Tearing Stability Prediction Combining Toroidal Calculations With a Two-Fluid Slab Layer

Abstract

A new classical TM stability simulation workflow has been developed that solves the resistive inner-layer equations in a plasma slab to yield a linear, quasi-toroidal TM growth rate $γ$ and mode rotation frequency $ω$. This workflow combines two-fluid and drift MHD effects in a slab approximation of the resistive inner layer (SLAYER) with an effective tearing stability index as $Δ(γ,ω) = Δ' - Δ_\mathrm{crit}$. SLAYER is used to calculate the inner-layer $Δ(γ,ω)$, the STRIDE code is used to calculate a toroidal $Δ'$ that includes shaping effects, and the toroidal $Δ_\mathrm{crit}$ incorporates effects of thermal conduction on Glasser stabilization. This workflow is rapid and numerically robust across reactor-relevant plasma conditions, and yields growth rates that closely align with analytic predictions in well-documented linear growth rate regimes. Using synthetic equilibria, TM stability was calculated across scans of plasma $β$, inverse aspect-ratio, and toroidal current profile gradient. These scans effectively benchmarked this STRIDE+SLAYER workflow against existing models and showed reliable stability predictions in shaped H-mode-like plasmas. This capability to quickly and robustly predict classical tearing stability in tokamaks will facilitate the mapping of TM stable operational regimes and design of safe discharge trajectories in future devices.

Figures (9)

• Figure 1: STRIDE+SLAYER workflow schematic showing that a combination of outer layer tearing drive ($\Delta'$) and inner-layer response ($\Delta$) are needed to calculate the linear tearing growth rate $\gamma$. Inclusion of a proxy for Glasser stabilization ($\Delta_{\mathrm{crit}}$) in the dispersion relation is optional.
• Figure 2: SLAYER $( \omega, \gamma)$ space growth rate root find. Shaded red and blue contours are computed using Re($\Delta$). The dominant TM growth rate (real-imaginary contour intersection) is marked with a star. Two stable solutions are also visible near $\pm110$ kHz. Poles with asymptotic $\Delta$ yield undefined solutions to the dispersion relation and are therefore rejected.
• Figure 3: Comparison of SLAYER vs. analytic dimensionless growth rates $\hat{\gamma}$. (a) As viscosity $P$ increases, the linear growth rate regime switches from semi-collisional (SC) to diffusive-resistive (DR) to viscous-resistive (VR). (b) As total normalized diamagnetic rotation $Q_*$ increases, the regime switches from diffusive-resistive (DR) to semi-collisional (SC). Analytic limits are shown as dashed lines. Regions of validity for analytic limits are shown in color, while invalid regions are plotted at low opacity.
• Figure 4: Full ($\hat{Q}_*$, $\hat{P}$) TM growth rate maps across DR, VR, SC, and RI regimes. (a) Analytic map showing discrete linear growth rate regimes as calculated by equations \ref{['eq:DR']}--\ref{['eq:RI']}. (b) SLAYER map showing smooth transitions between regimes and alignment with analytic theory at tokamak-relevant frequencies (i.e., low $\hat{Q}_*$).
• Figure 5: STRIDE+SLAYER vs TJ $\beta$ scan benchmark, showing good alignment in the 2/1 and 3/1 growth rates calculated by both codes.