Neutron Flux in the Reactor Cores

For the evaluation of the fuel composition over burn-up in the future EFIT reactor, an approach already made by others was taken: two EFIT-like fuel elements are placed in the MYRRHA in-pile test sections (IPS) (Sarotto et al. 2013). But this approach implies that the neutron fluxes in the in-pile test sections of the MYRRHA reactor core can be compared to the fluxes in the future EFIT reactor. This assumption is tested simulating the MYRRHA and the EFIT core with fresh fuel and no spallation source present. For both cores, the same number of source particles is used.

The neutron flux distribution is calculated at different positions in each core. The results are plotted in arbitrary units in Figure 7.4. The energy range was chosen according to preliminary calculations of the neutrons spectrum in the core. For the EFIT core, the relative neutron flux is depicted for one exemplary fuel element from the inner, the intermediate and the outer core zone. As expected, the value is lowest in the outermost core zone. The behavior of the flux is quite similar for all three graphs in the medium energy range. For high and low energies, the statistical variation of the flux is much higher due to the lower number of scores per energy bin.

Looking at the neutron flux from the EFIT-like fuel element7in the IPS section MYRRHA reactor, the same behavior of the energy distribution can be seen, but the normalized flux is about one magnitude higher than in the EFIT reactor. The neutron flux in the MOX element also shows one important difference: the dip at around 90 keV is missing. In the EFIT fuel elements, it is caused by the inert magnesium matrix. Magnesium-24, comprising nearly 80 % of natural magnesium, has a neutron absorption resonance at 83 keV8.

10-4 0.001 0.010 0.100 1 10 10-11 10-10 10-9 10-8 10-7 10-6 10-5 Energy in MeV N e u tr o n F lu x in A rb it ra ry U n it s

Figure 7.4.: The neutron flux distribution in the EFIT and MYRRHA sub-critical cores. The position of the elements in the EFIT core affects the absolute flux they are exposed to. For the MYRRHA reactor, the neutron flux distribution for one EFIT-like and one MOX fuel element is plotted. The MOX fuel does not show the characteristic dip at around 90 keV like the magnesium oxide matrix fuels. Absolute values depend on the actual power density in the reactor core.

There are different reasons why the flux curves for the two reactor cores differ so much. On the one hand, the different fuel compositions in the total core result in different probabilities for certain reactions. In the P&T-fuel present in the MYRRHA IPS and the EFIT elements (high content of plutonium and minor actinides), the probability of capture per source neutron is doubled compared to the MOX fuel elements. On the other hand, less neutrons introduce fission reactions (about 10 % less reactions per source particle in the Monte Carlo simulation).

This is also mirrored by the different criticality levels of the reactor cores. At EOL with fresh fuel,

k_{e f f} for EFIT is only at 0.96 while for MYRRHA k_{e f f} (in BOC configuration, which is used in equilibrium operation) it is nearly one (0.99). The different values connotate indirectly the number of fissions that is induced per source neutron. Thus, starting the same number of particles does not equal the same number of fissions which also explains the lower level of the flux in the EFIT reactor. For EFIT an extremely low source efficiency of only 0.52 is published in Artioli et al. (2007). Therefore, a high proton beam is needed to achieve the targeted power output. To allow for a

7 _{EFIT-like fuel elements have a reduced number of fuel pins to fit into the MYRRHA fuel element geometry.}

8 _{It seems strange that the inert matrix magnesium has such a strong influence on the neutron spectrum. To}

verify the statement, several calculations of the neutron flux distribution with different fuel compositions were performed.

smaller particle accelerator and a more economic operation of the reactor, it is quite likely that in the ongoing design process efforts will be taken to increase the source efficiency. For the MYRRHA core in BOC configuration, the calculation of the source efficiency results in a value of 0.97. For a given energy output equal to a certain number of fissions in the fuel, significantly fewer neutrons from the spallation source are needed.

The fact that the absolute magnitude of the neutron fluxes differs to such a high degree complicates the translation of the fuel element exposure from the MYRRHA IPS to the future EFIT core as for example done in Sarotto et al. (2013). Figures depending on the absolute neutron flux the material is exposed to must be careful analyzed to ensure commensuration. In the following, this will be either done by evaluating the material after a range of irradiation times or, if possible, by using reference values that are mostly independent of the absolute value of the neutron flux.

7.3.4 Source Efficiency

One figure usually easily obtained from the burn-up calculations is the criticality of the system over burn-up. This does not hold true for a sub-critical system driven by a spallation source. Even the newest version of MCNPX (MCNP6) is not capable of doing criticality calculations while at the same time external neutrons, e.g. by a spallation source, are produced and tracked. The importance of the source neutrons increases with decreasing criticality over burn-up (reactivity swing). To keep the same power level during one sub-cycle, it is possible to increase the beam current. To calculate the source efficiency and the beam current, the knowledge of the effective multiplication factor

k_{e f f} is required. Consequently, for one sub-cycle during equilibrium operation of the MYRRHA reactor explicit criticality calculations were performed.

One sub-cycle consists of 90 days of irradiation and a subsequent 30 day maintenance period. Corresponding to the time steps in the burn-up calculation, the criticality, source efficiency, and beam current were calculated every 30 days, beginning at BOC. Table 7.6 shows the results. The reactivity swing over burn-up can be clearly seen. Criticality of the core increases again with the insertion of fresh fuel. All criticality values lie in the range between 0.95 and 0.97 as desired for safe reactor operation.

Directly connected to the neutron multiplication in the core is the source efficiencyφ∗as described in section 4.3.2. The source efficiency denotes the importance of the external supplied neutrons compared to the neutrons produced in the core. It can be calculated using equation 3.15. By definition it is only usefully described in a sub-critical reactor where an external neutron source is present. For the MYRRHA reactor core, the calculated values range from 1.19 to 1.28 at the end of the sub-cycle. With decreasing intrinsic reactivity of the core due to burn-up the external source neutrons become more important for core dynamics. For comparison, a source efficiency of 1.08, calculated at BOL with ke f f = 0.995, is given in IAEA (2015, p. 45).

Table 7.6.: Evolution of the effective multiplication factork_{e f f}, the source efficiency and the beam current over one arbitrary sub-cycle in equilibrium mode of the MYRRHA reactor model.

k_{e f f} Source Efficiencyφ∗ Beam Current I

0 0.971 1.19 2.21 mA

+30 Days 0.964 1.24 2.65 mA

+60 Days 0.959 1.24 3.10 mA

+90 Days 0.954 1.28 3.43 mA

+120 Days 0.971 1.19 2.23 mA

The proton current supplied by the particle accelerator is used to balance the reactivity swing during reactor operation. The neutron production is proportional to the beam current on the

spallation target.The beam current I in particles per second is calculated using equation 3.17. Hereby, average values of 2.95 for the number of released neutron per fission and 200 MeV for the released energy per fission are taken. As also shown in Table 7.6, the resulting beam currents range between 2.21 mA and 3.43 mA. For the MYRRHA core, the planned maximum current is 4 mA.