Magnetic relaxation in spheromaks using spectral expansions in cylindrical geometry

Abstract

Abstract. A code has been developed to study self-organization in spheromaks using the Galerkin method in which the magnetic and velocity fields appearing in the incompressible dissipative MHD equations are expanded in a spectrum of Chandrasekhar–Kendall eigenstates of the curl. The ultimate goal is to apply the Galerkin method in actual spheromak geometry to calculate turbulence levels and associated transport. The present work employs the straight-cylinder approximation, known to give a good representation of internal ideal MHD modes in spheromaks and applied here to resistive tearing modes. Our main result to date is a demonstration that the Galerkin method can exhibit tearing island formation with only a few states in the spectrum. Example quasilinear calculations are presented for a decaying spheromak and for a spheromak created by gun injection.