Nonlinear Analysis of the Solutions of the Hasegawa-Wakatani Equations

TL;DR

This paper applies centre manifold analysis to the nonlinear Hasegawa-Wakatani equations, simplifying the complex plasma confinement models to predict stability and behavior of hot plasma systems.

Contribution

It introduces a method to analyze the nonlinear Hasegawa-Wakatani models using centre manifold theory, enabling easier stability analysis of plasma confinement systems.

Findings

Centre manifold analysis simplifies the Hasegawa-Wakatani equations.

Projection operators are defined using the linear structure of the equations.

The method provides qualitative stability predictions for plasma models.

Abstract

The Hasegawa-Wakatani models are used in the study of confinement of hot plasmas with externally imposed magnetic fields. The nonlinear terms in the Hasegawa-Wakatani models complicate the analysis of the system as they propagate local changes across the entire system. Centre manifold analysis allows us to project down onto much smaller systems that are more easily analysed. Qualitative information about the behaviour of the reduced system, such as whether it is stable or unstable, can be used to predict the behaviour of the original full system. We show how the simple structure of the linear part of the Hasegawa-Wakatani equations can be used to define these projection operators. The centre manifold analysis will be used on a few examples to highlight certain properties of the Hasegawa-Wakatani models.