Anderson Localization of Ion-Temperature-Gradient Modes and Ion Temperature Clamping in Aperiodic Stellarators

TL;DR

This paper proposes a model linking Anderson localization to ion temperature clamping in stellarators, explaining how aperiodic geometry causes temperature saturation independent of heating power.

Contribution

It introduces a minimal model based on Anderson localization to explain ion temperature clamping in stellarators, connecting geometry to plasma behavior.

Findings

A quasiperiodic Hill equation describes ITG mode structure in stellarators.

The model predicts a three-threshold ordering: instability, localization, and temperature clamp.

A power-independent lower bound on the ion temperature gradient is suggested.

Abstract

Ion temperature clamping -- the saturation of the ion temperature regardless of heating power -- is observed across stellarator experiments. We propose a minimal model based on Anderson localisation. Starting from a reduced fluid model for drift waves [Phys. Fluids 26, 880 (1983)], we show that aperiodic stellarator geometry leads to a quasiperiodic Hill equation for the ion-temperature-gradient (ITG) mode structure. In a tight-binding approximation this equation reduces to an Aubry--Andre--Harper difference equation, suggesting an Anderson-localisation mechanism for ITG eigenfunctions. We identify a three-threshold ordering: the linear instability threshold lies below the Anderson localisation threshold, which lies below the observed clamp. This is conjectured to create a low-transport second regime above the instability threshold, qualitatively analogous to the second stability regime of MHD ballooning theory, and provides a power-independent lower bound on the observed gradient.