# Neutral Beam Coupling with Plasma in a Compact Fusion Neutron Source
## 6 Fast Ions Losses and Toroidal Effects  
In the FNS-ST compact tokamak design, plasma is confined by a toroidal magnetic field of about 1-1.5 T. Moderate field values impair the fast particles confinement, especially at the plasma low field side. In spherical tokamaks, in contrast to the conventional (i.e., higher aspect ratio) tokamaks, the toroidal magnetic configuration causes the essential fraction of ions captured towards the trapped orbits, which are not closed around the MES axis. The trapped (or unclosed, or banana) particle fractions, as opposed to the population of passing particles, drive no direct current in the toroidal direction. The orbital losses of  
Figure 16: NB shine-through power density maps at FNS-ST first wall for parallel beamlet aiming (NB port size 0.2 \(\times\) 0.4 m\({}^{2}\)) in two operation cases: (**a**) ideal beam alignment, total power—0.066 MW, peak density—1.13 MW/m\({}^{2}\); (**b**) beam nominal misalignment (error) \(4/-6\) mrad in horizontal and vertical planes, total power—0.065 MW, peak density—1.45 MW/m\({}^{2}\). For BTR power density profiles, the axes X, Y and Z correspond to NBI coordinates shown in Figure 2.  
Figure 15: NB shine-through power density maps at FNS-ST first wall (NB port size 0.2 \(\times\) 0.4 m\({}^{2}\)) in two operation cases: (**a**) ideal beam alignment, total power—0.070 MW, peak density—1.16 MW/m\({}^{2}\); (**b**) beam nominal misalignment (error) \(4/-6\) mrad in horizontal and vertical planes, total power–0.069 MW, peak density—1.50 MW/m\({}^{2}\). For BTR power density profiles, the axes X, Y and Z correspond to NBI coordinates shown in Figure 2.  
fast particles in spherical tokamaks typically exceed those in conventional tokamaks by several times. The initial fast ions energy released in FNS-ST from NB atom injection is \(\sim\)100-150 keV. Their Larmor radius in a magnetic field of \(\sim\)1 T is about several centimeters, so the fast ions born at the plasma periphery with a small pitch angle cosine escape from being captured by plasma already during the first Larmor circle. When the number of rescued ions is large, the total efficiency of NB heating and current drive decrease according to the lost ion fraction. The minimum (or critical) pitch angle cosine value, allowing the ion to be captured within the separatrix, i.e., the last closed magnetic surface (LCMS), is evaluated for a given beam particles energy and the magnetic field configuration. Based on the critical pitch, the lost ions fraction due to Larmor rotation is calculated for a given injection geometry defined by the beam shape and tangential aiming. A similar procedure is applied to the calculation of bounding pitch for ions passing, and to the trapped (banana) losses estimation. The beam fast ions with a pitch cosine less than the critical value are considered to be lost (or cut-off) within the \"loss cones\". Note the loss cone in a toroidal magnetic trap is inversed compared to the loss cone in mirror plasma devices. The fast beam ions trapped to banana trajectories, together with the ions escaping on the first Larmor, are considered as not driving the toroidal current, but they are supposed to contribute to the neutron generation. Accurate fast ion drift simulation is very expensive, especially in spherical tokamaks where the fast ion Larmor radius is comparable to the magnetic field inhomogeneity scale, and the drift approximation is not very applicable. BTOR implements the following simple procedure which boosts the fast ion loss evaluation speed: the fast ion loss diagram for a given magnetic configuration is calculated (Figure 17a), the two-dimensional distribution of the ion source over the radial coordinate (\(\psi\)) and pitch angle cosine (Figure 17b,c) are reconstructed, and finally both maps are overlapped (yellow shade in Figure 17c). The fast ion tracks are reconstructed by BTOR by combining the circulation along the field line and Larmor rotation.