Application is made to the straight field line case and to a z pinch with no axial field. In the high‐frequency limit (ωd≪ω), the usual ideal magnetohydrodynamic modes are recovered. In the low‐frequency limit (ω≪ωd), an interchange‐type instability is identified in the z‐pinch case.