Application of the "Functional Monte Carlo" Method to Estimate Continuous Energy k-Eigenvalues and Eigenfunctions

In Monte Carlo simulations of k-eigenvalue problems, the eigenfunctions are often poorly estimated for optically thick fissile systems with a large dominance ratio, i.e. when the ratio of the second largest to the largest eigenvalue is close to unity. In this case, Monte Carlo estimates of the fission source may never converge unless an extraordinarily large number of particles is used per fission generation. We have proposed a new “functional Monte Carlo” (FMC) method to address this difficulty. The 1-D, monoenergetic FMC results were published in the journal “Nuclear Science and Engineering” in 2008. In the present paper, we extend the FMC method to continuous-energy k-eigenvalue problems. The continuous-energy approach has several noticeable differences compared with the monoenergetic approach. In this hybrid FMC method, energy-integrated nonlinear functionals are estimated using standard Monte Carlo techniques with continuous energy. These functionals are then used in an energy-independent low-order equation to estimate the eigenvalue and the energy-integrated flux. The resulting continuous energy FMC estimates of eigenvalue and energy-integrated flux have very small energy truncation errors and statistical errors. However, the FMC method has no spatial or angular truncation errors. Our numerical examples show that the energy-integrated flux converges orders of magnitude faster in the FMC approach than with the standard Monte Carlo approach. The FMC method also produces much more accurate estimates of the eigenvalue.