# Neutral Beam Coupling with Plasma in a Compact Fusion Neutron Source
## 2 NBI Scheme for FNS-ST and the Source Beam Structure
### Neutral Beam Structure  
The shape of the beam and its internal structure are determined by beamlet focusing provided by the ion-optical system (IOS) and by the beamlets' internal angular dispersion. The ion beam, initially formed by the plasma emitter and accelerated in a multi-grid multi-aperture IOS, consists of 400 beamlets in accordance with the apertures setup across the extraction and acceleration grids (electrodes). In the FNS-ST injector unit based on positive ions, the source beam is organized as a vertical column of five rectangular sections (beamlet clusters) with 80 beamlets each. To ensure efficient beam transmission to the tokamak without overheating the beamline elements, the beamlet focusing is rather complex. All the beamlets throughout the IOS column in a horizontal plane are aimed at NBI port center-point, while in a vertical plane, within each cluster, the beamlets axes are parallel to the cluster axis, and the clusters' axes are steered to reduce the entire beam cross-section at NBI port plane in tokamak. The beamlet focusing scheme is shown in Figure 2.  
Figure 2: FNS-ST NBI beamlets axes focusing (BTR main screen). The ion current within each beamlet is supposed to have a normal distribution along the polar angle, and the sum of Gaussian fractions fits the beam angular shape in all NBI schemes. For example, the positive ion beam in FNS-ST is well matched by a two-dimensional Gaussian profile (with different standard deviations along horizontal and vertical axes), while a negative ion beam, combined by two angular fractions (core and halo) can be reproduced by a sum of one-dimensional profiles versus polar angle from the beamlet axis:  
\[j(\theta)=\frac{1-H}{\pi\Delta_{c}^{2}}e^{-\theta^{2}/\Delta_{c}^{2}}+\frac{H }{\pi\Delta_{h}^{2}}e^{-\theta^{2}/\Delta_{h}^{2}}\, \tag{1}\]  
where \(\theta\) is a polar angle from the beamlet axis, \(H\) is so called halo fraction, and \(\Delta_{c}\) and \(\Delta_{h}\) are the angular widths of the core \(h\) halo. Note that the Gaussian width in our notation is not the same as the standard deviation \(\sigma\) for normal distribution. The positive ion beam in FNS-ST is supposed to carry a single core fraction, with no halo. The positive ion beamlet angular width in the FNS-ST NBI is assumed to be 15 mrad, which implies that at a distance of 11.5 m, i.e., at the NB port plane, each beamlet footprint is \(\sim\)33 cm in diameter; therefore, the nominal NB port width was chosen to be 30 cm. With the beamlets perfect alignment towards the center-point of the 30 \(\times\) 60 cm\({}^{2}\) NBI window, the calculated beam transmission efficiency is \(\sim\)76%, with an injected power of 3.5 MW. If the beamlets' alignment is not perfect (the beam is \"misaligned\"), with errors of \(\pm\)4 mrad in the horizontal and \(\pm\)6 mrad in the vertical direction, the NB power delivered to plasma reduces down to 3.3 MW (with the beam transmission \(\sim\)71%), as shown in Figure 3.  
Since a reduced size of the injection port is highly preferred, an option of NB injection through a window size 20 \(\times\) 40 cm\({}^{2}\) was considered and compared with the window nominal size 30 \(\times\) 60 cm\({}^{2}\). The result profiles of beam power delivered are shown in Figure 4. With perfect beam alignment to the 20 \(\times\) 40 cm\({}^{2}\) injection port center-point, the calculated beam transmission was \(\sim\)50%, with an injection power of \(\sim\)2.3 MW, which corresponds to a one third decrease from the nominal case. With misalignment of 4/\(-\)6 mrad along horizontal/vertical axes, the power input to the plasma reduces down to 2.1 MW (reduced 36% from the nominal port size, with NB transmission decay down 46%). Taking into account the neutralization yield \(<\sim\)50%, the overall NBI performance was about 25%, and all the injector units delivered only \(\sim\)6 MW to FNS-ST plasma.