Author: Rahul Gaur
Requested Type: Consider for Invited
Submitted: 2022-03-07 11:47:17
Co-authors: W.D. Dorland, I.G. Abel
University of Maryland, College Park
3324 AV Williams Building
College Park, MD 20742
The power density of tokamaks scales with the plasma beta as β^2 which makes high-β operation an attractive choice for
future high-power-density tokamak devices [Menard et al. Nucl. Fusion 22].
Ultra-high-beta(β ~ 1) configurations have previously [Hsu. et al.] been explored at the level of asymptotic MHD equilibria by solving the Grad-Shafranov equation in the limit (δ_Hsu)^2 ~ ε/(βq^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 ideal-ballooning and linear gyrokinetic analysis of ultra-high-beta(β~1) equilibria for tokamaks.
In the first part, we examine ideal ballooning stability. We find that alpha_MHD ~ 1/(δ_Hsu)^2 >> 1 is large enough to make them "second-stable" to the ideal ballooning mode. Upon ensuring ideal ballooning stability, we examine their stability to 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(β~0.1) and a low-beta(β~0.01) equilibrium at two different radial locations: the inner core(Norm. radius ρ = 0.5) and the outer core(ρ = 0.8) for two triangularities:δ = 0.4 and δ = -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.
Next, we perform a linear electromagnetic study of all the nominal local equilibria to explore the possible effects of kinetic ballooning modes. We find that all the ultra-high beta equilibria are still linearly stable whereas the β~0.1 equilibria show strong KBM instability.
Using a full gyrokinetic code for linear studies at k⊥ρi≪ 1 can be relatively expensive. Therefore, as an alternative, we numerically solve the KBM equations of Tang et al. including the trapped electron effects in the limit ωbi ≲ ω < ωbe and compare the results with GS2