On the radiative collapse phenomenon

For a pinch under equilibrium, the Pease-Braginskii current limit sets the ceiling when the ohmic heating rate is balanced by the bremsstrahlung loss rate. Under a dynamical condition. Shearer showed that, when the pinch current exceeds the Pease-Braginskii limit, the difference in ohmic heating and bremsstrahlung loss rate could lead to the phenomenon of radiative contraction, producing a plasma structure of ultra high energy density. The work was extended by Haines and Robson independently to describe the conditions for radiative collapse. These analytical results show that under certain circumstances, a high temperature pinch can be self-compressed to an extremely high density, limited only by photon self-absorption or electron degeneracy. In this paper, we present an analysis on the radiative collapse formalism including the effect of an external circuit. It is shown that the degree of contraction is governed by the intrinsic rate of energy delivery to the system. Two expressions are derived which define the ultimate pinch dimension with the plasma parameters and that of the electrical circuit.