Diffusion, creation and decay processes in plasma dynamics: Evolution towards equilibria and the role of bifurcated states

It is the purpose of the present contribution to introduce a new technique of analysis based on a central expansion in the spatial variable for a bounded state of a fusion plasma. The technique considerably simplifies the description of the dynamics as well as the determination of equilibria. For particular cases of practical interest, combining effects of alpha particle heating, external heating, ohmic heating and bremsstrahlung, explicit analytic results are obtained for equilibrium distributions. The analytic results are complementary to those of extensive direct computer calculations and useful as checks or for interpretation. The problem of studying nonlinear partial differential equations of a reaction-diffusion type is transformed to a description in terms of three characteristic dynamic variables which depend only on time and which are governed by three coupled nonlinear first-order differential equations. A unified description is given in one, two and three spatial dimensions and assumes radial symmetry for 2D and 3D cases. (orig./HSI)