# Neutral Beam Coupling with Plasma in a Compact Fusion Neutron Source
## 1 Introduction
The release point radius and initial pitch angle (the angle between the ion velocity and the magnetic field vector) of the fast particles result in a wide scattering across the beam constituent rays, which can lead to a lower FI fraction captured to the most favorable magnetic orbits, with higher CD efficiency and neutron output. The overall performance of a _thick_ (realistic) NB shape is essentially lower compared to classical _thin_ beam models (e.g., traditional pencil-like representation [10]). In compact tokamak devices, including spherical design, the size of the beam envelope cross section can be of the same order as the plasma cross section, so the shaping effects are generally more pronounced. The enhanced orbital losses stem from the combination of the beam ions statistics in 6-dimensional phase space and the magnetic field topology. It is important to add that NBI optimum operating range is predominantly based on currently available and cost-effective neutral beam production technologies. The NB composition and spectra are commonly defined by the NB creation scheme. Several efficient NBI models and codes have been presented recently, which are capable to calculate NBI fast ion distribution almost in real time, due to simplified fast ion birth procedure, very low ion orbits statistics for interpolation, and analytical solution of the Fokker-Planck equation, e.g., as implemented in RABBIT code [11]. To speed up the calculation, the effect of beam shaping is included analytically. The RABBIT code is reported to run \(\sim\)1000 times faster compared with NUBSAM code [12], showing small deviations (\(\sim\)10%) between the results, which is supposed to be acceptable for many applications. However, a more sophisticated approach of beam geometry representation [13] has proved to offer a more reliable and accurate NBI simulation, especially for studying three-dimensional beam-plasma phenomena. Finally, in the context of integrated tokamakmodelling frameworks, there are NBI models based on simplified (narrow-beam) approach, with generalization to a realistic NBI geometry, e.g., NEMO code [14]. The main advantage of the mixed approach is its modularity, with the possibility to work with any tokamak equilibrium and injector geometry; it can also be integrated in a workflow with any global transport code. To study the geometry impact on NB response and performance in tokamak plasmas, we propose a light-weighted technique of multi-ray beam tracing (LNB, Lite Neutral Beam) [15], which strikes a balance between the best features of the present-day advanced NBI models, i.e., high accuracy, flexibility, almost real-time performance, and finally the ability to be integrated in a calculation workflow. The LNB approach is generalized in a software package BTR-BTOR. The beam statistics are normally represented by 10\({}^{5}\)-10\({}^{9}\) particles derived from BTR code [16; 17]. BTR code was developed 25 years ago to target the issues of NBI design [18], and has been actively used since 2005 until now, especially in ITER NBI design and study [19]. In BTOR pipeline (Beam in TORoids) [20], the numerical methods for particle tracing and transformations, as well as the input beam model itself are inherited from BTR code. The numerical procedures are deterministic and easy tractable, all the results can be reproduced and easily explained. The BTOR code takes the BTR data set containing the detailed NB atoms statistics, composed of phase coordinates and current fraction, and next, \"propagates\" the beam data flow through tokamak plasma: through the beam ionization, and the slowing down until relaxation. This approach allows for calculation of particle distributions in the phase space, beam losses estimation, NB heating efficiency, NBCD, beam-plasma fusion rates, and other beam induced effects. The main idea of BTR-BTOR workflow was to apply a highly efficient BTR technique to all beam-driven events, i.e., to the source beam simulation, atom ionization, fast ion slowing down and fusion probability calculation.