Evolution of α particle distribution in burning tokamaks including energy dependent α transport effects

Standard Fokker-Planck codes describing the α particle distribution function evolution describe the simple balance between the fusion source term and the collision operator. The lack of terms describing radial diffusion implies perfect α confinement neglecting prompt α orbit losses, various α ripple loss mechanisms and anomalous α diffusion during slowing down (such as that produced by resonant Alfven wave turbulence), not to mention neoclassical losses due to banana pitch angle scattering below the critical energy Ec. A tractable reduced description of radial α diffusion has been developed previously which describes the distribution of the α particles as a function of the α energy (E), radial flux label (ρ) and time. In the present worked, various energy dependent α ripple or anomalous model coefficients of diffusion in velocity space, D=D(E) will be implemented and studied. The source term in the Fokker-Planck equation is written as Qα=Qfusion + Qin, where Qin(ρ,E) is a loss term describing further α particle and heat transport models. The effect of energy dependence of the spatial α diffusion coefficient will also be studied using a multi-group set of continuity equations. We find strong sensitivity of the α evolution to the energy dependence of Dα(E). Figs