Micro-depletion data generation

Micro-depletion data is generated for Ants simultaneously with spatial homoge- nization. Data is included in the GenPoly library in the post-processing phase of homogenization. The library itself is then sufficient for providing all necessary information for the Ants micro-depletion method. The method requires homogenized microscopic reaction cross sections, homogenized nuclide number densities, fission yield tables, and decay data. The scope of the data set is dependent on the size of the depletion system.

Serpent calculates microscopic cross sections into a few-group structure according to user input. The input requires the universe of the homogenized material, volume, list of materials, and a list of nuclides and reactions. Separate micro-depletion systems can be defined with multiple input cards. The user is responsible for listing appropriate reactions to create sensible transmutation chains for the modeled system.

The pre_2.2.1 development version of Serpent that was used in this thesis has an input option for listing all possible reactions for all nuclides in the homogenized material. In principle, this should be sufficient for creating all required transmutation chains for fuel depletion and it was used to create the initial micro-depletion input.

However, the following changes had to be made to the input to create a consistent depletion system for fuel.

1. Only a subset of all neutron reactions were included and the rest were filtered away. In general, only reactions removing the original nucleus and forming a new one should be included. The list of allowed reactions is shown in table 3.3.

2. For some nuclides, the total fission-reaction cross section is not available in the nuclear data library. In this case, Serpent can calculate the total fission based on the sum of 1st-, 2nd-, 3rd-, and possibly 4th-chance fission cross sections.

However, the automatically generated input only includes nth-chance fissions.

The input was processed by removingnth chance fission reaction numbers and adding the total fission reaction number.

3. Some nuclides have radiative neutron capture reactions separately listed for the ground state and metastable excited state. The automated input erroneously lists these reactions only for the ground state. In this thesis, the list was modified by adding the neutron capture to exited state for nuclides that had the ground state already listed.

For all reactions and all nuclides, Ants forms the depletion matrix by calculating the removal rate for the target nuclide and the production rates for reaction products. If the reaction does not have any end product, the target nucleus is removed without any product. For example, including elastic scattering in the micro-depletion input will lead to huge errors. The third point is also related to the same phenomenon.

If neutron capture reaction to the ground state is only included, the metastable state is not produced at all. As a result, the total amount of the product nuclide is underestimated.

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Table 3.3: List of allowed reactions in fuel transmutation chains. Reactions and their descriptions are based on ENDF neutron reaction numbers. The list contains all reactions which change the target nucleus to another. Reaction MT 45 (n, npα) was unintentionally not included in the list. However, it is a rare reaction and it should not have a significant impact on results.

MT Reaction Description

11 (n, 2nd) production of two neutrons and a deuteron 16 (n, 2n) production of two neutrons

17 (n, 3n) production of three neutrons 18 (n, fission) Total fission

22 (n, nα) production of a neutron and an alpha particle 23 (n, n3α) production of a neutron and three alpha particles 24 (n, 3nα) production of two neutrons and an alpha particle 25 (n, 3nα) production of three neutrons and an alpha particle 28 (n, np) production of a neutron and a proton

29 (n, n2α production of a neutron and two alpha particles 30 (n, 2n2α) production of two neutrons and two alpha particles 32 (n, nd) production of a neutron and a deuteron

33 (n, nt) production of a neutron and a triton 34 (n, n³He) production of a neutron and a ³He particle

35 (n, nd2α) production of a neutron, a deuteron, and two alpha particles 36 (n, nt2α) production of a neutron, a triton, and two alpha particles 37 (n, 4n) production of four neutrons

41 (n, 2np) production of two neutrons and a proton 42 (n, 3np) production of three neutrons and a proton 44 (n, n2p) production of a neutron and two protons 102 (n, γ) radiative capture

103 (n, p) production of a proton 104 (n, d) production of a deuteron 105 (n, t) production of a trition 106 (n, ³He) production of a ³He particle 107 (n, α) production of an alpha particle 108 (n, 2α) production of two alpha particles 109 (n, 3α) production of three alpha particles 111 (n, 2p) production of two protons

112 (n, pα) production of a proton and an alpha particle 113 (n, t2α) production of a triton and two alpha particles 114 (n, d2α) production of a deuteron and two alpha particles 115 (n, pd) production of a proton and a deuteron

116 (n, pt) production of a proton and a triton

117 (n, dα) production of a deuteron and an alpha particle

The second point requires a more detailed description of how fission yields are treated. Fission yield energy dependence is taken into account by dividing the fission reaction artificially into different reactions that have different yields. Then, few-group homogenized microscopic cross sections for these reactions are evaluated such that the total fission yield is equal to the way Serpent treats different fission yields. For instance, the total fission reaction cross section is labeled with MT number 18. It is listed in the micro-depletion input as 181, 182, 183, ... where the last number indicates which fission yield table should be used for that reaction. Each of these reactions has a different homogenized microscopic reaction cross section reflecting the fission yield energy dependence. Other fission reaction cross sections are treated similarly, like 1st chance fission with MT 19 and 2nd chance fission MT 20. Output for these reactions would be 191, 192, 193, ... and 201, 202, 203, ... respectively.

The labeling of fission reactions with different yields might conflict with other MT numbers. Numbers from 152-200 are unassigned, thus total fission MT numbers 181, 182, 183, ... and 1st chance fission 191, 192, 193, ... are fine. However, reaction numbers for 2nd chance fission 201, 202, and 203 conflict with total neutron, gamma, and proton production reaction numbers. There are also conflicts with 3rd chance fission, but 4th chance fission should be in unassigned space again. Thus it was decided to use only total fission reaction numbers for micro-depletion input for consistency and to avoid unexpected results.

In addition to homogenized microscopic cross sections, Serpent output for each calculation contains smeared nuclide densities, fission yield tables, and decay data.

Homogenized microscopic cross sections change as a function of burnup and feedback variables. Therefore they are also parameterized with the polynomial fit (3.2) and historical effects are corrected with the plutonium-indicator method. Decay data and fission yield tables can be simply read from a single point to the final GenPoly library.

The final micro-depletion input for each fuel assembly contained at most three different micro-depletion transmutation chains or micro-depletion regions. The first was the simple transmutation chain from²³⁸U to ²³⁹Pu and related reactions needed for the plutonium correction method. The second micro-depletion region contained all nuclides and reactions for fuel depletion. The third region was optional and it was defined for the depletion of burnable absorbers. It was included in all assemblies with burnable absorber rods, but the analysis was left out of the scope of this thesis.

The micro-depletion data input for fuel depletion was extensive. The total number of different nuclides included in fuel micro depletion was 1463. From these nuclides, 1270 had decay data and 376 had reaction data. The sum of all distinct reactions was 4346 and the total number of distinct fission yield tables was 108.

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