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It is well known that the process of construction of quasisymmetric magneticfields in magnetostatic equilibrium with isotropic pressure suffers from theproblem of overdetermination. This has led to the widespread belief that globalquasisymmetric solutions are likely not to exist. We develop a generalnear-axis expansion procedure that does not rely on the assumption ofmagnetostatic equilibria with isotropic pressure. We then demonstrate that inequilibria with anisotropic pressure, it is possible to circumvent the problemof overdetermination and carry out the power-series solutions to higher order.This suggests, contrary to current belief, that the existence of globallyquasisymmetric fields is likely if one relaxes the assumption of magnetostaticequilibria with isotropic pressure.

Solving the problem of overdetermination of quasisymmetric equilbrium solutions by near-axis expansions: I. Generalised force balance