Jan Dufek

Numerical Stability of Existing Monte Carlo Burnup Codes in Cycle Calculations of Critical Reactors

Abstract We show that major existing Monte Carlo burnup codes are numerically unstable in cycle calculations of critical reactors; spatial oscillations of the neutron flux can be observed even when relatively small time steps are used. This is caused by using the explicit Euler or midpoint method that appear to be numerically unstable with the step sizes common in cycle calculations. More stable methods that are common in deterministic burnup calculations, like the modified Euler method, can easily be introduced into the Monte Carlo burnup codes.

Stochastic Approximation for Monte Carlo Calculation of Steady-State Conditions in Thermal Reactors

Abstract A new adaptive stochastic approximation method for an efficient Monte Carlo calculation of steady-state conditions in thermal reactor cores is described. The core conditions that we consider are spatial distributions of power, neutron flux, coolant density, and strongly absorbing fission products like 135Xe. These distributions relate to each other; thus, the steady-state conditions are described by a system of nonlinear equations. When a Monte Carlo method is used to evaluate the power or neutron flux, then the task turns to a nonlinear stochastic root-finding problem that is usually solved in the iterative manner by stochastic optimization methods. One of those methods is stochastic approximation where efficiency depends on a sequence of stepsize and sample size parameters. The stepsize generation is often based on the well-known Robbins-Monro algorithm; however, the efficient generation of the sample size (number of neutrons simulated at each iteration step) was not published yet. The proposed method controls both the stepsize and the sample size in an efficient way; according to the results, the method reaches the highest possible convergence rate.

Fission source sampling in coupled Monte Carlo simulations

Abstract We study fission source sampling methods suitable for the iterative way of solving coupled Monte Carlo neutronics problems. Specifically, we address the question as to how the initial Monte Carlo fission source should be optimally sampled at the beginning of each iteration step. We compare numerically two approaches of sampling the initial fission source; the tested techniques are derived from well-known methods for iterating the neutron flux in coupled simulations. The first technique samples the initial fission source using the source from the previous iteration step, while the other technique uses a combination of all previous steps for this purpose. We observe that the previous-step approach performs the best.

Performance of the Explicit Euler and Predictor-Corrector–Based Coupling Schemes in Monte Carlo Burnup Calculations of Fast Reactors

Abstract We present a stability test of the explicit Euler and predictor-corrector–based coupling schemes in Monte Carlo burnup calculations of the gas fast reactor fuel assembly. Previous studies have identified numerical instabilities of these coupling schemes in Monte Carlo burnup calculations of thermal spectrum reactors due to spatial feedback–induced neutron flux and nuclide density oscillations, where only sufficiently small time steps could guarantee acceptable precision. New results suggest that these instabilities are insignificant in fast-spectrum assembly burnup calculations, and the considered coupling schemes can therefore perform well in fast-spectrum reactor burnup calculations even with relatively large time steps.

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10. A. SASAHARA, T. MATSUMURA, G. NICOLAOU, J. P. GLATZ, E. TOSCANO, and C. T. WALKER, “Post Irradiation Examinations and Computational Analysis of High Burn-up UOX and MOX Spent Fuels for Interim Dry Storage,” Proc. 10th Pacific Basin Nuclear Conference, Kobe, Japan, October 20–25, 1996, pp. 1072–1080 ~1996!. Reply to “Comments on ‘Numerical Stability of Existing Monte Carlo Burnup Codes in Cycle Calculations of Critical Reactors’”