Non-Linear Thermal Instability in Optically Thin

This paper contains a study of the stability of a slab like thermal structure constituted by an optically thin plasma with solar abundances in which there is generation and loss of energy, and a thermal diffusion of heat dependent on both density and temperature. The analysis is carried out by means of a second order approximation. A general expression for the Landau constant is obtained. Close to the first order marginal state this constant is completely determined by the power of the heat diffusion law and the first and second order derivatives respect to density and temperature of the heat/loss function. Normally, near the first-order marginal state, the second order is such that cooling perturbations are enhanced. However, it is possible to find circumstances where a finite perturbation may lead to the enhancement of heating. First and second order bifurcation points are determined when this function has a power dependence on density and temperature. The regions with different kind of instability or stability have been determined on the plane defined by the ratios between the dynamical and the relaxation time scale (α) and between the dynamical and the heating time scale (). Additionally, the time evolution at the onset of the nonlinear regime is analysed