Calculating the linear critical gradient for the ion-temperature-gradient mode in magnetically confined plasmas

A first-principles method to calculate the critical temperature gradient for onset of ion-temperature-gradient mode (ITG) in linear gyrokinetics is presented. We find that conventional notions connection length previously invoked tokamak research should be revised and replaced by a generalized correlation explain this stellarators. Simple numerical experiments gyrokinetic theory show localized ‘spikes’ shear, hallmark stellarator geometry, are generally insufficient constrain parallel mode. ITG modes localize within bad drift curvature wells have set peak also observed. case study near-helical stellarators increasing field period demonstrates can indeed controlled manipulating magnetic but underscores need general framework evaluate gradient. conclude average global shear resonant near absolute gradient, physics which included through direct solution equation. Our method, handles geometry more efficient than solvers, could applied future studies turbulence optimization.