Stability of finite-sized radiating plasmas

It is shown that the onset of instabilities in a finite-sized, optically thin, radiating plasma coincides with the loss of uniqueness of solutions to the governing nonlinear differential equations. Furthermore, conditions on the luminosity function are derived for the existence of metastable states of such plasmas with dimensions smaller than the critical maximum size derived from conventional normal mode stability analysis. The results are applied to a simple configuration modelling free-free emission from a confined radiating, high-temperature plasma.