JAEA-Conf 2011-002 - 日本原子力研究開発機構

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2. Foundation of sensitivity analyses In the present study, only criticality k is treated as an integral parameter. Sensitivity coefficients of k to the nuclear data , k S , can be easily calculated by the first order perturbation theory with forward and adjoint neutron fluxes. Usually k S is interpreted as a relative change in k due to a relative change in , and is defined as dk k d S k . This definition is however inappropriate to describe sensitivities to higher order Legendre coefficients of scattering matrices l a since a l can take both positive and negative values, and a value close to zero. Thus the definition of sensitivity coefficients is modified as dk k d S k in the present study. The so-called library effect is calculated as follows. Let us consider two multi-group libraries, LIB1 and LIB2. Here criticalities calculated with these two libraries are written as LIB2 k . A difference in these criticalities coefficients of elastic scattering matrices are calculated as k, LIB1 k S l , g g ' n l1 g g' LIB1 k and LIB 2 LIB1 k k k due to differences in Legendre LIB2 LIB1 a a l, gg ' l, gg ' LIB1 0, gg ' , (1) where n denotes nuclides, l denotes the Legendre order, g and g ' denote energy groups, respectively. This k corresponds to the library effect of higher order Legendre coefficients. Usually, higher order Legendre components of scattering matrices l, g g ' are stored in multi-group cross section libraries. Thus Legendre coefficients of scattering matrices a ' l, g g are derived from scattering matrices stored in multi-group libraries as al , g g ' l, g g ' 0, g g ' . Note that infinite dilution cross sections are used for the present library effect calculations as usual. If we focus on a difference in Legendre components (cross sections), not in Legendre coefficients, of scattering matrices, a library effect is calculated with the following equation: k , LIB1 k S l , g g ' n l1 g g' JAEA-Conf 2011-002 LIB2 LIB2 LIB1 LIB1 a a l, g g ' 0, g g ' l, g g ' 0, g g ' 3. Numerical procedure The following are fast neutron systems for which sensitivity analyses are carried out in the present study. The specifications of these systems are derived from the ICSBEP handbook [1]: - HEU-MET-FAST-001 (Godiva): a bare sphere of highly enriched uranium. .
- PU-MET-FAST-001 (Jezebel): a bare sphere of plutonium-239 metal. - U233-MET-FAST-001 (Jezebel-233): a bare sphere of uranium-233 metal. - HEU-MET-FAST-028 (Flattop-U): a highly enriched uranium sphere reflected by normal uranium. - PU-MET-FAST-006 (Flattop-Pu): a plutonium sphere reflected by normal uranium. - U233-MET-FAST-006 (Flattop-233): a uranium-233 sphere reflected by normal uranium. - HEU-MET-FAST-003-011: a highly enriched uranium sphere reflected by tungsten-carbide. - HEU-MET-FAST-021: a highly enriched uranium sphere reflected by iron. - PU-MET-FAST-040: a plutonium sphere reflected by copper. - HEU-MET-FAST-027: a highly enriched uranium sphere reflected by lead. 70-group sensitivity coefficients are derived with forward and adjoint neutron fluxes calculated by using an in-house discrete ordinates neutron transport code. In the discrete ordinates neutron transport calculations, Legendre coefficients of scattering matrices are accounted for up to the fifth order, and the 32-point double Gaussian angular quadrature set is used. Effective cross sections used for the neutron transport calculations are obtained by using the SLAROM-UF code [2] and UFLIB-J4.0 based on JENDL-4.0. Figure 1 shows a sensitivity of the HEU-MET-FAST-028 criticality to Legendre coefficients of elastic scattering cross sections of uranium-238. Library effects are calculated according to Eq.(1) with the sensitivity coefficients and the infinite dilution cross sections stored in UFLIB. JENDL-4.0 is treated as a base library, and differences of the other libraries to JENDL-4.0 are evaluated. 4. Result of sensitivity analysis Table 1 shows differences in criticalities due to differences in each order of Legendre coefficient of elastic scattering matrices. Large effects over 0.001 are written in a bold style. While library effects due to differences in higher order Legendre coefficients are generally small, non-negligible effects are observed in PU-MET-FAST-006 with JENDL-3.3 and ENDF/B-VII.0, and HEU-MET-FAST-021 with all the libraries. The former is due to the difference in the uranium-238 data and the latter is due to the difference in the iron-56 data. Please remember that the above library effect calculations are carried out by using infinite dilution cross sections. Since medium-heavy nuclides such as iron-56 have resonance cross sections in the energy range above 0.1MeV, which is a dominant range in the present benchmark systems, the resonance self-shielding effect should be considered for accurate evaluation of library effects. Thus, a library effect calculation is again carried out for HEU-MET-FAST-021 with shielded cross sections. In the resonance self-shielding factor calculation, background cross sections for iron isotopes are set at 50, 0.5, 150 and 1,000 barns for iron-54, -56, -57 and -58, respectively. These values are evaluated for the reflector medium of HEU-MET-FAST-021. In this case, a library effect is calculated with the following equation: k , LIB1 k S l , g g ' n l 1 g g' k , LIB1 S l , g g ' n l1 g g' LIB 2 LIB1 a a f l, g g ' LIB2 t1, g LIB 2 l, g g ' l, g g ' f LIB 2 g JAEA-Conf 2011-002 f LIB1 g LIB 2 0, g g ' LIB1 0, g g ' f LIB1 t1, g LIB1 l, g g ' f LIB1 g LIB1 0, g g ' f LIB1 g LIB1 0, g g ' ,
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JAEA-Conf 2011-002 Proceedings of t
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JAEA-Conf 2011-002 31. Preliminary
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6.2 Measurement of neutron-induced
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JAEA-Conf 2011-002 Table 1 Comparis
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JAEA-Conf 2011-002 (T1/2=8,900,000
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JAEA-Conf 2011-002 Though words too
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JENDL-3.3 showed better applicabili
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ENDF. Thus this cross section store
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Acknowledgement JAEA-Conf 2011-002
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In the MALIBU program, isotope conc
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some minor actinides. For major act
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JAEA-Conf 2011-002 code MVP-BURN an
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JAEA-Conf 2011-002 [3] Measurements
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3.1 Experimental Set up JAEA-Conf 2
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References JAEA-Conf 2011-002 [1] N
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JAEA-Conf 2011-002 was large. The a
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JAEA-Conf 2011-002 4. Results and D
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Acknowledgments Present study inclu
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Fig. 1 A conceptural picture of the
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4. Theoretical studies Theoretical
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JAEA-Conf 2011-002 Fig.9 Comparison
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Ion source JAEA-Conf 2011-002 LE
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JAEA-Conf 2011-002 3. Readiness
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JAEA-Conf 2011-002
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JAEA-Conf 2011-002 Figure 1. An exa
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JAEA-Conf 2011-002 Figure 6. Compar
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JAEA-Conf 2011-002 calculation of d
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JAEA-Conf 2011-002 equilibrium emis
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JAEA-Conf 2011-002 Cowley et al. [1
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4. Conclusions We have compared nuc
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of MeV region with highest cosmic-r
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JAEA-Conf 2011-002 events can be id
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JAEA-Conf 2011-002 models and its p
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JAEA-Conf 2011-002
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JAEA-Conf 2011-002 xx
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JAEA-Conf 2011-002 1. The recent ac
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JAEA-Conf 2011-002 4. Conceptual de
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The Institute's staff of about 280
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3. Nuclear Theory Laboratory JAEA-C
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JAEA-Conf 2011-002 References [1] P
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JAEA-Conf 2011-002 reaction 6 Li +
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Using the approximated distribution
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momentum of the constituents of P.
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dσ/dΩ (mb/sr) c.m. scattering ang
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JAEA-Conf 2011-002 [2] N. Austern,
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moderating fast neutrons emitted fr
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JAEA-Conf 2011-002 3. Results and d
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JAEA-Conf 2011-002 the detection de
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Fig.1. Experimental arrangement for
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in this work was confirmed. (2) 153
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Neutron Capture Cross Section of 15
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ENDF resonance parameters are based
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sample changer. The measured flux s
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REFERENCES JAEA-Conf 2011-002 [1] W
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JAEA-Conf 2011-002 Fig. 4: The rela
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Fig. 10: The PHITS2 calculation geo
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for such a low energy region should
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MCNPX calculation was performed bas
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JAEA-Conf 2011-002 We measured dou
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1mm-thick carbon target 22mm in dia
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JAEA-Conf 2011-002 Figure 2 shows e
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The double-differential (n,xp) and
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JAEA-Conf 2011-002 forward angles.
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Fig.3. Two-dimensional plot of PI v
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JAEA-Conf 2011-002 Fig. 7. Deuteron
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JAEA-Conf 2011-002 The new detector
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4. Off line data analysis Double di
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eports of data of carbon-ion incide
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Count [-] 4 10 3 10 2 10 10 1 Charg
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Acknowledgement We are grateful to
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Beam Line BM1 Copper Target BM2 5×
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φ = φbm · ρtof · ρmulti (2) E
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References [1] K. Ishibashi, H. Tak
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JAEA-Conf 2011-002 hint at the orig
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Neutron Dose Rate [Sv/hr/src neutro
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JAEA-Conf 2011-002 radiation protec
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Ztarget, Atarget are the numbers fo
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We described our formalism for calc
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2. Model
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JAEA-Conf 2011-002
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Page 192 and 193: analysis of integral experiments [6
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JAEA-Conf 2011-002 - 日本原子力研究開発機構

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