Since a fast reactor core with uranium-plutonium fuel is not in its most reactive configuration under operating conditions, redistribution of the core materials (fuel, steel, sodium) during a core disruptive accident (CDA) may lead to recriticalities and as a consequence to severe nuclear power excursions. The prevention, or at least the mitigation, of core disruption is therefore of the utmost importance. In the current paper, we analyze an innovative fast reactor concept developed within the CP-ESFR European project, focusing on the phenomena affecting the initiation and the transition phases of an unprotected loss of flow (ULOF) accident. Key phenomena for the initiation phase are coolant boiling onset and further voiding of the core that lead to a reactivity increase in the case of a positive void reactivity effect. Therefore, the first level of optimization involves the reduction, by design, of the positive void effect in order to avoid entering a severe accident. If the core disruption cannot be avoided, the accident enters into the transition phase, characterized by the progression of core melting and recriticalities due to fuel compaction. Dedicated features that enhance and guarantee a sufficient and timely fuel discharge are considered for the optimization of this phase.

In this paper, the mechanism of traveling wave reactors (TWRs) is investigated from the mathematical physics point of view, in which a stationary fission wave is formed by radial fuel drifting. A two dimensional cylindrically symmetric core is considered and the fuel is assumed to drift radially according to a continuous fuel shuffling scheme. A one-group diffusion equation with burn-up dependent macroscopic coefficients is set up. The burn-up dependent macroscopic coefficients were assumed to be known as functions of neutron fluence. By introducing the effective multiplication factor k_eff, a nonlinear eigenvalue problem is formulated. The 1-D stationary cylindrical coordinate problem can be solved successively by analytical and numerical integrations for associated eigenvalues k_eff. Two representative 1-D examples are shown for inward and outward fuel drifting motions, respectively. The inward fuel drifting has a higher k_eff than the outward one. The 2-D eigenvalue problem has to be solved by a more complicated method, namely a pseudo time stepping iteration scheme. Its 2-D asymptotic solutions are obtained together with certain eigenvalues k_eff for several fuel inward drifting speeds. Distributions of the neutron flux, the neutron fluence, the infinity multiplication factor k_inf and the normalized power are presented for two different drifting speeds.