The effect of a subsonic flow, inherent to most stellarators because of a radial electric field, on their ideal magnetohydrodynamic (MHD) stability properties is studied employing the quasi-Lagrangian picture developed by Frieman and Rotenberg (1960 Rev. Mod. Phys.32 898). The Mach number of the perpendicular E × B flow in stellarators is of order 0.01 and, therefore, admits the usage of a subsonic approximation in form of a static equilibrium. A mathematical formulation of the weak form of the stability equation with flow has been implemented in the ideal-MHD stability code CAS3D. This formulation uses magnetic coordinates and does not involve any derivatives across magnetic surfaces. In addition to the expected Doppler shift of frequencies, properties of the spectrum of the ideal MHD force operator, which are already known for tokamaks, but now also shown in the stellarator case, are: firstly, the appearance of unstable flow-induced continua stemming from the coupling of sound and Alfvén continuum branches with equal mode numbers; and, secondly, the existence of flow-induced, global, stable modes near extrema of sound continuum branches, the extrema, in turn, being generated by the influence of a sheared flow on the static sound continua.
Nonlinear Magnetohydrodynamics