Shear Alfvén Waves in Chaotic Magnetic Fields

Abstract

The shear Alfvén 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 Alfvén 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.

Figures (11)

• Figure 1: Poincaré plot of the magnetic field including the perturbation from equation \ref{['eqn:B_perturbation']}, with $k=1.3\times10^{-3}$.
• Figure 2: Quadratic-Flux-Minimising (QFM) surfaces on Poincaré map with $k=1.3\times10^{-3}$ (a) and Poincaré map with the same magnetic field, in QFM coordinates (b).
• Figure 3: Key metrics vs number of QFM surfaces. Chosen number of surfaces is based on minimising $(B^s)^2$ while maintaining a smooth Jacobian.
• Figure 4: Change of the Poincaré map (left column) and corresponding continuum (right column) for increasing perturbation amplitude $k$. Specific solutions are highlighted in the continuum plots that are localised to the flux surfaces highlighted in the Poincaré maps. Continuum plots are constructed in QFM coordinates, $(s, \vartheta, \zeta)$, while Poincaré maps are computed in original cylindrical coordinates, $(\psi, \theta, \varphi)$.
• Figure 5: Specific solution residing on $\iota_1$ as $k$ increases. Left column shows the Fourier harmonics in QFM coordinates, $(s, \vartheta, \zeta)$. Right column shows contour plot mapped back to original cylindrical coordinates, $(\psi, \theta, \varphi)$, at $\varphi=0$.