Authors & Affiliations
Elshin A.V., Tenischeva N.V.
The Institute of Nuclear Power Engineering, “St. Petersburg Polytechnic University named after Peter the Great”, Sosnoby Bor, Russia
In the papers dedicated to the use of surface harmonic method, the so-called reciprocity relations are applied to get finite-difference equations that describe neutron distribution and importance in the heterogeneous reactor. These relations state that matrices consisting of average neutron group «levels” at the boundary of the cells calculated for the testing functions that are used in the method, are equal to the transpose of similar levels of neutron importance. The proof of these relations is based on the property of neutron transport operator conjugacy. In order to demonstrate the conjugacy, special boundary conditions are usually used, namely: the importance of neutrons released from the reactor is equal to zero. In testing functions these boundary conditions are not used, so it does not seem obvious that the reciprocity relations are met. In this paper the attempt is demonstrated with simple examples (special cases) to check meeting the above-mentioned reciprocity relations.
Surface harmonic method, neutron distribution, heterogeneous reactor, reciprocity relations, neutron transfer operator, neutron importance
1. Elshin A. The Evolution of the Surface Harmonic Method to Derive Equations for a Distribution of Neutrons and their Importance in a Heterogeneous Reactor. Proceeding of International Topical Meeting on Mathematics and Computations, Supercomputing, Reactor Physics and Nuclear and Biological Applications, Avignon, France, 2005.
2. El'shin A.V. Poluchenie konechno-raznostnykh uravnenij geterogennogo reaktora s prostranstvennoj kinetikoj [Finite-Difference Equations of a Heterogeneous Reactor with Spatial Kinetics]. Atomnaya energiya - Atomic Energy. 2007, Vol. 103, no. 4, pp. 222-232.
3. Laletin N.I. Ob uravneniyakh geterogennogo reaktora [On the Heterogeneous Reactor Equations]. Voprosy atomnoy nauki i tekhniki. Ser. Fizika yadernykh reaktorov - Problems of atomic science and technology. Series: Physics of Nuclear Reactors. 1981, Vol. 5, no. 18, pp. 31-46.
4. El'shin A.V., Abdullaev A.M. O sootnosheniyakh vzaimnosti i vysokikh priblizheniyakh metoda poverhnostnykh garmonik [On Reciprocity Relations and High Approximations of the Surface Harmonic Method]. Trudy konf. «Nejtronika-2012. Nejtronno-fizicheskie problemy atomnoj energetiki» [Proc. conf. “Neutronics-2012. Neutronic Problems in Nuclear Power”] Obninsk, 2012, pp. 22-23.