# Neutral Beam Coupling with Plasma in a Compact Fusion Neutron Source
## 1 Introduction  
Spherical tokamaks (ST) can provide high neutron flux density and good compatibility with fission blankets at a lower cost than conventional tokamaks. A neutron source FNS-ST with a compact design based on a spherical tokamak [1] is expected to provide a stationary neutron flux of \(\sim\)10\({}^{18}\) n/s. The device operating parameters (T\({}_{\rm e}\) = 5 keV, n\({}_{\rm e}\) = 10\({}^{20}\) m\({}^{-3}\)) are chosen accounting for a high neutral beam (NB) contribution to non-inductive current drive (CD). The estimated NB contribution to neutron yield is up to 99%, coming from deuterium-tritium (DT) fusion between hot beam particles and relatively cold plasma, with a Maxwell velocity distribution [2]. NB tangential injection is also an efficient current driver, since the fast ions produced and captured by plasma create a current parallel to the magnetic field during their circulation and deceleration (slowing down) in the plasma. The beam ion current, together with the bootstrap current fully substitutes the inductive current in FNS-ST plasma, ensuring the steady-state operation of the device [3]. However,additional heating and CD systems significantly increase the cost of the entire machine. In addition, due to the low aspect ratio (R/a) and moderate values of the toroidal magnetic field, the relative fraction of fast particle losses in a spherical tokamak significantly exceeds that in tokamaks with a high aspect ratio (classical or conventional) [4], since the Larmor radius of fast ions at the low field side of torus can be comparable with a rather low minor radius, and with the magnetic field variation scale. In order to minimize the losses of fast particles and to boost the injected power, the parameters of NB injection need to be chosen accounting for the beam efficient penetration to plasma, and to ensure the most favorable beam deposition within the plasma core volume. For an efficient neutral beam current drive (NBCD), the beam energy should exceed by a factor of 3-5 [5] the so-called critical energy [6], the latter depends on the plasma electron temperature and on the normalized beam mass (i.e., the ratio of the beam to the background ion mass). NBCD increases with higher electron temperature and lower plasma density, which extend the fast ion thermalization time. Taking into account the toroidal geometry and the strong inhomogeneity of parameters across plasma cross section, all the beam-driven effects, including NBCD, beam-plasma fusion rates, heating and plasma rotation, are sensitive to instant fast ions (FI) deposition in plasma. The FI spatial distribution produced by the beam, or NB footprint, is defined by the beam atom penetration depth in plasma, or rather, the average path of individual groups of fast atoms before their ionization point. As a result, factors such as beam penetration depth, FI circulation time, and direct losses of fast atoms and released ions, finally determine the choice of the beam-plasma mode operation and NB aiming tuning in a beam-driven tokamak. The problem of geometry impact on beam-plasma interaction is highlighted in [7], where different calculation models of NBI are compared, and the results show a visible discrepancy in the fast ion distribution and loss of NB performance between various beam models applied to the same beam-plasma system. In addition, the experimental data, which are not in a perfect agreement with NBCD simulation, especially for off-axis tangential injection [8; 9], also motivated us to perform a more detailed study of beam-plasma geometry impact on NB efficiency. The beam spatial shape and angular distribution (6-dimensional NB geometry in a phase space) have an essential impact on the beam ions release in plasma and their final capture by the magnetic field.