THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENT OF PHYSICS

Transcription

1 THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENT OF PHYSICS TESTING THE LAWRENCE LIVERMORE NATIONAL LABORATORY SIMULATION OF NEUTRON AND GAMMA RAY EMISSION FROM FISSION AND PHOTOFISSION IN MCNPX ROBERT ALLEN WELDON JR. SPRING 2013 A thesis submitted in partial fulfillment of the requirements for a baccalaureate degree in Physics with honors in Physics Reviewed and approved* by the following: Jorge Sofo Professor of Phyiscs Thesis Supervisor Richard Robinett Professor of Physics Honors Adviser * Signatures are on file in the Schreyer Honors College.

2 i ABSTRACT MCNP is the foremost radiation transport code in use today. Used in nuclear engineering, radiology, physics, and other fields, MCNP can be found throughout the world, and is constantly being upgraded. Lawrence Livermore National Laboratory (LLNL) developed a physics model for the simulation of neutron and gamma ray emission from fission and photofission that was included in MCNPX 2.7.B in The LLNL multiplicity capability provided the ability for MCNPX to simulate neutron and gamma-ray distributions for neutron induced, spontaneous and photonuclear fission reactions. This thesis examines and supports the accuracy of LLNL s physics model by comparison with experiment and similar physics models already in MCNP. The components of the LLNL capability tested included the multiplicity capability, the four different multiplicity options, and the correlation options. The LLNL multiplicity capability was tested and compared with experiment. The percent difference between the capability and experiment was less than 6% in the first five multiplicities for the neutron induced fission of U- 233, U-235, Pu-239, and Pu-241. For the spontaneous fission of U-238, Pu-238, Pu-240, Cm-242 and Cm-244, the percent error was less than 3% in the first five multiplicities. The testing of the five FISM options with the LLNL capability showed LLNL as having the closest results to consensus experimental data for neutron induced fission for U-235 with a percent difference in the first five multiplicities of less than 8%. The four multiplicity options tested showed general agreement with experiment. The average value for the energy of fission neutrons induced by thermal neutrons was 2.06 MeV for U-235, which is within the accepted value of 2.0 to 2.1 MeV. The runs conducted for photons emitted in fission reactions produced by thermal neutrons gave an average of 6.00 photons being

3 ii produced per fission event which is within the accepted range of 6 to 8 photons produced per fission reaction. The correlation options tested showed agreement between Beck and Vogt.

4 iii TABLE OF CONTENTS List of Figures... iii List of Tables... iv Acknowledgements... v Chapter 1 MCNP, Fission, Neutron Multiplicity, and the LLNL Capability Fission Neutron Multiplicity The Lawrence Livermore Simulation Applications of the LLNL Capability and Testing... 6 Chapter 2 Initial Multiplicity Testing... 8 Chapter 3 FISM Options Chapter 4 Options in the LLNL Source Code Neutron-induced Fission Data Spontaneous Fission Data Neutron Energy Conservation Chapter 5 Summary of Results Appendix A Complete FISM Option Results Appendix B Complete Correlation Option Results REFERENCES... 38

5 iv LIST OF FIGURES Figure 1.1 Nubar values of U-235 and Pu Figure 2.1 Benchmarking method used for the initial testing Figure 3.1 Output of Test for FISM set to 1 (right) and FISM Set to 5 (left) Figure 4.1 LLNL Multiplicity Source Code Options Figure 4.2 Input Deck Used for Nudist Runs Figure 4.3 U-235 Weight/Bin Width vs. Upper Energy Value for Bin for Neutrons Figure 4.4 U-235 Weight/Bin Width vs. Upper Energy Value for Bin for Photons..21 Figure 4.5 Cross-section for U Figure 4.6 Graph of Weight/Bin Width vs. Upper Energy Value for Bin for U Figure 4.7 Graph of Weight/Bin Width vs. Upper Energy Value for Bin for U

6 v LIST OF TABLES Table 1.1 Values of,, and for U Table 2.1 Percent Error of Neutron Induced Fission Multiplicity as Compared to Experiment Table 2.2 Percent Error of Spontaneous Fission Multiplicity as Compared to Experiment Table 3.1 Percent Difference Between FISM options 5 (LLNL), 1, 2, 3 and Consensus for U-235 (neutron-induced fission)...12 Table 3.2 Percent Difference Between FISM Options 1, 2, 3,4, 5 (LLNL) and Consensus for U-238 (Spontaneous Fission) Table 3.3 Example of Print Table 38 from U-235 Output File..15 Table 4.1 Percent Differences Between 5 MeV Thermal and 15 MeV Thermal for Each Nudist Option.19 Table 4.2 Percent Differences Between 5 MeV Thermal and 15 MeV Thermal with Thermal set to Nudist= Table 4.3 Results of ndistoption.24

7 vi ACKNOWLEDGEMENTS I would first like to thank Dr. Michael Fensin. His guidance as my research mentor while at Los Alamos National Laboratory was superb in every way. The hands-on style of mentoring he used helped me to learn a large quantity of material in a short amount of time and to be able to produce high quality work. I would also like to thank the Department of Homeland Security for providing the funding for my internship at Los Alamos. Finally, I would like to thank Jorge Sofo and Richard Robinett for guiding me in my research and throughout my time here at Penn State.

8 1 Chapter 1 MCNP, Fission, Neutron Multiplicity, and the LLNL Capability Monte Carlo N-Particle code (MCNP) is a radiation transport code used for neutron, photon, electron, or coupled neutron/photon/electron transport. That is, it models the interaction of radiation with materials. With uses such as reactor and accelerator modeling, MCNP is the flagship transport code for modeling in the field of nuclear engineering. The code was initially created in the 1950s and has continued to be upgraded and used since that time. Currently there are two forms of the code, MCNP5 and MCNPX. The two codes share the same basic structure with some differences in data acquisition, the use of high energy cross-sections, and other areas. For the testing reported in this paper, all the work was done with MCNPX 2.7.0, the current software version. MCNPX (MCNP extended) is a Fortran90 (F90) Monte Carlo radiation transport computer code created to transport all known particles at all energies. [1] The history of MCNPX is summarized in the user manual: The MCNPX program began in 1994, when several groups in the Los Alamos X, T and LANSCE divisions proposed a program of simulation and data tool development in support of the Accelerator Production of Tritium Project. The work involved a formal extension of MCNP to all particles and all energies, improvement of physics simulation models, extension of neutron, proton and photonuclear libraries to 150 MeV, and the formulation of new variance reduction and data analysis techniques. The proposal also included a program of cross section measurements, benchmark experiments, deterministic code development, and improvements in transmutation code and library tools through

9 the CINDER 90 project. Since the closure of the APT project, work on the code has continued under the sponsorship of the AAA and other programs. [1] Fission As a particle transport code (and originally just a neutron transport code), the basis of MCNP is the fission reaction. Fission is when a nucleus receives enough energy such that the nucleus can become energetic enough to split. This splitting can occur by two different processes: neutron-induced or spontaneous. In neutron-induced fission, a neutron is absorbed into an actinide. This causes the actinide with mass number A, to briefly turn into an excited actinide with a mass number A+1 with excitation energy provided by the kinetic energy of the neutron and the forces that bind the neutron. After this brief binding, the actinide splits into fast moving lighter elements and releases neutron and gamma rays. The release of neutrons and photons is dependent on the energy of the incident neutron. Approximately 6-8 MeV is required in order to overcome the nuclear strong force (or binding energy) holding an atom together. When this happens, any excess energy in the splitting is given off in the form of neutrons and photons. Neutrons are released until the excitation energy is less than the binding energy of the nucleus. The daughter nuclei and neutrons released during fission do not account for all of the energy though. The additional energy is released in the form of photons and the kinetic energy of the fission fragments. Fission can also occur spontaneously. In spontaneous fission the nucleus will split into two nearly equal fragments releasing neutrons and a large amount of energy in the process. While spontaneous fission is theoretically possible for elements with atomic masses greater than 92 amu, it is only seen in elements with atomic masses of 230 amu or greater.

10 3 1.2 Neutron Multiplicity As was mentioned in the previous section, when fission occurs neutrons are released. The number of neutrons released is any given fission reaction is not exact, but can range generally between zero and seven. Since an exact number of neutrons is not released, the neutron multiplicity is used to describe a particular nuclide. The neutron multiplicity is the average number of neutron produced in a fission event of a nuclide. It is denoted by the symbol and is generally a decimal number. The value of the neutron multiplicity is unique for each isotope for a given incident neutron energy as displayed in Figure 1.1 below. The value of the neutron multiplicity is also different for spontaneous and neutron-induced fission in the same isotope. For U-235 the value of for spontaneous fission is 1.86 while for neutron-induced fission (with thermal neutrons) is Figure 1.1 Nubar values of U-235 and Pu-239. U-235 and Pu-239 have distinct values of nubar at all energies. When recording, the values and are usually also recorded. is the number of neutrons released per fission event. It is always an integer number, since only an integer number of neutrons can be released. Like, is different for both spontaneous and induced fission. The

11 4 neutron probability distribution,, is the probability that a given fission will result in the emission of a discrete amount of neutrons. That is to say, is the probability that neutrons will be released in a fission event.. Table 1.1 below displays how the values,, and are generally recorded in the literature. Table 1.1 Values of,, and for U-235. Here is listed as <nu>, is the probability that a given multiplicity (0-7) will occur. [2] Gwin 84 Boldeman 84 Consensus Std. Dev P P P P P P P P <nu> <nu(nu-1)>/2! <nu(n-1)(n-2)>/3! Because each isotope has a specific value for, it can be used as an invaluable tool in isotope detection. This is known as neutron multiplicity counting. In its simplest definition, neutron multiplicity counting is a neutron detection technique that leverages the multiplicity emissions of neutrons from fission to identify various actinides in a lump of material. The ability to identify certain actinides in a mass of material is of the utmost importance to nuclear nonproliferation agencies.

12 5 1.3 The Lawrence Livermore Simulation Lawrence Livermore National Laboratory (LLNL) developed a physics model for the simulation of neutron and gamma ray emission from fission and photofission that was included in MCNPX 2.7.B [3] as an undocumented feature and then as a documented feature in MCNPX 2.7.C. [4] The LLNL multiplicity capability provided the ability for MCNPX to simulate neutron and gamma-ray distributions for neutron induced, spontaneous and photonuclear fission reactions. [5] It also allows for prompt gammas from photofission, correlation of neutrons and photons from fission, and neutron and photon multiplicity so that the number of emitted particles is not just the integer closest to the average value. [6] The original testing on the model for implementation into MCNPX was conducted by McKinney and Hendricks. [7] The model is an encapsulation of measured data with the default of the neutron multiplicity distribution drawing its data for neutron multiplicity distributions from Gwin et al. [2] along with the data from Zucker and Holden. [8] One of the founding principles of MCNPX was that it would have several redundant capabilities, providing the means of testing and including various physics packages. Though several multiplicity sampling methodologies already existed within MCNPX, the LLNL fission multiplicity was included to provide a separate capability for computing multiplicity as well as including several new features not already included in MCNPX. These new features include: (1) prompt gamma emission/multiplicity from neutron-induced fission; (2) neutron multiplicity and gamma emission/multiplicity from photofission; and (3) an option to enforce energy correlation for gamma neutron multiplicity emission. The multiplicity sampling used in the LLNL capability is different from the other options offered in MCNPX in that it uses experimental neutron multiplicity values. The default option in MCNPX is an integer floor/ceiling method in which the average integer value of the emitted

13 6 neutrons is used. For the fissioning of U-235 the average number of neutrons emitted is 2.4 per fission, and so MCNPX record the emission of either 2 or 3 neutrons. The other available options all use variations on fitting a Gaussian and truncating it or shifting it to adjust for the average. The LLNL Capability offers a method that can be much more exact in it measurements since the number of emitted neutrons is based on the experimental data, rather than on averages and fits. The new photofission option (2 above) has three distinct advantages over the default MCNPX treatment: (1) prompt photofission gammas are produced; (2) photonuclear neutrons and gammas are correlated; and (3) the correct multiplicity of photofission neutrons and gammas is used, while the number of secondaries is correctly sampled rather than being the number just above or below the average. [3] The use of exact modeling of the photofission process enables coincidence counting of photofission neutrons and gammas. One of the main advantages of the LLNL neutron fission model is that neutron-induced photons are correlated with the fission event. The LLNL fission model is the only MCNPX method emitting spontaneous fission prompt photons. These are neglected in the MCNPX default FMULT spontaneous fission source. 1.4 Applications of the LLNL Capability and Testing The identification of individual actinide concentrations, especially U-235 and Pu-239, is of the utmost importance to the International Atomic Energy Agency s mission of, verifying through inspection systems that States comply with their commitments, under the Non- Proliferation Treaty and other non-proliferation agreements, to use nuclear material and facilities only for peaceful purposes. [9] Capabilities such as the Lawrence Livermore multiplicity capability allow for the modeling of neutron and photon multiplicities which can be applied to isotope identification devices.

14 7 The capabilities in the LLNL fission model also allow correlated signal detection for identifying presence of special nuclear material (SNM). Therefore, these new capabilities help meet the missions of the Domestic Nuclear Detection Office (DNDO), which is tasked with developing nuclear detection strategies for identifying potential radiological and nuclear threats. The LLNL capability provides new simulation abilities that can be directly applied to detection strategies by the DNDO. The testing performed on the LLNL capability was funded by the Department of Homeland Security and was conducted at Los Alamos National Lab. The testing included: (1) an initial test of the capability s default settings; (2) testing the capability against the other multiplicity distribution options (FISM options) available in MCNPX; (3) testing the neutron induced fission data (nudistoption); (4) testing the spontaneous fission data (ndistoption); and testing the neutron energy conservation options (correlationoption).

15 8 Chapter 2 Initial Multiplicity Testing Two types of tests were created to test the default LLNL neutron multiplicity capability: neutron-induced fission tests and spontaneous fission tests. Figure 1.1 below shows the benchmarking method used for the tests. Figure 2.1 The benchmarking method used for the initial testing. The input deck on the left was used for neutron induced fission and the input deck on the right was used for spontaneous fission. Both cases set the 6th entry on the PHYS:N card to 5 (i.e. use LLNL multiplicity). The neutron-induced fission tests utilized a simple cm radius sphere where ev neutrons were released at the sphere center. Neutrons were forced to immediately collide in the sphere and release all progeny from the sphere, without further collision, using the LCA card, LCA 7j -2 (therefore density and size of the sphere are irrelevant). Enough particles were run to ensure that the average error of any specific multiplicity did not exceed 0.36%. Neutron-induced fission

16 9 multiplicities were computed for U-233, U-235, Pu-239, and Pu-241. The spontaneous fission tests also used the same spherical geometry, except: (1) the LCA card was removed; (2) the density of the sphere was set to g/cm3; and (3) instead of emitting a thermal neutron, the PAR keyword was set to PAR=SF. The purpose of the small density was to ensure that the spontaneous fission neutrons would not further interact and induce fissions (i.e. the mean free path greatly exceeded the size of the sphere). Enough particles were run to ensure that the average error of any specific spontaneous multiplicity did not exceed 0.23%. Spontaneous fission multiplicities were computed for U-238, Pu-238, Pu-240, Pu-242, Cm-242, and Cm-244. All of the computed results were compared against experimental results compiled by Holden at Brookhaven National Laboratory. [10] Since the LLNL multiplicity capability only uses experimental data, the comparison between the consensus data recorded by Holden and the results of running the capability should only have small percent differences between them. Table 2.1 displays the percent difference of the LLNL multiplicity capability compared to experiment for neutron induced fission multiplicity, where is the neutron emission multiplicity distribution. The maximum error is for U-233 at 220%, but for the 7th multiplicity. The first four multiplicities of U-233 are all within 6%. Pu-239 has the smallest error never exceeding 2% (and never exceeding 1% for most multiplicities). U-235 has larger than 5% error for 0, 1 and >3 multiplicities. The large errors for U-233 and U-235 in the last three multiplicities are not as meaningful as the errors for the first three multiplicities (the mean neutrons per fission is between 2-3 resulting in the dominant amount of emissions being from the 2 and 3 multiplicity; furthermore, higher multiplicities may not be currently utilized in coincidence counting). Pu-241 has percent errors below 10% for the first six multiplicities and over 13% for the 6 and 7 multiplicities. The percent errors for ν and higher moments are below 5% for all four actinides (U-235 and Pu-239 are below 1%).

17 10 Table Percent Error of Neutron Induced Fission Multiplicity as Compared to Experiment. U-233 U-235 Pu-239 Pu-241 P0 1.33% 7.11% 0.28% 9.99% P1 3.60% 7.41% 0.25% 0.30% P2 1.67% 0.90% 0.16% 0.66% P3 3.50% 3.23% 0.03% 1.04% P4 5.44% 4.58% 0.21% 2.25% P % 5.81% 0.10% 1.69% P % 19.70% 1.23% 13.37% P % 45.90% 1.69% 30.89% <ν> 0.46% 0.94% 0.10% 0.45% <ν(ν-1)>/2! 1.93% 1.58% 0.28% 0.89% <ν(ν-1)(ν-2)>/3! 4.96% 0.43% 0.71% 1.17% Table Percent Error of Spontaneous Fission Multiplicity as Compared to Experiment. U-238 Pu-238 Pu-240 Pu-242 Cm-242 Cm-244 P0 0.02% 4.14% 0.01% 1.55% 0.05% 0.05% P1 0.00% 2.57% 0.00% 6.94% 0.01% 0.01% P2 0.01% 0.13% 0.01% 3.03% 0.00% 0.00% P3 0.01% 1.07% 0.01% 11.59% 0.00% 0.00% P4 0.00% 2.94% 0.00% 49.57% 0.00% 0.00% P5 0.05% 5.34% 0.03% 29.55% 0.01% 0.01% P6 0.00% 99.92% 0.07% 0.07% P7 0.07% 0.02% P8 0.30% <ν> 0.00% 1.04% 0.00% 0.00% 0.00% 0.00% <ν(ν-1)>/2! 0.00% 2.10% 0.00% 2.01% 0.00% 0.00% <ν(ν-1)(ν-2)>/3! 0.00% 3.20% 0.00% 6.52% 0.00% 0.00% Table 2.2 displays the percent difference of the LLNL multiplicity capability compared to experiment for spontaneous fission emission multiplicity. All multiplicities for U-238, Pu-240, Cm-242, Cm-244 are very accurate, never exceeding 0.052%. Pu-238 has percent errors of less than 5%, while Pu-242 has a range of percent errors from less than 7% for the 0, 1 and 2 multiplicities and as a greater than 10% for the 3-6 multiplicities. The percent errors of ν are

18 11 extremely accurate for most actinides (<<0.01% except for Pu-238 and Pu-241 which are 1.04% and 23.27% respectively). The higher moments of ν are extremely accurate except for Pu-238 (<5%) and Pu-242 (<10%). The results of the tests show that multiplicities for Pu-239 neutron induced fission and U- 238, Pu-238, Pu-240, Cm-242 and Cm-244 spontaneous fission are computed very accurately. U-233, U-235, Pu-241, and Pu-242 have larger percent errors, exceeding 30.89%, but the large errors are all in the final four multiplicities. The first three multiplicities of each are less than 10%. The percent errors for ν and the higher moments are also within 10% for all the actinides.

19 12 Chapter 3 FISM Options MCNPX offers five different FISM options for dealing with fission multiplicity control. The options are laid out in the MCNPX manual. [1] If fism=0, the MCNP treatment is used, which assumes an integer number of neutrons per fission; if fism=1, the sampled nubar is corrected to preserve the average; if fism=2, the multiplicity is preserved by increasing the nubar threshold; if fism=3, the Gaussian distribution is sampled without correction; if fism=4, the MCNP method is used in the presence of spontaneous fission or the FMULT card; if fism=5, the LLNL fission model is used for neutron-induced, spontaneous, and photonuclear fission. Tests were run comparing the different FISM options applicable. The results for the neutron-induced fission of U-235 are displayed in Table 3.1. Table Percent Difference Between FISM options 5 (LLNL), 1, 2, 3 and Consensus for U- 235 (neutron-induced fission). Consensus values were taken from Gwen et al. [2] % Difference (LLNL, Consensus) %Diff. (FISM 1, Cons.) %Diff. (FISM 2, Cons.) The table shows the results for four of the five FISM options (the 4th FISM option only applies to spontaneous fission) and the percent difference when compared with the consensus value from %Diff. (FISM 3, Cons.) Consensus Std. Dev LLNL FISM 1 FISM 2 FISM 3 P E E E % 28.80% 41.12% 27.73% P E E E % -6.97% -9.88% -7.40% P E E E % -3.74% -3.87% -3.87% P E E E % 1.17% 1.36% 1.36% P E E E % 7.90% 8.45% 8.45% P E E E % 6.54% 7.45% 7.45% P E E E % 3.16% 4.40% 4.40% P E E E % % % % P8 2.26E E E-06 P9 2.36E E E-08 <nu> E E E % 0.94% 0.94% 1.12% <nu(nu-1)>/2! E E E % 3.30% 3.66% 3.66% <nu(n-1)(n-2)>/3! E E E % 5.45% 6.02% 6.02%

20 13 Zucker and Holden. [5] The LLNL option gives the most accurate results with the percent errors below 8% in the first three multiplicities. FISM options 1, 2, and 3 displayed percent differences greater than 27% for the first multiplicity, which was to be expected since they use averaging techniques that cause P0 to have higher probability. For spontaneous fission the results of the FISM option runs showed the same values for options one through four and only a slight difference for option 5. This is displayed in table 3.2 below. Table Percent Difference Between FISM Options 1, 2, 3,4, 5 (LLNL) and Consensus for U- 238 (Spontaneous Fission). Consensus values were taken from Gwen et al. [2] Consensus Std. Dev LLNL FISM 1 FISM 2 FISM 3 FISM 4 P E E E E E-02 P E E E E E-01 P E E E E E-01 P E E E E E-01 P E E E E E-02 P E E E E E-03 <nu> E E E E E E+00 <nu(nu-1)>/2! E E E E E E+00 <nu(n-1)(n-2)>/3! E E E E E E-01 % Diff. (LLNL, Consensus) %Diff. (FISM 1, Cons.) %Diff. (FISM 2, Cons.) %Diff. (FISM 3, Cons.) %Diff. (FISM 4, Cons.) 0.02% 0.02% 0.02% 0.02% 0.02% 0.00% 0.00% 0.00% 0.00% 0.00% -0.01% -0.01% -0.01% -0.01% -0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.00% 0.00% 0.00% 0.00% 0.00% -0.05% -0.05% -0.05% -0.05% -0.05% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

21 14 With the significant digits used for table 4 the five FISM options appeared to be exactly the same. Upon inspection of the output files it was clear that options one through four were exactly the same while option five was slightly different. This difference can be seen in figure 1. Figure Output of Test for FISM set to 1 (right) and FISM Set to 5 (left). For the FISM option set to 1 there were 19,897,991 neutron source tracks, while with FISM set to 5 there were 19,897,988 giving a difference of three between them. There were also differences under the fission section in the last digits of fissions, fission neutrons, and multiplicity fraction which is circled in red in figure 3.1. The reason for the values for option first four options being exactly the same is related to print table 38 in the output file. Table 3.3 shows an example of print table 38. Neutron-induced fission uses the width and watt parameter from the table and gets nubar from the Evaluated Nuclear Data Files (ENDF). Because of this, the values for FISM 1, 2, and 3 for neutron-induced fission are different. Spontaneous fission should use the width, watt, and sfnu parameters from table 38. The problem is, for cases where columns greater than column six exist in print table 38,

22 15 the additional columns are uses instead of the width, watt, and sfnu parameters. The values that occupy the columns greater than column six are the same between the FISM options. This was the problem in the cases run to test the spontaneous fission FISM options. Table Example of Print Table 38 from U-235 Output File. Whenever more than 6 columns are occupied, as shown below, the values of the width, watt, yield, and sfnu columns are replaced by the values of the final columns of the table. zaid width watt1 watt2 yield sfnu E E E E * E E E E E E E E E E E E E E E E E E E E E E Because of this the options 1 4 are exactly the same. Option 5 (LLNL) uses the same cumulative distribution function as listed in print table 38 but with one extra significant digit, which accounts for the very slight difference between option 5 and the others.

23 16 In addition to the actinides U-235 and U-238, tests for the FISM options were also performed for U-233, Pu-239, and Pu-241. The full results of all the FISM options tests for the five actinides are recorded in Appendix A. The tests for U-233, Pu-239, and Pu-241 were completed for neutron-induced fission and not for spontaneous fission.

24 17 Chapter 4 Options in the LLNL Source Code The LLNL source code allows data to from different sources for neutron-induced fission, spontaneous fission for Cf-252, and energy correlation between neutrons and gammas. These options do not currently have keywords on an MCNPX input card, and the options can only be selected by altering the source code. To test these options the source code was changed and recompiled. Print statements were added to the code to ensure that the changes were taking effect. The three options changed in the code were the nudistoption, ndistoption, and correlationoption. Figure 4.1 shows the options as they appear in the LLNL capability source code. Figure LLNL Multiplicity Source Code Options.

25 Neutron-induced Fission Data Four options are provided for the neutron-induced fission data. To conduct the tests the value for nudistoption was set in the source code from 0 to 3 and was run for U-233, U-235, Pu-239, and Pu-241. For each of the isotopes runs were performed with the energy set to 2.53e-8 MeV, 5MeV, and 15 MeV. Additional runs were conducted for U-235 with erg=7 MeV. An example of the input deck used is show in figure 3. The only difference between the input deck used here and the initial input decks used to test the neutron multiplicity is the added neutron current tally circled in red. Figure Input Deck Used for Nudist Runs. Tests were run for the actinides U-233, U-235, Pu-239, and Pu-241. Several methods of comparison were used to check the results of the tests. The first method of comparison was to ensure that the tests were yielding reasonable results. This was done by comparing the results of the runs for options 0 3 of 5MeV with thermal and then 15MeV with thermal. The results for U-235 are shown in Table 4.1.

26 19 Table Percent Differences Between 5 MeV Thermal and 15 MeV Thermal for Each Nudist Option. % Difference 5 MeV, Thermal %Difference 15 MeV, Thermal nudist=0 nudist=1 nudist=2 nudist=3 nudist=0 nudist=1 nudist=2 nudist=3 P % % % % % % % % P % % % % % % % % P % % % % % % % % P3 8.82% 7.63% 7.79% 5.42% -8.56% -9.59% % % P % 71.89% 76.34% 73.43% % % % % P % % % % % % % % P % % % % % % % % P % #DIV/0! % % % #DIV/0! % % P % P % <nu> 25.89% 24.75% 24.99% 24.98% 60.52% 59.08% 86.14% 86.22% <nu(nu-1)>/2! 64.47% 62.35% 61.95% 62.59% % % % % <nu(n-1)(n-2)>/3! % % % % % % % % Table Percent Differences Between 5 MeV Thermal and 15 MeV Thermal with Thermal set to Nudist=3. %Difference 5 Mev, Thermal (nudist=3) %Difference 15 MeV, Thermal (nudist=3) nudist=0 nudist=1 nudist=2 nudist=3 nudist=0 nudist=1 nudist=2 nudist=3 P % % % % % % % % P % % % % % % % % P % % % % % % % % P3 5.41% 5.44% 5.34% 5.42% % % % % P % 72.59% 73.84% 73.43% % % % % P % % % % % % % % P % % % % % % % % P % % % % % % % % P % % P % % <nu> 24.73% 24.71% 25.05% 24.98% 59.03% 59.03% 86.22% 86.22% <nu(nu-1)>/2! 61.93% 61.86% 62.78% 62.59% % % % % <nu(n-1)(n-2)>/3! % % % % % % % % The second method of comparison used was to compare the value for thermal neutrons with nudist = 3 to 5 MeV and 15 MeV for nudist = 0, 1, 2, 3. The results are shown in Table 4.2.

27 20 In the tables above, the large percent errors (>1000% in some cases) are to be expected since we are making a comparison between energies and different neutron distribution options. The point to note in the tables is that the percent difference between 5 MeV and thermal nubar is approximately 25% while the percent difference between 15 MeV and thermal nubar is much greater falling between 59% and 86%. This is exactly as it should be since nubar increases as the incident neutron energy increases. Also note in tables 4.1 and 4.2 for the results of 15 MeV there is a jump in the percent difference from around 59% for nudist set to 0 and 1 up to 86% for nudist set to 2 and 3. The reason for this is that for nudist options 0 and 1 for any energy greater than 10 MeV the nubar value for 10 MeV is used. For options 2 and 3 the value of nubar for 15 MeV is used. [4] The third method used to compare the result was graphical. Figures 4.3 and 4.4 below are the graphs of the weight divided by the bin width versus the upper energy value for the bin for neutrons and photons respectively. Figure 4.3 U-235 Weight/Bin Width vs. Upper Energy Value for Bin for Neutrons. The values were taken from the output of the MCNPX run. The integral of the curves gives the average energy of the neutrons emitted.

28 21 Figure 4.4 U-235 Weight/Bin Width vs. Upper Energy Value for Bin for Photons. The values were taken from the output of the MCNPX run. The integral of the curves gives the average energy of the photons created. The importance of the two graphs above was not in the peaks, but in the integral of the graphs. The integral of the curve in Figure 4.3 for neutrons at thermal energies was 2.06 MeV, 1.29 MeV for neutrons at 5 MeV, 1.62 MeV for neutrons at 7 MeV, and 2.38 MeV for neutrons at 15 MeV. These results are not immediately evident and were taken from the output file of the MCNPX nudist runs. There is an obvious trend in Figure 4.3 with the integral increasing as the energy increases. This is true except for thermal energies which has an integral greater than both 5 MeV and 7 MeV. Beyond this the measured average value for the energy of neutrons released in fission is 2 MeV. The value of the thermal neutrons was close to this, but the other energies differed significantly. The reason for this was made evident by looking at the cross-sections of the reactions.

29 22 Figure 4.5 Cross-section for U-235. Here mt 18 is the total fission cross section, -2 is the absorption cross-section, -3 is the elastic cross-section, and -1 is the total cross-section. The cross-section in figure 4.5 shows that at thermal energies the total cross-section is dominated by the fission cross section. At 5 MeV and 7 MeV the fission cross section makes a noticeable decrease, and the total cross-section is dominated by the elastic cross-section. This difference between thermal and the other energies caused the integral of the graph of the energy at thermal to be greater than at 5 or 7 MeV. In MCNPX fission is not always forced to happen. Since elastic scattering is more dominant at 5 and 7 MeV, the average energy is lower because the energy released from elastic scattering of neutrons is much less than that produced in a fission reaction. A similar argument as for the neutrons of Figure 4.3 is true for the graph of the photons in Figure 4.4. Here the integral of the curves give the average number of photons released per fission event. The integral of the photon curves were 6.00 for thermal neutrons, 3.22 for 5 MeV

30 23 neutrons, 4.72 for 7 MeV neutrons, and 7.89 for 15 MeV neutrons. The number of photons released of photons released in a fission reaction is generally between 6 and 8. As with the neutron graph, the trend of the average increasing for low energy neutrons to high energy neutron is evident, with thermal being out of place. The high fission cross-section at thermal energies is again the cause of this, but here it is limiting the number of photons produced. Each of the methods of comparison proved that the nudistoption in the LLNL capability yielded reasonable results. In the first two types of comparisons used, the various energies all gave different results with percent differences that would be expected between them. The graphs of the neutron and photon energies also proved to give results close to the experimental averages of both neutron and photon energies. 4.2 Spontaneous Fission Data The spontaneous fission data available in the LLNL capability is given by Verbeke on page 6 of his report. The LLNL source code uses tabulated data for spontaneous fission. The ndistoption in the source code allows the user to select between the use of experimental multiplicity data for Cf-252 by Spencer et al. [11] or Boldeman. [12] Tests were conducted for this option using the same input deck as was used for spontaneous fission in the initial multiplicity testing (Figure 2.1). Table 4.3 gives the results of the tests which show close agreement between the sources and LLNL s capability s ndistoption results.

31 24 Table 4.3 Results of ndistoption. Spencer Error Boldeman Error ndist 0 Rel. Error ndist 1 Rel. Error % Difference (ndist 0, Spencer) %Diff. (ndist 1, Boldeman) P E E E E E E % -1.31% P E E E E E E % 0.92% P E E E E E E % -0.41% P E E E E E E % 0.66% P E E E E E E % -0.69% P E E E E E E % -0.11% P E E E E E E % 1.68% P E E E E E E % -2.63% P E E E E E E % 5.01% P E E % <nu> E E E E E % 0.00% 4.3 Neutron Energy Conservation The LLNL source code offers four options for correlating the energy between neutrons and gamma-rays in fission (correlationoption). With correlationoption equal to 0 there is no correlation between neutron and photons (this is the default), for 1 the total fission neutron energy and total fission gamma-ray energy are sampled from normal distributions of means given in Beck et al. [10], for 2 the total fission neutron energy and total fission gamma-ray energy are sampled from normal distributions of means given in Vogt, [11] and 3 was to give total correlation between neutrons and gamma-rays. Option 3 was thought to be fully completed and included in the source code, but we found that while the option exists, it has yet to be completed. Options 1 and 2 correlate the energy between the neutron and gamma-rays, but they offer no correlation between the number of neutrons and the number of gamma-rays.

32 25 Representative results of the correlation testing are shown in the figures below for U-235 with the default option (nudist=3). Figure 4.6 displays the neutron energy distribution. There are three main observations to be made for the graph. First, correlation option 0, 1, and 2 follow very similar paths as would be expected. Correlation option 1 and 2 use very similar methods in calculating energy conservation, and their results are similar to the result obtained when the neutron energies are sampled independently (option 0). Second, the methods used by Beck and Vogt are cut off at 10 MeV as seen in the graph. Option 0 has no such limitations, and so it increases beyond 10 MeV. Third, the large peak at the beginning can be ignored. It is the result of thermal scattering and is insignificant when compared to the rest of the graph. It appears as a large and significant peak, but this due to the log-log set up of the graph. The integral under the curve (the average neutron energy) is determined by energy values greater than approximately 1,000 ev. The peak is well below this, and so can be ignored. Figure 4.6 Graph of Weight/Bin Width vs. Upper Energy Value for Bin for U-235 Neutrons. The graph is of a similar form to Figure 4.3 but is a log-log graph to emphasize the divergence of correlation option 0 from 1 and 2 at higher energies.

33 26 Figure 4.7 is a graph of the photon energy distribution for the fission of U-235. The peaks show the average energy for photons in a given fission event. The average energy of photons emitted in fission is 7 MeV for U-235, so the values for correlation options 0, 1 and 2 are all within an acceptable range of the average, but correlation option 0 is higher than would be expected. Figure Graph of Weight/Bin Width vs. Upper Energy Value for Bin for U-235 Photons.

34 27 Chapter 5 Summary of Results The results of the testing proved to be positive. Multiplicities, using the LLNL multiplicity capability, were computed and compared to experimental data for ten different isotopes. Multiplicities for Pu-239 neutron induced fission and U-238, Pu-238, Pu-240, Cm-242 and Cm-244 had a percent difference of less than 1% when compared with consensus data. The large U-233, U-235, Pu-241, and Pu-242 errors were all in the final four multiplicities, with the first three multiplicities of each being less than 10%. The error for the higher moments of was also within 10% for all the actinides. For the tests performed on the FISM option it was found that if there are columns greater than column 6 in print table 38 of the MNCPX output file, then FISM options are not applicable for spontaneous fission. FISM=5 was slightly different for spontaneous fission from the other options because of the cumulative distribution in LLNL which is slightly different from that in MCNPX The results for neutron induced fission showed general agreement between the options. The results of the nudist runs also proved to yield reasonable results. When the nudist options were compared between each other the differences were evident at both 5 and 15 MeV. When the same option was compared at various energies the percent differences between energies was exactly the expected difference. Finally, the average energies of the neutrons and the average number of photons emitted were found to be accurate when compared to the experimental averages once the effects due to the dominating cross-sections were taken into account.

35 28 The results of the correlation option testing show agreement between Beck (option 1) and Vogt (option 2). Since they use similar methods in calculating the correlation, this was to be expected. Option 0 (no correlation) proved to have results greater than either Beck or Vogt. The main result is that there is no correlation option for the number of neutron and gammas, as was originally thought when the LLNL capability was added to MCNPX. The main conclusions of the testing are that the LLNL capability accurately models neutron and photon multiplicities using experimental data sets, the neutron and photon distribution options are accurate when compared with the other options in MCNPX, and there is no correlation option for the number of neutrons and gammas. With the use of data sets instead of mathematical models the LLNL capability sets itself apart from the other option available in MCNPX, while proving to be a very useful and accurate modeling tool.

36 29 Appendix A Complete FISM Option Results U-233 Consensus Std. Dev LLNL (5) Rel. Error % Difference (LLNL, Consensus) P P P P P P P P <nu> <nu(nu-1)>/2! <nu(n-1)(n- 2)>/3!

37 U-233 continued 30 FISM 1 Rel. Error % Diff. (FISM 1, Cons.) % Diff. (FISM 2, Cons.) FISM 3 Rel. Error % Diff. (FISM 3, Cons.) P P P P P P P P E E P E E P E E <nu> <nu(nu-1)>/2! <nu(n-1)(n-2)>/3! U-235 Consensus Std. Dev LLNL Rel. Error % Difference (LLNL, Consensus) P E E-02 P E E-02 P E E-03 P E E-02 P E E-02 P E E-02 P E E-01 P E E-01 <nu> E E-03 <nu(nu-1)>/2! E E-02 <nu(n-1)(n-2)>/3! E E-03

38 31 U-235 Continued FISM 1 Rel. Error %Diff. (FISM 1, Cons.) FISM 2 Rel. Error %Diff. (FISM 2, Cons.) FISM 3 Rel. Error %Diff. (FISM 3, Cons.) P0 4.09E % 4.48E % % P1 1.60E % 1.55E % % P2 3.24E % 3.23E % % P3 3.08E % 3.08E % % P4 1.37E % 1.38E % % P5 2.84E % 2.87E % % P6 2.72E % 2.75E % % P7 1.17E % 1.19E % % P8 2.26E E % P9 2.36E E % <nu> 2.44E % 2.44E E % % <nu(nu-1)>/2! 2.40E % 2.40E % % <nu(n-1)(n-2)>/3! 1.20E % 1.20E % %

39 32 U-238 Consensus Std. Dev LLNL Rel. Error % Difference (LLNL, Consensus) FISM 1 Rel. Error %Diff. (FISM 1, Cons.) P E % 4.82E % P E % 2.49E % P E % 4.25E % P E % 2.28E % P E % 4.23E % P E % 7.25E % <nu> E E % 1.99E % <nu(nu-1)>/2! E E % 1.44E % <nu(n-1)(n-2)>/3! E E % 4.70E % U-238 Continued FISM 2 Rel. Error %Diff. (FISM 1, Cons.) FISM 3 Rel. Error %Diff. (FISM 1, Cons.) FISM 4 Rel. Error %Diff. (FISM 1, Cons.) P0 4.82E % 4.82E % 4.82E % P1 2.49E % 2.49E % 2.49E % P2 4.25E % 4.25E % 4.25E % P3 2.28E % 2.28E % 2.28E % P4 4.23E % 4.23E % 4.23E % P5 7.25E % 7.25E % 7.25E % <nu> 1.99E % 1.99E % 1.99E % <nu(nu-1)>/2! 1.44E % 1.44E % 1.44E % <nu(n-1)(n-2)>/3! 4.70E % 4.70E % 4.70E %