Linear Chain Method for Numerical Modelling of Burnup Systems

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.

Automated summary

Theoretical aspects of the linear chain method for numerical modelling of nuclear transmutation systems, particularly in regards to transmutation trajectory analysis (TTA), are presented. The TTA method, an advanced version of the linear chain method, has been implemented globally with various numerical improvements and alternative forms of solutions. The paper aims to introduce the background of the developed method, clarify misunderstandings, and suggest unexplored options in the implementation of numerical algorithms.