Equilibrium and Steady State of Dense Z-Pinches Superposing a Small Amount of Axial Flux

Abstract

The pressure equilibrium and steady state of z-pinches trapping a small amount of axial magnetic flux are studied. The Bennett relation and the Pease–Braginskii-current are modified, taking into account the superposed axial field. The line energy density decreases in the modified Bennett relation, but the decrease is only of the order ε2, where ε = (the axial field strength at the axis)/(the azimuthal field strength at the plasma periphery) ≪ 1. On the other hand, the current in the steady state can increase without being limited by the Pease–Braginskii-current. Hence, the radiation collapse is prevented. The decrease of line energy density in the modified Bennett relation is almost canceled in the steady state.