Benchmark of the Kilowatt Reactor Using Stirling TechnologY (KRUSTY) Component Critical Configurations

Abstract

Kilowatt Reactor Using Stirling TechnologY (KRUSTY) was a prototype for the U.S. National Aeronautics and Space Administration’s Kilopower Program. KRUSTY has a highly enriched uranium–molybdenum alloy (with 7.65 wt% molybdenum) annular core reflected by beryllium oxide with an outer stainless steel shield. Five configurations from the experimental campaign were chosen to be evaluated as benchmark cases. Uncertainties were evaluated in five categories: (1) criticality measurement, (2) mass and density, (3) dimensions, (4) material compositions, and (5) positioning. The largest contribution to the overall uncertainty in each case was from the radial alignment of the movable platen. A simplified model was created to increase computational efficiency, and an average bias of –16 pcm was calculated due to the simplifications. Sample calculations were completed for each case using MCNP6.2, COG, and MC21, all with ENDF/B-VIII.0 nuclear data. For MCNP6.2, the average difference (absolute value) between the calculated and experimental k_eff for the five configurations was 14 pcm for both the detailed and the simplified models. The k_eff results from all three codes are within 1σ of the benchmark values. KRUSTY’s value as a benchmark is due to its sensitivity to beryllium and molybdenum. For beryllium, KRUSTY adds an 18th benchmark with a total cross-section sensitivity greater than 0.05%/%/(unit lethargy). For molybdenum, KRUSTY adds a 9th benchmark with a total cross-section sensitivity greater than 0.004%/%/(unit lethargy).

Keywords:

• KRUSTY
• benchmark
• U-8Mo
• BeO
• neutron sensitivity

I. INTRODUCTION

Recent advances in nuclear reactor technology have been focused on making smaller and smaller reactors. The majority of these advances have been directed toward the development of small modular reactors (SMRs), which typically produce power in the range of 100 to 300 MW(electric). The general purpose for these reactors is to provide power to smaller markets. SMRs are projected to be more economical, safer, and easier to build than full-scale light water reactors.¹

More recently, researchers have been looking at the possibility of making even smaller reactors, in the range of 1 to 20 MW(thermal). These microreactors have been designed to be fully contained and, ideally, built in a factory-type setting for ease of deployment and transport.^2–4 Many diverse applications have been proposed for microreactors, including powering remote locations in Alaska and Canada, powering islands and coastal areas affected by natural disasters, and powering a colony on the surface of the moon or Mars.^5–9

With this last goal in mind, the U.S. National Aeronautics and Space Administration (NASA) teamed with the U.S. National Nuclear Security Administration (NNSA) to design a microreactor for space applications. This resulted in the prototype and proof-of-concept assembly named Kilowatt Reactor Using Stirling TechnologY (KRUSTY).¹⁰ Component manufacturing and dry fitting of KRUSTY began in the summer of 2017. Finally, KRUSTY was fully assembled, and experiments were conducted from November 2017 to March 2018.

The KRUSTY experiments were conducted across four phases: component critical, cold critical, warm critical, and high temperature.^11–14 The component critical phase was used to determine the reactivity worth of various components using a simplified version of KRUSTY. Upon completion of the first phase, the cold critical phase was conducted to confirm the reactivity worth of the same components when the full version of KRUSTY was assembled. The warm critical phase consisted of three free runs at 15 ¢, 30 ¢, and 60 ¢ of reactivity. These free runs were used to validate the results of the reactor physics codes, which had to be confirmed before the project could move forward into phase four. The high-temperature demonstration conducted during phase four was a full-powered test that ran for an uninterrupted 28 h, with temperatures reaching 800°C.

The KRUSTY benchmark summarized in this paper includes 5 configurations selected from the 60 total configurations completed during the component critical experiments phase¹⁵ (of those 60, 59 were at or above critical¹¹). This phase was performed at the National Criticality Experiments Research Center (NCERC) between November 2017 and February 2018. Preliminary results from the benchmark have been reported previously.^16–18 This paper summarizes the experimental configurations, experimental uncertainties, benchmark model simplifications and bias, and sample calculations from the approved International Criticality Safety Benchmark Evaluation Project (ICSBEP) benchmark evaluation of the KRUSTY component critical experiments.^15,a The benchmark evaluation of KRUSTY is important to the microreactor design community as it provides detailed results on novel materials and designs that are being considered for commercial use.

This paper is organized as follows. Section II presents an overview of the KRUSTY assembly. Section III discusses the experimental configurations used in the benchmark. Section IV provides a discussion on the uncertainty evaluation procedure. Section V discusses the simplified model. The experimental k_eff and benchmark k_eff are presented in Sec. VI. The results of sample calculations are provided in Sec. VII. Section VIII presents the cross-section sensitivities and discusses why KRUSTY is a much-needed benchmark. Last, Sec. IX provides the summary and conclusions.

II. KRUSTY ASSEMBLY OVERVIEW

A rendering of the KRUSTY component critical assembly is shown in Fig. 1, and an axial cross section of the central core column is provided in Fig. 2. KRUSTY’s core is created from three annular pieces of highly enriched uranium alloyed with an average of 7.65 wt% molybdenum (U-7.65Mo). The U-7.65Mo core, which was enriched to 93.1 wt% ²³⁵U, had a total mass of 32.200 kg and an average density of 17.34 g/cm³. The total core height was 25.00122 cm (9.843 in.) with an outer diameter of 10.99820 cm (4.330 in.) and inner diameter of 3.98780 cm (1.570 in.). The core pieces also had eight slots on the outer edge at 45-deg angles that would contain heat pipes in the later phases of the KRUSTY experimental campaign. In the component critical phase discussed here, four of the slots contained stainless steel support rods. The entire central core column was suspended from the upper shields via the support rods, as shown in Fig. 2.

Fig. 1. Axial cross section of KRUSTY assembly.

Fig. 2. Axial cross section of KRUSTY’s central core column.

Surrounding the core was an annular beryllium oxide (BeO) reflector assembly with an inner diameter of 14.48562 cm (5.703 in.) and a radial thickness of 11.80719 cm (4.6485 in.). As shown in Fig. 1, this assembly actually comprised two rings with the outer ring composed of four interlocking pieces. The height of the BeO reflector rings was varied by adding or removing pieces from the top. The individual rings came in thicknesses of 2.54 cm (1.000 in.), 0.635 cm (0.250 in.), and 0.3175 cm (0.125 in.). In the configurations evaluated, the height varied from 28.62834 to 29.26334 cm (11.271 to 11.521 in.). The individual masses and dimensions of each ring can be found in Sec. I of the KRUSTY benchmark evaluation.¹⁵

Outside the BeO reflector rings was a cylindrical stainless steel ring shield called the outer stainless steel shield, which was composed of four large stainless steel pieces. This ring had an inner radius of 20.48002 cm (8.063 in.), a radial thickness of 30.48000 cm (12.000 in.), and a height of 63.10630 cm (24.845 in.). This ring acted not only as the largest radiation shield in the assembly but also as the last layer of reflection.

In addition to the aforementioned major components, other smaller components located above and below the fuel were included in the KRUSTY central core assembly. These components included axial reflectors and shields made of aluminum, BeO, boron carbide (B₄C), and stainless steel. The components were part of the central core column and were suspended along with the fuel (Fig. 2).

The lower shielding assembly was placed beneath the BeO reflector rings and was composed of nine circular plates placed on the movable platen (Fig. 1). The two center shields were composed of B₄C, and the other seven shields were manufactured from stainless steel. All of these shields had an outer diameter of 39.6875 cm (15.625 in.), and the top four shields had an inner diameter of 14.2875 cm (5.625 in.) to allow the shielding assembly to wrap around the bottom of the central core column. All of the shielding plates in the lower shielding assembly had a thickness of 2.54 cm (1.000 in.).

The remainder of the shielding assembly was stacked on top of the outer stainless steel shields. These shields were B₄C plates sandwiched between stainless steel plates. The lower stainless steel shield plate was a rectangular plate with dimensions of 76.2 $\times$ 63.5 $\times$ 1.27 cm (30.00 $\times$ 25.00 $\times$ 0.50 in.) with a central hole of diameter 20.955 cm (8.250 in.). The upper stainless steel shield plate was a rectangular plate with dimensions of 93.98 $\times$ 76.2 $\times$ 3.81 cm (37.00 $\times$ 30.00 $\times$ 1.50 in.) with the same size hole. The B₄C shielding in the center was composed of three pieces: a main shield and two side pieces. The main shield was a rectangular plate with dimensions of 76.2 $\times$ 63.5 $\times$ 5.08 cm (30.00 $\times$ 25.00 $\times$ 2.00 in.)with the same size hole as the steel plates, and the side pieces were 76.2 $\times$ 15.24 $\times$ 5.08 cm (30.00 $\times$ 6.00 $\times$ 2.00 in.). The hole in the center of the upper assembly was added to allow the central core column to be dropped into the KRUSTY assembly and anchored to the top of the upper shielding assembly.

KRUSTY was installed on the Comet vertical-lift machine. Criticality was achieved by lifting the platen and BeO reflector rings into position around the suspended central core column. A more thorough and detailed description of KRUSTY is available in the benchmark evaluation.¹⁵

III. EXPERIMENTAL CONFIGURATIONS

The five configurations evaluated in the benchmark differed in the reflecting material at the bottom of the central core column and the height of the BeO reflector ring. Two configurations also had an AmBe neutron source in the middle of the fuel. The full breakdown of the experimental configurations as well as the date they were performed and the measured reactor period are presented in Table I. The reported reactor period measurements are the average of three compensated ion chambers (referred to as linears since they display data on a linear scale), each located at least 3 m from the assembly, and the reactivity was calculated based on the Inhour equation, the delayed neutron data for ²³⁵U fast fission as given by Keepin,¹⁹ and the measured prompt neutron decay constant.²⁰ A lengthy discussion regarding the applicability and associated uncertainty analysis of using Keepin’s delayed neutron data can be found in Sec. 2.1 of the KRUSTY benchmark evaluation.¹⁵

TABLE I Parameters of Evaluated Benchmark Configurations

Configuration	Date	Reactor Period(s)	Reactivity(¢)	BeO Height(in [cm])^a	Source Present	Top Axial Reflector Plug Material^b	Bottom Axial Reflector Plug Material^b
1	November 16, 2017	99.8	+9.7	11.250 (28.575)	Yes	BeO	BeO
2	December 4, 2017	4.9	+51.9	11.375 (28.8925)	Yes	BeO	BeO
3	December 5, 2017	505.8	+2.4	11.250 (28.575)	No	BeO	BeO
4	December 20, 2017	145.5	+7.1	11.375 (28.8925)	No	Al	BeO
5	December 21, 2017	19.4	+28.3	11.500 (29.21)	No	Al	Al

^aDesign value, not actual value.

^bLocated in the BeO bottom axial reflector (see Fig. 2).

IV. EVALUATION OF UNCERTAINTIES

The sensitivity effects for the five configurations were evaluated using the Monte Carlo N-Particle^b ® (MCNP®) code version 6.2.0 and ENDF/B-VIII.0 neutron cross-section libraries, including thermal scattering [S(α,β)] data for Be in BeO and for O in BeO (Refs. 21 through 24). Calculations used 1 000 000 histories per cycle with 1200 active cycles and 50 inactive cycles, which resulted in a 1σ statistical uncertainty of ±0.00002.

For some parameters, the standard uncertainty in k_eff, u_k,i, due to uncertainty in parameter i with reference value x_i,0, was calculated as the difference between the perturbed values of k_eff divided by the number of standard deviations:

(1) $u_{k,i}=\frac{\pm u_i}{2\delta x_i}\left[k_{eff}\left(x_{i,0}+\delta x_i\right)-k_{eff}\left(x_{i,0}-\delta x_i\right)\right],$(1)

where u_i is the standard uncertainty in the parameter being perturbed and δx_i is the value of the perturbation. The scaling factor 2δx_i/u_i is the range of the positive and negative perturbations in units of standard deviations of the parameter x_i (in other words, the number of standard deviations by which x_i,0 was perturbed). The difference in Eq. (1)(1) $u_{k,i}=\frac{\pm u_i}{2\delta x_i}\left[k_{eff}\left(x_{i,0}+\delta x_i\right)-k_{eff}\left(x_{i,0}-\delta x_i\right)\right],$(1) is given as ∆k_eff in the uncertainty tables in the benchmark evaluation.¹⁵ Sensitivity effects are judged to be negligible when the calculated value of ∆k_eff is within the Monte Carlo uncertainty (usually ±0.00003). In addition, if u_k,i is less than 0.000005, the effect is also judged to be negligible (regardless if |∆k_eff| > 0.00002).

Equation (1)(1) $u_{k,i}=\frac{\pm u_i}{2\delta x_i}\left[k_{eff}\left(x_{i,0}+\delta x_i\right)-k_{eff}\left(x_{i,0}-\delta x_i\right)\right],$(1) is an uncertainty multiplied by a central-difference approximation of a derivative, which can be written

(2) $u_{k,i}=\pm u_i{\left.\frac{\mathrm{\partial }{k}_{eff}}{\mathrm{\partial }{x}_i}\right|}_{x_i=x_{i,0}}.$(2)

Equations (1)(1) $u_{k,i}=\frac{\pm u_i}{2\delta x_i}\left[k_{eff}\left(x_{i,0}+\delta x_i\right)-k_{eff}\left(x_{i,0}-\delta x_i\right)\right],$(1) and (2(2) $u_{k,i}=\pm u_i{\left.\frac{\mathrm{\partial }{k}_{eff}}{\mathrm{\partial }{x}_i}\right|}_{x_i=x_{i,0}}.$(2) ) can also be written

(3) $u_{k,i}=\pm \frac{u_i}{x_{i,0}}{k}_{eff,0}{S}_{k,x_i},$(3)

where $k_{eff,0}=k_{eff}\left(x_{i,0}\right)$ [in the notation of Eq. (1(1) $u_{k,i}=\frac{\pm u_i}{2\delta x_i}\left[k_{eff}\left(x_{i,0}+\delta x_i\right)-k_{eff}\left(x_{i,0}-\delta x_i\right)\right],$(1) )] and $S_{k,x_i}$ is the relative sensitivity of k_eff with respect to x_i, defined by

(4) $S_{k,x_i}\equiv \frac{x_{i,0}}{k_{eff,0}}{\left.\frac{\mathrm{\partial }{k}_{eff}}{\mathrm{\partial }{x}_i}\right|}_{x_i=x_{i,0}}.$(4)

For some parameters, the relative sensitivity $S_{k,x_i}$ of Eq. (4)(4) $S_{k,x_i}\equiv \frac{x_{i,0}}{k_{eff,0}}{\left.\frac{\mathrm{\partial }{k}_{eff}}{\mathrm{\partial }{x}_i}\right|}_{x_i=x_{i,0}}.$(4) can be computed using adjoint methods. Whenever adjoint-based derivatives were available, Eq. (3)(3) $u_{k,i}=\pm \frac{u_i}{x_{i,0}}{k}_{eff,0}{S}_{k,x_i},$(3) was used for the uncertainties. If u_k,i is less than 0.000005, the uncertainty is judged to be negligible.

Uncertainties were evaluated in five categories: (1) criticality measurement, (2) mass and density, (3) dimensions, (4) material compositions, and (5) positioning. Uncertainties in category 1 were evaluated using the reproducibility of the experiments and the uncertainties in the nuclear data used to infer k_eff from the measurements. Uncertainties in categories 2 and 4 were evaluated using first-order adjoint-based sensitivity analysis using Eqs. (3)(3) $u_{k,i}=\pm \frac{u_i}{x_{i,0}}{k}_{eff,0}{S}_{k,x_i},$(3) and (4(4) $S_{k,x_i}\equiv \frac{x_{i,0}}{k_{eff,0}}{\left.\frac{\mathrm{\partial }{k}_{eff}}{\mathrm{\partial }{x}_i}\right|}_{x_i=x_{i,0}}.$(4) ) (Ref. 25). Uncertainties in categories 3 and 5 were evaluated using first-order finite difference–based sensitivity analysis, otherwise known as direct perturbations or brute force, using Eq. (1)(1) $u_{k,i}=\frac{\pm u_i}{2\delta x_i}\left[k_{eff}\left(x_{i,0}+\delta x_i\right)-k_{eff}\left(x_{i,0}-\delta x_i\right)\right],$(1) .

The largest and total uncertainties (not necessarily in each category) for Cases 1 through 5 are listed in Tables II through VI, respectively. Uncertainty contributions greater than 0.00008 in magnitude are listed. The relative uncertainties given for the standard k_eff uncertainties were propagated from Monte Carlo statistical uncertainties. The total asymmetric uncertainty was approximated by adding the symmetric uncertainties in quadrature with the positive and negative contributions, as appropriate. Interesting conclusions from the uncertainty analysis are summarized in Secs. IV.A and IV.B.

TABLE II Largest Uncertainties for Case 1

Parameter	Category^a	keff Combined Standard Uncertainty^b
Platen radial alignment	5	+0.00045 ± 3.63%
Central core column axial alignment	5	±0.00039 ± 3.25%
Mass of outer stainless steel shields	2	±0.00029 ± 0.93%
Fuel dimensions	3	±0.00025 ± 1.19%
Fuel composition	4	±0.00017 ± 0.30%
Axial central core column gaps, positive contributions	5	+0.00016 ± 17.18%
Axial BeO gaps, outer BeO ring	5	–0.00011 ± 25.71%
Stainless steel outer shield composition	4	±0.00009 ± 2.68%
Axial BeO gaps, inner BeO ring	5	+0.00008 ± 35.36%
Axial central core column gaps, negative contributions	5	–0.00008 ± 34.05%
Other	1, 2, 3, 4, 5	+0.00020/–0.00019 ± 3%
Total	1, 2, 3, 4, 5	+0.00078/–0.00062 ± 2%

^aSee text.

^bAsymmetric uncertainty bounds due to positioning uncertainty.

TABLE III Largest Uncertainties for Case 2

Parameter	Category^a	keff Combined Standard Uncertainty^b
Platen radial alignment	5	+0.00046 ± 3.54%
Central core column axial alignment	5	±0.00040 ± 3.14%
Mass of outer stainless steel shields	2	±0.00028 ± 0.96%
Fuel dimensions	3	±0.00025 ± 1.24%
Fuel composition	4	±0.00017 ± 0.30%
Axial central core column gaps, positive contributions	5	+0.00014 ± 20.47%
Criticality measurement, positive contribution	1	+0.00016 ± 0.00%
Axial central core column gaps, negative contributions	5	–0.00010 ± 28.43%
Stainless steel outer shield composition	4	±0.00009 ± 2.69%
Axial BeO gaps, outer BeO ring	5	–0.00008 ± 35.36%
Other	1, 2, 3, 4, 5	+0.00020/–0.00019 ± 6%
Total	1, 2, 3, 4, 5	+0.00079/–0.00062 ± 2%

^aSee text.

^bAsymmetric uncertainty bounds due to positioning uncertainty.

TABLE IV Largest Uncertainties for Case 3

Parameter	Category^a	keff Combined Standard Uncertainty^b
Platen radial alignment	5	+0.00049 ± 3.33%
Central core column axial alignment	5	±0.00040 ± 3.21%
Mass of outer stainless steel shields	2	±0.00029 ± 0.93%
Fuel dimensions	3	±0.00025 ± 1.23%
Fuel composition	4	±0.00018 ± 0.34%
Axial central core column gaps, positive contributions	5	+0.00017 ± 16.90%
Stainless steel outer shield composition	4	±0.00009 ± 2.71%
Axial central core column gaps, negative contributions	5	–0.00008 ± 35.92%
Other	1, 2, 3, 4, 5	+0.00021/–0.00020 ± 5%
Total	1, 2, 3, 4, 5	+0.00081/–0.00062 ± 2%

^aSee text.

^bAsymmetric uncertainty bounds due to positioning uncertainty.

TABLE V Largest Uncertainties for Case 4

Parameter	Category^a	keff Combined Standard Uncertainty^b
Platen radial alignment	5	+0.00044 ± 3.72%
Central core column axial alignment	5	±0.00038 ± 3.37%
Mass of outer stainless steel shields	2	±0.00029 ± 0.95%
Fuel dimensions	3	±0.00024 ± 1.24%
Fuel composition	4	±0.00018 ± 0.30%
Axial central core column gaps, positive contributions	5	+0.00017 ± 16.22%
Stainless steel outer shield composition	4	±0.00009 ± 2.71%
Other	1, 2, 3, 4, 5	+0.00020/–0.00021 ± 6%
Total	1, 2, 3, 4, 5	+0.00076/–0.00060 ± 2%

^aSee text.

^bAsymmetric uncertainty bounds due to positioning uncertainty.

TABLE VI Largest Uncertainties for Case 5

Parameter	Category^a	keff Combined Standard Uncertainty^b
Platen radial alignment	5	+0.00044 ± 3.72%
Central core column axial alignment	5	±0.00038 ± 3.33%
Mass of outer stainless steel shields	2	±0.00028 ± 0.97%
Fuel dimensions	3	±0.00024 ± 1.20%
Fuel composition	4	±0.00017 ± 0.32%
Axial central core column gaps, positive contributions	5	+0.00017 ± 16.93%
Criticality measurement, positive contribution	1	+0.00010 ± 0.00%
Axial BeO gaps, inner BeO ring	5	+0.00009 ± 31.43%
Stainless steel outer shield composition	4	±0.00008 ± 2.72%
Other	1, 2, 3, 4, 5	+0.00018/–0.00021 ± 7%
Total	1, 2, 3, 4, 5	+0.00076/–0.00059 ± 2%

^aSee text.

^bAsymmetric uncertainty bounds due to positioning uncertainty.

IV.A. Positioning Uncertainty Dominates and Leads to Asymmetric Uncertainty Bounds

Four of the top eight contributions to the total uncertainty are due to positioning uncertainty, including gaps. The largest uncertainty in each case was due to the platen radial alignment. The platen is designed to be centered radially, i.e., aligned on the assembly axis. Misalignment in any radial direction causes an increase in k_eff. Thus, uncertainty in the platen location leads to a one-sided uncertainty in k_eff. The distance that the platen could travel in the radial direction before contacting another part is 0.25 in. This was taken as a bounding uncertainty for the platen radial misalignment. It is a large value, and the assembly is sensitive to the location of the platen. The gap was needed to ensure that the experiment could be assembled without friction between the stationary and moving components.

Another source of asymmetric uncertainty bounds is the possible presence of gaps. It is assumed there are no gaps, so introducing gaps in a certain location causes k_eff to move in only one direction. The nine potential gap locations, shown Fig. 3, in the central core column (Fig. 2) were evaluated independently. Some caused k_eff to increase, but some caused it to decrease, as summarized in Table VII. A detailed discussion on determining the size of the different gaps is provided in Sec. 2.5 of the KRUSTY benchmark evaluation.¹⁵

TABLE VII Uncertainty u_k and Uncertainty of Central Core Column Axial Gaps

Gap Number	Case	Deviation Used(in.)	Δkeff ± 1σMC	1σ Uncertainty (in.)	Final uk
1	1	+0.0143/√3	0.00012 ± 0.00003	±0.0143/√3	+0.00012
	2	+0.0143/√3	0.00010 ± 0.00003	±0.0143/√3	+0.00010
	3	+0.0143/√3	0.00013 ± 0.00003	±0.0143/√3	+0.00013
	4	+0.0143/√3	0.00015 ± 0.00003	±0.0143/√3	+0.00015
	5	+0.0143/√3	0.00014 ± 0.00003	±0.0143/√3	+0.00014
2	1	+0.0083/√3	0.00010 ± 0.00003	±0.0083/√3	+0.00010
	2	+0.0083/√3	0.00009 ± 0.00003	±0.0083/√3	+0.00009
	3	+0.0083/√3	0.00010 ± 0.00003	±0.0083/√3	+0.00010
	4	+0.0083/√3	0.00007 ± 0.00003	±0.0083/√3	+0.00007
	5	+0.0083/√3	0.00008 ± 0.00003	±0.0083/√3	+0.00008
3	1	+0.0019/√3	0.00001 ± 0.00003	±0.0019/√3	Negligible
	2	+0.0019/√3	0.00001 ± 0.00003	±0.0019/√3	Negligible
	3	+0.0019/√3	0.00003 ± 0.00003	±0.0019/√3	+0.00003
	4	+0.0019/√3	0.00000 ± 0.00003	±0.0019/√3	Negligible
	5	+0.0019/√3	0.00001 ± 0.00003	±0.0019/√3	Negligible
4	1	+0.0012/√3	−0.00008 ± 0.00003	±0.0012/√3	−0.00008
	2	+0.0012/√3	−0.00003 ± 0.00003	±0.0012/√3	−0.00003
	3	+0.0012/√3	−0.00003 ± 0.00003	±0.0012/√3	−0.00003
	4	+0.0012/√3	−0.00004 ± 0.00003	±0.0012/√3	−0.00004
	5	+0.0012/√3	−0.00003 ± 0.00003	±0.0012/√3	−0.00003
5	1	+0.0012/√3	−0.00001 ± 0.00003	±0.0012/√3	Negligible
	2	+0.0012/√3	−0.00005 ± 0.00003	±0.0012/√3	−0.00005
	3	+0.0012/√3	−0.00004 ± 0.00003	±0.0012/√3	−0.00004
	4	+0.0012/√3	−0.00006 ± 0.00003	±0.0012/√3	−0.00006
	5	+0.0012/√3	−0.00002 ± 0.00003	±0.0012/√3	Negligible
6	1	+0.0019/√3	0.00001 ± 0.00003	±0.0019/√3	Negligible
	2	+0.0019/√3	−0.00006 ± 0.00003	±0.0019/√3	−0.00006
	3	+0.0019/√3	−0.00006 ± 0.00003	±0.0019/√3	−0.00006
	4	+0.0019/√3	0.00001 ± 0.00003	±0.0019/√3	Negligible
	5	+0.0019/√3	−0.00006 ± 0.00003	±0.0019/√3	−0.00006
7a, 7b	1	+0.0113/√3	−0.00002 ± 0.00003	±0.0113/√3	Negligible
	2	+0.0113/√3	−0.00005 ± 0.00003	±0.0113/√3	−0.00005
	3	+0.0113/√3	−0.00001 ± 0.00003	±0.0113/√3	Negligible
	4	+0.0113/√3	0.00002 ± 0.00003	±0.0113/√3	Negligible
	5	+0.0113/√3	0.00003 ± 0.00003	±0.02/√3	+0.00005
8	1	+0.02/√3	0.00005 ± 0.00003	±0.02/√3	+0.00005
	2	+0.02/√3	0.00003 ± 0.00003	±0.02/√3	+0.00003
	3	+0.02/√3	0.00001 ± 0.00003	±0.02/√3	Negligible
	4	+0.02/√3	0.00005 ± 0.00003	±0.02/√3	+0.00005
	5	+0.02/√3	0.00003 ± 0.00003	±0.02/√3	+0.00003
9	1	+0.0026/√3	0.00000 ± 0.00003	±0.0026/√3	Negligible
	2	+0.0026/√3	−0.00002 ± 0.00003	±0.0026/√3	Negligible
	3	+0.0026/√3	0.00001 ± 0.00003	±0.0026/√3	Negligible
	4	+0.0113/√3	−0.00001 ± 0.00003	±0.0113/√3	Negligible
	5	+0.02/√3	−0.00002 ± 0.00003	±0.02/√3	Negligible

Fig. 3. Gap number used for axial central core column gap uncertainty.

Gaps in the BeO reflector rings also had a nonnegligible contribution to the overall uncertainty. The maximum size of the axial gaps in the BeO reflector rings was estimated by comparing measurements of the stack height with measurements of the individual part heights. (In contrast, the maximum size of the axial gaps in the central core column was estimated using measurements of the flatness and parallelism of adjacent parts.) The bounding uncertainty in the size of the gaps between each layer in the inner and outer BeO rings was +0.0018 in. and +0.005 in., respectively. For Case 1, inserting a gap of +0.0018/√3 in. between each layer in the BeO inner rings resulted in a Δk_eff = +0.00008 ± 0.00003. Inserting a gap of +0.005/√3 in. between each layer in the BeO outer rings resulted in a Δk_eff = –0.00011 ± 0.00003. These values (and analogous values for the other cases) were used separately as one-sided uncertainties in the total uncertainties of Tables II through VI.

IV.B. Outer Stainless Steel Shields Are Important

The outer stainless steel shields are enormous when compared to the size of the core. As these components were too large for the scales available, the masses were not measured. A density of 8.00 g/cm³ was assumed,^26,27 and an uncertainty of ±1.5% was applied. Another reason the outer stainless steel shields are important in the uncertainty quantification is that the compositions were measured but uncertainties were not given, so the following uncertainties were applied: ±1% on the iron content, ±5% on chromium and nickel, and ±20% on all other impurities. The outer stainless steel shields contributed about as much to the total uncertainty as the fuel did. Gaps in the outer stainless steel shields had a very small contribution to the total uncertainty.

V. SIMPLIFIED MODEL

The detailed model takes about 2 h 10 min to run on 288 processors on the high-performance Grizzly machine at Los Alamos National Laboratory (LANL). A simplified model was developed to reduce this computational time. Simplifications were made in seven broad categories:

1. Fuel annuli: Use average fuel material definition with most impurities removed and one solid piece.

2. BeO reflector rings (geometry and density): Use average density and one single piece for inner BeO reflector rings, preserving total mass. Use average density and one single piece for outer BeO reflector rings, removing grooves on outer surface while preserving total mass. The overall outer dimensions of the inner and outer rings were preserved. There remains a radial gap between the rings.

3. BeO reflector rings (material): Remove most impurities.

4. Structure (geometry): Simplify the geometry, introducing cylindrical symmetry where possible.

5. Type 304 stainless steel (SS304), Type 4140 stainless steel (SS4140), and Type 316 stainless steel (SS316) (material): Remove some impurities.

6. Aluminum (material): Remove some impurities.

7. Air (material): Replace air with void.

When impurities were removed, the atom density of the material was reduced by the atom density of the removed nuclides.

Simplifying the fuel geometry and materials had the largest effect on k_eff; simplifying the BeO reflector rings had the second-largest effect. This is shown in Table VIII, which lists the k_eff of the model with the simplification minus the k_eff of the model with all of the preceding simplifications. The bias was calculated as the k_eff of the model with the simplification minus the k_eff of the base case, which is the detailed model without any simplifications, also shown in Table VIII. The base k_eff for each detailed model was the average of ten independent calculations, and the k_eff of each simplified case was the average of four independent calculations. For the final total simplification bias, the k_eff of each simplified case was the average of ten independent calculations. The final simplification bias is shown in italic print in Table VIII.

TABLE VIII Cumulative Simplification Bias for Detailed to Simplified Model*

Simplification	Case	Δkeff ± 1σMC (Difference from Preceding Simplification)	Δkeff ± 1σMC (Difference from Detailed Model)
Smooth outer stainless steel shield outer boundary; remove air	1	—	–0.00005 ± 0.00003
	2	—	–0.00002 ± 0.00003
	3	—	–0.00003 ± 0.00003
	4	—	–0.00006 ± 0.00003
	5	—	–0.00003 ± 0.00003
Fuel annuli (geometry and materials)	1	0.00022 ± 0.00003	0.00017 ± 0.00003
	2	0.00021 ± 0.00003	0.00019 ± 0.00003
	3	0.00021 ± 0.00003	0.00018 ± 0.00003
	4	0.00024 ± 0.00003	0.00018 ± 0.00003
	5	0.00022 ± 0.00003	0.00019 ± 0.00003
Structure (geometry)	1	–0.00008 ± 0.00003	0.00009 ± 0.00003
	2	–0.00009 ± 0.00003	0.00010 ± 0.00003
	3	–0.00011 ± 0.00003	0.00007 ± 0.00003
	4	–0.00014 ± 0.00003	0.00004 ± 0.00003
	5	–0.00014 ± 0.00003	0.00005 ± 0.00003
Simplify SS4140 and SS316 (material)	1	–0.00002 ± 0.00003	0.00007 ± 0.00003
	2	0.00000 ± 0.00003	0.00010 ± 0.00003
	3	0.00000 ± 0.00003	0.00007 ± 0.00003
	4	0.00002 ± 0.00003	0.00006 ± 0.00003
	5	0.00000 ± 0.00003	0.00005 ± 0.00003
Simplify aluminum (material)	1	0.00003 ± 0.00003	0.00010 ± 0.00003
	2	0.00002 ± 0.00003	0.00012 ± 0.00003
	3	0.00003 ± 0.00003	0.00010 ± 0.00003
	4	0.00002 ± 0.00003	0.00008 ± 0.00003
	5	–0.00001 ± 0.00003	0.00004 ± 0.00003
Simplify other steel (material)	1	–0.00011 ± 0.00003	–0.00001 ± 0.00003
	2	–0.00012 ± 0.00003	0.00000 ± 0.00003
	3	–0.00011 ± 0.00003	–0.00001 ± 0.00003
	4	–0.00013 ± 0.00003	–0.00005 ± 0.00003
	5	–0.00009 ± 0.00003	–0.00005 ± 0.00003
BeO reflector rings (geometry and density)	1	–0.00019 ± 0.00003	–0.00020 ± 0.00003
	2	–0.00019 ± 0.00003	–0.00019 ± 0.00003
	3	–0.00019 ± 0.00003	–0.00020 ± 0.00003
	4	–0.00019 ± 0.00003	–0.00024 ± 0.00003
	5	–0.00019 ± 0.00003	–0.00024 ± 0.00003
BeO reflector rings (material)	1	0.00005 ± 0.00003	–0.00015 ± 0.00003
	2	0.00005 ± 0.00003	–0.00014 ± 0.00003
	3	0.00004 ± 0.00003	–0.00016 ± 0.00003
	4	0.00005 ± 0.00003	–0.00019 ± 0.00003
	5	0.00004 ± 0.00003	–0.00020 ± 0.00003

*Each simplification includes the preceding simplifications.

The simplified model takes about 50 min to run on the same computing configuration, a 62% savings. Most of the savings come from geometric simplifications. The slots for accommodating heat pipes and the support rods prevent the simplified KRUSTY model from being cylindrically symmetric.

VI. EXPERIMENTAL AND BENCHMARK k_eff

The benchmark experiment k_eff and its uncertainty were determined based on the measured asymptotic reactor period reported in Table I. The experiment uncertainty is calculated as discussed in Sec. IV and is provided again in Tables IX and X. The listed simplification bias for the detailed model, Table IX, is based on the temperature difference between the experiment and the nuclear data set used. The simplification bias for the simplified model, Table X, includes the temperature difference and the bias introduced from the simplification of geometry and materials, as described in Sec. V. The bias is applied to the experimental k_eff to obtain the benchmark k_eff for both models.

TABLE IX Summary of Experimental and Benchmark k_eff, Uncertainty, and Bias for the Detailed Model

Case	Experiment keff	Experiment Uncertainty	Simplification Bias	Benchmark Model keff
1	1.00064	+0.00078/ –0.00062	0.00001 ± 0.00001	1.00065 +0.00078/–0.00062
2	1.00344	+0.00079/ –0.00062	0.00001 ± 0.00001	1.00345 +0.00079/–0.00062
3	1.00016	+0.00081/ –0.00062	0.00001 ± 0.00001	1.00017 +0.00081/–0.00062
4	1.00047	+0.00076/ –0.00060	0.00001 ± 0.00001	1.00048 +0.00076/–0.00060
5	1.00188	+0.00076/ –0.00059	0.00001 ± 0.00001	1.00189 +0.00076/–0.00059

TABLE X Summary of Experimental and Benchmark k_eff, Uncertainty, and Bias for the Simplified Model

Case	Experiment keff	Experiment Uncertainty	Simplification Bias^a	Benchmark Model keff
1	1.00064	+0.00078/ –0.00062	–0.00014 ± 0.00003	1.00050 +0.00078/–0.00062
2	1.00344	+0.00079/ –0.00062	–0.00013 ± 0.00003	1.00331 +0.00079/–0.00062
3	1.00016	+0.00081/ –0.00062	–0.00015 ± 0.00003	1.00001 +0.00081/–0.00062
4	1.00047	+0.00076/ –0.00060	–0.00018 ± 0.00003	1.00029 +0.00076/–0.00060
5	1.00188	+0.00076/ –0.00059	–0.00019 ± 0.00003	1.00169 + 000076/–0.00059

^aIncludes the simplification bias from Table IX.

VII. SAMPLE CALCULATIONS

The results of sample calculations using MCNP6.2 for the five cases are shown in Table XI for the detailed benchmark model and Table XII for the simplified benchmark model. The calculations used continuous-energy ENDF/B-VIII.0 nuclear data with thermal scattering [i.e., S(α,β)]. Each calculated result (of both the detailed and the simplified models) is the average of ten independent calculations with 1 000 000 neutron histories per generation with 1200 active generations and 50 skipped generations. One standard deviation is given; for the reported benchmark values, the standard deviation is based on the results of the uncertainty evaluation, and for the stated sample calculations, the standard deviation reported is the Monte Carlo error.

TABLE XI Sample Calculation Results for the Detailed Model Using MCNP6.2

Code(Cross-Section Set)→	Benchmark	MCNP6.2 (Continuous-Energy ENDF/B-VIII.0)^a
Case ↓	keff	keff	Calculated – Experimental (pcm)
1	1.00065 +0.00078/–0.00062	1.00043 ± 0.00002	–22
2	1.00345 +0.00079/–0.00062	1.00325 ± 0.00002	–20
3	1.00017 +0.00081/–0.00062	1.00017 ± 0.00002	0
4	1.00048 +0.00076/–0.00060	1.00033 ± 0.00002	–15
5	1.00189 +0.00076/–0.00059	1.00174 ± 0.00002	–15

^aIncluding thermal scattering [S(α,β)] data for Be in BeO and for O in BeO.

TABLE XII Sample Calculation Results for the Simplified Model Using MCNP6.2

Code (Cross-Section Set)→	Benchmark	MCNP6.2 (Continuous-Energy ENDF/B-VIII.0)^a
Case ↓	keff	keff	Calculated – Experimental (pcm)
1	1.00050 +0.00078/–0.00062	1.00028 ± 0.00002	–22
2	1.00331 +0.00079/–0.00062	1.00311 ± 0.00002	–20
3	1.00001 +0.00081/–0.00062	1.00001 ± 0.00002	0
4	1.00029 +0.00076/–0.00060	1.00014 ± 0.00002	–15
5	1.00169 +0.00076/–0.00059	1.00154 ± 0.00002	–15

^aIncluding thermal scattering [S(α,β)] data for Be in BeO and for O in BeO.

The results of sample calculations using the Monte Carlo code²⁸ COG 11.3 for the five cases are shown in Table XIII for the detailed benchmark model and Table XIV for the simplified benchmark model. The calculations used continuous-energy ENDF/B-VIII.0 nuclear data with thermal scattering. The calculations used 15 000 neutron histories per generation with 699 900 active generations and 100 skipped generations.

TABLE XIII Sample Calculation Results for the Detailed Model Using COG 11.3

Code (Cross-Section Set)→	Benchmark	COG 11.3 (Continuous-Energy ENDF/B-VIII.0)^a
Case ↓	keff	keff	Calculated – Experimental (pcm)
1	1.00065 +0.00078/–0.00062	1.00029 ± 0.00001	–36
2	1.00345 +0.00079/–0.00062	1.00313 ± 0.00001	–32
3	1.00017 +0.00081/–0.00062	1.00005 ± 0.00001	–12
4	1.00048 +0.00076/–0.00060	1.00019 ± 0.00001	–29
5	1.00189 +0.00076/–0.00059	1.00163 ± 0.00001	–26

^aIncluding thermal scattering [S(α,β)] data for Be in BeO and for O in BeO.

TABLE XIV Sample Calculation Results for the Simplified Model Using COG 11.3

Code (Cross-Section Set) →	Benchmark	COG 11.3 (Continuous-Energy ENDF/B-VIII.0)^a
Case ↓	keff	keff	Calculated – Experimental (pcm)
1	1.00050 +0.00078/–0.00062	1.00042 ± 0.00001	–8
2	1.00331 +0.00079/–0.00062	1.00327 ± 0.00001	–4
3	1.00001 +0.00081/–0.00062	1.00018 ± 0.00001	17
4	1.00029 +0.00076/–0.00060	1.00033 ± 0.00001	4
5	1.00169 +0.00076/–0.00059	1.00171 ± 0.00001	12

^aIncluding thermal scattering [S(α,β)] data for Be in BeO and for O in BeO.

The results of sample calculations using the Monte Carlo code²⁹ MC21 9.00.02 for the five cases are shown in Table XV for the simplified benchmark model. The calculations used continuous-energy ENDF/B-VIII.0 nuclear data with thermal scattering. The calculations used 500 000 neutron histories per generation with 1000 active generations and 50 skipped generations.

TABLE XV Sample Calculation Results for the Simplified Model Using MC21 9.00.02

Code (Cross-Section Set) →	Benchmark	MC21 9.00.02 (Continuous-Energy ENDF/B-VIII.0)^a
Case ↓	keff	keff	Calculated – Experimental (pcm)
1	1.00050 +0.00078/–0.00062	1.00028 ± 0.00003	–22
2	1.00331 +0.00079/–0.00062	1.00316 ± 0.00003	–15
3	1.00001 +0.00081/–0.00062	1.00005 ± 0.00003	4
4	1.00029 +0.00076/–0.00060	1.00015 ± 0.00003	–14
5	1.00169 +0.00076/–0.00059	1.00149 ± 0.00003	–21

^aIncluding thermal scattering [S(α,β)] data for Be in BeO and for O in BeO.

The MCNP6.2, COG, and MC21 results are all within 1σ of the benchmark model k_eff.

The reactor kinetics parameters (computed using the iterated fission probability method, invoked with the KOPTS option in MCNP6.2) are given in Table XVI for the detailed model and in Table XVII for the simplified model.

TABLE XVI Sample Reactor Kinetics Calculation Results for the Detailed Model

Code (Cross-Section Set) →	MCNP6.2 (Continuous-Energy ENDF/B-VIII.0)
Case ↓	Generation Time (μs)	Rossi-α (1/μs)^a	βeff
1	5.18963 ± 0.00589	−1.32831E-03 ± 3.10736E-06	0.00689 ± 0.00001
2	5.26417 ± 0.00594	−1.31163E-03 ± 3.05813E-06	0.00690 ± 0.00001
3	5.20395 ± 0.00590	−1.32166E-03 ± 3.08973E-06	0.00688 ± 0.00001
4	5.27333 ± 0.00596	−1.30889E-03 ± 3.05484E-06	0.00690 ± 0.00001
5	5.30315 ± 0.00599	−1.29921E-03 ± 3.03127E-06	0.00689 ± 0.00001

^aThis is the α corresponding to the delayed critical k_eff reported in Table XI, not to be confused with an experimental inference or simulation.

TABLE XVII Sample Reactor Kinetics Calculation Results for the Simplified Model

Code (Cross-Section Set) →	MCNP6.2 (Continuous-Energy ENDF/B-VIII.0)
Case ↓	Generation Time (μs)	Rossi-α (1/μs)^a	βeff
1	5.20414 ± 0.00599	−1.32725E-03 ± 3.13567E-06	0.00691 ± 0.00001
2	5.27053 ± 0.00606	−1.30859E-03 ± 3.09406E-06	0.00690 ± 0.00001
3	5.21459 ± 0.00604	−1.32763E-03 ± 3.14757E-06	0.00692 ± 0.00001
4	5.27134 ± 0.00608	−1.31069E-03 ± 3.09003E-06	0.00691 ± 0.00001
5	5.30395 ± 0.00610	−1.29778E-03 ± 3.06928E-06	0.00688 ± 0.00001

^aThis is the α corresponding to the delayed critical k_eff reported in Table XII, not to be confused with an experimental inference or simulation.

Prompt neutron decay constant measurements were performed on the KRUSTY experiment using four ³He tubes placed in the heat pipe channels of the core not occupied by the support rods. Although there was a central cavity in the fuel, there was no way to instrument detectors in this location. Because of this positioning, the system had many reflected neutrons incident upon it, which led to saturation of the detectors from what are in essence uncorrelated source neutrons near critical, so no direct measurement was attempted.

The measured value of Rossi-α for the KRUSTY experiment is –1136.5 ± 16.1 s⁻¹. The calculated Rossi-α results agree well with the experimental measurements reported in Ref. 20, as shown in Table XVIII. As demonstrated in Ref. 20, there typically exists a 10% to 20% negative bias in the measured versus simulated values of Rossi-α, which matches well with the results of the KRUSTY experiment.

TABLE XVIII Comparison of Experimental and Calculated Values of Rossi-α

Case	Experiment Rossi-α (1/μs)	MCNP6.2 for Detailed Model Rossi-α (1/μs)^a	$\frac{C-E}{E}$
1	−1.1365E-03 ± 1.6100E-05	−1.32831E-03 ± 3.10736E-06	0.1688
2	−1.1365E-03 ± 1.6100E-05	−1.31163E-03 ± 3.05813E-06	0.1541
3	−1.1365E-03 ± 1.6100E-05	−1.32166E-03 ± 3.08973E-06	0.1629
4	−1.1365E-03 ± 1.6100E-05	−1.30889E-03 ± 3.05484E-06	0.1517
5	−1.1365E-03 ± 1.6100E-05	−1.29921E-03 ± 3.03127E-06	0.1432

^aFrom Table XVI.

VIII. NUCLEAR DATA AND SENSITIVITIES

KRUSTY’s value as a benchmark is due to its sensitivity to beryllium and molybdenum. Figures 4 and 5 show heat maps of the number of benchmarks in the 2016 edition of the ICSBEP Handbook that are sensitive to various reactions involving beryllium and molybdenum.³⁰ It can be seen in Fig. 4 that there are 30 total benchmarks that are sensitive to ⁹Be elastic scattering and 28 benchmarks sensitive to elastic scattering of beryllium in BeO. Figure 5 shows a maximum of 16 total benchmarks that are sensitive to any molybdenum isotope.

Fig. 4. Heat map showing number of benchmarks sensitive to beryllium.

Fig. 5. Heat map showing number of benchmarks sensitive to molybdenum.

The relative sensitivity of k_eff in these benchmarks to the total cross section of ⁹Be or elemental molybdenum is compared with KRUSTY in Figs. 6 and 7, respectively, to show the importance of KRUSTY to the community. Figures 6 and 7 are intended to show where the KRUSTY sensitivities fall among the previous benchmarks; the details of the previous benchmarks are unimportant for this purpose. For beryllium, there are 17 benchmarks that have a sensitivity greater than 0.05%/%/(unit lethargy) between 0.5 and 0.82 MeV. KRUSTY adds an 18th benchmark. The sensitivity spectra for the current benchmarks and KRUSTY are plotted in Fig. 6. For molybdenum, there are eight benchmarks with a sensitivity greater than 0.004%/%/(unit lethargy) between 1.85 and 2.354 MeV with KRUSTY adding a ninth benchmark with a sensitivity of 0.0054%/%/(unit lethargy) at 1.94 MeV. These sensitivity spectra are provided in Fig. 7. (Figures 6 and 7 include only the benchmark with the largest sensitivity in a series, and the examined benchmarks are from the 2016 edition of the ICSBEP Handbook.)

Fig. 6. Comparison of the relative sensitivity of k_eff to the ⁹Be total cross section with previous benchmarks.

Fig. 7. Comparison of the relative sensitivity of k_eff to the elemental molybdenum total cross section with previous benchmarks.

As shown in the ENDF/B-VIII.0 criticality testing, of the benchmarks sensitive to elastic scattering in BeO, the simulated k_eff values generally decreased when ENDF/B-VII.1 data were replaced with ENDF/B-VIII.0 data.²² As there are so few experiments sensitive to elastic scattering in BeO, it is not clear if these changes are actually matching experiments better or not. A detailed analysis of the KRUSTY sensitivities (more detailed than is provided in this paper) should help resolve these questions. No changes to the molybdenum cross sections are mentioned in the ENDF/B-VIII.0 paper.²²

IX. SUMMARY AND CONCLUSIONS

As the only successful test of a microreactor, KRUSTY represents the future of nuclear technology both on Earth and other planets. This joint NASA/NNSA experimental campaign was executed at NCERC from November 2017 to March 2018 in four distinct phases. Five configurations from the first phase, component critical experiments, were chosen to be evaluated as a benchmark for inclusion in the ICSBEP Handbook.

These configurations were evaluated across five distinct categories [listed in Sec. IV as (1) criticality measurement, (2) mass and density, (3) dimensions, (4) material compositions, and (5) positioning] to determine the overall experiment uncertainty. Additionally, biases associated with the benchmark model simplifications were determined. Once the uncertainty and simplification biases were applied to the experimental k_eff, the benchmark k_eff was calculated. MCNP6.2 was used for all of the neutron transport simulations. The largest difference between the computational and experimental k_eff was –22 pcm for both the detailed and simplified models. Results from the COG 11.3 and MC21 9.00.02 Monte Carlo codes using ENDF/B-VIII.0 cross sections are also provided. The calculated k_eff results from MCNP6.2, COG 11.3, and MC21 9.00.02 are all within 1σ of the benchmark model k_eff.

The KRUSTY assembly will be a valuable addition to the ICSBEP Handbook because of its sensitivity to beryllium and molybdenum, to which relatively few current benchmarks are sensitive.

Acknowledgments

The authors are grateful to Soon Kim, Lawrence Livermore National Laboratory, for providing COG results. The authors are also grateful to Szelim Kong, Naval Nuclear Laboratory, for providing MC21 results.

This material is based upon work supported in part by the U.S. Department of Energy (DOE) Nuclear Criticality Safety Program, funded and managed by the NNSA for the DOE. This work was also supported by the NASA Space Technology Mission Directorate and an Integrated University Program Graduate Fellowship. We would like to acknowledge the work of the KRUSTY evaluation’s external reviewers, John Bess (Idaho National Laboratory) and Dave Heinrichs (Lawrence Livermore National Laboratory), and we would like to acknowledge the work of Gary Harms (Sandia National Laboratories), who also reviewed the evaluation.

Notes

^a As all benchmark evaluations are subject to revision, consult the latest edition of the ICSBEP Handbook for the most recent values.

^b MCNP® and Monte Carlo N-Particle® are registered trademarks owned by Triad National Security, LLC, manager and operator of LANL. Any third-party use of such registered marks should be properly attributed to Triad National Security, LLC, including the use of the designation as appropriate. For the purposes of visual clarity, the registered trademark symbol is assumed for all references to MCNP within the remainder of this paper.