## 4 Consistent Model for Calculating Fluxes in the Fuel Cycle  
The FC-FNS code [15; 20; 21] is used to calculate the fluxes of the fuel components in the FNS-ST fuel cycle and the accumulation of tritium in the FC systems. The code is adopted for calculating the FNS-ST parameters. It uses the data on the particle fluxes in the plasma, calculated with the SOLPS4.3 [16; 22] and ASTRA [23] codes using built-in models of the bulk and divertor plasmas. The SOLPS4.3 code package realizes a 2D model of the edge (SOL and divertors) plasma in the assumption of the toroidal symmetry, involving the fluid description of the electrons and ions and the Monte Carlo modeling of the atoms and molecules. In the ASTRA code, a 1.5D approximation is used - that is, the one-dimensional (radial) transport of energy, particles, and current is modeled using the metric coefficients calculated from the 2D plasma equilibrium consistent with the plasma pressure and current profiles. The SOLPS run results relevant for the core-edge coupling are parameterized to form scalings for the plasma parameters at the separatrix, and these scalings form the boundary conditions for ASTRA [24]. This approach was previously used for analyzing the FC of the DEMO-FNS facility [16; 25; 26], and in this work, it is used for the FNS-ST facility. To describe adequately in ASTRA the heat and particle fluxes in the bulk plasma, we use the Bohm/gyro-Bohm transport model [27] that takes into account the effects of nonlocal transport. This model developed for JET was successfully implemented for spherical tokamaks such as START [28] and MAST [29]. The diffusivity of the plasma particles and the average plasma density are varied to determine the possible range of variation of the fluxes in the FC. The particle diffusivity is taken to be proportional to the electron heat conductivity and is varied in the range of \(D/\chi_{e}=0.2\)-0.6 according to the research done on different devices [30; 31]. The average plasma density is varied inside the range of \(n_{e}=7.0\)-10.0 \(\times\) 10\({}^{19}\) m\({}^{-3}\), which, together with the variation of the diffusivity, determines the possible range of the fluxes in the FC. The plasma density profile is then determined by the electron heat conductivity together with the particle sources from the gas influx across the separatrix, pellet injection, and NBI. The gas influx is calculated in the SOLPS code, and the profile of the corresponding ion source is calculated in ASTRA and depends on the density and temperature profiles inside the separatrix. The radial profile of the ion source from the pellet injection is pre-defined, with the maximum at some distance from the separatrix and the magnitude as the external parameter. The radial profile of the ion source from the neutral beam is calculated with the NUBEAM code [32] built in ASTRA. An example of the resulting density profile for a D beam case is shown in Figure 1. No density profile difference between the D and D + T beam cases is observed in our calculations. Note that the density profile shape has a minor impact on the neutron yield that is dominated by the beam-plasma interaction. The resulting dimensionless plasma parameters, such as the collisionality of \(\sim\)0.02 and the normalized ion Larmor radius of -0.03-0.04 in FNS-ST (with the central ion temperature of 6-8 keV), are not far from those in the shots from the database analyzed in [30; 31], thus justifying the implementation of this transport model for FNS-ST.  
We use the FC-FNS code developed at the NRC Kurchatov Institute (Russian Federation) to simulate the balance of particles in the core and divertor plasma (based on the results calculated by the ASTRA and SOLPS codes) as well as the flows in all fuel cycle systems (in steady-state mode) and, accordingly, the calculation of the T inventory in them.