离子温度梯度模态和离子温度钳制在非周期星形场中的安德森局域化
Anderson Localization of Ion-Temperature-Gradient Modes in Aperiodic Stellarators
AI总结：
研究非周期星形场中离子温度梯度模态的安德森局域化机制，揭示离子温度钳制的三阶段阈值结构及低输运第二 regime 的物理机制。
摘要：
离子温度钳制--无论加热功率如何，离子温度饱和的现象在星形场实验中被观测到。本文基于安德森局域化提出最小模型。从漂移波简化流体模型出发，证明非周期星形场导致离子温度梯度（ITG）模态的准周期性Hill方程。在紧束缚近似下，该方程简化为 Aubry--Andre--Harper 差分方程，表明 ITG 特征函数的安德森局域化机制。识别出三阶段阈值：线性不稳定性阈值低于安德森局域化阈值，后者低于观测到的钳制。这被推测创造了一个低输运第二 regime，类似于MHD膨胀理论的第二稳定性 regime，提供了一个与功率无关的观测梯度下界。
英文摘要：
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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