Impact of delayed neutron constants on reactivity effects measured in a fast reactor

Delayed neutron parameters of fast VENUS-F reactor core configurations are determined with Monte Carlo calculations using various nuclear data libraries. Differences in the calculated effective delayed neutron fraction and the impact of the delayed neutron data (6or 8-group precursors) that are applied in the experimental data analysis on the measured reactivity effects are studied. Considerable differences are found due to application of U and U delayed neutron data from JEFF, JENDL and ENDF evaluations.


Introduction
Analysis of experimental data measured in numerous nuclear reactor physics experiments require the knowledge of core averaged kinetic parameters. Deterministic [1] or Monte Carlo methods [2,3] can be used to calculate the effective delayed neutron fraction  eff , decay constants  i and abundances  i of the precursor groups for a specific reactor core configuration as they depend on fuel composition and neutron spectrum.
Evaluated delayed neutron data (delayed neutron multiplicity  d , half-lives and abundances of precursors, delayed neutron spectra  d ) are available in general purpose nuclear data libraries (e.g. JEFF, JENDL, ENDF). The delayed neutron spectra are given in energy-group format (usually 16 groups of Hansen-Roach set [4]). The evaluated decay constants and abundances are given in time-group format (usually 8 groups [5] or 6 groups [6]). The group constants (as well as the fission yields) are evaluated at three energies: thermal, fast (fission), high (fusion). This study is focused on fast fission in 235 U and 238 U.
The influence of delayed neutron data on thermal reactor parameters has been widely investigated (e.g. [7,8]). In fast reactors the influence of delayed neutron spectra was studied [9,10], benchmarks for  eff were carried out at MASURCA and FCA critical facilities [11] and used for adjustment of delayed neutron yields [12]. In this paper, we describe the impact of delayed neutron data on the analysis of reactivity measurements at the fast zero-power VENUS-F reactor located at the Belgian Nuclear Research Center SCK•CEN. VENUS-F has been extensively used for fast neutron data validation [13][14][15][16][17] serving as a mockup of the MYRRHA fast reactor/accelerator driven system [18,19]. Sensitivity and uncertainty analysis of  eff were recently studied for the specific cases of the VENUS-F [20] and MYRRHA reactors [21].

Delayed neutron data
The half-lives and abundances of delayed neutron precursors are represented either with 6 groups (isotope-dependent half-lives) or 8 groups (identical half-lives for all the fissionable isotopes). Each nuclear data library makes its own best estimate based on various evaluated data available for each of the fissile and fertile isotopes in three energy regions. The current status of the delayed neutron parameters of 235 U and 238 U (relevant for the present study) adopted in the main nuclear data libraries is the following.
The JEFF library (since version 3.1) [22] uses Spriggs data (both decay constants and abundances) in 8-group format [4,5]. The JENDL library (since version 3.2) [23] uses the 6-groups data: decay constants of Keepin [6] and abundances evaluated on the basis of a large set of experimental and evaluated data. The ENDF library (since version VII.0) [24] uses the 6-groups data that come from summation calculations, which use decay constants and delayed neutron emission probabilities from the evaluated experimental data file NuBase2003 [25]; if not available, the data are calculated using quasi-particle randomphase approximation and the statistical gross theory [26]. One of the most remarkable features in ENDF is the remarkably short first group half-life compared to the other two evaluations, see Table 1. Other libraries like BROND-3.1, CENDL-3.1, TENDL-2017 adopted the same decay constants as in ENDF.
There are no uncertainties of the decay constants and group abundances in the evaluated data libraries. Only the original Spriggs data [5] contain uncertainties of the group abundances (group half-lives are fixed, thus, their uncertainties are reflected in the uncertainties of the abundances), which further leads to the uncertainty of the average halflife of the delayed neutrons (9.10 s ± 1% for fast 235 U and 5.3 s ± 3% for fast 238 U fissions). Although the group constants evaluated for thermal (25 meV) and high (14 MeV) energy have unambiguously defined energy, the mean energy of the fast spectrum specified in the evaluations is not always clear because of a wide variation in the mean energies of the experimental setups used in integral data studies. The 235 U evaluations in the fast spectrum correspond to a mean energy of hundreds of keV (some evaluations refer to 200 keV [4], 400 keV [22], 500 keV [24] or a range from 50 keV to 7 MeV [23]). However, the fast spectrum values for 238 U rather correspond to energies slightly above 1 MeV (although the evaluations again refer to 400 or 500 keV, which is not realistic due to the 238 U fission threshold energy). The energy dependence of the group decay constants was extensively measured [27].  4 30 In general, the delayed neutron production has a non-trivial energy dependence, especially above 1 MeV, see 235 U in Fig. 1. Below 10 keV,  d is constant and JENDL and ENDF give nubar about 2% smaller than JEFF. Between 10 and 50 keV,  d increases according to JENDL and ENDF, while it stays constant in JEFF evaluation. Between 50 keV and 1 MeV, ENDF gives  d about 2-3% bigger than JEFF and JENDL. The sharp decrease of  d above 4 MeV is likely to be caused by the second chance fission process. The  d covariances in JENDL lead to 3.5% uncertainty below 20 keV and 7 % uncertainty between 20 keV-3 MeV, which is significantly bigger than the differences between various evaluations.
The delayed neutron production in 238 U is about 3 times bigger than in 235 U with differences up to 5% between the evaluations.

Experiment
VENUS-F [28] is a fast zero-power reactor loaded with 30% wt. metallic uranium fuel. The core configuration presented in this paper used solid Bi as a coolant simulator and lead as reflector, see Fig. 2 (detailed description of fuel assembly composition and the entire core can be found in [15]).
For measurements of reactivity effects, either the compensation method [29] or the MSM method [30] are used. Both require the application of the delayed neutron parameters. The former through the calibration of control rods with a period measurement (the inhour equation). The latter requires the determination of a reference sub-critical state. For that purpose, a rod drop method is applied (see further).
The VENUS-F reactor was operated in a critical state at a stable power for sufficiently long time for the neutron population and precursor concentrations to reach equilibrium (about 20 min). Fission chambers [31] inserted in experimental channels in the reflector (see Fig. 2 left) were used to record a constant count rate n 0 .
Then, an absorber rod (made of B 4 C powder) located in the reflector (see Fig. 2) was rapidly inserted (the rod drop took 0.4 s). Detector count rates n(t) were measured as a  4 30 function of time after the rod drop (t = 0) until counting only background counts, i.e. the complete decay of the precursors, see Fig. 3 left.
The reactivity of the sub-critical configuration was determined using the integral counting method: (1) that requires the knowledge of the effective delayed neutron fraction  eff and the relative abundances of each precursor group  i =  i eff / eff (the number of groups being G = 6 or 8) characterized by the decay constants  i (calculated using the Monte Carlo method, see next section).
The expression ∑ i / i in equation (1) represents the mean life time of a delayed neutron  d = 1/ d = T 1/2 /ln (2). Its uncertainty combined with the uncertainty of the counting statistics of n 0 and the integral of n(t) after the rod drop contribute to the total uncertainty of the measured reactivity in units of $. The uncertainty of  eff needs to be added if the reactivity in units of pcm is required. Fig. 2. Left: radial cut through the VENUS-F reactor configuration discussed in this paper. The cut passes through the core midplane (marked with a dashed line in the right-hand side figure). The assembly pitch is 8 cm, both the core diameter and height are 160 cm. Right: axial cut through the core at the plane passing the rod drop and two safety rods (marked with a dashed line in the left-hand side figure). The depicted situation is after the rod was dropped (i.e. it is fully inserted in the core). Fuel assemblies -violet, B 4 C control rods (CR) and rod drop systemyellow, B 4 C safety rods (SR) -orange, lead reflector -green, experimental channels with fission chambers -white circles, stainless steel casing -black.

Calculation tools
The MCNP5-1.60 code [32] was used to calculate the kinetic parameters averaged over the VENUS-F core (i.e. spectrum and isotope averaged) with the iterated fission probability (IFP) approach [33]. The KOPTS card [34] with the number of cycles in blocks for adjoint weighting equal to 10 was used. Each criticality calculation consisted of 1850 active cycles preceded by 50 inactive, each of them having 10 6 neutrons. Such high number of histories was chosen to suppress the statistical uncertainties of the calculated kinetic parameters. The uncertainty of the calculated  eff is 2 pcm (i.e. 0.3%) in all cases.
It was tested at various VENUS-F core configurations that the IFP approach gives the same result of  eff as the prompt method [2]. An extensive verification of the Serpent-2 code against MCNP performed with the first VENUS-F critical core [35] provided a confidence in consistency of results, among others,  eff results of both codes agree within 1.
Cross-sections from the following evaluated nuclear data libraries were used in the MCNP calculations:  JEFF-3.1.2 (released in 2012 [36]) that is taken as a reference library in the next section; the same delayed neutron data were adopted in the newest release JEFF-3.3 (Nov 2017 [37]);  JENDL-4.0 (released in 2010 [23]);  ENDF/B-VII.1 (released in 2011 [24]) -the same delayed neutron data were adopted in the newest release ENDF/B-VIII.0 (Feb 2018 [38]), the only difference being the added  d covariances.

Results
First, the core averaged kinetic parameters calculated with different libraries are compared. Then their influence on the measured reactivity effects is discussed and the experimental results are compared with the MCNP calculations of the reactivity effects.

Effective delayed neutron fraction
The calculation with JEFF-3.  4 30 the kinetic parameters were measured [39]. All the calculations agree with the experimental value  eff = (730±11) pcm within the uncertainties.
That is the situation if cross sections and delayed neutron parameters of all the isotopes are used from a single library. In order to distinguish between the impact of both uranium isotopes and to investigate whether the cross sections have any impact on the core averaged kinetic parameters, new calculations were performed having JEFF-3.1.2 as a reference library and altering either the cross sections and the delayed neutron data or only the delayed neutron data of JEFF-3.1.2 with those of ENDF/B-VII.1 and JENDL-4.0 for 235 U and 238 U isotopes separately, see Table 2.
Replacing any of the JEFF-3.1.2 235 U or 238 U cross-sections or the delayed neutron data with those of JENDL-4.0 (while keeping everything else from JEFF-3.1.2) leads to the  eff value decreases by 1 %. No statistically significant influence of the 235 U and 238 U cross sections on  eff was observed.
If the delayed neutron data from ENDF/B-VII.1 are used for 235 U or 238 U, then the  eff value increases by 1 % or decreases by 2%, respectively. Such a strong influence of 238 U can be explained by the fast neutron spectrum (about 10% of fissions in the fuel happens in 238 U, see Fig. 3 right) and the bigger delayed neutron multiplicity than 235 U. The opposite effects of 235 U and 238 U partially cancel out and lead to a  eff value that is 1 % smaller when ENDF/B-VII.1 is used for all the isotopes compared to JEFF-3.1.2.

Precursor groups
Core averaged abundances of delayed neutron precursors calculated using the three main libraries are compared in Fig. 4. Only the 1 st and the 4 th group from ENDF and JENDL have similar values. The 2 nd and the 3 rd group in JENDL have abundances bigger by 20% than in ENDF, while the 5 th and the 6 th group in ENDF have abundances bigger than JENDL by 20% and 40%, respectively. ENDF has thus more weight on the shorterliving precursors and, as a consequence, the average delayed neutron half-life is shorter: 7.05 s for ENDF, 8.22 s for JENDL, 8.18 s for JEFF.
Mixing the delayed neutron data for fissionable isotopes in 6 and 8 groups in one calculation, as it was done in the previous section, can lead to absurd core averaged group half-lives. JEFF-3.1.2 used as a reference has the same half-lives of the 8 groups for both 235 U and 238 U. If ENDF or JENDL data in 6 groups are applied for one of the isotopes, then  4 30 the core averaged half-lives of the 1 st -6 th groups change, while those of the 7 th and the 8 th groups remain the same. That can cause the 6 th group having shorter half-life than the 7 th group, see example in Table 3.
In fact, such mixing is not an artificial thing. In JEFF, delayed neutron data in the 8 groups format are used for the well-known fissionable isotopes, however, for some other isotopes the delayed neutron data are evaluated in the 6 groups format [37]. Even in one of the test versions of JEFF-3.3, the 6 groups format was considered for 235 U and the 8 groups format for 238 U [37].

Reactivity effects
The evaluated delayed neutron data have impact on the measured rod drop reactivity, see equation (1). The reactivity (in $) is linearly proportional to the mean delayed neutron life time  d . As shown in the previous section,  d of the investigated VENUS-F core has almost the same values (difference of 0.6 %) when calculated with 8 groups of JEFF and 6 groups of JENDL delayed neutron precursor data. Therefore, the application of JEFF and JENDL lead to the same measured reactivity in $ and ENDF gives about 14% smaller reactivity in $. For reactivity in pcm, the difference between JEFF and the other two libraries increases by 1 %, see section 5.1.  4 30 MCNP calculations of the rod drop are compared with the experimental results in Table  4. A small variation (not more than 2 %) in the calculated rod drop reactivity was found when different libraries were used in the calculations.
When delayed neutron data from JEFF or JENDL were applied in the analysis of experimental data, then the calculations underestimate such experimental results (by 6-8 %). In case of ENDF, the calculations overestimate the experiment by 6 %.
The core averaged delayed neutron data from mixed libraries (discussed in sections 5.1 and 5.2) were also applied to the experimental reactivity determination, see Table 4. Replacing the JEFF delayed neutron data of 235 U by JENDL does not change the reactivity value, while replacing by ENDF leads to a significant change and overestimation of the experiment by 9 %. On the contrary, replacing the JEFF delayed neutron data of 238 U by either JENDL or ENDF leads to a perfect agreement between experiment and calculation.