Optimization Model for Radioactive Waste Transmutation in Advanced Fuel Cycle Anna G. Golovkina ∗ Igor V. Kudinovich ∗∗ Dmitri A. Ovsyannikov ∗∗∗ ∗ Saint Petersburg State University, Universitetsky pr. 7/9, Saint Petersburg, 199034 Russia (e-mail: a.golovkina@spbu.ru) ∗∗ Saint Petersburg State University, Universitetsky pr. 7/9, Saint Petersburg, 199034 Russia (e-mail: i.kudinovich@spbu.ru) ∗∗∗ Saint Petersburg State University, Universitetsky pr. 7/9, Saint Petersburg, 199034 Russia (e-mail: d.a.ovsyannikov@spbu.ru) Abstract: Optimization approach to effective radioactive waste management in advanced fuel cycle is proposed in the paper. This approach is based on the optimal control theory. The considered controlled system contains a system of ordinary differential equations, describing radioactive isotopes concentration change in time and a number of switching points in which the system state can be changed. The values of variables in the switching points are the optimizing parameters, subjected to determination. Moreover, because the recycling of nuclear waste is supposed to fulfill in subcritical reactor, the constraints on effective multiplication factor are also taken into account during numerical calculations. . Keywords: Fuel control, radioactive waste management, advanced fuel cycle, ADS, optimization problem. 1. INTRODUCTION Advanced fuel cycle is an important aspect of sustain- able nuclear energy, because its implementation leads to resources preservation, significant waste minimization and improved economy Salvatores and Palmiotti (2011). The mentioned points are achieved due to recycling of spent nuclear fuel. Normally it contains a lot of long-lived transuranic elements (TRU) and fission products (FP). The TRU constitute about 1% of the nuclear waste mass, but its radiotoxicity is about 20000 times higher than radiotoxicity of FP after 1000 years Herczeg (2003). Hence, considerable reduction of the total waste radiotoxicity can be achieved by TRU extraction during the recycling process and the following transmutation Kudinovich et al. (2014). Transmutation is a conversion of long-lived radionuclides into short-lived or stable isotopes by neutral or charged particle fluxes Herczeg (2003). Ordinary this process is considered to be realized in fast nuclear reactors. However traditional reactors have several disadvantages that bring into question transmutation feasibility. The main short- comings are the limitation on actinides amount that can be loaded in the transmuter (due to safety reasons) and the fact that fissile isotope burnup does not exceed 25% in traditional reactors Kudinovich et al. (2014). In this regard, it is widely proposed to use hybrid systems for transmutation. One of the most promising facilities of that type is Accelerator Driven System (ADS). ADS consists of subcritical reactor, neutron producing target and charged particle accelerator Nifenecker et al. (2003); Golovkina et al. (2012, 2014b, 2013, 2014a). The subcritical core con- ADS Spent fuel separation Fuel fabrication Cooling pond Temporary storage Long-term storage U 238 U 235 U 238 ? ? LWR … 1 2 3 4 Fig. 1. The Scheme of advanced fuel cycle with ADS as a waste burner considered in this paper figuration of the ADS would allow burning up some atypi- cal actinide mixtures. Also in order to start the operation of ADS it is not necessary to reach some reactivity excess, because the external source gives the required neutron supply to maintain the reaction Golovkina et al. (2016). It should be noted that the intensity of the external neutron source depends on accelerator-driver characteristics, which can also be subjected to optimization Ovsyannikov (1997, 2012); Balabanov et al. (2018). The principal scheme of advanced fuel cycle with ADS as a waste burner is shown in Fig. 1.