UW-CPTC 09-7 Drift-resistive-inertial ballooning modes in the HSX Stellarator

A linear stability theory of non-ideal magnetohydrodynamic (MHD) ballooning modes is investigated using a two fluid model for electron-ion plasmas. Drift-resistive-inertial ballooning mode (DRIBM) eigenvalues and eigenfunctions are calculated for a variety of equilibria including axisymmetric shifted circular geometry (ŝ− model) as well as for three dimensional configurations relevant for the Helically Symmetric Stellarator (HSX) [F.S.B. Anderson, A.F. Almagri, D.T. Anderson, P.G. Mathews, J.N. Talmadge, and J.L. Shohet, Fusion Technology 27, 273 (1995)]. For typical HSX parameters, characteristic ballooning mode growth rates exceed the electron collision frequency. In this regime, electron inertial effects dominate plasma resistivity and produce an instability whose growth rate scales with the electromagnetic skin depth. However, as plasma is increased, the resistive and inertial effects become unimportant. Under these conditions, the mode is completely stabilized by drift frequency effects, which dominate resistivity and inertia. Numerical results indicate that in the absence of drift effects, RIBM modes are purely growing and persist in regimes where ideal MHD ballooning modes are stable. It is found that the magnitudes of the linear growth rates are not sensitive to the addition of the mirror term in the description of the HSX stellarator configuration. The eigenvalues and eigenvectors in the strong ballooning approximation are used together with a quasi-linear mixing length estimate to determine particle flux and particle diffusivity. The particle diffusivity increases with rising density gradient and collisionality in a plasma with a low electron temperature. This increase in transport is consistent with the increase observed in the edge region of HSX plasmas. The magnitude of the particle diffusivity is computed to be in the range 5 to 10 m2/s, which is consistent with the experimental measured particle diffusivity at the edge of HSX plasmas.