The strong dependence of fusion reaction rate on ion temperature leads to a thermalinstability of D T burning plasma.Mathematical qualites are discussed for the non-linear differential equations describing the steady state power balance of a D T burning plasma.Shooting method is used to obtain equilibrium solution and eigenvalue of the linearized equation about temperature pertubation around equilibrium.How ever,the solution obtained by the above method can be different from the time-dependent one for t→∞.This provides a typical example of a kind of unsolved non-linear mathematical problem.

Combined with the overall energy balance equation of the background plasma,the multi energy group equations which evolve the distribution function of α particles during slowing down are employed to perform self consistent numerical investigation of the burining plasma temperature profiles of importance to fusion reactors.By simulating both the dynamic and steady state plasma operating regime,it is showed that the burning plasma temperature profiles tend to be more peaked than that of the experimentally derived profiles.Such a feature is persisted whether or not there is significant diffusion of α particles during their slowing down and should be taken into account in future rigorous analyses of the behaviors and effects of α particles in fusion reactors.