## 4 Modelling and Simulation Results
This result demonstrates both the large breeding which takes place in this system (see the Pu accumulation in Figure 5) and the tremendous effect of the fission product accumulation on system criticality (see Figure 6). The general form of the breeding curve is comparable to results for other breeding based systems, such as sodium cooled fast reactors [34], while the detailed result is dominated by the core size/leakage and the correlation between fertile and fissile load in the system. The detailed Pu breeding (Figure 5) shows the growth of the plutonium content from zero in the initial composition to almost 10,000 ppm at the final burnup composition. Long term all Pu isotopes show an asymptotic approach to a steady-state value characterised by the specific balance between the breeding and the fission processes. The plutonium vector is mainly dominated by Pu-239. The higher Pu isotopes take longer to form but long-term, Pu-240 shows an increased steady-state amount due to its lower fission cross section, whilst Pu-241, with its significantly higher fission cross section, has a lower steady-state amount. The fission product accumulation, Figure 6 is seen to be almost linear with burnup for 5 leading fission product elements. In general, it is not surprising that the amount of fission products formed is directly proportional to the number of fission events that have taken place and thus to the amount of energy produced in the system (the burnup). Thinking a bit further into the future, this behaviour would change to asymptotic behaviour, with element concentration plateauing at a steady state value, if some constant share of the specific fission product element could be removed by a salt clean-up system. For the full investigation of fission product accumulation, the 142 isotopes of the highest concentration were evaluated from the POLARIS calculation as tested in [26]. The  
Figure 6: Accumulation of elements over burnup for selected leading fission products. accumulation of these isotopes was analysed in detail and the leading isotopes of up to 37 elements have been considered. The criticality effect of each of the different elements was determined through the use of a very specific procedure that has been developed and tested recently in [24]. At the target burnup of 100 GWd/tHM, the detailed composition was reproduced as a new starting input for a follow up calculation. This base case including all fission products indicated a criticality value of \(k_{ref}\) = 0.99224, used as the reference value. Based on this input a series of steady state calculations were then initiated to study the effect of the removal of the different fission product elements. Each time an element x was removed and the calculation was repeated, based on the new criticality value, \(k_{x}\), \(\Delta k_{eff}\) in pcm was generated using Equation (1). \[\Delta k_{eff}[pcm]=\frac{k_{x}-k_{ref}}{k_{ref}\cdot k_{x}}\cdot 10^{5} \tag{1}\]  
All major elements which result in a more than 50 pcm criticality effect (change in \(k_{eff}\)) are given in Table 1. The comprehensiveness of the chosen isotope and element set can be observed in the last two lines of the table. The line sum indicates the summed values of all considered isotopes in the table while the line whole indicates the effects when the whole isotope set of the POLARIS code is used. Thus, the considered isotope and element set given in the table considered 93% of the overall fission product concentration and 95% of the criticality reduction due to the fission product accumulation. The concentrations of these leading elements, in terms of their poisoning effect, can be seen to vary from Zirconium (at almost 4500 ppm) to Europium (\(\sim\)50 ppm) which reflects the widely differing neutron capture cross sections of these isotopes. One approach, in terms of developing potential separation methods, could be to only consider those elements with a significant concentration (say more than 500 ppm). This reduces the number of elements from 20 to 16.