Equilibrium and stability in a high-current discharge in a dense plasma under conditions of radiative conduction

Abstract

Equilibrium and stability are examined for a high-current self-compressed discharge:in a dense, optically opaque plasma of finite conductivity, with allowance for dissipation via radiative heat transfer. If the thermal conductivity is high, the plasma temperature is virtually constant throughout the cross-section of the discharge, whereas the density and pressure fall off fairly rapidly away from the axis. The spectrum for small oscillations shows that such an equilibrium discharge is unstable with respect to short-wave hydrodynamic oscillations (bending and necking) if the plasma conductivity is low. Instability can develop only for long-wave perturbations in a cylindrical discharge, and also for a nonequilibrium discharge when the rise time is iess than the equilibration time. A planar equilibrium discharge is stable, while a cylindrical equilibrium discharge in a dense low-temperature plasma is more stable than one in a high-temperature plasma.

There have been several discussions of the use of high-current discharges in dense plasmas as light sources for laser pumping. The choice of discharge dimensions is governed by the temperature T of the radiating surface, which should be 3–10 eV. Only ohmic heating can allow one to keep a plasma at such a temperature for a sufficiently long time (around 100 vsec). On the other hand, hydrodynamic instabilities (bends, necks, hot spots) can arise in a dense plasma carrying a current, which can lead to current interruption and plasma dispersal (see [1] for literature). Stability is therfore a major problem in the use of such discharges as light sources. However, it is not correct to apply the theory of [1] to such discharges, since this theory is for a not very dense, hot. transparent plasma under conditions such that radiation does not play a major part in the development of the discharge, whereas a discharge in a dense, optically opaque plasma is best as a light source. Such a plasma can have considerable radiative energy transfer, which can influence the entire character of the discharge. Moreover, effects due to the finite conductivity (diffusion of electric and magnetic fields) may play major parts at these relatively low temperatures. Here we present a theoretical discussion of the equilibrium and stability of a high-current discharge in a dense, optically opaque plasma having a finite conductivity and considerable radiative heat transfer.