The hot-electron closure of the moment-based gyrokinetic plasma model

TL;DR

This work derives a hot-electron limit (HEL) closure for the gyro-moment (GM) hierarchy used in gyrokinetics by expanding the gyroaveraging kernels in the small-temperature-ratio limit $\tau = T_i/T_e \ll 1$ and retaining only $\mathcal{O}(\tau)$ terms to yield a closed four-moment system (density, parallel velocity, and parallel/perpendicular temperatures). In Z-pinch geometry the HEL-closure GM is analytically equivalent to the Ivanov fluid model, with numerical benchmarks confirming accurate linear growth rates, nonlinear heat transport, and low-collisionality dynamics. Extending to tokamak $s-\alpha$ geometry and comparing with GK simulations at $\tau = 1$ shows that HEGS qualitatively preserves transport and temporal structure but fails to reproduce the Dimits shift, underscoring the importance of higher-order moments in zonal-flow physics and the geometry-driven coherence of zonal flows. The results suggest a systematic path to higher-order HEL closures to recover Dimits-like behavior in tokamaks and provide a concrete bridge between gyrokinetic and reduced gyrofluid formulations.

Abstract

We derive the hot-electron-limit (HEL) closure for the moment hierarchy used to solve the gyrokinetic equations, known as the gyromoment (GM) approach. By expanding the gyroaveraging kernels in the small temperature ratio limit, τ = Ti/Te << 1, and retaining only the essential O(τ) terms, we obtain a closed system for the density, parallel velocity, and parallel and perpendicular temperatures. In a Z-pinch geometry, the GM system with the HEL closure is analytically equivalent to the one developed by Ivanov et al. (2022). Numerical benchmarks confirm the closure's accuracy, reproducing established linear growth rates, nonlinear heat transport, and low collisionality dynamics. An extension to the tokamak-relevant s-α geometry and a comparison with gyrokinetic simulations reveal the capabilities and limitations of the HEL-closed GM model: while transport levels and temporal dynamics are qualitatively preserved even at τ=1, the absence of higher-order kinetic moments prevents an accurate prediction of the Dimits shift and of transport suppression.

Figures (6)

• Figure 10: Convergence of the heat flux with respect to the parallel resolution in the three-dimensional Z-pinch geometry for $\kappa_T=0.8$ (blue) and $\kappa_T=3.0$ (red), setting $\chi=0.1$ and $L_\parallel=2$.
• Figure 11: Linear growth rates of ITG simulations in the $s-\alpha$ geometry with the GK simulations (solid) and HEGS (dashed).
• Figure 12: Time traces of the radial heat flux of the Cyclone Base Case with the GK simulations (solid) and HEGS (dashed).
• Figure 13: Mixing length estimate $\gamma/k^2$ of the maximal growth rate (blue) and the saturated heat flux level (red) for different temperature gradient values. We compare the HEGS (solid) with the GK simulations (dashed).
• Figure 14: Linear growth rates of ITG simulations in the Z-pinch geometry with the GK simulations (solid) and HEGS (dashed). The hybrid geometry (green) is obtained with the $s-\alpha$ geometry setting $q_0=100$, $\epsilon=0.001$ and $\hat{s} =0$.