# Fast Ion Speed Diffusion Effect on Distributions of Fusion Neutrons
## 3 Calculation Results
Therefore, the low-energy parts of darker and lighter surfaces in Figure 1 coincide as well as the low-energy contours shown by dashed and solid lines in Figure 2.  
Modelling of the \({}^{2}\)H(\({}^{2}\)H,n)\({}^{3}\)He reaction was performed assuming mono-directional injection of monoenergetic 130 keV deuterons into Maxwellian deuterium target plasma, with equal electron and ion temperatures 7 keV and the electron density \(n_{e}=10^{14}\) cm\({}^{-3}\). The injection angle \(90^{\circ}\) was used as a sample case, and the fraction of suprathermal tail deuterons was 2.5%. Figure 3a shows 3D plots of two anisotropic distributions of velocities of deuterium nuclei calculated for the same conditions. The dark-blue surface corresponds to the simplified model (2) without taking into account the speed diffusion. The light-blue surface corresponds to the semianalytical model based on (13), taking into account the speed diffusion effect. The presence of a high-energy tail in the vicinity of the injection angle can be seen. The tail is extending for the light-blue surface further than for the dark-blue surface. Figure 3b illustrates these same deuteron velocity distributions as 2D plots for three selected pitch angles: \(30^{\circ}\), \(60^{\circ}\), and \(90^{\circ}\). Figure 2: Contour plots of the anisotropic distributions of fuel nuclei shown in Figure 1 without the speed diffusion (dashed lines) and with the speed diffusion (solid lines). (**a**) Deuteron velocity distribution functions; (**b**) triton velocity distribution functions. Double differential reactivities with respect to neutron energy \(E_{n}\) and laboratory emission angle \(\vartheta_{n}\) are shown as surface plots in Figure 4a,b for \({}^{3}\)H(\({}^{2}\)H,n)\({}^{4}\)He reactions and for \({}^{2}\)H(\({}^{2}\)H,n)\({}^{3}\)He reactions, correspondingly. Blue surfaces show the results obtained with the fast ion speed diffusion effect and grey surfaces show the results obtained without the fast ion speed diffusion effect. The presence of extra tails of suprathermal ions with somewhat higher energies in the former case is responsible for a slight increase in the reactivities; however, the shapes of the surfaces do not significantly differ, qualitatively. Figure 4: Energetic and angular distributions of fusion neutrons calculated with fast ion speed diffusion effect (blue surfaces) and without fast ion speed diffusion effect (grey surfaces). (**a**) For \({}^{3}\)H(\({}^{2}\)H,n)\({}^{4}\)He reactions corresponding to velocity distributions of deuterons and tritons shown in Figures 1 and 2; (**b**) for \({}^{2}\)H(\({}^{2}\)H,n)\({}^{3}\)He reactions corresponding to velocity distributions of deuterons shown in Figure 3.  
Figure 3: Anisotropic distributions of deuterons without taking into account the speed diffusion (dark blue) and with the speed diffusion taken into account (light blue) for the case of injection energy 130 keV, suprathermal fraction 2.5%, and injection angle 90\({}^{\circ}\), depicted as: (**a**) surface plots; (**b**) velocity distribution functions of deuterons with pitch angles 30\({}^{\circ}\), 60\({}^{\circ}\), and 90\({}^{\circ}\). For clarity, the difference between the neutron distributions obtained with and without the effect of speed diffusion of fast deuterium and tritium ions is shown in Figure 5 for the \({}^{3}\)H(\({}^{2}\)H,n)\({}^{4}\)He reaction and in Figure 5 the \({}^{2}\)H(\({}^{2}\)H,n)\({}^{3}\)He reaction. Angularly resolved energy spectra of neutrons produced in \({}^{3}\)H(\({}^{2}\)H,n)\({}^{4}\)He reactions and in \({}^{2}\)H(\({}^{2}\)H,n)\({}^{3}\)He reactions are shown in Figure 6 and in Figure 6, correspondingly, for the cases when calculations were made using the simplified model (2) not taking into account the speed diffusion effect, and using a more sophisticated model (13), taking into account the speed diffusion in velocity space of fuel nuclei. Although noticeable differences in fusion product spectra can be observed, the obtained results demonstrate similar qualitative behaviour.