\section{Production mechanisms for the nuclides relevant for the source term of the MYRRHA FA}
In this sections the production paths of the nuclides relevant for the analysis of the source term of a MYRRHA FA are described.
The nuclides taken into account belong to three categories:
\begin{itemize}
    \item volatile fission products important in case of accidental release;
    \item nuclides contributing to the decay heat in the FA after;
    \item plutonium isotopes and minor actinides relevant for the spent fuel management.
\end{itemize}

The production mechanisms are investigated by a thorough analysis of the the reaction rates involved in the depletion process.
A limit of this study is that only the critical operation mode is analysed, and that all the nuclear reactions for neutrons with energies above 20 MeV are not taken into account.
This assumption is deemed to be acceptable for the analysis of the fuel source term.
An insight of the difference in the production mechanisms present in the critical and sub-critical mode of operation is presented in appendix \ref{h3comments} for specific nuclides ($^{3}H$).\\
The considered volatile nuclides are produced mainly by fission either as direct fission products or as indirect fission products following the isobaric decay process. $^3$H is produced by ternary fission.
Their production via neutron capture is generally negligible.

The outlier of this category is $^{134}$Cs, which results from neutron capture in $^{133}$Cs.\\
The same conclusion can be drawn for the fission products relevant for decay heat, with their production being mainly linked to the fission of plutonium isotopes.\\
\begin{figure}[h!]
    \centering
    \begin{minipage}{0.9\textwidth}
        \includegraphics[width=\linewidth]{images/plots/FA/2D_fa/pu_bu.png} 
    \end{minipage}
    \hfill
    \begin{minipage}{0.9\textwidth}
        \includegraphics[width=\linewidth]{images/plots/FA/2D_fa/am_bu.png}
    \end{minipage}
        \begin{minipage}{0.9\textwidth}
        \includegraphics[width=\linewidth]{images/plots/FA/2D_fa/cm_bu.png}
    \end{minipage}
\caption{Buildup of actinides during irradiation, normalized on the \acrshort{EoI} concentration.}
\label{fig:actinides_buildup}
\end{figure}

Minor actinides appear from the neutron-induced transmutation of the uranium and plutonium isotopes contained in the fresh \acrshort{MOX}.
The MOX fuel considered for MYRRHA is made by 30\% of plutonium, which drives the nuclear fission chain with isotopes $^{239}$Pu and $^{241}$Pu.
In parallel, plutonium is bred and depleted through neutron capture reactions.
The buildup of plutonium isotopes is shown in the first plot of Fig. \ref{fig:actinides_buildup}. The most depleted isotope of plutonium is $^{241}$Pu since its participates to fissions and its production mechanism is less effective than for $^{239}$Pu since more neutron captures are necessary.
$^{238}$U is the is the most abundant nuclide in the fresh fuel and a continuous source of $^{239}$Pu via neutron capture.
The reaction chain is shown in eq. \ref{eqDC}.\\
\begin{equation}
^{238}U \xrightarrow{(n,\gamma)}\ ^{239}U \xrightarrow{(\beta_{-})}\ ^{239}Np \xrightarrow{(\beta_{-})}\ ^{239}Pu
\label{eqDC}
\end{equation}
Minor actinides are concerning for \acrshort{SNF} management.
$^{241}$Am is the main contributor to decay heat at 70 years of cooling because of its half-life. It is produced by $^{241}$Pu $\beta_{-}$ decay both during irradiation and after discharge of the fuel assembly.
Additional neutron captures in $^{241}$Am lead to the production of other minor actinides such as $^{242}$Cm, as shown in eq.~\eqref{eq2}.
\begin{equation}
^{241}Pu \xrightarrow{(\beta_{-})}\ ^{241}Am \xrightarrow{(n,\gamma)}\ ^{242m}Am \xrightarrow{(\beta_{-})}\ ^{242}Cm
\label{eq2}
\end{equation}
\\
$^{242}$Cm  ($t_{\frac{1}{2}} = $ 163 d) is important for the FA decay heat following the considerations in Sect.~ref{coreDH}. It is produced by the radioactive decay of $^{242m}$Am and, because of its half-life, it reaches its peak concentration at intermediate burnup levels, i.e., before the FA discharge. Its irregular buildup curve is to be associated by its decay constant.\\   
$^{243}$Cm is produced by neutron capture in $^{242}$Cm, while only a small amount of $^{244}$Cm ( $t_{\frac{1}{2}} = $ 18.00 y) follows this chain.
The $^{244}$Cm dominant production path is from the $\beta$-decay of $^{244}$Am ( $t_{\frac{1}{2}} = $ 10.1 hr), generated by successive captures in $^{242m}$Am.
Heavier curium isotopes are produced through neutron capture in $^{244}$Cm with a strong non-linear dependence on burnup.\\
$^{243}$Cm and $^{245}$Cm ( $t_{\frac{1}{2}} = $ 8255.49 y) have larger (non-threshold) fission cross sections compared to other curium isotopes, and they can also fission spontaneously.
However, because of their tiny concentration in the nuclear fuel their major depletion mechanism is $\alpha$ decay.
\begin{center}
\fbox{\begin{minipage}{0.98\textwidth}
The nuclides relevant for the source term of the MYRRHA FA were divided into three categories.
Volatile fission products, as well as fission products important for the decay heat are directly produced by fission.\\
The minor actinides that pose a burden for the spent fuel management are generated from the nuclear transmutation of the plutonium driver fuel.
\end{minipage}}
\end{center}
