# ON SOLUTION TO THE PROBLEM OF REACTOR KINETICS WITH DELAYED NEUTRONS BY MONTE CARLO METHOD

23rd Symposium of AER on VVER Reactor Physics and Reactor Safety (2013, Štrbské Pleso, Slovakia)

Advances in spectral and core calculation methods

## Abstract

Submitted paper is devoted to initial value problem for both the neutron transport equation

and the system of equations that describe behaviour of emitters of delayed neutrons.

Examination of the solution to this problem is based on several main suppositions which

concern behaviour of macroscopic effective cross-sections that describe reaction of neutron

with medium, the temperature of medium and the other parameters of the equations.

Formulation of these suppositions is sufficiently general and is in agreement with properties

of all known models of physical quantities mentioned. Among others the suppositions admit a

dependence of both macroscopic effective cross-sections and temperature on spatial

coordinates and time that can be arbitrary to a great extent.

Original mathematical formulation of the problem is the set of integro-differential

equations. At first the problem is transposed into equivalent one to solve certain linear integral

equation for neutron flux. Then solution to that integral equation is found by the method of

successive iterations and its uniqueness is proven.

Numeric solution to the integral equation by Monte Carlo method consists in finding a

functional of the exact solution. In the paper a random process is constructed and several

random variables are proposed to this purpose. Then it is proven that each of these variables is

unbiased estimator of that functional.