Subcriticality Measurement by Neutron Source Multiplication Method ...

Subcriticality Measurement by Neutron SourceMultiplication Method with Detected-NeutronMultiplication FactorNagoya UniversityKyoto UniversityTomohiro Endo,Akio YamamotoCheol Ho Pyeon,Takahiro Yagi2012 ANS Winter Meeting, DATA ANALYSIS IN NUCLEAR CRITICALITY SAFETY—II, Nov. 15, 2012 1

Contents• Neutron source multiplication method(NSM)• Detected-neutron multiplication factork det• NSM expression using k det• NSM experiment at Kyoto UniversityCritical Assembly (KUCA)• Numerical result of k det =k eff map• Experimental result of NSM2012 ANS Winter Meeting, DATA ANALYSIS IN NUCLEAR CRITICALITY SAFETY—II, Nov. 15, 2012 2

Neutron source multiplication method(NSM)• Subcriticality measurement technique based onCRSSkSk2 S1kCR :count rate, k : neutron multiplication factorS :neutron source strength, :detector efficiency• Features• Simple technique by neutron source and detector• Reactivity difference Dr can be measured from thereference state where k eff is known beforehand2012 ANS Winter Meeting, DATA ANALYSIS IN NUCLEAR CRITICALITY SAFETY—II, Nov. 15, 2012 3

Modified NSM [1]• Neutron count ratecalculated neutron fluxat target subcritical stateCRCR k Seff 1 kk1eff Sd calcSf †1 F k†calccalceffCorrection to extract fundamental modecomponent of l-eigenvalue equationcalcfundamentaladjoint eigenfunction[1] Mizoo, N., 1977. JAERI-M 7135, (JAERI).2012 ANS Winter Meeting, DATA ANALYSIS IN NUCLEAR CRITICALITY SAFETY—II, Nov. 15, 2012 4

Purpose of this study• Issues of Modified NSM• Numerical results has uncertainties• size, nuclide compositions, cross-sections• analytical models• Estimated correction factors have also uncertainties• Purpose• To clarify appropriate detector positions to reducethe impact of correction factors in NSM experiment• Ideally, correction factors nearly equal to unity• Reconsideration of definition of measured“neutron multiplication factor”2012 ANS Winter Meeting, DATA ANALYSIS IN NUCLEAR CRITICALITY SAFETY—II, Nov. 15, 2012 5

Decomposition of neutron fluxsource-flux term fission-flux term ( r,E,)(r,E,) ( r,E,)s fdd s d fNeutron detectordetection of primaryneutron due to sourcedetection of fissionneutron2012 ANS Winter Meeting, DATA ANALYSIS IN NUCLEAR CRITICALITY SAFETY—II, Nov. 15, 2012 6

Detected-neutron multiplication factor [2]kdetddfII††A• Ratio of “detected fission-neutron” to “detectedall neutron”• Similar to the definition of “Subcritical mulitiplicationfactor: k sub[3]”s• Note: reaction rate of neutron detection is usedin the difinition of k det[2] T. Endo, et al., Ann. Nucl. Energy, 38, pp.2417-2427 (2011).[3] K. Kobayashi and K. Nishihara, Nucl. Sci. Eng., 136[2], pp.272-281 (2000).F2012 ANS Winter Meeting, DATA ANALYSIS IN NUCLEAR CRITICALITY SAFETY—II, Nov. 15, 2012 7sA annihilation operatorF production operator†I detector importance

Relationship betweenneutron count rate and k det k kk2 ds1d dd det dddfs s1kdet• Detected total neutron count rate canrigorously expressed by summation ofInfinite geometric series• 1 st term:detected primary neutron due toemission of external source• Common ratio: k detd det d fssdet2012 ANS Winter Meeting, DATA ANALYSIS IN NUCLEAR CRITICALITY SAFETY—II, Nov. 15, 2012 8

NSM expression using k detkTarget state• Correction factor for source-fluxfs1d s,targeteff, targetdtarget 1 fs1fc,target1kdet,targetds,targetReference statefdc,refdks,refrefeff, refd1kdds,refdet,refreftarget• Conversion factor from k det to k efff kcdetkeff• Note: f s & f c can be evaluated by only forwardcalculations, without adjoint ones2012 ANS Winter Meeting, DATA ANALYSIS IN NUCLEAR CRITICALITY SAFETY—II, Nov. 15, 2012 9

Appropriate detector position inNSM experimentk1k 11ffkkf keff, eff, target s11eff, targets1fc,targeteff,refc,refk d d ref ref deff, refddtargetdreftarget• Detector position where k det =k eff• Conversion factor f c is equal to unity• This search can be achieved by only forwardcalculations at reference state• Detector position where f s =1 is better• Note: need for forward calculations for target state2012 ANS Winter Meeting, DATA ANALYSIS IN NUCLEAR CRITICALITY SAFETY—II, Nov. 15, 2012 10

How to numerically solve k detsource0.1.01001001001001-07-08-09-10-11-12fuel0.00010.000010.000001- 1E-071E-081E-091E-101E-111E-12-30 -10 10 30source0.10.1 0.01 0.01 fuel0.001s 0.001f0.00010.000010.000001= 1E-071E-081E-091E-101E-111E-12-30 -10 10 301. Forward external source problem withfission2. Forward external source problem withoutfisison (n f =0 or n=0)3. f is evaluated by s4. k det =< d f >/< d >-30 -10 10 302012 ANS Winter Meeting, DATA ANALYSIS IN NUCLEAR CRITICALITY SAFETY—II, Nov. 15, 2012 11

CfNSM experiment at Kyoto UniversityCritical Assembly(KUCA)FC#1FC#2UIC#5FC#2UIC#5UIC#6FC#2UIC#5UIC#6FC#3FC#3C3UIC#6S4C2C3 F F F F F FF F Cf F F F FF F F Cf F F C1 FS4 F F F F F FC2FC#3C3S4C2F F F F FF F F F FF F F F FF F Cf F FUIC#4F F F F F C1UIC#4F F F F FS5F F F F S6 FS5C1S6S5S6UIC#4NFC#1NFC#1Nreference targetstateFCfCSNFCUICFuelFCfFuelFuel+Cf NFuel+CfPolyethylene Tritium targetPolyethyleneDeuteron beam lineControl rodCSNControl rodSafety rod FCAm-BeSafety rodAm-BeTritium targetHe-3 detectorTritium targetDeuteron beam lineFCUICCSUICDeuteron beam lineFission chamberFission chamberUIC detectorUIC detectorHe-3 detectorFuel+CfHe-3 detectorPolyethyleneControl rodSafety rodAm-BeFission chamberUIC detectorUnit cell(6.34 mm)1/16” EU×2(3.17 mm)Polyethylene (PE)(481.92 mm)…Polyethylene (PE)(482.11 mm)1/8”PE1” Al plate 1/8”PE+1/2”PE×4(3.17 mm)1/8”PE+1/2”PE×5Reflector 548.59 mm(Upper)Fuel 375.66 mm(Unit cell 60 times)Reflector 561.49 mm(Lower)2012 ANS Winter Meeting, DATA ANALYSIS IN NUCLEAR CRITICALITY SAFETY—II, Nov. 15, 2012 12

#2k det =k eff map for Am-Be sourceby SRAC/DANTSYS,16-group Sn transport calc.#1◎FC#3Am-BeHe-3 detectorfission chamberAm-BeHe-3 detectorfission chamber#3#3#4○He#3#2#1◎FC#3○He#3#3#3#3#4#2#3#4#2#1#2#1#2#2#1×FC#1#1×FC#1only C3 rod inreference stateAll rods in2012 ANS Winter Meeting, DATA ANALYSIS IN NUCLEAR CRITICALITY SAFETY—II, Nov. 15, 2012 13

(-ρ ) by NSM [Δk /k ](-ρ) by NSM [Δk/k](-ρ ) by NSM [Δk/k]Result of NSM for Am-Be sourcecontrol 1% rod 3%rth [Δk/k]6%5%4%3%2%1%0%He#1He#2He#3He#4FC#1FC#2FC#36%5%4%3%2%1%0%0% 1% 2% 3%(-ρ ) by control rod worth [Δk /k ]without corerction-1% 1% 3%(-ρ) by control rodworth [Δk/k]2012 ANS Winter Meeting, DATA ANALYSIS IN NUCLEAR CRITICALITY SAFETY—II, Nov. 15, 2012 146%5%4%3%2%1%0%r by NSM can beimproved with f s & f cHe#1He#2He#3He#4FC#1FC#2FC#3failed0% 1% 2% 3%(-ρ ) by control rod worth [Δk /k ]with f s & f c correction

#2k det =k eff map for Cf-souceby SRAC/DANTSYS,16-group Sn transport calc.Cf#1#1He-3 detectorfission chamberCfHe-3 detectorfission chamberAlmost same f c =k det /k eff value for all detectors#3#3#4#2#3#3#3#4#2#3#4#2#1#2#1#2#2#1#1only C3 rod inreference stateAll rods in2012 ANS Winter Meeting, DATA ANALYSIS IN NUCLEAR CRITICALITY SAFETY—II, Nov. 15, 2012 15

(-ρ ) by NSM [Δk /k ](-ρ ) by NSM [Δk /k ]Result of NSM for Cf-source4%He#14%r by NSM can beimproved with f s & f c3%He#2He#33%He#42%FC#1FC#22%FC#3control 1% rod 3%rth [Δk/k]1%1%0%0%0% 1% 2% 3% 0% 1% 2% 3%(-ρ ) by control rod worth [Δk /k ](-ρ ) by control rod worth [Δk /k ]without corerctionwith f s & f c correction2012 ANS Winter Meeting, DATA ANALYSIS IN NUCLEAR CRITICALITY SAFETY—II, Nov. 15, 2012 16

Conclusion• NSM based on k det• Good results without corrections at detector positionwhere k det =k eff• position can be searched by calculation for reference state• Correction factors can be evaluated by only forwardcalculations without adjoint ones• Future works• Evaluation of k det and correction factors usingcontinuous energy Monte Carlo code• Uncertainty Analysis for k det and correction factors2012 ANS Winter Meeting, DATA ANALYSIS IN NUCLEAR CRITICALITY SAFETY—II, Nov. 15, 2012 17

Acknowledgement• This work has been carried out in partunder the Visiting Researcher’s Programof the Research Reactor Institute, KyotoUniversity, FY2011.2012 ANS Winter Meeting, DATA ANALYSIS IN NUCLEAR CRITICALITY SAFETY—II, Nov. 15, 2012 18