An analytic model of radiative collapse of a Z-pinch

There is a critical current IPB of about 1 MA (the Pease-Braginskii current) at which Ohmic heating and bremsstrahlung losses balance in a Z-pinch under pressure equilibrium. An analytic zero-dimensional model shows the process of radiative collapse when the prescribed current exceeds the critical current. In particular for a linearly rising current radiative collapse is complete when the current is 3 IPB. However, in practice the voltage limitation imposed by an external circuit prevents such a total collapse, and by including this in the model a maximum density (1030-1032 m-3)can occur followed by an expansion and damped oscillation about an equilibrium at which the current equals the Pease-Braginskii current. In the absence of alpha-particle pressure the maximum density is limited by the resistance of the narrow column, the large voltage across which (∼108V) is balanced essentially bu a large negative LI; it occurs when the current is IPB [(δ-1)/(δ-2)]1/2 where δ=7/3+4/3 In(R/a), where a is the pinch radius and R is the radius of the current return. The minimum current following maximum density is shown to be greater than IPB/√2. Degeneracy effects can be included in the model. (author) 5 refs., 1 fig