On the nonlinear theory of the long-wavelength radiative condensation instability

Nonlinear evolution of the radiative condensation instability (RCI) of an optically thin plasma is investigated in the framework of a one-dimensional model. The model is applicable for motions either along a sufficiently strong magnetic field, when the transverse heat conduction is suppressed, or perpendicular to a straight, shear-free magnetic field. The long-wavelength limit of the RCI is considered when the characteristic radiative cooling time is much shorter than the acoustic (or magnetoacoustic) time. The case when the isochoric thermal mode is damped, while one of the two "acoustic" (or "magnetoacoustic") modes is unstable, is studied. Two different problems of the instability are considered. In the first, the heat conduction is negligible and the instability is described by a reduced set of equations, which formally coincide with those of a gas whose effective compressibility as a function of the density is of alternating sign. The study starts with small perturbations and follows them numerically into the nonlinear regime. It is shown that, during the first stage of the instability, cool plasma condensations develop, these being surrounded by rarefied and hot plasma regions. Subsequently the condensations expand unless mass inflow into the system is disallowed. The condensation boundaries represent a new type of shock wave which develops in such a "normal-anomalous" gas dynamics. These shock waves have a monotonic density profile, but a nonmonotonic pressure profile. Properties of the shock waves are investigated analytically and numerically. If the mass inflow is disallowed, stable equilibrium condensations develop, the boundaries of which represent contact discontinuities. In the second problem, the heat conduction is relatively large, so that direct crossover between the long-wavelength limit and the heat conduction-dominated short-wavelength limit occurs. In this case also either static or expanding plasma condensations are shown to develop, depending on the boundary conditions. An analytical description of the static equilibria is presented.