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.

A new method for nonlinear random vibration-the Monte Carlo method based on the path-integral formalism is presented. The statistics of response of nonlinear systems to white noise excitation is represented in the path-integral forms. Then the Monte Carlo method is used for calculation. Due to the natural combination of the path-integral formalism and the Monte Carlo method, the new method is very concise and straightforward.Some aspects related to applications are discussed, and two numerical examples give the verification of the new method.