# Shear Alfv\'en and acoustic continuum in general axisymmetric toroidal geometry

## TL;DR

This paper develops a general framework for analyzing shear Alfvén and ion sound wave continua in axisymmetric toroidal plasmas, extending previous models to include complex geometries and equilibrium effects, with applications to tokamak stability.

## Contribution

It introduces a novel formulation in ballooning space that extends continuum spectrum analysis to include gyrokinetic and 3D effects, building on and generalizing earlier work.

## Key findings

- Excellent agreement with MARS code results
- Continuum structures linked to plasma inertia
- Method applicable to complex 3D geometries

## Abstract

The equations describing the continuous spectrum of shear Alfv\'en and ion sound waves propagating along magnetic field lines are introduced and solved in the ballooning space for general geometry in the ideal MHD limit. This approach is equivalent to earlier analyses by Chu et al. 1992 [Phys. Fluids B 4, 3713 (1992)] but the present formulation in the ballooning space allows to readily extend it to include gyrokinetic and three-dimensional equilibrium effects. In particular, following Chen and Zonca 2017 [Phys. Plasmas 24, 072511 (2017)], the MHD limit is adopted to illustrate the general methodology in a simple case, and the equations are solved within the framework of Floquet and Hill's equation theory. The connection of shear Alfv\'en and ion sound wave continuum structures to the generalized plasma inertia in the general fishbone like dispersion relation is also illustrated and discussed. As an application, the continuous frequency spectrum is calculated for a reference equilibrium of the Divertor Tokamak Test facility. The results are compared with those obtained by the MARS code adopting the standard methodology, demonstrating excellent agreement.