# Neutral Beam Coupling with Plasma in a Compact Fusion Neutron Source
## 6 Fast Ions Losses and Toroidal Effects
The example ion orbits in the FNS-ST tokamak configuration for a reduced magnetic field value (B = 0.5 T, to make the Larmor radius wider) are shown in Figure 18a,b; they correspond to the ion passing along the magnetic line without collisions. Figure 18a refers to the fast ion released at the periphery, while Figure 18b shows the orbit of fast ion born in the vicinity of the magnetic axis. In the first case (Figure 18a) the ion is produced with a lower pitch cosine and, if it does not escape from the plasma at the first Larmor, it can be captured either to passing or to a trapped orbit depending on the poloidal coordinate of the birth. The fast ion released closer to the magnetic axis (Figure 18b) is passing, as its velocity vector is more parallel to the magnetic field vector and almost equal to the maximum pitch cosine value (see Figure 18c), while the mirror ratio at the axis is minimum: \(\Pi=\mathrm{B_{max}}/\mathrm{B_{min}}\sim\)1. The overall number of fast ions lost in spherical tokamaks due to orbital effects can reach 70-80%. These losses strongly depend on the beam energy, the NB shape and aiming geometry (radius, axis inclination). While Larmor losses can be reduced by increasing the magnetic field, ion capture onto trapped orbits is predetermined by the toroidal magnetic configuration and, therefore, cannot be totally avoided. For given tokamak parameters, the beam energy and aiming can be tuned to reduce overall beam losses and increase NBI performance. It should be noted that the optimum conditions for NBCD and for neutron generation typically differ and even necessarily overlap in parameter space. Figure 17: Fast ion orbital loss computation in BTOR: (**a**) loss cones due to Larmor (red) and banana (purple); (**b**) ion source distribution in a poloidal plane; (**c**) ion source over the radial coordinate (\(\psi\)) and pitch angle with overlapped loss cones (yellow shaded). Upper row = thin beam; lower row = thick beam 30 \(\times\) 60 cm\({}^{2}\). Figure 18: Fast ions orbits (BTOR plots): (**a**) at the plasma periphery (low magnetic field B\({}_{\rm t}\), low pitch cosine); (**b**) at the plasma core (high B\({}_{\rm t}\), high pitch cosine). (**c**) The magnetic vector direction (green arrows), beam ray pitch cosine variation (green profile) along the beam ray (blue arrow), and the fast ion release profile along the beam ray (red). For fast ions slowing down in plasma, neoclassical (toroidal) effects occur by magnetic field variation along the magnetic field line. For low inverse aspect ratio (\(\varepsilon=\mathrm{r}/\mathrm{R}\)) values, in the area close to the magnetic axis the toroidal effects almost vanish, while they grow at the plasma periphery. The ion current toroidal correction produces an additional strong impact on the current drive profile and the overall beam efficiency [24]. For each MES with a specific \(\varepsilon\)-value, the fast ions with a pitch cosine below the critical level (see Figure 17a) are trapped to banana orbits and do not drive toroidal current. Fast ions with a higher pitch cosine go on passing and circulating around the main toroidal axis. Their parallel velocity oscillates cyclically during their motion along the magnetic field line (see Figure 19), and the amplitude of oscillation depends on the pitch cosine at \(\mathrm{B_{min}}\) point (at the poloidal coordinate \(\Theta=0\)) and on the magnetic field mirror ratio \(\Pi=\mathrm{B_{max}}/\mathrm{B_{min}}\) along the magnetic field line. Figure 19 shows that the decrease of the average parallel velocity of the fast ions circulating around the torus, even without accounting for deceleration, depends on the ion initial pitch angle and on the MES mirror ratio \(\Pi=\mathrm{B_{max}}/\mathrm{B_{min}}\).