From hybrid-kinetic theory an eigenvalue equation for electromagnetic perturbations with ω ≈ ωci in collisionless theta-pinches with anisotropic ion energy was recently derived. This equation is presently reduced to two ordinary second-order linear differential equations by an expansion in the thermal ion Larmor radius. The leading-order correction terms contain Cherenkov resonances absent in the homogeneous case, which are reached for speeds ≈ υ| β|-½ and wave-numbers typical for unstable modes in the homogeneous case, indicating the importance of Cherenkov resonance on the stability of modes driven by ion energy anisotropy. These equations are supplemented by appropriate boundary conditions for the case when the plasma is surrounded by a cylindrical, perfectly conducting wall. For weak inhomogeneities a local dispersion equation is obtained. The physical mechanism underlying the influence of Cherenkov resonance parallel to the confining magnetic field as a FLR effect on stability behaviour is illustrated.
Two-fluid and finite Larmor radius effects on high-beta tokamak equilibria with flow in reduced magnetohydrodynamics
