Line-tying of interchange modes in a hot electron plasma

Abstract

The dispersion relation of low-frequency (ω≪ωci) electrostatic flute-like interchange modes in a mirror cell with a fraction α of hot bi-Maxwellian electrons, with bulk line-tying to cold (nonemitting) end walls, has been solved using a slab model and the local approximation. In the absence of line-tying, hot-electron interchange modes are never completely stabilized (in contrast to the conventional theory [Phys. Fluids 9, 820 (1966); Phys. Fluids 19, 1255 (1976)], which assumes monoenergetic hot electrons and has little relevance to real plasmas). In the presence of line-tying, hot-electron interchange modes are more effectively stabilized than magnetohydrodynamic (MHD) interchange modes, because (1) the line-tying is enhanced by a factor of (ω/νe)1/2 when the wave frequency ω is greater than the cold-electron collision frequency νe; and (2) hot-electron interchange modes can be completely stabilized, rather than merely having their growth rates reduced, if there is a spread of hot-electron-curvature drift velocities. Predictions of the minimum α needed for instability and of the first azimuthal mode number m to go unstable, and of the scaling of these quantities with neutral gas pressure, are in good quantitative agreement with observations of hot-electron interchange instabilities in the Tara tendem mirror experiment [Bull. Am. Phys. Soc. 30, 1581 (1985)], provided a correction is made for the fact that the modes in Tara are not flute-like, but should have higher amplitudes in the plug than in the central cell. The theory may also explain observations in other experiments [Phys. Fluids 27, 1019 (1984); Phys. Fluids 19, 1203 (1976)]. Increasing the ion temperature Ti should have a modest stabilizing effect. In addition to the hot-electron interchange modes, there are also ion-driven interchange modes, which are unstable even in the absence of hot electrons, but generally have low growth rates, much less than MHD growth rates. Even these modes may be completely stabilized by finite Larmor radius and line-tying when Ti is sufficiently great.