A simplified approach to pinch equilibrium

The fundamental quantity in the usual MHD model is the magnetic field. The authors propose a formulation of pinch equilibrium in terms of the currents instead. An integral formulation of pinch equilibrium gives new kinetic pressure profiles for plasma configurations in a cylinder. This simplified method of computing magnetostatic equilibrium offers an alternative to solving the Grad-Shafranov equation. Its distinct logic leads to closed-form expressions obtained analytically. Results include the explicit dependence of equilibrium on the externally-generated field Bo, and field-reversal appears as an intrinsic feature of Screw-pinches. Basic insight into Z-pinches, Screw-pinches, and F-Θ relations comes from the same formalism