## 4 Modelling and Simulation Results  
The first step was to define a reasonable base case close to the eutectic composition 45%NaCl-38.5%UCl\({}_{4}\)-16.5%UCl\({}_{3}\) which achieves a significant burnup and results in a sufficient amount of fission products to create a sufficient effect on criticality by each fission product. As well as being important to obtain a reliable estimation of the effect each fission product element has on criticality, it is also required to obtain insight into the likely concentrations of fission products as a basis for the design of a future separation (clean-up) system. The analysis is based on the standard case of [26] at the lowest planned temperature level of 930 K, with a system radius of 213 cm, a target burnup of 100 GWd/tHM, an initial U-235 enrichment of 11.78 at% which has been found in an iterative approach to create a critical system at this temperature. The system size was iterated in a multi-stage approach. The first iteration is used to determine an enrichment which delivers an initial criticality for each size within an accuracy of <10 pcm, while in the second stage a burnup case was run to determine the maximum criticality achieved through the burnup with the aim of determining the radius that delivers a maximum \(k_{\mathit{eff}}\) of 1.006 at the point of highest criticality, see Figure 3.  
The used model shows a typical burnup behaviour of a breeder system (see Figure 3, or [26]) which is characterised by a profile starting with growth in criticality until a single, central peak followed by a continuous decrease, cause dby the fission product accumulation and the effect of removing all fission products, see Figure 4. The curve starts at criticality (iteration condition) with the degree of criticality rising initially caused by the breeding of new fissile material from the fertile U-238, see Figure 5. In general, the breeding and burnup behaviour of a reactor core is characterised by a competition between different processes: (a) the formation of new fissile material, (b) the consumption of fissile and fertile material, and (c) the progressive build-up of fission products which has an increasingly strong and long term effect. Thus, the first part of the curve is dominated by breeding, which delivers an increase in criticality, whilst the second part is dominated by fission  
Figure 3: Criticality of the 2D finite system, as measured by \(k_{\mathit{eff}}\), as a function of burnup (time) for different system radii for the close to eutectic composition 45%NaCl–38.5%UCl\({}_{4}\)–16.5%UCl\({}_{3}\). product accumulation, see Figure 6 (and the slow decrease in the amount of fertile U-238, which slightly slows the breeding) which delivers a progressive decrease in criticality. Figure 4: Criticality over burnup for the base case (213 cm from Figure 2) for the investigation compared to criticality development for a virtual system without fission products. Figure 5: Accumulation of isotopes over burnup for selected leading breeding products. An extended burnup curve at the standard evaluation temperature of the study, 980 K, is given in Figure 4. The curve using the higher temperature is used to create a balance between the over and under critical areas of the curve to obtain the best possible representation of breeding with the least influence of the \(k_{\mathit{eff}}\) normalization on breeding. The reference (base) case radius of 213 cm is again showing the initial increase in criticality caused by breeding and the longer-term reduction of the criticality due primarily to fission product accumulation as given in the black curve of Figure 3 (observe in addition to the slight reduction in the initial criticality due to the fuel temperature change from Figure 3 to Figure 4). To identify the potential maximal effect of a clean-up system that would remove all fission products, the criticality development of a theoretical system without fission product accumulation is then given for comparison.