Abstract
A first-principles method to calculate the critical temperature gradient for the onset of the ion-temperature-gradient mode (ITG) in linear gyrokinetics is presented. We find that conventional notions of the connection length previously invoked in tokamak research should be revised and replaced by a generalized correlation length to explain this onset in stellarators. Simple numerical experiments and gyrokinetic theory show that localized ‘spikes’ in shear, a hallmark of stellarator geometry, are generally insufficient to constrain the parallel correlation length of the mode. ITG modes that localize within bad drift curvature wells that have a critical gradient set by peak drift curvature are also observed. A case study of near-helical stellarators of increasing field period demonstrates that the critical gradient can indeed be controlled by manipulating the magnetic geometry, but underscores the need for a general framework to evaluate the critical gradient. We conclude that average curvature and global shear set the correlation length of resonant ITG modes near the absolute critical gradient, the physics of which is included through direct solution of the gyrokinetic equation. Our method, which handles the general geometry and is more efficient than conventional gyrokinetic solvers, could be applied to future studies of stellarator ITG turbulence optimization.
Highlights
Energy transport resulting from small-scale electrostatic fluctuations is a major impediment to sustaining nuclear fusion in magnetic confinement devices
The mode structures along the field line for the critical modes are plotted in figure 6(c). It can be inferred from these results that the lower bound on the critical gradient of the ion-temperature-gradient mode (ITG) mode, which pertain to broad-along-the-field-line, low-ky resonant modes, is set by global shear
We found that traditional connection length estimates often do not adequately capture the physics of the onset of the linear electrostatic ITG mode, and that instead the correlation length L, which emerges in the solution of the integral equation (2.8), is the appropriate reference length that sets the critical gradient through the damping frequency vT/L
Summary
Energy transport resulting from small-scale electrostatic fluctuations is a major impediment to sustaining nuclear fusion in magnetic confinement devices. The ion-temperature-gradient mode (ITG mode) has been singled out as a leading cause of transport in magnetic fusion devices. Much of the work just mentioned, as well as current efforts towards turbulence optimization of which we are aware, involve modelling turbulence itself This is a challenging problem to crack, especially at the level of generality needed for stellarator design. While some plasma instabilities are susceptible to sub-critical turbulence that bring this onset below the linear threshold, it appears that the opposite occurs in the case of the ITG mode, with the onset occurring at a somewhat larger value of the gradient (Dimits et al 2000). A specific gradient might be targeted so that modest turbulence is present in the desired operating regime, which may, in certain cases, help flush out impurities (Garcia-Regaña et al 2021)
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