An analytical local approach to flux-conserving tokamak equilibrium

A solution to the Grad-Shafranov equation is obtained by expanding the MHD equilibrium functions in half-integer powers of the poloidal flux, about the magnetic axis. The poloidal angle dependence of the expansion coefficients is solved for, from a sequence of ordinary linear differential equations with constant coefficients. Flux conservation is achieved after calculating the inverse rotational transform, by requiring it to be invariant during the pressure rise.