The different analytical solutions without space-time separation foreseen for the analysis of ADS experiments are described. The SC3A experiment in the YALINA-Booster facility is described and investigated. For this investigation the very special configuration of YALINA-Booster is analyzed based on HELIOS calculations. The results for the time dependent diffusion and the time dependent equation are compared with the experimental results for the SC3A configuration. A comparison is given for the deviation between the analytical solution and the experimental results versus the different transport approximations. To improve the representation to the special configuration of YALINA- Booster, a new analytical solution for two energy groups with two sources (central external and boundary source) has been developed starting form the Green's function solution. Very good agreement has been found for these improved analytical solutions. 1. Introduction Different current and planned experiments (MUSE [1], YALINA [2], GUINEVERE [3]) are designed to study the zero power neutron physical behavior of accelerator-driven systems (ADSs). The detailed analysis of the kinetic space-time behavior of the neutron flux is important for the evaluation of these ADS experiments. Current analysis for all these experiments is based on the standard methods [4]—Sj？strand method [5] and Slope method [6]—both are based on the point kinetics equations [7]. The point kinetics equations are developed from different approximations to the transport equation. Nevertheless, all these partial differential equations of the transport equation are solved by the separation of space and time to derive the point kinetics equations. The separation of space and time does not provide useful results for cases with strongly space-time dependent external source [8]. In recent years, two big projects have been launched to solve the problem of subcriticality determination in ADS experiments and during ADS operation for the future. In the 6th European Framework program in the integrated project EUROTRANS, the domain 2, ECATS [9] has been dedicated to ADS experiments and the analysis methods for the experiments. In the same time frame, the IAEA has launched the coordinated research project “Analytical and Experimental Benchmark Analyses of Accelerator Driven Systems (ADS)” [10]. Different correction methods based on Monte Carlo Results for the YALINA-Booster system have been derived for the Sj？strand method as well as for the Slope method in EUROTRANS/ECATS [11, 12]. Good results have been achieved with this
References
[1]
R. Soule, W. Assal, P. Chaussonnet et al., “Neutronic studies in support of accelerator-driven systems: the MUSE experiments in the MASURCA facility,” Nuclear Science and Engineering, vol. 148, no. 1, pp. 124–152, 2004.
[2]
A. I. Kievitskaia, et al., “Experimental and theoretical research on transmutation of long-lived fission products and minor actinides in a subcritical assembly driven by a neutron generator,” in Proceedings of the 3rd International Conference on ADTTA, Praha, Czech Republic, 1999.
[3]
H. A？t Abderrahim and P. Baeten, “The GUINEVERE-project at VENUS, project status,” in ECATS Meeting, Cadarache, France, Januray 2008.
[4]
C. M. Persson, P. Seltborg, A. ？hlander et al., “Analysis of reactivity determination methods in the subcritical experiment Yalina,” Nuclear Instruments and Methods in Physics Research, Section A, vol. 554, no. 1–3, pp. 374–383, 2005.
[5]
N. G. Sj？strand, “Measurements on a subcritical reactor using a pulsed neutron source,” Arkiv f？r Fysik, vol. 11, p. 13, 1956.
[6]
B. E. Simmons and J. S. King, “A pulsed neutron technique for reactivity determination,” Nuclear Science and Engineering, vol. 3, p. 595, 1958.
[7]
K. Ott and R. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, La Grange Park, Ill, USA, 1985.
[8]
B. Merk and F. P. Wei？, “A three-scale expansion solution for a time-dependent P1 neutron transport problem with external source,” Nuclear Science and Engineering, vol. 163, no. 2, pp. 152–174, 2009.
[9]
G. Granget, et al., “EUROTRANS/ECATS or neutronic experiments for the validation of XT-ADS and EFIT monitoring: status, progress and first assessments,” in OECD Nuclear Energy Agency International Workshop on Technology and Components of Accelerator Driven Systems, Karlsruhe, Germany, March 2010.
[10]
Analytical and Experimental Benchmark Analyses of Accelerator Driven Systems (ADS), http://www.iaea.org/inisnkm/nkm/aws/fnss/crp/crp7.html.
[11]
P. Gajda, “Pulsed neutron source measurement in YALINA-subcritical facility,” in Proceedings of the 3rd Environmental Compatible Air Transport System Progress Meeting (ECATS' 10), Mol, Belgium, March 2010.
[12]
V. Bécares, “Analysis of pulsed neutron source experiments,” in Proceedings of the 3rd Environmental Compatible Air Transport System Progress Meeting (ECATS' 10), Mol, Belgium, March 2010.
[13]
V. Bécares, D. Villamarín, M. Fernández-Ordó？ez, E. M. González-Romero, and Y. Fokov, “Correction methods for reactivity monitoring techniques in Pulsed Neutron Source (PNS) measurements,” in Proceedings of the International Conference on the Physics of Reactors (PHYSOR '10), pp. 914–928, Pittsburgh, Pa, USA, May 2010.
[14]
Y. Gohar, et al., “‘Argonne analyses of YALINA-booster’, YALINA-thermal, and LEU YALINA-booster,” in IAEA Meeting, Mumbai, India, February 2010.
[15]
Summary of the Technical Meeting on, “‘Use of Low Enriched Uranium (LEU Fuel in Accelerator Driven Sub-Critical Assembly (ADS Systems’, and 3rd RCM of the CRP on ‘Analytical and Experimental Benchmark Analyses of Accelerator Driven Systems’,” Mumbai, India, February 2010.
[16]
A. M. Weinberg and E. P. Wigner, The Physical Theory of Neutron Chain Reactors, University of Chicago Press, Chicago, Ill, USA, 1958.
[17]
D. G. Duffy, Green’s Functions with Application, Chapman & Hall/CRC, 2001.
[18]
M. N. ？zi？ik and B. Vick, “Propagation and reflection of thermal waves in a finite medium,” International Journal of Heat and Mass Transfer, vol. 27, no. 10, pp. 1845–1854, 1984.
[19]
B. Merk, “Time dependent analytical approximation solutions for a pulsed source problem: P1 transport versus diffusion,” in IEEE Nuclear Science Symposium, Dresden, Germany, 2008.
[20]
B. Merk, “An analytical solution for a one dimensional time-dependent neutron transport problem with external source,” Transport Theory and Statistical Physics, vol. 37, no. 5–7, pp. 535–549, 2008.
[21]
B. Merk, “An analytical approximation solution for a time-dependent neutron transport problem with external source and delayed neutron production,” Nuclear Science and Engineering, vol. 161, no. 1, pp. 49–67, 2009.
[22]
B. Merk, V. Glivici-Cotru？ǎ, and F. P. Wei？, “A solution for the telegrapher's equation with external source: application to Yalina—SC3A and SC3B,” in International Conference on the Physics of Reactors (PHYSOR '10), pp. 3053–3065, Pittsburgh, Pa, USA, May 2010.
[23]
B. Merk, V. Glivici-Cotruta, and F. P. Wei？, “A solution for Telegrapher's equation with external source: development and first application,” Nuovo Cimento della Societa Italiana di Fisica B, vol. 125, no. 12, pp. 1547–1559, 2010.
[24]
B. Merk, V. Glivici-Cotru？？, and F.-P. Wei？, “Application of a two energy group analytical solutions to the YALINA experiment SC3A,” in Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (MC '11), Rio de Janeiro, Brazil, 2011.
[25]
B. Merk, V. Glivici-Cotru？？, and F.-P. Wei？, “A three scale expansion solution for the Telegrapher’s equation with external source: development and first application,” in Proceedings of the 21st International Conference on Transport Theory, Torino, Italy, 2009.
[26]
HELIOS Methods, Studsvik Scandpower, 2003.
[27]
V. Bécares Palacios, et al., “Analysis of PNS measurements at the YALINA-Booster subcritical facility,” in Proceedings of the 2nd EUROTRANS ECATS Progress Meeting, Aix-en-Provence, France, January 2009.
[28]
B. Merk and F. P. Wei？, “A two group analytical approximation solution for an external source problem without separation of space and time,” Annals of Nuclear Energy, vol. 37, no. 7, pp. 942–952, 2010.
[29]
FREYA: Fast Reactor Experiments for hYbrid Applications, http://freya.sckcen.be/en.
[30]
V. Glivici-Cotruta and B. Merk, “An analytical solution of the time dependent diffusion equation in a composite slab,” submitted to: Transport Theory and Statistical Physics.
[31]
C. Bergl？f, “YALINA-booster: pulsed neutron source characterization,” in Proceedings of the 2nd EUROTRANS ECATS Progress Meeting, Aix-en-Provence, France, 2009.
