Alpha eigenvalue calculations with Tripoli-4®

Characterizing the time behavior of neutron transport is crucial in several technological issues, such as for instance reactor start-up analysis, reactivity measurements, or kinetics studies of accelerator-driven systems. Basically, this amounts to computing the spectrum of the Boltzmann operator: analytical techniques, though quite ingenuous, are often restricted to simple geometries and one-speed transport, so that numerical solutions become mandatory to this aim. In this paper we develop a Monte Carlo method for determining the dominant eigenvalue of the Boltzmann operator and the associated fundamental mode for arbitrary geometries, materials, and boundary conditions; this is done in view of adding such capabilities to the Monte Carlo code Tripoli-4®. Extensive verification and validation tests are performed on multiplying and moderating media, and a critique of the algorithm is proposed.