Modeling Temperature Profiles in the Pedestal of NSTX with Reduced Models

Abstract

This paper describes new modeling capabilities for predicting H-mode pedestal profiles in spherical tokamaks. Temperature profiles for NSTX discharges 132543 and 132588 are modeled by coupling the \textsc{astra} transport solver with neoclassical transport and gyrokinetic-based reduced models for electron temperature gradient (ETG) and kinetic ballooning mode (KBM) instabilities. A quasi-linear surrogate model for ion-scale transport is developed using linear \textsc{gene} simulations, requiring only a single free parameter calibrated to one discharge. Time-evolving the temperatures with fixed density yields good agreement with experiments for both discharges. Systematic analysis of the transport mechanisms reveals that neoclassical transport is huge across the entire pedestal region for the ion channel. ETG turbulence is large in the plasma edge and low density gradient region, contributing substantially to the electron channel. However, KBM/MHD-like modes also drive significant transport in both the ion and electron thermal channels, making them essential for accurate pedestal modeling. Further refinements, including explicit $E \times B$ shear suppression and scaled ETG transport, produce quantitative but not qualitative improvements. This work lays the foundation for predictive modeling of future devices.

Figures (16)

• Figure 1: Scatter plot comparing the heat flux from the simple reduced ETG model (y-axis) with numerous nonlinear gyrokinetic simulations from GENE and CGYRO (x-axis) for NSTX. The red line demonstrates that multiplying the calculated heat fluxes from the simple model by a factor of two ($2 \times Q_{\mathrm{model}}$) provides an improved fit to the nonlinear simulations for NSTX. Because the model is stiff with respect to the temperature gradient, these magnitude differences in heat flux result in very small differences for the overall profile prediction. (Simulations performed with the gene code).
• Figure 2: $T_e$ profile prediction from the unscaled baseline model using ASTRA with fixed $T_i$ and $n_e$. The predicted profiles find reasonable agreement with experimental measurements, though some minor differences remain for (a) shot 132543 and (b) shot 132588.
• Figure 3: Thermal diffusivity ($\chi_e$) profiles driven by ETG for (a) 132543 and (b) 132588. The results show that the ETG-driven transport is particularly strong and highly localized in the steep gradient region of the pedestal.
• Figure 4: The electron-ion energy exchange rate per unit volume ($P_{ei}$) for (a) 132543 and (b) 132588. Note the sign convention where $P_{ei}$ represents energy transfer into the ions from the electrons. $P_{ei} < 0$ indicates energy is transferred to the electrons in the steep gradient region, while $P_{ei} > 0$ indicates energy is transferred to the ions in the regions with a smaller $T_e$ gradient.
• Figure 5: $T_e$ profiles predicted with different density profiles (increasing or decreasing the density gradients by $\pm 20\%$). Panels (a) 132543 and (b) 132588 use a pivot point for the density profile adjustment at $\rho=1.0$ from the original one. Panels (c) 132543 and (d) 132588 use a pivot point at $\rho=0.9$. Overall, the $T_e$ profile is highly resilient and does not change much.