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Theoretical research on low-frequency drift Alfvén waves in general Tokamak equilibria

Yang Li

TL;DR

The paper develops a unified kinetic framework for low-frequency drift Alfvén waves in tokamak plasmas based on a generalized fishbone-like dispersion relation. It constructs a general model with arbitrary magnetic geometry and finite ion orbit width, plus a circular-geometry reduced model that retains full circulating and trapped ion effects, with limiting cases reproducing earlier theories. The inertial-layer analysis yields a second-order equation for the perturbed flux and a Lambda^2 inertia term that combines fluid, circulating, and trapped contributions, with orbit-averaged quantities linking electrostatic and magnetic perturbations. The framework enables numerical treatment directly from orbit data, provides benchmarks for simulations, and offers a path to incorporating neoclassical and finite orbit width effects as well as geometric shaping in DAW dynamics.

Abstract

We developed kinetic models based on general fishbone-like dispersion relations. Firstly, a general model for arbitrary magnetic configuration and ion orbit width is presented. Then, by disregarding ion orbit width and approximating the magnetic geometry as circular, we introduce a simplified model that fully incorporates circulating/trapped ion effects. Finally, by considering the limit of ions being well-circulating or deeply trapped, the results directly revert to those observed in earlier theoretical studies.

Theoretical research on low-frequency drift Alfvén waves in general Tokamak equilibria

TL;DR

The paper develops a unified kinetic framework for low-frequency drift Alfvén waves in tokamak plasmas based on a generalized fishbone-like dispersion relation. It constructs a general model with arbitrary magnetic geometry and finite ion orbit width, plus a circular-geometry reduced model that retains full circulating and trapped ion effects, with limiting cases reproducing earlier theories. The inertial-layer analysis yields a second-order equation for the perturbed flux and a Lambda^2 inertia term that combines fluid, circulating, and trapped contributions, with orbit-averaged quantities linking electrostatic and magnetic perturbations. The framework enables numerical treatment directly from orbit data, provides benchmarks for simulations, and offers a path to incorporating neoclassical and finite orbit width effects as well as geometric shaping in DAW dynamics.

Abstract

We developed kinetic models based on general fishbone-like dispersion relations. Firstly, a general model for arbitrary magnetic configuration and ion orbit width is presented. Then, by disregarding ion orbit width and approximating the magnetic geometry as circular, we introduce a simplified model that fully incorporates circulating/trapped ion effects. Finally, by considering the limit of ions being well-circulating or deeply trapped, the results directly revert to those observed in earlier theoretical studies.
Paper Structure (12 sections, 88 equations, 2 figures)

This paper contains 12 sections, 88 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Theoretical model
  3. Guiding center motion
  4. Kinetic equation in ballooning space
  5. Governing equations
  6. General solution in singular layer
  7. An application to circular geometry
  8. Reduced model
  9. Canonical angle and pseudo-orthogonality
  10. Solutions for circular configuration
  11. Limiting case
  12. Summary and discussion

Figures (2)

  • Figure 1: $M$ function for $\sigma=1$ and reverse aspect ratio $\epsilon=0.1$
  • Figure 2: $L$ and $L/\theta_{b}$ functions for reverse aspect ratio $\epsilon=0.1$