  We explore the existence of quasisymmetric magnetic fields in asymmetric
toroidal domains. These vector fields can be identified with a class of
magnetohydrodynamic equilibria in the presence of pressure anisotropy. First,
using Clebsch potentials, we derive a system of two coupled nonlinear first
order partial differential equations expressing a family of quasisymmetric
magnetic fields in bounded domains. In regions where flux surfaces and surfaces
of constant field strength are not tangential, this system can be further
reduced to a single degenerate nonlinear second order partial differential
equation with externally assigned initial data. Then, we exhibit regular
quasisymmetric vector fields which correspond to local solutions of anisotropic
magnetohydrodynamics in asymmetric toroidal domains such that tangential
boundary conditions are fulfilled on a portion of the bounding surface. The
problems of boundary shape and locality are also discussed. We find that
symmetric magnetic fields can be fitted into asymmetric domains, and that the
mathematical difficulty encountered in the derivation of global quasisymmetric
magnetic fields lies in the topological obstruction toward global extension
affecting local solutions of the governing nonlinear first order partial
differential equations.
