1. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft Subcriticality level inferring in the ADS systems: spatial corrective factors for Area Method F. Gabrielli Forschungszentrum Karlsruhe, Germany Institut für Kern- und Energietechnik (FZK/IKET) Second IP-EUROTRANS Internal Training Course June 7 – 10, 2006 Santiago de Compostela, Spain 1

2. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft Layout of the presentation Principle of Reactivity Measurements MUSE-4 Experiment PNS Area Method: a static approach  Analysis of the Experimental results: Area method analysis PNS α-fitting method:  and  p evaluation  Analysis of the Experimental results: Slope analysis by α-fitting method Conclusions 2

3. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft Principle of Reactivity Measurements If point kinetics assumptions fail, correction factors are needed. MUSE-4 experiment supplied a lot of information about this subject  Reactivity does not depend on the detector position, detector type, …  Some quantities, i.e. the mean neutron generation time Λ which is used in the slope method, do not depend on the subcritical level. Several static/kinetics methods are available to infer the reactivity level of a subcritical system. All these methods are based on the point kinetics assumption, then assuming that: 3

4. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft In this case, corrective spatial factors, evaluated by means of calculations, should be applied to the experimental results analyzed by means of one of the point kinetics based methods, in order to infer the actual subcriticality level of the system. Depending on the used method, corrective factors may have a different amplitude. Thus, from a theoretical point of view, the reliability of a method for inferring the reactivity will be given by the magnitude of the corrective factors to be associated. Depending on the subcriticality level and on the presence of spatial effects, the subcriticality level of the system may not be inferred by the detectors responses in different positions on the basis of a pure point kinetics approach. Principle of Reactivity Measurements 4

5. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft MUSE-4 experiment: layout MUSE (MUltiplication avec Source Externe) program was a series of zero-power experiments carried out at the Cadarache MASURCA facility since 1995 to study the neutronics of ADS. The main goal was investigating several subcritical configurations (k eff is included in the interval 0.95-1) driven by an external source at the reactor center by (d,d) and (d,t) reactions, the incident deuterons being provided by the GENEPI deuteron pulsed accelerator. 5

6. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft MUSE-4 experiment: layout and objectives In particular, the MUSE-4 experimental phase aimed to analyze the system response to neutron pulses provided by GENEPI accelerator (with frequencies from 50 Hz to 4.5 kHz, and less than 1 μs wide), in order to investigate by means of several techniques the possibility to infer the subcritical level of a source driven system, in view of the extrapolation of these methods to an European Transmutation Demonstrator (ETD). 6

7. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft α-fitting method Area method Experimental techniques analyzed 7

8. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft is based on the following relationship relative to the areas subtended by the system responses to a neutron pulse: PNS Area Method Concerning the method (which does not invoke the estimate of Λ ), it is not possible "a priori" to evaluate the order of magnitude of correction factors even if the system response appears to be different from a point kinetics behaviour. This aspect is strictly connected with the integral nature of the PNS area methods Because of spatial effects, reactivity is function of detector position. These spatial effects can be taken into account by solving inhomogeneous transport time- independent problems. 8

9. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft PNS Area Method: a static approach * [*][*] S. Glasstone, G. I. Bell, ‘Nuclear Reactor Theory’, Van Nostrand Reinhold Company, 1970 Neutron source is represented by Q(r, ,E,t)=Q(r, ,E) δ + (t) and a signal due to prompt neutrons alone is considered The prompt flux  p (r, ,E,t) satisfies the transport equation With the usual free-surface boundary conditions and the initial condition  p (r, ,E,t)=0 Defining the prompt neutron flux Φ p (r,Ω,E)= ∫ Φ p (r,Ω,E,t)dt and after integrating over the time… Where the initial condition was used and the fact that lim (t  ) Φ p =0 because the reactor is subcritical Therefore, the time integrated prompt-neutron flux satisfies the ordinary time- indipendent transport equation Hence, it can be determined by any of standard multigroup methods ~ 0 ∞ 9

10. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft Prompt Neutron Area = ∫ D(r,t)dt= ∫∫∫ σ d (r,E)Φ p dVdΩdE ∞ ~ 0 PNS Area Method: a static approach * The time integrated prompt-neutron flux satisfies the ordinary time-independent transport equation The total time-integrated flux Φ(r,Ω,E) satisfies the same equation with χ p (1-β) replaced by χ Delayed Neutron Area = - ρ ($)= Prompt Neutron Area Delayed Neutron Area ~ ∫∫∫ σ d (Φ - Φ p )dVdΩdE ~ ~ [*][*] S. Glasstone, G. I. Bell, ‘Nuclear Reactor Theory’, Van Nostrand Reinhold Company, 1970 10

11. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft ERANOS (European Reactor ANalysis Optimized System) calculation description A XY model of the configurations was assessed The reference reactivity level was tuned via buckling JEF2.2 neutron data library was used in ECCO (European Cell Code) cell code 33 energy groups transport calculations were performed by means of BISTRO core calculation module 11

12. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft MUSE-4 SC0 1108 Fuel Cells Configuration – DT Source The configuration with 3 SR up, SR 1 down and PR down was analyzed Reference Reactivity: -12.53 $ (Evaluations based on MSA * /MSM + measurements in a previous configuration) Experimental data from E. González-Romero et al., "Pulsed Neutron Source measurements of kinetic parameters in the source-driven fast subcritical core MASURCA", Proc. of the "International Workshop on P&T and ADS Development", SCK-CEN, Mol, Belgium, October 6-8, 2003. F. Mellier, ‘The MUSE Experiment for the subcritical neutronics validation’, 5 th European Framework Program MUSE-4 Deliverable 6, CEA, June 2005. 12 *Modified Source Approximation +Modified Source Multiplication

13. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft Sc0 results Reactivity ρ($)Dispersion DetectorExperimental [*] Calculated ExperimentalCalculated(E-C)/C (%) I-14.3-13.10.87620.9561 +7.5 L-12.9-13.00.97130.9658 -0.6 F-11.9-11.81.05291.0603 +0.7 M-12.7-12.80.98660.9783 -0.8 G-13.0-12.40.96381.0121 +5.0 N-12.1-11.81.03551.0587 +2.2 H-12.6-12.10.99441.0369 +4.3 A-12.7-12.40.98661.0140 +2.8 B-13.0-12.80.96380.9824 +1.9 MUSE-4 SC0 1108 cells configuration, D-T Source, 3 SR up SR1 down PR down Dispersion means the ratio ρ(MSM)/ ρ(AREA) exp or calc. [*] E. Gonzáles-Romero (ADOPT ’03) 13 Mean/St.Dev: -12.6 ± 0.4

14. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft MUSE-4 SC2 1106 Fuel Cells Configuration – DT Source Reference Reactivity (Rod Drop + MSM) : -8.7 ± 0.5 $ 14

15. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft SC2 results Reactivity ρ($)Dispersion DetectorExperimental [*] Calculated ExperimentalCalculated(E-C)/C (%) I-8.6 1.012 0.0 L-8.8-8.90.9890.978 1.1 F-8.9-9.00.9780.967 1.1 C-8.7-8.81.0000.989 1.1 G-9.0-8.80.9670.989 -2.2 D-8.9-8.70.9781.000 -2.2 H-8.9-8.70.9781.000 -2.2 A-8.9-8.80.9780.989 -1.1 B-9.0-8.80.9670.989 -2.2 MUSE-4 SC2 1106 cells configuration, D-T Source Dispersion means the ratio ρ(Reference)/ ρ(AREA) exp or calc. [*] E. Gonzáles-Romero, ADOPT ‘03 15 Mean/St.Dev: -8.86 ± 0.16

16. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft MUSE-4 SC3 1104 Fuel Cells Configuration – DT Source Reference Reactivity (Rod Drop + MSM) : -13.6 ± 0.8 $ 16

17. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft SC3 results MUSE-4 SC3 972 cells configuration, D-T Source Dispersion means the ratio ρ(Reference)/ ρ(AREA) exp or calc. [*] From Y. Rugama Reactivity ρ($)Dispersion DetectorExperimental [*]CalculatedExperimentalCalculated(E-C)/C (%) I-12.9-13.01.0541.046 0.8 L-14.4-13.80.9440.986 -4.2 F-14.0 0.971 0.0 C-13.7 0.993 0.0 A-13.8-13.60.9861.000 -1.4 B-13.8-13.60.9861.000 -1.4 J-12.9 1.054 0.0 K-12.9-12.81.0541.063 -0.8 17 Mean/St.Dev: -13.7 ± 0.5

18. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft Experimental results for α-fitting analysis 18

19. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft PNS α-fitting analysis in MUSE-4 Concerning the PNS α-fitting method (which invokes the evaluation of Λ), three types of possible MUSE-4 responses to a short pulse may be obtained: a)The system responses show the same 1/τ-slope in all the positions (core, reflector and shield), thus the system behaves as a point. b)The system responses show a 1/τ-slope only in some positions, but not all the slopes are equal; the system does not show an ‘integral’ point kinetics behavior and a reactivity value position-depending will be evaluated. Thus, corrective factors have to be applied in order to take into account the reactivity spatial effects. c)The system responses do not show any 1/τ-slopes; the system does not behave anywhere as a point and only experimental data fitting can try to solve the problem. As in the previous case, corrective factors have to be applied. 19

20. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft Corrective factors approach to the α-fitting analysis When PNS α-fitting method is performed, we assumed that, at least in the prompt time domain, the flux behaves like: if we are coherent with this hypothesis, we have to perform the substitution of our factorised flux into: Consequently in the prompt time domain, the (time-constant) shape of the flux obeys the eigenvalue relationship: 20

21. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft Corrective factors approach to the α-fitting analysis: flow chart Directly evaluated by the α-eigenvalue equation “Prompt version” of the inhour equation (  p >> i ) 21

22. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft Corrective factors approach to the α-fitting analysis: flow chart It is possible to follow the standard way to calculate α p starting from the k eigenvalue equation: 22

23. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft Prompt α Calculation procedure performed by means of ERANOS ERANOS core calculation transport spatial modules (BISTRO and TGV/VARIANT) solve the k eigenvalue equation: While, for our purpose, the following eigenvalue relationship has to be solved: K=1 …that means performing the following substitution if ERANOS is used 23

24. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft Prompt α Calculation procedure: MUSE-4 SC0 analysis k eff ρβ eff Λ K (ms) α p,k (s -1 ) k calculation0.95970-0.042000.003350.4683-96821 kdkd ρβ eff,d Λ d (ms) α p (s -1 ) α calculation 0.95843-0.043370.003681.0069-46730 Red data indicate eigenvalues directly evaluated by ERANOS (XY model) +47% -48% 1108 Fuel Cells Configuration (3 SR up, SR 1 down and PR down) – DT Source Reactivity values calculated by using φ K and ψ eigenfunctions are similar (compensation in the product α · Λ) 24

25. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft 25 Spectra in the shielding and in the reflector ψ eigenfunctions (α calculation) φ k eigenfunctions (k calculation) ReflectorShielding According to the theory, differences between ψ and φ k eigenfunctions energy profiles at low energies are mainly observed in the reflector and in the shielding regions: in fact, besides the different fission spectrum, the main differences will be localized in the spatial and energetic regions where α/v is equal or greater than the Σ t term. Such happens at low energies and inside, or near, reflecting regions at low absorption, where the profile of the ψ shapes functions spectra will be more marked than those of the φ k functions, because of the lower absorptions.

26. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft Comparison among the calculated results y=exp(α p t) Results seem to provide a coherent picture concerning the system location where α-fitting method (with refined Λ evaluation) could be applied, i.e. far from the source. In any case, point kinetics α p slope seems to agree with exponential 1/τ- slope only in the shield and for a short time period. 26

27. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft MCNP Vs Experimental results Reflector and shield experimental slopes show a double exponential behavior which is not reproduced by MCNP calculations; on the contrary, it looks evident a good agreement for a short time period. Experimental results show that for large subcriticalities, 1/τ-slopes are different for core, reflector and shield detectors positions. MCNP results well reproduce in the core the experimental responses. 27

28. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft Conclusions 1.For large subcriticalities, PNS area method seems to be more reliable respect to a-fitting method, for what concerns the order of magnitude of the spatial correction factors (about  5%). 2.Concerning the application to the ADS situation, because of the beam time structure required for an ADS, it does not allow an on-line subcritical level monitoring, but can be used as “calibration” technique with regards to some selected positions in the system to be analyzed by alternative methods, like Source Jerk/Prompt Jump (which can work also on-line). 3.Codes and data are able to predict the MUSE time-dependent behavior in the core region. The presence of a second exponential behavior in the reflector and shield regions is not evidenced either by the deterministic or by the MCNP simulations. 28

29. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft THANK YOU FOR YOUR KIND HOSPITALITY

30. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft Prompt α Calculation procedure: pre-analysis Reflector NA/SS MOX1 Radial Shielding Axial Shielding 169.6 159 148.4 137.8 121.9 116.6 100.7 95.4 84.8 74.2 63.6 42.4 31.8 21.2 10.6 8.28 18.5 33.1 39.7 55.9 97.03 Lead MOX3 Homogenized Beam Pipe MUSE-4 Sub-Critical ERANOS RZ model: symmetry axis around the Genepi Beam Pipe axis Z (cm) R (cm) Positions for neutron spectra analysis Core 17 cm,92.8 cm Reflector 57.5 cm, 92.8 cm Shield 66.4 cm, 129.9 cm a1

31. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft Prompt α Calculation procedure: pre analysis results Red data indicate eigenvalues directly evaluated by ERANOS (RZ model) k eff ρβ eff Λ K (ms) α p,k (s -1 ) k calculation 0.97124-0.029610.003350.51634-63834 kdkd ρβ eff,d Λ d (ms) α p (s -1 ) α calculation 0.97166-0.029160.003690.81633-40240 +37% -37% a2

32. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft α p / α p,k Ratio at Different Reactivity Levels α p / α p,k k eff Far from criticality, the deviation is mainly due to the differences between the mean neutron generation times Λ K and Λ d evaluated using respectively φ K and ψ eigenfunctions. α p /α p,k ratio deviates from the unity depending on the subriticality level a3

33. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft Spectra in the core Core ψ eigenfunctions (α calculation) φ k eigenfunctions (k calculation) a4

34. Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft Spectra in the shielding and core selected positions ψ eigenfunctions (α calculation) φ k eigenfunctions (k calculation) ReflectorShielding According to the theory, differences between ψ and φ k eigenfunctions energy profiles at low energies are mainly observed in the reflector and in the shielding regions: in fact, besides the different fission spectrum, the main differences will be localized in the spatial and energetic regions where α/v is equal or greater than the Σ t term. Such happens at low energies and inside, or near, reflecting regions at low absorption, where the profile of the ψ shapes functions spectra will be more marked than those of the φ k functions, because of the lower absorptions. a5