Force balance and quasi-symmetry of Boozer realizations

Determine whether magnetic fields realizing a prescribed Boozer-coordinate magnitude satisfy force-balance relations such as the magnetohydrostatic equation, characterize the relationship between the two free single-variable functions in the local realizability theorem and the usual free functions in magnetohydrostatic solutions with nested flux surfaces, and determine the consequences of additionally requiring quasi-symmetry.

Background

The local realizability theorem allows an arbitrary positive analytic field-strength function in Boozer coordinates, together with admissible analytic flux-function coefficients. This freedom is geometric and does not impose the magnetohydrostatic force-balance equation.

The paper proves a separate characterization showing that admitting Boozer coordinates alone is weaker than satisfying force balance. It also notes that quasi-symmetric field-strength functions are locally realizable, while the resulting flux-surface geometries may nevertheless be constrained. The compatibility of realizability with magnetohydrostatic balance and quasi-symmetry remains unresolved.