Towards A New Theory Of Plasma Equilibrium

An integral formulation of pinch equilibrium gives new kinetic pressure profiles for the simplest cylindrical plasma configurations. This derivation presents an alternative to the Grad-Shafranov equation. Z-pinches, screw-pinches, and F-Θ relations all come from the same formalism. Results include the explicit dependence of equilibrium on the externally-generated B
₀
, and field-reversal arises as an intrinsic feature of screw-pinches. In sharp contrast to the usual procedure in ideal MHD of having to integrate a non-linear partial differential equation numerically, the new equation is immediately integrable (analytically) in one step. The present treatment of equilibrium is a first step in setting up an entirely new approach to plasma descriptions. By assigning the primary role to the current rather than the magnetic field, some old ambiguities are cleared up. Errors with the magnetic field at the elementary stages of conventional formulations permeate the whole theory, even though all subsequent details may be correct.