High-mode-number ballooning modes in a heliotron/torsatron system. II. Stability

Abstract

As described in the companion paper [N. Nakajima, Phys. Plasmas 3, 4545 (1996)], in heliotron/torsatron systems that have a large Shafranov shift, the local magnetic shear is found to have no stabilizing effect on high-mode-number ballooning modes at the outer side of the torus, even in the region where the global shear is stellarator-like in nature. The disappearance of this stabilization, in combination with the compression of the flux surfaces at the outer side of the torus, leads at relatively low values of the plasma pressure to significant modifications of the stabilizing effect due to magnetic field-line bending on high-mode-number ballooning modes—specifically, that the field-line bending stabilization can be remarkably suppressed or enhanced. In an equilibrium that is slightly Mercier-unstable or completely Mercier-stable due to peaked pressure profiles, such as those used in standard stability calculations, high-mode-number ballooning modes are destabilized due to these modified stability effects, with their eigenfunctions highly localized along the field line. Highly localized mode structures such as these cause the ballooning mode eigenvalues ω2 to have a strong field line dependence (i.e., α-variation) through the strong dependence of the local magnetic curvature, such that the level surfaces of ω2(ψ,θk,α) (≤0) become spheroids in (ψ,θk,α) space, where ψ labels flux surfaces and θk is the radial wave number. Because the spheroidal level surfaces for unstable eigenvalues are surrounded by level surfaces for stable eigenvalues of high-mode-number toroidal Alfvén eigenmodes, those high-mode-number ballooning modes never lead to low-mode-number modes. In configuration space, these high-mode-number modes are localized in a single toroidal pitch of the helical coils, and hence they may experience substantial stabilization due to finite Larmor radius effects.