Application of backtracking algorithm to depletion calculations

Based on the theory of linear chain method for analytical depletion calculations, the burn-up matrix is decoupled by the divide and conquer strategy and the linear chain with Markov characteristic is formed. The density, activity and decay heat of every nuclide in the chain can be calculated by analytical solutions. Every possible reaction path of the nuclide must be considered during the linear chain establishment process. To confirm the calculation precision and efficiency, the algorithm which can cover all the reaction paths of the nuclide and search the paths automatically according to to problem description and precision restrictions should be sought. Through analysis and comparison of several kinds of searching algorithms, the backtracking algorithm was selected to search and calculate the linear chains using Depth First Search (DFS) method. The depletion program can solve the depletion problem adaptively and with high fidelity. The solution space and time complexity of the program were analyzed. The new developed depletion program was coupled with Monte Carlo program MCMG-II to calculate the benchmark burn-up problem of the first core of China Experimental Fast Reactor (CEFR). The initial verification and validation of the program was performed by the calculation. (author)