\section{Activity of an irradiated MYRRHA FA}\label{Activity_FA}
The activity of a FA as a function of the decay time is evaluated from its source term as described in eq. \eqref{act_dh}.
\begin{figure}[H]
    \centering
    \begin{minipage}{0.94\textwidth}
        \includegraphics[width=\linewidth]{images/plots/FA/ref_activity/crit_ass.png} 
    \end{minipage}
    \hfill
    \begin{minipage}{0.94\textwidth}
        \includegraphics[width=\linewidth]{images/plots/FA/ref_activity/sc_ass.png}
    \end{minipage}
\caption{FA activity as a function of discharge burnup and decay time. Critical configuration in the top figure, sub-critical in the bottom.}
\label{fig:batch_act}
\end{figure}
As already discussed, this work has the objective to investigate all the possible discharge situations of an irradiated FA. The evolution of the FA activity for 70 years of decay in critical and sub-critical configuration is drawn in Fig. \ref{fig:batch_act}.\\

\textit{Envelope activity}\\
The envelope activity is determined considering the FA conveying the largest activity in every step of the decay. Fig. \ref{fig:env_act_sc} shows the evolution of the envelope curve and the associated FA burnup. 
\begin{figure}[h!]
\centering
\includegraphics[width=0.95\textwidth]{images/plots/FA/ref_activity/env_sc.png}
\caption{Evolution of envelope activity in sub-critical configuration.}\label{fig:env_act_sc}
\end{figure}
The curve describes the the sub-critical configuration --- i.e., the operation mode that gives the larger activity. The FA activity for the critical case is omitted since the same considerations can be drawn.\\
In the first period of decay the activity is dominated by the assembly with lower burnup, that underwent only one irradiation cycle but at the highest power in the central core position. On the contrary the most irradiated assemblies (largest burnup) contribute the most in the long term.\\

\textit{Contributors to envelope activity}\\
The activity in the short period is dominated by short-lived fission products, while at longer decay times it is dominated by $^{241}$Pu.
The longer the cooling time the more the effects of burnup are important. The FA with the largest burnup is responsible for the envelope curve for decay times greater than three years, when the most of the activity is produced by the actinides.
This behaviour is underlined in Fig. \ref{fig:frac_sc}, showing the contribution of fission products and actinides to the FA envelope activity curve.\\
\begin{figure}[h]
\centering
\includegraphics[width=0.95\textwidth]{images/plots/FA/ref_activity/frac_sc.png}
\caption{Fractional evolution of major contributors to the envelope activity. The actinides are drawn with solid line while the fission products with dashed.}\label{fig:frac_sc}
\end{figure}
The figure shows the nuclides contributing for more than 5\% to the envelope activity in the period ranging from 1 to 70 days of decay. Some fission products are in a secular equilibrium \cite{SecularEquilibrium}, that is,  one parent nuclide with a relatively long half-life decays in a very short-lived daughter nuclide. In this case such nuclides are considered together as a source of activity (and decay heat).
The decay chain $^{95}$Zr ( $t_{\frac{1}{2}} = $ 64.03 d) / $^{95}$Nb ( $t_{\frac{1}{2}} = $ 34.99 d) gives the largest activity contribution at 90 days of decay. At more than 100 d the dominant contribution comes from $^{241}$Pu. It decays in $^{241}$Am than takes over after 70 years of decay. For longer time periods most of the activity is associated to americium and plutonium isotopes.\\
The same approach employed to present the activity of a MYRRHA FA is also adopted in the next section to show the decay heat results.

\begin{center}
\fbox{\begin{minipage}{0.98\textwidth}
The time evolution of the activity of a MYRRHA FA was parametrically quantified as a function of the FA burnup to produce an envelope activity curve. In the short term the FAs with low burnup provide the largest activity because of the abundance of short-lived fission products. For longer time scales the FAs with high burnup produce the largest activity because of  $^{241}$Pu. FAs with intermediate burnup values make up the envelope activity curve in the decay range 30-1000 days. 
\end{minipage}
}
\end{center}