# On the Dimensions Required for a Molten Salt Zero Power Reactor Operating on Chloride Salts
## 3 Results and Discussion  
### 2-D Criticality Versus Dimension Studies  
The first important information for designing a small scale zero-power core is the demanded size, the required salt amount, and the related amount of nuclear material. The required core size is studied through the variation of the enrichment, followed by the determination of the radius required to achieve a critical configuration in the 2-D system with an iteration accuracy of \(\pm\)100 pcm. The thickness of the reflector has been kept identical at 30 cm for each step of the study. The mentioned size of the core is strongly dependent on the salt composition--eutectic composition versus heavy metal rich composition, and on the fissile enrichment in the uranium chloride salt. The system radius and thus the required amount of salt is, as expected, to be continuously decreasing with increasing U-235 enrichment showing a kind of asymptotic behaviour for very high enrichment; see Figure 6.  
The observation holds for the reflected and the unreflected system (modelled by replacing the reflector material with a vacuum) as well as for the eutectic and the heavy metal rich system. The volume gain  
\[volume\;gain=\frac{vol_{HMR}-vol_{ET}}{vol_{HMR}}\;[\%]\]  
for the heavy metal rich (HMR) system stays almost constant with a volumetric reduction of approximately 30% compared to the eutectic system (ET), while for the 20% enriched system, the volume gain is slightly higher. The slight variation in the curves seem to be a result of the iteration limit for the dimensional iteration (\(\pm\)100 pcm). From the point of the required salt volume, a good gain can be achieved by increasing the U-235 enrichment to 35%--thus, a value higher than the safeguarding limit of 20%. The effect of going to higher values does not seem to give the required significant improvement to justify moving to a higher enriched fissile material.  
Figure 5: The general 2-D (left and centre) Monte-Carlo model of the configuration (left, top view x-y, centre front view x-z) and 3-D (left and right) Monte-Carlo model of the configuration (left, top view x-y, right front view x-z) with molten salt fuel core—blue, stainless steel vessel—light green, reflector—yellow, and vacuum—grey used for the validation of the results and the 3-D studies.  
The second step of the study analyses the efficiency of the reflector dependent on the U-235 enrichment and the two different salt configurations (Figure 7). For this step, all reflected critical configurations of the last step have been recalculated with the reflector region filled with vacuum, while the thickness of the reflector itself has been kept identical at 30 cm for each step. The figure indicates a clear change in the effect of the reflector with the expected growing gain caused by the reflector effect with increasing U-235 enrichment and the correlated decrease of the size of the critical system. The k\({}_{\text{eff}}\) of the drop caused by eliminating the reflector reaches up to more than 20,000 pcm for the highest enrichment, while the effect starts to saturate at high enrichments. The effect of removing the reflector is slightly stronger for the heavy metal rich system for lower enrichments, while this difference disappears for higher enrichment. The results of this step indicate a good opportunity to use the reflector as a future control system for a zero-power reactor in the case the enrichment is sufficiently high, at least 35% or higher. The control- and shut-down  
Figure 6: 2-D system radius for the eutectic and the heavy metal rich system depending on uranium enrichment for the reflected and the unreflected systems as well as the volume gain per step archived by changing from the eutectic to the heavy metal rich system (calculated through POLARIS).  
system will be discussed and analysed deeper in a second part of this study [21] and the effects of the use of different reflector materials in a third part [22].