Version 1.0 Revised on Nov. 19, 1992 IAEA Benchmark Problem Based on the Time-of-Flight Experiment on Beryllium Slabs at FNS/JAERI Yukio OYAMA and Hiroshi MAEKAWA Fusion Reactor Physics Laboratory Department of Reactor Engineering Japan Atomic Energy Research Institute Tokai-mura, Naka-gun, Ibaraki-ken, 319-11 Japan (Phone) 81-292-82-6075 (for Y.O.) or -6015 (for H.M.) (Telefax) 81-292-82-5709 (BITNET) oyama@fnshp.tokai.jaeri.go.jp (for Y.O.) maekawa@fnshp.tokai.jaeri.go.jp (for H.M.) 1. Numerical Data and Their Format a) Datafiles: BETOFTG.DAT ----- Source neutron spectrum BETOF5.DAT ------ 50.8 mm-thick angular neutron flux BETOF15.DAT ----- 152.4 mm-thick angular neutron flux ENERGY.DAT ---------- Boundary energy b) Units of the data Source spectrum [n/sr/lethargy/source] Angular flux [n/sr/cm2/lethargy/source] c) Data format for experimental data Comment 1 line 20A4 Energy (mid-point) [MeV] I = 1, 150 6E12.4 Angular flux [See above] I = 1, 150 6E12.4 Error (fraction) [%] I = 1, 150 6E12.4 d) Number of data set BETOFTG.DAT 1 0 degree BETOF5.DAT 4 0, 24.9, 42.8, 66.8 degrees BETOF15.DAT 5 0, 12.2, 24.9, 42.8, 66.8 degrees *In the case of 50.8 mm-thick and 12.2 degree, it was revealed that the measured flux was contaminated by some of direct neutrons from the target and too difficult to analysis. Therefore the data of 50.8 mm-thick and 12.2 degree is not included in the file. e) Data format for boundary energy (ENERGY.DAT) Comment 1 line 20A4 Boundary energy [MeV] I = 1, 151 8F9.5 2. Flight Path and Effective Measured Area The flight path and effective measured area are summarized as follows. The meaning of them is described in the references. These data are useful for Monte Carlo calculations. Table Flight path and measured area 50.8 mm-thick Assembly ---------------------------------------------- Angle Flight Path [cm] Measured Area [cm**2] ---------------------------------------------- 0.0 738 85.88 24.9 740 86.34 41.8 744 87.26 66.8 753 89.33 ---------------------------------------------- 152.4 mm-thick Assembly ---------------------------------------------- Angle Flight Path [cm] Measured Area [cm**2] ---------------------------------------------- 0.0 728 83.57 12.2 729 83.80 24.9 731 84.26 41.8 736 85.41 66.8 748 88.18 ---------------------------------------------- 3. Calculational Model The calculational model is of course depend on the code used. Basic data are as follows: Radius of assembly : 31.5 cm Thickness of assembly : 5.08 and 15.24 cm Distance between target and assembly : 20 cm Be atom density : 1.215x10**23 atoms/cm**3 Area of detector : (pai)x2.54**2 [cm**2] 4. How to Calculate the Angular Flux (1) Neutron source You can use the data of "BETOFTG.DAT" as the source. Before you start the calculation you should interpolate the spectrum to adjust it to the group structure used. It is notable that the integrated source spectrum multiplied by 4x(pai) is not unity (1.0) but about 1.12. The source neutrons are generated isotropically at the target position. (2) Two-demensional discrete ordinate code such as DOT3.5 You can easily understand from the reference 4) how to do. It is important to average over the measured area when the calculated angular flux is compared with the measured one. (3) Monte Carlo calculation You can see a sample of method in the reference 1). 5. Comparison Two types of comparison will be done for this benchmark problem. (1) To compare the measured and calculated angular fluxes directly in graph. (2) To compare the integrated flux over following four energy regions in C/E values (Ratio of calculated to experimental values); Table Integrated Angular Flux 50.8 mm-thick Assembly ---------------------------------------------------------------------- Energy* 10.183 (14) 1.9557 (47) 0.5070 (74) 0.0974 (107) Angle --------------------------------------------------------------- 0.0 3.922-4#(0.18%) 1.302-5 (0.90%) 8.831-6 (0.85%) 3.847-6 (1.53%) 24.9 2.566-5 (0.55%) 6.180-6 (1.08%) 5.093-6 (0.88%) 3.765-6 (1.00%) 41.8 1.016-5 (0.92%) 5.746-6 (1.20%) 5.022-6 (0.94%) 3.484-6 (1.15%) 66.8 4.567-6 (1.10%) 5.423-6 (0.91%) 4.706-6 (0.71%) 3.140-6 (0.88%) ---------------------------------------------------------------------- 152.4 mm-thick Assembly ---------------------------------------------------------------------- Energy* 10.183 (14) 1.9557 (47) 0.5070 (74) 0.0974 (107) Angle --------------------------------------------------------------- 0.0 7.727-5 (0.21%) 5.759-6 (0.74%) 5.091-6 (0.62%) 4.171-6 (0.74%) 12.2 2.330-5 (0.33%) 4.941-6 (0.67%) 4.591-6 (0.54%) 3.642-6 (0.64%) 24.9 1.041-5 (0.51%) 4.581-6 (0.70%) 4.362-6 (0.55%) 3.524-6 (0.62%) 41.8 4.748-6 (0.72%) 3.961-6 (0.74%) 4.002-6 (0.56%) 3.153-6 (0.66%) 66.8 1.336-6 (2.08%) 2.657-6 (1.20%) 2.940-6 (0.76%) 2.399-6 (0.66%) ---------------------------------------------------------------------- *Lower energy boundary for each region in MeV and the group number of lower boundary from the higher energy group. #Read as 3.922x10**(-4). 6. References When you publish the results using this numerical data, you should refer at least following references 1) and 2). 1) Oyama Y., Maekawa H.: "Measurement and Analysis of an Angular Neutron Flux on a Beryllium Slab Irradiated with Deuteron-Tritium Neutrons," Nucl. Sci. Eng., 97, 220-234 (1987). 2) Oyama Y., Yamaguchi S., Maekawa H.: "Experimental Results of Angular Neutron Spectra Leaking from Slabs of Fusion Reactor Candidate Materials (I)," JAERI-M 90-092 (1990). 3) Oyama Y., Maekawa H.: "Measurements of Angle-Dependent Neutron Spectra from Lithium-Oxide Slab Assemblies by Time-of-Flight Method," JAERI-M 83-195 (Nov. 1983). 4) Oyama Y., Yamaguchi S., Maekawa H.: "Analysis of Time-of-Flight Experiment on Lithium-Oxide Assemblies by a Two-Dimensional Transport Code DOT3.5," JAERI-M 85-031 (March 1985). 5) Oyama Y., Maekawa H.: "Spectral Measurement of Angular Neutron Flux on the Restricted Surface of Slab Assemblies by the Time-of-Flight Method," Nucl. Instr. Methods, A245 173-181 (1986). 6) Oyama Y., Yamaguchi S., Maekawa H.: "Measurements and Analyses of Angular Neutron Flux Spectra on Graphite and Lithium-Oxide Slabs Irradiated with 14.8 MeV Neutrons," J. Nucl. Sci. Technol., 25, 419-428 (1988). 7) Oyama Y.: "Experimental Study of Angular Neutron Flux Spectra on a Slab Surface to Assess Nuclear Data and Calculational Methods for a Fusion Reactor Design," JAERI-M 88-101 (June 1988). Attachment 1 Calculational model for MCNP code FNS-TOF/31.4 CM(R)*5.06 CM(Z)-BE CYL./FIXED CONE BIAS/5 PT DETECTORS C ************************************** C * CELL CARAD * C ************************************** C ******* EXTERNAL VOID **************** 1 0 -4 : +4 -2 +3 : +10 : +2 -10 +5 +6 +7 +8 +9 C ******* SOURCE VACUUM REGION ********* 2 0 -3 +4 -1 C ******* MATERIAL REGION ************** 3 1 1.215-1 -3 +1 -2 C ******* DETECTOR VACUUM REGION ******* 4 0 +2 -10 -5 : +2 -10 -6 : +2 -10 -7 : +2 -10 -8 : +2 -10 -9 C ------- THE FOLLOWING IS A BLANK DELIMETER C ************************************** C * SURFACE CARD * C ************************************** 1 PZ -5.06 2 PZ 0 3 CZ 31.4 4 PZ -50 5 CZ 5.228 6 1 CZ 5.235 7 2 CZ 5.242 8 3 CZ 5.270 9 4 CZ 5.332 10 SO 1000 C ------- THE FOLLOWING IS A BLANK DELIMETER C ************************************** C * MODE CARD - NEUTRON ONLY * C ************************************** MODE 0 C ************************************** C * TRANSFORMATION CARDS * C * ROTATION ABOUT THE Y AXIS BY THETA* C ************************************** *TR1 0 0 0 12.2 90 102.2 90 0 90 77.8 90 12.2 +1 *TR2 0 0 0 24.9 90 114.9 90 0 90 65.1 90 24.9 +1 *TR3 0 0 0 41.8 90 131.8 90 0 90 48.2 90 41.8 +1 *TR4 0 0 0 66.8 90 156.8 90 0 90 23.2 90 66.8 +1 C ************************************** C * CELL PARAMETER CARDS * C ************************************** IN 0 1 1 1 C **************************************************** C * SOURCE SPECIFICATION CARDS * C * SRC1=POINT ISOTROPIC OPTION * C * SDIR DIRC. BIASING - HEIGHT REDUCTION CONSIDERED* C * SI(ENG.) AND SP(PROB.) TAKEN FROM BETOF SOURCE * C * EXPT. DATA * C **************************************************** SRC1 0 0 -25.06 2 1.0 SDIR 0 0 1 1 0.5372231 SI 4.6308-02 5.2474-02 5.9461-02 6.7378-02 7.6349-02 8.6515-02 9.8035-02 1.1109-01 1.2588-01 1.4264-01 1.6163-01 1.8315-01 2.0754-01 2.3517-01 2.6649-01 3.0197-01 3.4217-01 3.8774-01 4.3936-01 4.9786-01 5.6415-01 6.3927-01 7.2438-01 8.2084-01 9.3013-01 1.0540+00 1.1943+00 1.3533+00 1.5335+00 1.7377+00 1.8498+00 1.9691+00 2.0961+00 2.2313+00 2.3752+00 2.5284+00 2.6914+00 2.8650+00 3.0498+00 3.2465+00 3.4559+00 3.6787+00 3.9160+00 4.1686+00 4.4374+00 4.7236+00 5.0282+00 5.3525+00 5.6978+00 6.0652+00 6.4564+00 6.8728+00 7.3161+00 7.7879+00 8.2902+00 8.8249+00 9.3940+00 9.9999+00 1.0157+01 1.0317+01 1.0480+01 1.0645+01 1.0812+01 1.0983+01 1.1156+01 1.1331+01 1.1510+01 1.1691+01 1.1875+01 1.2062+01 1.2252+01 1.2445+01 1.2641+01 1.2840+01 1.3042+01 1.3248+01 1.3456+01 1.3668+01 1.3883+01 1.4102+01 1.4324+01 1.4550+01 1.4779+01 1.5012+01 1.5248+01 1.5488+01 1.5732+01 1.5980+01 1.6231+01 1.6487+01 SP 0 0 0 0 0 0 0 5.045-05 1.197-04 1.745-04 2.433-04 2.511-04 3.572-04 4.063-04 5.016-04 6.489-04 7.416-04 8.517-04 1.041-03 1.208-03 1.454-03 1.694-03 1.851-03 2.077-03 2.229-03 2.337-03 2.381-03 2.537-03 2.614-03 1.386-03 1.362-03 1.333-03 1.278-03 1.262-03 1.267-03 1.326-03 1.757-03 2.744-03 4.302-03 2.974-03 1.100-03 1.072-03 1.009-03 8.938-04 8.675-04 8.483-04 7.534-04 6.830-04 6.709-04 6.652-04 6.191-04 5.136-04 4.860-04 5.057-04 5.266-04 6.163-04 7.539-04 2.027-04 2.446-04 2.567-04 2.599-04 3.287-04 3.745-04 3.789-04 5.094-04 6.856-04 6.933-04 8.102-04 1.166-03 1.184-03 1.248-03 2.430-03 2.467-03 2.504-03 5.970-03 6.696-03 6.824-03 1.731-02 2.364-02 2.396-02 6.401-02 1.159-01 1.180-01 1.271-01 1.538-01 1.564-01 1.535-01 2.881-02 2.918-02 0 C ********************************************* C * MATERIAL SPECIFICATION CARDS * C ********************************************* C ---- BERYLLIUM ----------------------------- M1 4009.33C 1.0 C DRXS C ********************************************** C * TALLY SPECIFICATION CARDS * C ********************************************** FC5 --- FLUXES AT 5 PT DTS(TH=0.0, 12.2, 24.9, 41.8, 66.8 DEG) F5 0.0 0 738.0000 1 156.16903 0 722.31035 1 311.5665 0 671.21257 1 495.90016 0 554.63414 1 692.10891 0 296.63826 1 DD 0.5 100 E0 4.6308-02 5.2474-02 5.9461-02 6.7378-02 7.6349-02 8.6515-02 9.8035-02 1.1109-01 1.2588-01 1.4264-01 1.6163-01 1.8315-01 2.0754-01 2.3517-01 2.6649-01 3.0197-01 3.4217-01 3.8774-01 4.3936-01 4.9786-01 5.6415-01 6.3927-01 7.2438-01 8.2084-01 9.3013-01 1.0540+00 1.1943+00 1.3533+00 1.5335+00 1.7377+00 1.8498+00 1.9691+00 2.0961+00 2.2313+00 2.3752+00 2.5284+00 2.6914+00 2.8650+00 3.0498+00 3.2465+00 3.4559+00 3.6787+00 3.9160+00 4.1686+00 4.4374+00 4.7236+00 5.0282+00 5.3525+00 5.6978+00 6.0652+00 6.4564+00 6.8728+00 7.3161+00 7.7879+00 8.2902+00 8.8249+00 9.3940+00 9.9999+00 1.0157+01 1.0317+01 1.0480+01 1.0645+01 1.0812+01 1.0983+01 1.1156+01 1.1331+01 1.1510+01 1.1691+01 1.1875+01 1.2062+01 1.2252+01 1.2445+01 1.2641+01 1.2840+01 1.3042+01 1.3248+01 1.3456+01 1.3668+01 1.3883+01 1.4102+01 1.4324+01 1.4550+01 1.4779+01 1.5012+01 1.5248+01 1.5488+01 1.5732+01 1.5980+01 1.6231+01 1.6487+01 FQ0 E F C ********************************************** C * ENERGY AND THERMAL CARDS * C ********************************************** ERGN 0 16.5 0 C *********************************************** C * PROBLEM CUTOFF CARDS * C *********************************************** CUTN 0 4.6308-02 -10 -0.01 NPS 1000000 CTME 8 C *********************************************** C * PERIPHERAL CRADS * C *********************************************** PRDMP 100000 100000 LOST 10 10 PRINT Attachment 2 Calculational model for GRTUNCL/DOT3.5 GRTUNCL *R-Z;AIR(O)20CM+BE(5.06CM);P5S16;I04=-6;JACKAS;* 1986/3/11 * O 1$$ 0 5 2 28 7 125 4 5 129 96 0 156 156 2 1 30000 10 0 1 0 18 0 0 16 2** -1.000 0. 0. T 1** F0.0 2** 1I0.0 4I20.0 25.06 3** 0.11899E-01 0.11667E-01 0.13899E+00 0.14184E+00 0.13951E+00 0.14529E+00 0.14597E+00 0.14346E+00 0.74153E-01 0.20786E-01 0.20505E-01 0.14429E-01 0.43117E-02 0.42303E-02 0.37340E-02 0.13519E-02 0.13318E-02 0.13118E-02 0.59588E-03 0.55969E-03 0.55086E-03 0.39958E-03 0.34917E-03 0.34531E-03 0.28599E-03 0.24272E-03 0.23991E-03 0.22796E-03 0.21412E-03 0.21152E-03 0.19871E-03 0.15024E-03 0.61135E-03 0.51448E-03 0.53488E-03 0.47013E-03 0.46368E-03 0.48406E-03 0.51280E-03 0.58653E-03 0.63566E-03 0.68752E-03 0.74331E-03 0.79038E-03 0.84608E-03 0.90432E-03 0.92786E-03 0.10015E-02 0.10731E-02 0.23636E-02 0.31292E-02 0.21772E-02 0.15062E-02 0.12211E-02 0.11807E-02 0.12276E-02 0.12688E-02 0.13252E-02 0.13042E-02 0.13686E-02 0.26939E-02 0.25974E-02 0.25060E-02 0.24072E-02 0.22341E-02 0.20166E-02 0.18107E-02 0.15900E-02 0.13654E-02 0.11712E-02 0.90967E-03 0.76861E-03 0.62969E-03 0.51194E-03 0.41351E-03 0.33151E-03 0.28512E-03 0.22243E-03 0.19177E-03 0.16966E-03 0.17002E-03 0.17582E-03 F0.0 4** 27I0.0 31.4 5** F1.0 6** 1.0 7** 1.0 8$$ 56R1 F2 10$$ 4I97 102 1Q6 4I103 108 5Q6 46I109 156 11$$ 6Z 4I25 30 6Z 4I19 24 4I31 36 4I91 96 4I43 48 4I67 72 48Z 12** 6Z 6R4.9220-5 6Z 6R1.2152-1 6R4.9813-4 6R7.7109-5 6R2.9013-5 6R2.4678-5 48Z 9$$ -97 -103 13** -0.97753 -0.90676 -0.82999 -0.74536 -0.64979 -0.53748 -0.39441 -0.14907 1M8 14** F1.0 T T **RZ; AIR(20 CM)+BE(5.06 CM); DZ= 1CM; P5S16; I04=6; JACKAS 3/11/'86** O 61$$ 0 5 2 28 7 125 4 5 129 96 2Z 156 0 160 2R1 3Z 1 10 15 4 6 2 4Z 2Z 0 0 0 3Z 0 0 3 3Z 0 5Z 2 2R1 5Z 18 8 0 62$$ 2 3 4 14 15 9 10 11 12 13 8 60000 0 0 63** 0.0 1.0-2 9Z 0.0 0.0 0.0 F0.0 T 7** -0.21082 -0.14907 1M1 -0.42164 -0.39441 -0.14907 1M2 -0.55777 -0.53748 -0.39441 -0.14907 1M3 -0.66667 -0.64979 -0.53748 -0.39441 -0.14907 1M4 -0.76012 -0.74536 -0.64978 -0.53748 -0.39441 -0.14907 1M5 -0.84327 -0.82999 -0.74536 -0.64979 -0.53748 -0.39441 -0.14907 1M6 -0.91894 -0.90676 -0.82999 -0.74536 -0.64979 -0.53748 -0.39441 -0.14907 1M7 -0.98883 -0.97753 -0.90676 -0.82999 -0.74536 -0.64979 -0.53748 -0.39441 -0.14907 1M8 1Q80 3R-0.97753 5R-0.90676 7R-0.82999 9R-0.74536 11R-0.64979 13R-0.53748 15R-0.39441 17R-0.14907 3R0.97753 5R0.90676 7R0.82999 9R0.74536 11R0.64979 13R0.53748 15R0.39441 17R0.14907 T 6** 0.0 0.13586-1 1N2 4R0.97681-2 0.0 0.64738-2 0.50390-2 0.64738-2 1N4 0.64634-2 0.71124-2 1N2 1N5 0.64634-2 0.14381-2 0.36342-2 0.14381-2 0.64634-2 1N6 0.64738-2 0.71124-2 0.36342-2 1N3 1N7 0.97681-2 0.50390-2 0.71124-2 0.14381-2 0.71124-2 0.50390-2 0.97681-2 1N8 0.13586-1 0.97681-2 0.64738-2 0.64634-2 1N4 1N8 1Q80 T 3** F0.0 T 1** F0.0 2** 1I0.0 4I20.0 25.06 4** 27I0.0 31.4 5** F1.0 8$$ 56R1 F2 10$$ 4I97 102 1Q6 4I103 108 5Q6 46I109 156 11$$ 6Z 4I25 30 6Z 4I19 24 4I31 36 4I91 96 4I43 48 4I67 72 48Z 12** 6Z 6R4.9220-5 6Z 6R1.2152-1 6R4.9813-4 6R7.7109-5 6R2.9013-5 6R2.4678-5 48Z 9$$ -97 -103 T T