Kinetic ballooning modes as a constraint on plasma triangularity in commercial spherical tokamaks

Abstract

To be economically competitive, spherical tokamak (ST) power plant designs require a high β (plasma pressure/magnetic pressure) and sufficiently low turbulent transport to enable steady-state operation. A novel approach to tokamak optimisation is for the plasma to have negative triangularity, with experimental results indicating this reduces transport. However, negative triangularity is known to close access to the “second stability” region for ballooning modes, and thus impose a hard β limit. Second stability access is particularly important in ST power plant design, and this raises the question as to whether negative triangularity is feasible. A linear gyrokinetic study of three hypothetical high β ST equilibria is performed, with similar size and fusion power in the range 500-800MW. By closing the second stability window, the negative triangularity case becomes strongly unstable to long-wavelength kinetic ballooning modes (KBMs) across the plasma, likely driving unacceptably high transport. By contrast, positive triangularity can completely avoid the ideal ballooning unstable region whilst having reactor-relevant β, provided the on-axis safety factor is sufficiently high. Nevertheless, the dominant instability at long wavelength still appears to be the KBM, though it could be stabilised by flow shear.

An adjoint-based method for optimising MHD equilibria against the infinite-n, ideal ballooning mode

“…We observe that the optimiser is moving toward a positive triangularity equilibrium, indicating that, for the similar values of the relevant parameters (given in table 4) positive triangularity high- equilibria are more stable than their negative triangularity counterparts. Our findings are consistent with recent observations by Davies, Dickinson & Wilson (2022), Nelson, Paz-Soldan & Saarelma (2022) and Saarelma et al. (2021) that negative triangularity equilibria are more unstable against the ideal ballooning mode compared with positive triangularity equilibria.…”

“…positive triangularity high-β equilibria are more stable than their negative triangularity counterparts. Our findings are consistent with recent observations by Davies, Dickinson & Wilson (2022), Nelson, Paz-Soldan & Saarelma (2022) and Saarelma et al (2021) that negative triangularity equilibria are more unstable against the ideal ballooning mode compared with positive triangularity equilibria. This behaviour prevents the formation of a steep pressure gradient, which limits the operational beta value of negative triangularity equilibria but also prevents the occurrence of edge localisedmodes.…”

Microstability of β ~ 1 tokamak equilibria

“…Recently, Davies, Dickinson & Wilson (2022) have published a study investigating access to high- spherical tokamak equilibria where they find that high-, negative-triangularity equilibria are more unstable and less accessible than their positive-triangularity counterparts. At first, this may seem to contradict our results.…”

Kinetic-ballooning-limited pedestals in spherical tokamak plasmas

“…Recent results from ELM-free negative triangularity operation [74] that aims to prevent ideal second stability access [75] may be modified by a larger KBM instability region [76], a phenomenon also seen in ST reactor studies [77,78]. Scaling expressions presented in this paper are summarized in table 2.…”