The SLBR-50 is conceptually designed for research. Several basic parameters of the reactor are shown in Table 1. Thermal power of the SLBR-50 is 50 MW. The hot-condition average temperature is 700 K. As for materials, 19.95% enrichment UO₂ is applied as the fuel. The uranium total weight is 3835.3 kg in the SLBR-50. B₄C is chosen as the control rod absorber material. In each pin cell, stainless steel is conducted as the clad material. Outside of the active core, BeO is applied as the reflector and stainless steel is conducted as the barrel. Heavy metal lead is adopted as the coolant in the lead-based reactor SLBR-50. Other parameters will be introduced in geometry modeling.

The geometry modeling of the SLBR-50 is divided into the pin cell, the lattice, and the whole core. The basic pin cell geometry is shown in Figure 1. The radius of the fuel region is 4.0 mm. The thickness of the air gap between the fuel and the clad is 0.1 mm, which is hard to show in the figure. The 0.6-mm-thick clad lies outside of the pin cell.

The hexagonal assembly geometry of the fuel, reflector, and control rod lattice are shown in Figure 2. The basic geometry is totally the same for these assemblies. 61 rods are arranged in regular matrix form. The thickness of the stainless steel assembly box is 2 mm. The assembly inner and outer distances are 88.0 and 92.0 mm separately. The assembly center distance is 93.5 mm.

The radial cut of SLBR-50 whole-core modeling is shown in Figure 3, and axial cuts of all rods out (ARO) and all rods in (ARI) cases are shown in Figure 4. The whole core consists of 144 fuel assemblies, 48 reflector assemblies, 18 control rod assemblies, and center guide tube assembly. Control rod assemblies are divided into three groups, including compensation, safety, and power adjustment. Besides, reflector assemblies are located outside of the active core. The barrel is explicitly modeled and the diameter of the barrel is 82 cm. In the axial cut, the height of the active core is 95 cm. On the top and the bottom of the active core, a 20-cm-high coolant reflector is arranged.

Nuclear design calculations for the power distribution and control rod worth were conducted using the Monte-Carlo code RMC. In the calculation, the ENDF-VII.0 library was adopted. 10 layers were divided in the axial direction of the active core. To obtain the detailed power distribution results, a relatively refined calculation condition was applied in the calculation. 8 billion active particles were used (800 generations consisting of 10 million neutrons per generation, of which 300 generations were skipped). Normalized radial assembly power and axial power distribution results of the ARO case are shown in Figures 5, 6. In the radial assembly power result, the maximum assembly power is 1.46, which lies in the center of the reactor. In the axial power distribution, the maximum power is 1.268.

In the control rod worth calculation, 60 million active particles are used (600 generations consisting of 100 thousand neutrons per generation, of which 200 generations are skipped). The control rod worth results are shown in Table 2. Three sets of control rods are calculated. Integral rod worth (IRW) results are 6,915, 4,114, and 16,022 pcm for compensation, power adjustment, and safety control rod sets separately. Both differential rod worth (DRW) and integral rod worth (IRW) results show the shutdown depth is adequate for reactor control.

Rationality of the primary design for the SLBR-50 is confirmed by these nuclear design results. Apparently, parameters in the reactor design need to be researched to improve the reactor characteristic. In this study, the spectral-shift effect is researched and analyzed based on the SLBR-50.

The burnup depth and critical rod position results for the small reactor design are shown in Table 3. Three sets of control rods are withdrawn in the order of safety rods, power adjustment rods, and compensation rods. The initial rod position is −95 cm, where the control rod absorbers are totally inserted. The fast-spectrum operation is from the beginning of life to 1500 EFPD. In 1500 EFPD, all control rod absorbers are withdrawn and the spectrum-shift operation begins. The spectral-shift effect can extend the cycle length from 1500 EFPD to 2600 EFPD, which has a 73.3% improvement for the cycle length with the same fuel weight. Besides, the spectral-shift design has the same shutdown margin as the fast-spectrum design.

The kernel of the spectral-shift effect is the energy spectrum shift. Therefore, the energy spectrums are analyzed in typical burnup steps, shown in Figure 10. Energy sections are divided by an order of magnitude, from 1.0e-9 to 10 MeV. Each line shows the energy spectrum along all energy sections for the certain burnup. The energy spectrum analyses need to match with the spectral-shift rod withdrawal procedure. Besides, the thermal-spectrum result is provided in the beginning of life with all moderator rods inserted. The thermal-spectrum result can be shown as a reference in the spectrum-shift analysis. In the fast-spectrum operation from 0 EFPD to 1500 EFPD, energy spectrums are similar. Control absorber insertion has little influence on the energy spectrum. In the spectral-shift operation from 1500 EFPD to 2600 EFPD, moderators are inserted, and the spectrum-shift phenomenon can be observed in the energy spectrum analyses. The energy spectrum distribution of 2600 EFPD is similar to the thermal spectrum. It can be concluded that the spectrum-shift control rod design takes advantage of the spectrum-shift effect sufficiently in the SLBR-50.

Nuclide density variation is an important result for the spectral-shift effect. In the nuclide density analysis, only the spectral-shift scheme is conducted because that is the only scheme influenced by the spectral-shift effect. Considering the breeding of ²³⁸U to ²³⁹Pu, the fission reaction of ²³⁵U, ²³⁸U, and ²³⁹Pu is the dominant nuclear reaction in the burnup. ²³⁵U, ²³⁸U, and ²³⁹Pu are analyzed as the typical nuclides. The nuclide densities for these three nuclides are listed in Table 4, and the utilization rate variations in the burnup are shown in Figure 11.

As is shown in the table, the nuclide density of ²³⁵U and ²³⁸U is decreasing both in the fast-spectrum operation and the spectrum-shift operation, and the nuclide density of ²³⁹Pu is increasing. The phenomenon is caused by the relatively hard energy spectrum. In the burnup procedure, even though the spectrum-shift effect makes the energy spectrum softer than the original fast spectrum, the spectrum-shift effect is unable to change the harder energy spectrum in the SLBR-50. Therefore, the breeding of ²³⁹Pu is stronger than the fission absorption in the burnup procedure. All in all, the spectral-shift improves the fuel utilization of ²³⁵U and ²³⁸U from 11.5 to 19.1% and from 2.06 to 3.47%.