Alpha particle distribution for full energy region

Abstract

The alpha particle distribution in the full energy region is studied in this work. The Fokker–Planck equation near the equilibrium state is analytically solved using an iteration method for alpha particles. The resulting distribution includes the Maxwellian part, the modified slowing down part, and the high energy tail part. The analytical results align with the conventional slowing down distribution in the high energy region vα>0.2vb and the Maxwellian distribution in the low energy region vα<0.1vb, where vα is the alpha particle velocity and vb is the birth velocity of alpha particles. In the range of 0.1vb<vα<0.2vb, the distribution is described by the sum of the Maxwellian part and modified slowing down part. Turbulent transport effects on the alpha particle distribution are studied through introducing a local sink term. A simplified analytical solution is provided, and the bump-on-tail distribution is observed under appropriate parameters. In both cases with and without transport effects, the Fokker–Planck equation is numerically solved. It is shown that the full temporal evolution of the system can be divided into three stages: the slowing down stage, thermalization stage, and quasi-steady state stage. The numerically obtained alpha particle distribution in the quasi-steady state stage agrees well with the theoretical results.