Front-curvature effects in the dynamics of confined radiatively bistable plasmas: Perfect patterns and Ostwald ripening.

Abstract

Front-curvature effects in the dynamics of a confined optically thin isotropic plasma, which is heated by an external energy source and cooled radiatively, are investigated under conditions of thermal bistability. Reduced governing equations for such a plasma are derived, based on the elimination of the acoustic modes. Possible large-scale equilibria, describing segregation of the plasma into two ``phases,'' dense and cool, and rarefied and hot, are found. Only objects with a constant mean curvature of their boundaries (the simplest of these are slabs, cylinders, and spheres) are shown to represent such equilibria. The curvature introduces a small correction to the ``area rule'' value of the equilibrium plasma pressure. The governing equations are reduced further and employed for stability analysis of individual equilibrium objects and of their ensembles. An equilibrium slab is found to be stable with respect to arbitrary perturbations. Similarly, a circular or spherical ``drop'' (or ``bubble'') is stable with respect to deformations of their shape. On the contrary, the same drop or bubble can be unstable with respect to a purely radial mode, and stability arguments determine the minimum possible radius of these objects. Ensembles of drops or bubbles show strong background-mediated competition (Ostwald ripening). Possible self-similar asymptotics of the time-dependent distribution of a large number of drops with respect to their radii are found. Two-dimensional numerical simulations of the dynamics of a confined bistable plasma are performed in a square ``box.'' When starting from a broadband noise perturbation around a uniform state, we observe radiative segregation of the plasma, followed by background-mediated competition and establishment of either the slab-type, or the drop (or bubble)-type equilibrium. Finally, deformation instability of planar ``evaporation'' fronts, similar to the Darrieus-Landau instability of the laminar flame propagation, is found.