NONLINEAR INSTABILITY OF NONHOMOGENEOUS THERMAL STRUCTURES

The set of families of steady state solutions of the energy equation w ith a heat diffusion term and a heat/loss term in a slab-like geometry have been obtained and their stability, up to the third order, analyz ed by applying Landau's method. For optically thin plasmas with solar abundances and with temperatures greater than 10(2) K, the kind of sta bility (instability) resulting for different heating mechanisms, as we ll as different heat diffusion laws, has been studied. In particular, the dependence of the linear rate, the second and third order Landau c onstants and the spatial temperature distribution of finite temperatur e disturbances on the degree of inhomogeneity of the initially steady state temperature distribution has been analyzed. A two parameter clas sification of the initially steady solutions has been obtained accordi ng to whether they show supercritical or asymptotic stability, or subc ritical or superexponential instability. In general? inclusion of inho mogeneity increases the variety of cases and. in particular, those cas es where the nonlinear stability is opposite to the linear stability. In many cases the second order is stable for positive perturbations, a nd unstable for negative perturbations, suggesting the formation of va rious types of condensations. (C) 1997 American Institute of Physics.