This paper describes the neutronic benchmarks and the results obtained by the various participants of the FP7 project EVOL and the ROSATOM project MARS. The aim of the benchmarks was two-fold: first to verify and validate each of the code packages of the project partners, adapted for liquid-fueled reactors, and second to check the dependence of the core characteristics to nuclear data set for application on a molten salt fast reactor (MSFR). The MSFR operates with the thorium fuel cycle and can be started with 233U-enriched U and/or TRU elements as initial fissile load. All three compositions were covered by the present benchmark. The calculations have confirmed that the MSFR has very favorable characteristics not present in other Gen4 fast reactors, like strong negative temperature and void reactivity coefficients, a low-fissile inventory, a reduced long-lived waste production and its burning capacities of nuclear waste produced in currently operational reactors.
The adjoint equation was introduced in the early days of neutron transport and its solution, the neutron importance, has ben used for several applications in neutronics. The work presents at first a critical review of the adjoint neutron transport equation. Afterwards, the adjont model is constructed for a reference physical situation, for which an analytical approach is viable, i.e. an infinite homogeneous scattering medium. This problem leads to an equation that is the adjoint of the slowing-down equation that is well-known in nuclear reactor physics. A general closed-form analytical solution to such adjoint equation is obtained by a procedure that can be used also to derive the classical Placzek functions. This solution constitutes a benchmark for any statistical or numerical approach to the adjoint equation. A sampling technique to evaluate the adjoint flux for the transport equation is then proposed and physically interpreted as a transport model for pseudo-particles. This can be done by introducing appropriate kernels describing the transfer of the pseudo-particles in phase space. This technique allows estimating the importance function by a standard Monte Carlo approach. The sampling scheme is validated by comparison with the analytical results previously obtained.
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