Prospects for H-mode inhibition in negative triangularity tokamak reactor plasmas

Abstract

Instability to high toroidal mode number (n) ballooning modes has been proposed as the primary gradient-limiting mechanism for tokamak equilibria with negative triangularity (δ) shaping, preventing access to strong H-mode regimes when δ is sufficiently negative. To understand how this mechanism extrapolates to reactor conditions, we model the infinite-n ballooning stability as a function of internal profiles and equilibrium shape using a combination of the CHEASE and BALOO codes. While the critical δ required for avoiding 2nd stability to high-n modes is observed to depend in a complicated way on various shaping parameters, including the equilibrium inverse aspect ratio, elongation and squareness, equilibria with negative triangularity are robustly prohibited from accessing the 2nd stability region, offering the prediction that that negative triangularity reactors should maintain L-mode-like operation. In order to access high-n 2nd stability, the local shear over the entire bad curvature region must be sufficiently negative to overcome curvature destabilization on the low field side. Scalings of the ballooning-limited pedestal height are provided as a function of plasma parameters to aid future scenario design.

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.…”

Available energy of trapped electrons in Miller tokamak equilibria

“…This is in line with findings of Saarelma et al. (2021) and Nelson, Paz-Soldan & Saarelma (2022), where the H-mode was found to be inaccessible in negative-triangularity tokamaks on the basis of the ballooning instability, though the physical reason is of course different. This rise in Æ in negative triangularity is perhaps unsurprising given that we have found that negative triangularity is stabilising in cases with significant positive shear, a weak pressure gradient, and a slight density gradient, exemplified in figures 8 and 11.…”

Geometric dependencies of the mean E × B shearing rate in negative triangularity tokamaks

“…This may contribute to the increase of the L-H power threshold for NT. This mechanism complements the one based on the loss of second stability of ideal MHD ballooning modes [9,10].…”

“…While this is observed at weak NTs, Hmode becomes completely inaccessible at strong NTs (δ u < −0.18), even if high power is applied. This has been linked to the loss of access to the second stability region of the infinite-n ideal ballooning modes [9,10]. This model is built upon a previous study predicting reduced pedestal height, clamped by degraded peeling ballooning (PB) and kinetic ballooning mode (KBM) stability, due to closed access to the second stability region for ballooning modes in the case of NT [11].…”