A Preliminary Study of an Improved Area Method, Adapted to Short Time Transients in Sub-Critical Systems.

Since the ’90s interest has grown in the characterization of sub-critical systems. Because they should not have control/shutdown devices, it is necessary to prevent by design neutron flux divergence in all conditions. Most of the available theoretical models on neutron kinetic behavior in multiplying systems are tailored on the description of critical systems; then they have decreasing validity as well as the system is far and far from criticality; as a consequence many of the available monitoring methods are of questionable use for sub-critical systems and give contradictory informations: this is true, among the others, for the Area Method. One of the difficulties in understanding the kinetic behavior of a sub-critical system is the scarcity of experimental measurements available. Then we decided to develop a full time-dependent MCNP6 simulation of a sub-critical core to obtain some ”phenomenological-like” data whose analysis leads to conclude that geometrical inhomogeneity of the system plays a key role in determining its time behavior over short time scales. Starting from an original observation by Weinberg andWigner, we conclude that, for the short time scale considered ( s), we cannot use the ”classical” diffusion approximation but a little bit more complicated formulation, similar to what is known as telegrapher’s equation: along this line we find a reasonable justification for the idea that, before using any analysis method grounded on the assumption that the system has relaxed into its fundamental mode, we could have to wait for a longer time than the prompt neutrons lifetime. We conclude that from an experimentalist’s point of view it should be at lest necessary to cut from the analysis the lowest part of the time interval before using the Area Method, but more refined analyses are needed.