Investigations on the migration mode method (MMM) for reactor calculations Aldo Dall’Osso a , Augusto Gandini b, * , Rossella Rotella c a AREVA NP, Tour Areva, 92084 Paris La De ´fense Cedex, France b DINCE, University of Rome ‘‘La Sapienza”, Piazzale Aldo Moro 5, 00185 Rome, Italy c S.R.S. GROUP S.r.l., Via dei Prefetti 26, 00186 Rome, Italy Abstract Current calculation codes for reactor analysis are based on the multi-group method to evaluate energy distribution of neutron flux. Usually a two energy group diffusion equation is adopted. This choice is adequate for PWRs associated to cross sections libraries tab- ulated versus fuel exposure and other state parameters as moderator density, fuel temperature, boron concentration. An improvement of this approach is represented by the migration mode method (MMM) by which the neutron spectrum is expanded in terms of base func- tions corresponding to the different modes of migration of the neutrons in the energy dimension. For a thermal reactor, three such func- tions may be easily identified: the Maxwellian distribution of the neutrons at thermal equilibrium with the moderator, the 1/E slowing down distribution (corrected to take into account resonance absorption effects) and the fission neutron spectrum. The (space-dependent) coefficients of the expansion are calculated by solving a differential equation which results having a structure similar to the one relevant to multi-group theory. The method can therefore be easily implemented adopting existing diffusion theory codes. With the present work, some investigations on the MMM are described relevant to UO 2 fuelled PWR systems. Demonstrative results are given to validate the potentiality of the method. 1. Introduction Current calculation codes for reactor analysis imple- ment the multi-group method (MGM) to evaluate the energy distribution of neutron flux and a two-group diffu- sion model is largely adopted for thermal reactors. In order to achieve accurate results the two-group model uses cross sections that conserve the reaction rates of fine multi-group calculations on an infinite medium condition. For this pur- pose the assembly cross sections are homogenized on the fine spectrum. Since the spectrum depends on the current conditions of the reactor, varying spatially, the cross sec- tions depend on several parameters as moderator density, fuel temperature, hard absorbers densities. This depen- dency is treated by tabulating the cross sections versus these parameters. But local spectrum variations in the reac- tor can also be due to the proximity of very different fuel types or to the proximity of the reflector or to the insertion of a control rod in the neighboring assembly. This depen- dency, usually called the leakage effect, is not seen by the cross sections, which are homogenized on an infinity med- ium spectrum. Since the leakage effect takes importance with reload strategies as MOX/UO 2 , AREVA NP has developed an innovative method (as an alternative of the multi-group method), the migration mode method (MMM) (Dall’Osso, 2003; Bruna et al., 2005), to implicitly represent the local spectrum variations produced by local conditions and leakage effects, basing on a heuristic approach. In order to further investigate on the benefits of this method, AREVA NP has recently launched a research action involving collaborations with universities. The benefits searched with this method are: * Corresponding author. Tel.: +39 066868095; fax: +39 066868489. E-mail address: augusto.gandini@uniroma1.it (A. Gandini). Annals of Nuclear Energy 35, 1306 (2008)