The AC/DC Module has a gauge fixing feature that is imposed by adding an extra scalar field variable ψ (not to be confused with Ψ used in the gauge transformation in The Gauge and Equation of Continuity for Dynamic Fields). The ψ field is used to impose a divergence constraint. In the most simple case, that is for magnetostatics, Ampère’s law for the magnetic vector potential reads:

The equation for ψ is used to impose the Coulomb gauge: ∇⋅ A = 0. However, to get a closed set of equations, ψ must be able to affect the first equation and this is obtained by modifying the first equation to:

The variable ψ can be seen as a Lagrange multiplier that not only imposes the Coulomb gauge but also eliminates any divergence in the externally generated current density, Je and makes it comply with the current continuity inherent in Ampère’s law.