Symmetric MHD Equilibria with Anisotropic Pressure and Currents with a Field-Aligned Component

Abstract:

We present a new formalism for symmetric magnetohydrodynamic equilibria with anisotropic pressure and currents with a field aligned component, which may have applications to planetary magnetospheres. While in this contribution we focus on translationally invariant equilibria, the method can also be extended to rotationally invariant systems. The current formalism defines the shear field component in terms of the magnetic field strength which leads to a Grad-Shafranov equation that is implicitly coupled to a secondary constraint equation. The new formalism bypasses this problem by considering the shear field component as a function of the poloidal magnetic field strength. One can then show that the problem is reduced to an equivalent problem without a shear field through the use of an effective parallel pressure, which makes it much easier to use the new method for modelling purposes.