Linear stability of ultra-high-beta (beta ~ 1) equilibria

The power density of tokamaks scales with the plasma beta as beta^2 which makes high-beta operation an attractive choice for future high-power tokamak devices. beta ~ 1 configurations have previously [Hsu. et al. PoP 96] been explored by solving the Grad-Shafranov equation in the limit epsilon/(beta q^2) << 1. We extend this by obtaining exact global equilibria numerically. However, various instabilities may limit the utility of such equilibria. To that end, we present an infinite-n, ideal-ballooning and linear gyrokinetic analysis of various equilibria for tokamaks. We find that alpha_MHD >> 1 is large enough to make them "second-stable" to the ideal ballooning mode. Next, we examine their stability to the two major sources of electrostatic turbulence: ITG and TEM, using the initial value code GS2. To understand the trend with a changing beta, we compare these equilibria with an intermediate-beta (beta~0.1) and a low-beta (beta~0.01) equilibrium at two different radial locations: the inner core (Normalized radius rho = 0.5) and the outer core (rho = 0.8) for two different triangularities: delta = 0.4 and delta = -0.4. We find that the ultra-high-beta equilibria are stable to both the ITG and TEM over a wide range of gradient scale lengths (R/L_T and R/L_n). Next, we perform a linear electromagnetic study of all the nominal local equilibria to explore the possible effects of Kinetic Ballooning Modes (KBMs). We find that all the high-beta equilibria become more unstable than their low-beta counterparts in the inner core but turn out to be much more stable than both the low or intermediate beta equilibria in the outer core. We also find that the negative-triangularity high-beta equilibria do not show any signs of KBMs. Using a gyrokinetic code for linear electromagnetic studies can be relatively expensive. Therefore, as an alternative, we numerically solve the KBM equations of Tang et al. as a reduced model for KBMs and compare the results with GS2.