On-the-Fly Doppler Broadening for Monte Carlo Codes

One of the primary challenges associated with the neutronic analysis of a nuclear reactor is accounting for temperature feedback due to Doppler broadening. This challenge is addressed by a new “on-the-fly” methodology that is applied during the random walk process in Monte Carlo codes with negligible impact on computational efficiency. The Monte Carlo code only needs to store 0 K cross sections for each isotope and the method will broaden the 0 K cross sections for any isotope in the library to any temperature in the range 77 to 3200 K for all incoming neutron energies up to 20 MeV. The methodology is based on a combination of Taylor series expansions and asymptotic series expansions. The type of series representation was determined by investigating the temperature dependence of ²³⁸U resonance cross sections in three regions: near the resonance peaks, midresonance, and the resonance wings. The coefficients for these series expansions were determined by a regression over the energy and temperature range of interest. Since the resonance parameters are a function of the neutron energy and the target nuclide, the ψ and χ functions in the Adler-Adler multilevel resonance model can be represented by series expansions in temperature only, allowing the least number of terms to approximate the temperature-dependent cross sections within a specified accuracy. The comparison of the broadened cross sections using this methodology with the NJOY cross sections was excellent over the entire temperature range (77 to 3200 K) and energy range. A Monte Carlo code was implemented to apply the combined regression model and used to estimate the additional computing cost, which was found to be <1%.