Progress in Nuclear Energy 124 (2020) 103343 Available online 8 April 2020 0149-1970/© 2020 Elsevier Ltd. All rights reserved. Contents lists available at ScienceDirect Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene Isotopic depletion calculation with generalized perturbation theory in subcritical systems driven by an external neutron source P.K. Taipe ∗ , F.C. Silva, A.C.M. Alvim Nuclear Engineering Program - COPPE, Federal University of Rio de Janeiro, Av. Horacio Macedo 2030, 21941-914, Rio de Janeiro, RJ, Brazil ARTICLE INFO Keywords: Subcritical system Burnup calculation Isotopic depletion calculation Generalized perturbation theory ABSTRACT Generalized Perturbation Theory (GPT) is used with the aim of proposing a perturbation method for isotopic depletion calculations. Changes in nuclide densities over time induce variations in the neutron flux and these lead to changes in reaction rates present in the evolution matrix. The proposed perturbation method treats these reaction rates as integral quantities and changes in these integral quantities as perturbations coming from changes in nuclide densities with fuel burnup. This method is applied to a subcritical system driven by an external neutron source. The results obtained by perturbation method show good agreement with the direct calculation. Considering that only a 1D problem was tested, other problems treating more energy groups and 2 or 3 spatial dimensions should be done in order to fully validate the method. 1. Introduction The methods of Perturbation Theory have been used in Reactor Physics, since the pioneering work of Wigner (1945). Since then, sev- eral other works have been developed with the objective of extending the applicability of this theory to treat other Reactor Physics problems. Among these works are those that gave rise to the so-called Gener- alized Perturbation Theory (Usachev, 1964; Lewins, 1965; Gandini, 1967 and 1983). One of the applications of perturbation theory is, for example, in isotopic depletion calculations (Williams, 1979; Silva and Thomé, 1987; Downar, 1992; Kallfelz et al., 1977). The isotopic composition of the reactor core has to be monitored during the fuel burnup, because heavy, high radiotoxicity elements are produced that accumulate as minor actinides (MA) and fission products (FP) in the nuclear waste at the end of the fuel cycle. Hybrid systems driven by an external neutron source (Rubbia et al., 1995; Bowman et al., 1992; Stacey, 2007) have been proposed to close the open (or once-through) fuel cycle (IAEA, 2018), to get rid of accu- mulation of MA and FP. These systems tackle this problem by burning MA and FP, and then reusing them together with fresh fuel during refueling. Two main examples of these systems are the Accelerator Driven Systems (ADS) (Gandini and Salvatores, 2002; MYRRHA, 1998) and the Fusion–Fission Reactor Systems (FFRS) (Mauer et al., 2004; Hoffman and Stacey, 2002; ITER, 1985). In this work, our main interest is to develop a method able to calculate nuclide densities using GPT, but without neglecting the prod- ucts of perturbed quantities, contrary to what is presently done up ∗ Corresponding author. E-mail addresses: ptorres@nuclear.ufrj.br (P.K. Taipe), fernando@nuclear.ufrj.br (F.C. Silva), alvim@nuclear.ufrj.br (A.C.M. Alvim). to now. In this sense, this method is a novel approach for treating reactor physics problems with GPT. For this, a perturbation method is proposed that treats reaction rates appearing in the evolution matrix as integral quantities. During the fuel cycle, nuclide densities change, inducing variations in the neutron flux which leads to variations in the integral quantities (or perturbations in the integral quantities), that are then determined applying GPT. Thus, in this method the iterative process of calculating the neutron flux is replaced by a GPT expression to obtain new reaction rates directly. Once the new reaction rates are found, the evolution matrix can be constructed for each time step, the depletion equations can be solved at each time, using the method proposed by Alvim et al. (2010), and finally, the nuclide densities can be obtained at the end of the burnup cycle. The method proposed by Alvim et al. (2010) to solve isotopic depletion equations, is part of the CNFR code (Portuguese acronym for National Code of Reactor Physics) (Silva et al., 2010; Prata et al., 2013; Heimlich et al., 2016 and 2018). This work is organized as follows. In Section 2 we describe the equations for isotopic depletion calculation. In Section 3 we formulate the perturbation method which will be used to make the depletion calculation. In Section 4 we show the applicability of our proposed method to a simple case. Finally, in Section 5 we present a summary and our conclusions. https://doi.org/10.1016/j.pnucene.2020.103343 Received 7 November 2019; Received in revised form 22 March 2020; Accepted 23 March 2020