Destabilization of magnetohydrodynamic modes with finite Larmor radius effects in tandem mirrors

Difficulties in the stabilization of ideal magnetohydrodynamic (MHD) ballooning modes by finite Larmor radius (FLR) effects are considered, in tandem mirror geometry for azimuthal mode numbers l>1. A kinetic formalism is used to obtain corrections to the long, thin approximation, when keeping terms of quadratic order in the curvature. If ηi =∂ ln Ti /∂ ln ni ≥0, with Ti, ni, the ion temperature and density, ion resonance effects eliminate absolute FLR stability, though the residual growth rates are substantially reduced from the MHD values. However, the residual modes are still important, and mixing length estimates of the confinement degradation from modes with l>l indicate they can still severely limit the achievement of reactor-grade operation near and above the threshold beta values predicted from the ideal MHD theory. This is most severe if the ion temperature decreases radially (ni>0), whereupon significant instabilities can even arise below the ideal threshold. However, if −2/3<η<0, the lowest order FLR theory suffices to produce stability.