Shear Alfv\'en Waves in Chaotic Magnetic Fields

TL;DR

This paper investigates how shear Alfvén waves behave in chaotic magnetic fields by numerically solving the eigenvalue problem in perturbed magnetic configurations, revealing wave spectrum changes as flux surfaces break down.

Contribution

It introduces a method to compute shear Alfvén spectra in chaotic magnetic fields using quadratic flux minimization and pseudo straight field line coordinates, highlighting spectral evolution with increasing chaos.

Findings

Spectrum varies with perturbation strength

Wave solutions remain stable on intact flux surfaces

Wave features persist even after flux surface destruction

Abstract

The shear Alfv\'en spectrum is computed in the presence of symmetry breaking perturbations that introduce chaotic magnetic field trajectories. Quadratic flux minimised surfaces allow the creation of pseudo straight field line coordinates in the chaotic region. With these coordinates, the reduced ideal MHD equations are cast into an eigenvalue problem and solved numerically. The spectrum is computed with varying perturbation strength, showing how shear Alfv\'en waves change as increasing number of flux surfaces are destroyed. Solutions on specific flux surfaces are shown to remain relatively unchanged while the flux surface remains intact, and retain some original features at large perturbations where the flux surface is destroyed.