Cartesian magnetostatic flux-function equilibrium
= Cartesian magnetostatic flux-function equilibrium
In a $y$-independent <magnetostatic equilibrium> with no axial pressure or gravitational force, $\nabla\psi\times\nabla B_y=0$. Thus $B_y=b(\psi)$ on a regular connected flux region. The remaining balance is $[\nabla^2\psi+bb']\nabla\psi/\mu_0+\nabla p+\rho\nabla\Phi=0$. Constancy on separate components of a level set does not automatically give one global single-valued $b$.