Flute-Mode Stability of Quadrupole-Anchored Tandem Mirror Plasmas

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We study the flute-mode stability of quadrupole-anchored tandem mirror plasmas. The present analysis is based on Newcombs Lagrangian density with an assumption of small Larmor radius of ions for paraxial approximation. A radial eigenmode equation for flute perturbations is derived without an eikonal approximation in flux coordinates, where effects of E × B plasma rotation due to an ambipolar electric field are considered. The obtained eigenmode equation is applicable to a mode with an arbitrary azimuthal mode number and can describe interchange, E × B rotational, and Kelvin-Helmholtz modes driven by the shear effect of E × B plasma rotation. A quadratic dispersion equation in perturbation frequency ω is derived based on a simplified cylindrical plasma model and is used to discuss the flute stability of quadrupole-anchored GAMMA 10 tandem mirror plasmas, where the anchor beta required for plasma stability is calculated for the m = 1 and 2 modes for different values of central-cell ambipolar potential.