# Onset of nonlinear structures due to eigenmode destabilization in tokamak plasmas

## TL;DR

This paper introduces a methodology to predict whether energetic-particle-driven instabilities in tokamak plasmas will produce frequency chirping or fixed-frequency oscillations, based on eigenstructure analysis and resonance surface stochasticity.

## Contribution

The paper presents a new criterion using eigenstructure calculations and resonance stochasticity to predict mode behavior in tokamak plasmas, aiding in understanding fast ion transport.

## Key findings

- Stochastic diffusion due to micro-turbulence can dominate energetic particle detuning.
- The criterion predicts the likelihood of chirping behavior consistent with experimental observations.
- Micro-turbulence strength influences whether modes exhibit chirping or fixed frequency.

## Abstract

A general methodology is proposed to differentiate the likelihood of energetic-particle-driven instabilities to produce frequency chirping or fixed-frequency oscillations. The method employs numerically calculated eigenstructures and multiple resonance surfaces of a given mode in the presence of energetic ion drag and stochasticity (due to collisions and micro-turbulence). Toroidicity-induced, reversed-shear and beta-induced Alfven-acoustic eigenmodes are used as examples. Waves measured in experiments are characterized and compatibility is found between the proposed criterion predictions and the experimental observation or lack of observation of chirping behavior of Alfvenic modes in different tokamaks. It is found that the stochastic diffusion due to micro-turbulence can be the dominant energetic particle detuning mechanism near the resonances in many plasma experiments, and its strength is the key as to whether chirping solutions are likely to arise. The proposed criterion constitutes a useful predictive tool in assessing whether the nature of the transport for fast ion losses in fusion devices will be dominated by convective or diffusive processes.