Coarse-grained gyrokinetics for the critical ion temperature gradient in stellarators

Abstract

We present a modified gyrokinetic theory to predict the critical gradient that determines the linear onset of the ion temperature gradient (ITG) mode in stellarator plasmas. A coarse-graining technique is applied to the drift curvature, entering the standard gyrokinetic equations, around local minima. Thanks to its simplicity, this novel formalism yields an estimate for the critical gradient with a computational cost low enough for application to stellarator optimization. On comparing against a gyrokinetic solver, our results show good agreement for an assortment of stellarator designs. Insight gained here into the physics of the onset of the ITG driven instability enables us to devise a compact configuration, similar to the Wendelstein 7-X device, but with almost twice the ITG linear critical gradient, an improved nonlinear critical gradient, and reduced ITG mode transport above the nonlinear critical gradient.

Global gyrokinetic simulations of electromagnetic turbulence in stellarator plasmas

“…2004) has been developed, which includes all components of the electromagnetic field perturbations. In this paper, results have been obtained for the first time showing saturated KBM turbulence in stellarator plasmas, even for plasma equilibria that have large-scale magnetohydrodynamic instability (Roberg-Clark, Plunk & Xanthopoulos 2022). The parallel component of the magnetic field perturbation, known to be important for KBMs, especially for the large-scale modes (Aleynikova et al.…”

Critical gradient turbulence optimization toward a compact stellarator reactor concept

“…To achieve turbulence optimization via shaping, several strategies have been developed to reduce the rate that turbulent transport increases ("stiffness") as a function of the ion temperature gradient [6][7][8][9][10]. Another approach is to target the onset ("critical") gradient of significant turbulent transport [11][12][13], which relies primarily on linear physics of ITG modes themselves [14][15][16][17] and avoids the hard problem of solving turbulence in the full range of toroidal geometries. Successful optimization has been recently demonstrated using a critical gradient (CG) approach, even leading to reduced stiffness of ITG turbulence in the nonlinear regime [12,18], but at the apparent cost of MHD stability via the loss of a vacuum magnetic well.…”

“…with F (b) defined as above. The quantities R eff and L are in practice computed by identifying and searching the drift wells along a particular field line as presented in [12], while a|∇α| is evaluated at the center of the drift well, effectively approximating it as a constant. In the small-b limit, F (b) is dominated by the constant term 2.84, close to the value of 2.66 determined or assumed in other works [12,14,29], at least for the case τ = 1.…”

“…The quantities R eff and L are in practice computed by identifying and searching the drift wells along a particular field line as presented in [12], while a|∇α| is evaluated at the center of the drift well, effectively approximating it as a constant. In the small-b limit, F (b) is dominated by the constant term 2.84, close to the value of 2.66 determined or assumed in other works [12,14,29], at least for the case τ = 1. In the large b limit, which applies to the flux tubes of both W7-X and HSX, we find, ignoring the small constant 0.04, that the formula effectively predicts a/L T,crit ∼ a 2 |∇α|/L .…”

First-principles based plasma profile predictions for optimized stellarators

“…This was achieved by coupling a global gyrokinetic code (GENE-3D), a neoclassical code (KNOSOS), and a transport code (TANGO), thus correctly capturing both neoclassical and 3D effects on plasma turbulence. This tool can be used to explore new optimized stellarator configurations [39][40][41] and identify the most efficient stellarator design able to optimize -at the same time -turbulent and neoclassical transport.…”