Quasisymmetric Equilibria in Anisotropic Magnetohydrodynamics

We study the existence of quasisymmetric magnetohydrodynamic equilibria in the presence of pressure anisotropy. When compared with isotropic magnetohydrodynamics, the tensorial nature of pressure enlarges the class of equilibrium magnetic fields. First, we show that any solenoidal vector field satisfying tangential boundary conditions solves anisotropic force balance provided that the pressure tensor is appropriately chosen. Hence, a quasisymmetric equilibrium can be achieved by constructing a quasisymmetric vector field in the domain of interest. Then, we derive a system of two coupled nonlinear first order partial differential equations expressing a family of quasisymmetric anisotropic magnetohydrodynamic equilibria in bounded domains, and exhibit regular quasisymmetric vector fields corresponding to local solutions of anisotropic magnetohydrodynamics such that boundary conditions are satisfied on a portion of the boundary. The problem of locality is also discussed: we find that the topological obstruction encountered in the derivation of global quasisymmetric magnetic fields is reflected by the local nature of the solutions of the governing nonlinear first order partial differential equations.