## 2 Transport Model  
The transport model used in the ASTRA code for heat is similar to previous simulations [13; 16]. To model the plasma density, in this work, ion transport equations are used,and the continuity equations are written separately for each of the isotopes of the main gas and each of the plasma fueling systems. Thus, a set of six continuity equations is formed,  
\[ \begin{array}{l}D^{+}:\left\{\begin{array}{l}\frac{\partial}{\partial t}n_{ beam}^{D^{+}}+\mathrm{div}\left(-D\
abla n_{beam}^{D^{+}}+Vn_{beam}^{D^{+}}\right)=S _{beam}^{D^{+}}-R_{beam}^{D^{+}},\\ \frac{\partial}{\partial t}n_{pel}^{D^{+}}+\mathrm{div}\left(-D\
abla n_{pel}^{ D^{+}}+Vn_{pel}^{D^{+}}\right)=S_{pel}^{D^{+}}-R_{pel}^{D^{+}},\\ \frac{\partial}{\partial t}n_{sep}^{D^{+}}+\mathrm{div}\left(-D\
abla n_{sep}^ {D^{+}}+Vn_{sep}^{D^{+}}\right)=S_{sep}^{D^{+}}-R_{sep}^{D^{+}},\\ \end{array}\right.\\ T^{+}:\left\{\begin{array}{l}\frac{\partial}{\partial t}n_{ beam}^{T^{+}}+\mathrm{div}\left(-D\
abla n_{beam}^{T^{+}}+Vn_{beam}^{T^{+}} \right)=S_{beam}^{T^{+}}-R_{beam}^{T^{+}},\\ \frac{\partial}{\partial t}n_{pel}^{T^{+}}+\mathrm{div}\left(-D\
abla n_{pel}^ {T^{+}}+Vn_{pel}^{T^{+}}\right)=S_{pel}^{T^{+}}-R_{pel}^{T^{+}},\\ \frac{\partial}{\partial t}n_{sep}^{T^{+}}+\mathrm{div}\left(-D\
abla n_{sep}^ {T^{+}}+Vn_{sep}^{T^{+}}\right)=S_{sep}^{T^{+}}-R_{sep}^{T^{+}},\\ \end{array}\right.\\ \end{array}  \tag{3}\]  
where \(n\) is the density of deuterium (\(D^{+}\)) or tritium (\(T^{+}\)) ions in the fast ion beam (_beam_), pellets (_pel_) or particles that arrive from the divertor zone through the separatrix (_sep_), \(S\) is the ionization source, \(R\) is the recombination sink, \(D\) is the diffusion coefficient, and \(V\) is the convection velocity (particle pinch). It is easy to see that the equations do not contain charge exchange terms (see, for example, [3]), since it is difficult to take them into account in the chosen approach. Estimates made for the typical parameters with which the simulations were performed (Section 3 et seq.) showed that the influence of the charge exchange effect (including charge exchange on beam atoms) can be neglected, given the other assumptions used, which seems to be acceptable at the moment. It is seen that the sum of the equations for each isotope gives the full continuity equation. Therefore, the solutions for the flux and total ion density are the same as in the case of solving the single full equation. Although the separation of one type of particle into \"partial\" components is quite artificial from the viewpoint of transport processes, such an approach allows one to quite naturally feed the answers obtained by the 1D plasma transport simulations into the 0D simulations of the tritium FC flows. For each equation, boundary conditions are set at the last closed magnetic surface,  
\[ \begin{array}{l}D^{+}:\left\{\begin{array}{l}n_{beam}^{D^{+}}(a)=0,\\ n_{pel}^{D^{+}}(a)=0,\\ n_{sep}^{D^{+}}(a)=\left(1-f_{sep}^{T}\right)\times n_{i}^{SOLPS},\\ \end{array}\right.\\ T^{+}:\left\{\begin{array}{l}n_{beam}^{T^{+}}(a)=0,\\ n_{pel}^{T^{+}}(a)=0,\\ n_{sep}^{T^{+}}(a)=f_{sep}^{T}\times n_{i}^{SOLPS},\\ \end{array}\right.\\ \end{array}  \tag{4}\]  
where \(f_{sep}^{T}=S_{sep}^{T^{+}}/(S_{sep}^{D^{+}}+S_{sep}^{T^{+}})\) is the fraction of the tritium source and \(n_{i}^{SOLPS}\) is the density of main gas ions at the plasma boundary obtained by SOLPS calculations [13]. Separation of the consistent value \(S_{sep}\) (\(S_{0 sep}\) in terms of [13], etc.) cannot be performed in the ASTRA code since \(S_{out}^{T}\) depends on \(S_{sep}^{T}\), which gives a nonlinear equation in the system.