# Neutral Beam Coupling with Plasma in a Compact Fusion Neutron Source
## 4 Beam Ionization and Fast Ions Deposition  
The model of NB multi-step ionization described in the previous section was applied to the calculation of fast ion release rates within the injection channel, which is the plasma volume containing the NB atom tracks. Beam atoms that pass the plasma without ionization create shine-through power losses. They produce a thermal load on the first wall of the tokamak chamber, which has to be evaluated for all possible scenarios of tokamak operation, especially in transient regimes with low plasma density.  
In a low aspect ratio tokamak, the beam spatial geometry and the internal angular structure (beam shaping), when combined with magnetic field topology effects, result in a complex beam deposition footprint, with a 3D structure completely different to \"thin\" beam geometry (or single ray beam). Therefore, the profiles of beam-driven current and neutron generation in compact and spherical devices cannot be approximated by thin (pencil-type, or narrow) beams, which can be a reasonable reduction for higher aspect devices, such as ITER. The beam finite size impact is illustrated in Figures 10 and 11, in which the beam attenuation, the fast ion release rate, and the resulting current are shown for thin (single ray) and thick (0.3 \(\times\) 0.6 m\({}^{2}\)) beam options. Figures 10a and 11a show the profiles along the NB axis, while Figures 10b and 11b show the corresponding radial profiles in plasma poloidal cross-section (RZ-plane).  
Figure 9: FNS-ST calculation model with plasma magnetic surfaces and the neutral beam box (BTOR). (**a**) The multi-ray neutral beam model (parallel beam cluster); (**b**) poloidal plasma cross-section with magnetic surfaces (LCMS is the last closed magnetic surface).  
The beam ionization footprints (2D) in poloidal RZ-plane for thin and thick beam options are shown in Figure 12 for deuterium beam energy E\({}_{\text{b}}\) = 200 keV, and for the beams on-axis targeting. It can be seen that these two beam options produce not only different shapes of the injection channel, but also different radial profiles of beam ionization (shown in red).  
Figures 10 and 11 also illustrate the change of the ion initial pitch cosine, i.e., the angle cosine between the initial ion velocity and the local magnetic field vector. This value is also impacts NBCD calculation, since it defines a parallel velocity component driving the current. With a finite beam thickness and internal angular dispersion (NB shaping effects), the ionization rate and total amount are varied across the tangential chords within the injection channel, due to difference in time of flight, plasma density along the chord, and pitch angle scatter. The beam shaping effects are also responsible for thermal load high asymmetry and power peaking at the tokamak first wall, which is produced by a non-uniform distribution of shine-through beam power losses along different NB rays tangential chords.  
Figure 11: Profiles of thick beam (real shape) penetration (BTOR): (**a**) along the horizontal axis; (**b**) the correspondent radial profiles in a poloidal cross-section.  
Figure 10: Profiles of thin beam (single ray) penetration (BTOR): (**a**) along the horizontal axis; (**b**) the correspondent radial profiles in a poloidal cross-section.