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The theoretical aspects of the linear chain method for the numerical modelling of nuclear transmutation systems, and particularly regarding the transmutation trajectory analysis (TTA), are presented. The theoretical background of the TTA method, as an advanced version of the linear chain method, with the detailed description of the applied mathematical set-up and graphical visualisation of transformation chains, is shown. As the TTA method was initially developed at the AGH University of Science and Technology almost 25 years ago, several numerical implementations were introduced worldwide, yet the mathematical improvements or alternative forms of solutions and numerical algorithms were reported since then. The method was also implemented and tested by different research groups, also in confrontation with alternative approaches to the nuclear transformation problem known as the matrix method. The aim of the paper is to present the background of the developed method and its advantages, clarify misunderstandings in the method perception and suggest unexplored options in numerical algorithm implementation.

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This paper deals with SiC detector simulation methodology for signal formation by neutrons and induced secondary radiation as well as its inverse interpretation. The primary goal is to achieve the SiC capability of simultaneous spectroscopic measurements of neutrons and gamma-rays for which an appropriate methodology of the detector signal modelling and its interpretation must be adopted. The process of detector simulation is divided into two basically separate but actually interconnected sections. The first one is the forward simulation of detector signal formation in the field of the primary neutron and secondary radiations, whereas the second one is the inverse problem of finding a representation of the primary radiation, based on the measured detector signals. The applied methodology under development is based on the Monte Carlo description of radiation transport and analysis of the reactor physics. The methodology of SiC detector signal interpretation will be based on the existing experience in neutron metrology developed in the past for various neutron and gamma-ray detection systems. Since the novel sensors based on SiC are characterised by a new structure, yet to be finally designed, the methodology for particle spectroscopic fluence measurement must be developed while giving a productive feed back to the designing process of SiC sensor, in order to arrive at the best possible design.

In this paper, we present a trajectory period folding method for numerical modelling of nuclear transformations. The method uses the linear chain method, commonly applied for modelling of isotopic changes in matter. The developed method folds two consecutive periods of time and forms linear chain representations. In the same way as in the linear chain method, the mass flow of straight nuclide-to-nuclide transitions following the formation of nuclide transmutation chains in every step is considered over the total period of interest. Therefore, all quantitative data about the isotopic transformations for the period beyond a particular calculation step are preserved. Moreover, it is possible to investigate the formation history of any isotope from the beginning of irradiation to the arbitrary time step, including cooling periods and multi-recycling for any designed nuclear fuel cycle. We present a case study for the transition from 238U to 239Pu and define the properties of the developed method and its possible applications in reactor physics calculations.