Equilibrium of the RFP Plasma, its Stability to the Interchange Mode, and a Scaling Law

An equilibrium configuration of a reversed field pinch (RFP) plasma, enclosed by a conducting shell, is derived. The plasma pressure and the toroidicity are taken into account. The flux function is obtained. The shift of the center of the flux surface from the center of the torus is also obtained. This equilibrium is a generalization of the force-free field. Magnetohydrodynamic (MHD) stability of the interchange mode is analyzed. Scaling laws for the pressure and other quantities, averaged over the plasma cross section, are derived.