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arXiv · 2604.08321

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

Amitava Bhattacharjee
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Abstract

The geometric coefficients of the ion-temperature-gradient (ITG) eigenmode equation along a magnetic field line are aperiodic because the line samples the full three-dimensional geometry. 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 ITG mode structure. In a tight-binding approximation this equation reduces to an Aubry--André--Harper difference equation, suggesting an Anderson-localization mechanism for ITG eigenfunctions. For the continuous equation the localization threshold is identified by the onset of a positive Lyapunov exponent of the transfer matrix at the drift-wave-resonant eigenvalue. The result is a structural property of the eigenvalue problem and is obtained on the drift-wave-resonant branch of the fluid model, at weak global and local magnetic shear. We discuss what bearing, if any, this transition may have on the observed clamping of the ion temperature in stellarators, a question that is not settled by this theory.

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Amitava Bhattacharjee. 2026-09-20. Anderson Localization of Ion-Temperature-Gradient Modes in Aperiodic Stellarators. https://arxiv.org/abs/2604.08321

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