On solution to the problem of reactor kinetics with delayed neutrons
21st Symposium of AER on VVER Reactor Physics and Reactor Safety (2011, Dresden, Germany)
Spectral and core calculations
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.
At first the problem is transposed into a linear integral equation for neutron flux. Next a
suitable linear space of functions is chosen to solution of that equation. In this domain,
solution to the integral equation is found by method of successive iterations and its
uniqueness is proven.
Numeric solution to the integral equation by Monte Carlo method consists in finding of one
or several functionals of the exact solution. To this purpose several types of random process
and random variables are constructed in the paper and consequently it is proven there that
these variables are unbiased estimators of those functionals.
Big space of the paper concerns construction of special random variable that can be treated
as a generalization of track length estimator.