# Neutral Beam Coupling with Plasma in a Compact Fusion Neutron Source
## 7 Fast Ion Distributions in Energy  
Since nuclear fusion between fast beam ions and thermal plasma ions is the main source of neutrons in FNS-ST tokamak, the fast ions energy distribution function (EDF) should contain an essential population with higher energies, or \"hot tail\" fraction, with a longer thermalization path and more probability to fuse until thermalization. The hot tail fraction grows when the beam is predominantly ionized and captured to passing orbits, and maximum neutron yield is achieved when all the beam rays are captured to passing tracks. The main steering parameters here are the beam energy and plasma density, with the operation range limited by the physical scenario and engineering aspects, such as the first wall overheating risks. Figure 21 shows the EDF of a deuterium beam for different energy ratios between the beam and plasma ions \(\text{E}_{\text{b}}/\text{T}_{\text{e}}\) (for a fixed plasma density \(\text{n}_{\text{e}}=1\times 10^{20}\) m\({}^{-3}\)). Thin colored lines correspond to the partial contribution of individual groups of slowing ions depending on the radial coordinate of their birth and circulation, whereas the bold black line shows the integral energy distribution across the slowing ions ensemble. Along each beam ray (atom track), the ion energy profile shape depends on the ion release radius (see Figure 21). A distribution peak at low energies can be normally observed for cold peripheral plasma layers, and a monotonic increase is more typical for the hotter core plasma layers. The larger the ratio (\(\text{E}_{\text{b}}/\text{T}_{\text{e}}\)) the smaller is the relative fraction of fast particles in the integral distribution, as is clearly seen from Figure 21b. The plasma temperature decrease for a fixed beam energy \(\text{E}_{\text{b}}\) leads to an expansion of a relatively cold plasma region from the periphery (\(\text  
from a thin beam option, especially for low aspect ratio systems. The initial distribution of fast ions and their velocity change along circulation, affected by the low aspect toroidal field, result in specific NBCD and neutron generation profiles, which are not specific for the conventional tokamak design. The total current drive and neutron yield in these systems are more sensitive to the beam shape. The beam thickness impact on NBCD in FNS-ST is illustrated in Figures 10-12 for E\({}_{\text{b}}\) = 100 keV/n. The FI path length in plasma and the driven current are roughly proportional to the ion slowing down time (\(\tau_{\text{s}}\)). Thus, the optimal conditions for current drive are naturally achieved for high beam relative energy (E\({}_{\text{b}}\)/T\({}_{\text{e}}\)\(>>\) 1), high plasma temperature and low plasma density, while the plasma density lower limit should be correlated with the beam energy (see Section 5). Figure 22 shows the influence of NB energy on the radial profile of the beam ion deceleration time, beam atom ionization and current drive. The overall current amplification due to FI circulation depends on the NB energy and on \(\tau_{\text{s}}\) profile. The initial fast ion orbital losses (see Section 6), including FI escape from the first Larmor circle and trapping to banana trajectories, reduce the current drive. The associated losses can be estimated with the fast ion release distribution map (Figure 17c). For spherical systems these losses amount to 70-80% if the NB energy is relatively low. The toroidal effects additionally reduce FI parallel velocity responsible for NBCD down by 20-30% (see Figure 20). If the atomic beam is produced from positive source ions (see Section 2), normally it consists of three energy fractions (E\({}_{\text{full}}\), E\({}_{1/2}\), and E\({}_{1/3}\)), contributing to the integral profiles of beam ionization, NBCD, and beam-plasma fusion. The NBCD efficiency of the three-component neutral beam was studied in detail in [25], with the NBCD estimated in FNS-ST plasma for the beam energy range E\({}_{\text{b}}\) = 100-140 keV accounting for NB composition.