Flute Stability Analysis of a Quadrupole-Anchored Tandem Mirror Plasma

We study flute mode stability of a quadrupole-anchored tandem mirror plasma. The present analysis is based on a Newcomb's Lagrangian density with the assumption of small Larmor radius of the ion in the paraxial approximation. A radial eigenmode equation for flute perturbations is derived without the eikonal approximation in the flux coordinates, where the effects of E×B plasma rotation due to an ambipolar electric field are taken into account. The obtained eigenmode equation is applicable to a mode with arbitrary azimuthal mode number, and can describe interchange modes, E×B rotational modes and also Kelvin -Helmholtz modes driven by the shear effect of E×B plasma rotation.