3.4 Axisymmetric equilibrium current density

Since J = μ₀⁻¹∇× B, the current density J can be inferred from a given magnetic field. The components of J (expressed in terms of g and Ψ) are given by Eqs. (50), (51) and (54) and these expressions can be further simplified by using the equilibrium constraints, such as g = g(Ψ) and △^∗Ψ = −μ₀R² −g. The simplified J expressions are given in A.8.

On the other hand, in the equilibrium reconstruction[18], it is the current that is first (partially) specified (e.g., by summing sources of current drive and bootstrap current) and then the current is used as constraints for the GS equation, i.e, constraints for the magnetic field.