# Neutral Beam Coupling with Plasma in a Compact Fusion Neutron Source
## 3 BTOR Software and LNB Computational Methods  
BTOR (Beam in TORoids) software was developed in 2019 [20] to study neutral beam injection performance in plasma accounting for detailed NB statistics, 3D plasma configuration, and toroidal magnetic field effects. BTOR simulates fast ion population behavior by applying the classical theory of ion deceleration [6], and is capable of delivering, in seconds, any particle ensemble distribution with a detailed resolution. This 'lite' approach allows efficient optimization and fine-tuning of beam-plasma operation parameters by applying only straightforward and easily interpreted methods. Despite phenatural simplicity of metod, the BTOR results showed good agreement with similar results of ASTRA calculations [22] both for NB ion capture and NBCD efficiency, although the current density in the vicinity of magnetic axis was typically lower when compared to ASTRA profiles [15]. The BTOR package was designed as a set of data flow processing routines, where the particles data passes through transformations, which imitate physical events by applying probability, defined by a relevant cross-section, including atom ionization, fast ion deceleration to thermal velocity, plasma heating, current drive and fusion. This data processing method is referred to as _\(\sigma\)-approach_. With all the probabilities (\(\sigma\)) tabulated or pre-calculated, BTOR methods become deterministic and fast. The statistical model of the neutral beam is referred to as the 'lite' neutral beam (LNB), which will be introduced in more detail through the next sections. In short, the BTOR concept is to study beam-related effects by mixing data processing (\(\sigma\)-approach) with efficient analytical or low-order (lite) methods of beam  
Figure 6: Beam source particles statistical distribution before neutralization, left to right: (X, Y), (@x, @y), (X, @x), (Y, @y), where X, Y—horizontal and vertical position in the plane, @x, @y—horizontal and vertical angle from the beam main axis. The beam source spatial dimensions (shown in the left plot) correspond to the plasma emitter rectangle W \(\times\) H = 18 \(\times\) 115 cm\({}^{2}\). Figure 7: Neutral beam distribution in the NBI port plane: (X, Y), (@x, @y), (X, @x), (Y, @y), where X, Y—horizontal and vertical position in the plane, @x, @y—horizontal and vertical angle from the beam main axis. representation. Here, it should be noted that the scaling laws actively used in the classical tokamak modelling are not always applicable to compact and spherical devices. In plasma physics, ab initio models are assumed to be resource-intensive and time-consuming. However, the reduced numerical ab initio models, such as LNB for beam-driven effects study, can significantly speed up massive calculations while staying within acceptable accuracy. The LNB beam model takes the beam particles statistics at the plasma entrance (Figure 7), calculated by BTR code, and propagates them step-by-step, i.e., simulates the fast ion (FI) population release and its slowing down. The fast ion distributions in time are converted to energy profiles, which are further used for CD evaluation and neutron source spatial distribution. Atom ionization in plasma and ion deposition is calculated using the Janev multi-step ionization model [23], with an effective stopping cross-section comprising the main channels of beam ionization on plasma species.