On The Nonlinear Theory Of The Radiation-Driven Thermal Instability Of A Magnetized Plasma

The nonlinear evolution of perturbations in a magnetized plasma subject to the radiation-driven thermal instability (RDTI) is investigated analytically in a simplified model. The perturbed plasma motions are assumed to be one-dimensional and perpendicular to the magnetic field. The intermediate- and long-wavelength limits of the RDTI are considered. In the former limit, the force balance sets in rapidly, on the magneto-acoustic time scale and we assume the total (thermal-magnetic) pressure remains constant. By transforming to Lagrangian variables, the problem is reduced to a single generalized reaction-diffusion equation, which is employed to analyze the two following stages of the RDTI. The first develops on the radiative time scale, when the heat conduction is insignificant, while the second usually occurs on a much longer, heat conduction-related time scale. For the first stage, a simple analytical solution is found, which describes the development of a strong plasma stratification (coexisting hot rarefied phase and cool dense phase) across the magnetic field. Slow erosion of the stratification in the form of almost uniform motion, collision and “annihilation” of the interphase boundaries generally occurs at the second stage. In the long-wavelength limit, local thermal equilibrium sets in first. Then, a slower unstable magneto-acoustic motion formally reduces to that of a one-dimensional flow of a gas whose effective pressure P is a non-monotonic function of the density p. Also, the case of direct crossover from the long- to the short-wavelength regime is studied. We report on numerical simulations, which follow the nonlinear evolution of an initially small perturbation and predict formation of strongly stratified final states, determined by the function P(p) and transverse heat conduction and/or viscosity.