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.
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.
The possibility of preparing fission chambers for the experimental determination of subcriticality without time-consuming corrections has been presented. The reactor detectors set consists of monoisotopic chambers. Each chamber is intended for a specific position in the system. Individual weights, rated a priori for all detectors in their positions, allow for quick calculation of whole system subcriticality. The inconveniences related to the spatial effect are minimized. This is achieved by computational simulation of the area method results, for each detector position and all possible fissionable and fissile nuclides. Next, one nuclide is selected, specific for the given position, presenting the smallest difference from the MCNP KCODE precisely estimated kkcode. The case study is made using the model of VENUS-F core.
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