Spallation Source

The spallation source is an essential part for the continuous operation of a sub-critical reactor. In the following, the options for the simulation of spallation sources in MCNPX are described and the procedure to calculate the source efficiency from the MCNPX output is explained.

4.3.1 Implementation in MCNPX

In the old MCNP versions, only neutron transport could be performed and energy ranges were restricted to ranges for which tabled cross sections were available. With the merge of the capabilities of the LAHET 2.8 program and MCNP-4B into MCNPX, more applications became possible. LAHET allows particle transport also for higher energies using different theoretical models. Since then, MCNPX is capable of simulating all particles and energies (Pelowitz 2011). When no tabled cross sections are present, which often is the case only up to 20 MeV, theoretical models to determine the reactions rates are used. The user can choose between several physics models.

For the implementation of the spallation source in the computer model, the example in the MCNPX User’s Manual (ibid., p. 373ff) comparing the different physics options is used as a reference for the resulting neutron production per incoming proton. In the base case, protons, neutrons and charged pions are transported. LAHET physics are used when no cross section data is present. The nucleon and pion interactions are also simulated using LAHET physics with the Bertini model based on the intra-nuclear cascade description of spallation processes. It is the most simplified model using only three different zones for the description of the charge in the nucleus. The CEM03 code increases this number to seven and the ISABEL code to 16 zones. For these different available physics models, the resulting neutron yield and computing time are tabled. Furthermore, one calculation also transporting light ions using the ISABEL INC model was documented (ibid.). It is shown that for the neutron production in a spallation target, the transport of protons, neutrons and charged pions is sufficient. The resulting values for the neutron yield n/p vary only slightly depending on the physics model.

It is recommended in the MCNPX User’s manual that the user tries the different options to decide which model is appropriate for the considered problem. Consequently, several calculations for the case of a spallation source in the center of a sub-critical reactor system were performed. The calculated values for n/p show only small variations and are consistent with published figures for the case of a spallation source (¸Sarer et al. 2013). Yet, because the CEM03 code is widely recommended to model the actual physics best, it was used for production calculations. Additionally, to account for higher energies than commonly present in reactor core calculations, the cut-off energy for neutrons protons was increased from 100 MeV to 1000 MeV.

The depletion code VESTA allows not only criticality sources in the Monte Carlo module as input for its depletion calculation, but all possible sources. Therefore, the spallation source could be simulated during burn-up and the influence of the high-energy tail of the spallation neutrons is represented in the material compositions derived from the simulation. But even with the newest MCNPX Version, the neutron multiplication factor can only be calculated with a specialized criticality source. Consequently, separate calculations for the criticality of the system were conducted at the beginning of life with fresh fuel and also with partly burnt spent fuel taken from the depletion calculation.

4.3.2 Calculation of the Source Efficiency

For the calculation of the source efficiency, it is necessary to determine the neutron yield n/p for the given problem. As already discussed, there are various ways to define a source neutron in a more complex geometry than a simple spallation target. In the MCNPX manual, two ways to calculate the neutron yield are described for a simple geometry (Pelowitz 2011). All necessary information is by default printed in the MCNPX output files.

The problem summary in the output file lists neutron creation and loss figures for elastic and inelastic nuclear reactions, denoted nuclear interactions and (n, xn) reactions6. All figures are given per source particle and averaged over the whole computer model. For the case of the simulation of a proton beam on a target, the source particles are the incoming protons and the problem only consists of the spallation target. The neutrons yield can then be calculated as

n

p = net nuclear interaction + net (n, xn) + tabular sampling. (4.2)

Tabular sampling herein accounts for the energy region where no cross sections are provided and only models are used. For the case of a sole spallation source, a simplified approach can be taken: since the only loss mechanisms for neutrons are escape and capture, these two values can be simply added up for the net neutron production. This does not hold true anymore when fissile material is present around the core. In this case, the loss and capture figures comprise fission reactions as well. Consequently, for the analysis of an accelerator-driven system, equation 4.2 is applied. It is simplified that the fission reactions occur in the sub-critical core. The nuclear interaction and (n, xn) reactions occur in the spallation target. Several preliminary calculations have shown the viability of this approach. Moreover, the consideration of fission figures in the shorter loss and

creation method yields the same results as equation 4.2.

Theoretically, even more reactions and factors could be taken into account. For instance, the problem summary also lists creation due to delayed fission separately. Its relative (per source particle) appearance in the core is considerably smaller than the figure for prompt fission. The change on n/p is affected more by the position of the spallation target in the core than by the less likely reactions in the core. These are neglected in the determination of its value.

For the calculation of the source efficiency according to equation 3.15, additional calculations for the determination of the multiplication factor ke f f were performed. The average neutron yield

per fission was set to 2.95 and the number of fissions per source neutron can be derived from the number of fission per source particle as listed in the MCNPX output file and the neutron yield n/p. The resulting values for the source efficiency can be used in a second step to estimate the beam power for a given power output and criticality of the system. According to definition 3.17, the beam power depends on the source efficiency and the neutron yield. If these two factors are explicitly inserted, some of the dependencies cancel each other out. The beam current then only depends

6 _{The from (n, xn) denotes the interaction of an incoming neutron with the target resulting in the production of x}

on the neutron loss per fission as provided in the MCNPX output file and constant parameters for the considered problem. This includes the average energy yield per fission Q_{f iss} and the power of the reactor system. The equation can thus be simplified for the considered reactor system with 100 MWth as

I= 0.5A · 1

loss to fission. (4.3)

It yields the beam current I in Ampere in dependence of one single figure from the computational output.