Shear Alfv\'en Waves in Chaotic Magnetic Fields

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.