On the use of Monte Carlo perturbation in neutron transport problems

Two methods to estimate the variations on the collision density between different configurations are presented: the 'multiple estimate method' and the 'Taylor expansion method'. First and foremost, we recall the bases of analogue simulation and present the notations used to define the collision density in the integral Boltzmann equation. In the second part we discuss the different non analogue techniques used to obtain a small variance. The third part of this work deals with correlated sampling that we call multiple estimate. The principle is similar to non analogue simulation when we introduce a biased law to simulate the propagation of particles. Finally, we calculate perturbed results owing to a Taylor expansion following Rief's nice representation. We extend the method to an arbitrary order of the Taylor expansion for one and two variables. We present several examples and bring in light the advantages and drawbacks of the 'multiple estimate method' and the 'Taylor expansion method'. In every case, we compare the collision densities estimated by these two methods with the collision densities estimated by independent simulations. (author)