Reduced kinetic model for ion temperature gradient instability in tokamaks with reversed magnetic shear

TL;DR

This paper develops a simplified yet accurate model for ion temperature gradient instabilities in tokamaks with reversed magnetic shear, revealing unique potential structures and resonance behaviors validated against gyrokinetic simulations.

Contribution

It introduces a Schrödinger-type differential equation model for ITG modes in RMS tokamaks, extending previous models with generalized invariance and benchmarking against global simulations.

Findings

Identification of a double-well potential in RMS profiles

Resonance of ITG modes with magnetic drift frequency

Maximum growth when rational surfaces are slightly separated

Abstract

Using the averaged magnetic drift model and a first-order finite Larmor radius (FLR) expansion, the eigenvalue equation for the ion temperature gradient (ITG) mode in tokamak plasmas is reduced to a Schr\"odinger-type differential equation. By invoking generalized translational invariance, the model is extended to reversed magnetic shear (RMS) configurations and benchmarked against global gyrokinetic simulations from GTC, showing good quantitative agreement. The analysis reveals a characteristic double-well potential unique to RMS profiles, which gives rise to the degeneracy between the lowest-order even and first-order odd eigenmodes when the two potential wells are sufficiently separated radially. The ITG instability is also found to resonate with the magnetic drift frequency, and its maximum growth occurs when the two rational surfaces are slightly separated. These results provide new physical insight into ITG mode behavior under reversed magnetic shear and offer a compact, accurate theoretical framework that bridges simplified analytic models and global simulations.