Evolution of temperature profiles in a fusion reactor plasma

The dynamics of plasma temperature profiles depends on the simultaneous processes of diffusion and creation, e.g. heating by alpha particles, as well as losses, e.g. bremstrahlung, and furthermore on the effects of boundaries, which play an essential role in the formation of equilibria. The temperature evolution is governed by a partial differential equation of the reaction-diffusion type. The heating by alpha particles is represented by a source term which depends on temperature to a certain power. The present contribution summarizes the concepts and recent results of a new technique of analysis based on a central expansion in the spatial variable. The problem of studying the nonlinear partial differential equation governing the evolution of a temperature profile is transformed to a description in terms of three characteristic dynamic variables (amplitude, width and shape) which depend only on time and which are governed by three coupled first order differential equations. Such equations allow for dynamic description of self-organisation in open as well as bounded systems. The technique simplifies the description of the dynamic properties of the temperature evolution of a burning fusion plasma. It provides physical insight in the dynamics of the system by analysis of the interplay between the various simultaneous processes. In particular, the problems of existence, accessibility and approach to possible equilibria can be studied by means of the new technique.