UDC:

УДК 621.039.516

Abstract:

tochastic differential equations of zerodimensional reactor kinetics have been

derived assuming that the discretetime and continuoustime branching processes

should have moments of distribution which converge up to the second order, inclusive.

The regular part of the equations derived is similar to that of the zerodimensional

reactor kinetics equations. The regular part is influenced by the totality of the Gaussian

white noise inputs with appropriate coefficients.

An approximated distribution of the continuoustime branching process values has

been derived by using a prompt neutron approximation from the onedimensional

equation for the characteristic function. Although this distribution may not have much

physical significance, it allowed the concept of the weak external neutron source to be

clarified more precisely.

An analysis has been made of the wellknown Cohn’s stochastic model, with reactivity

noise introduced by analogy with the Schottky effect. It has been shown that the model

works well due to a very small fraction of delayed neutrons emitted by all the fissionable

isotopes.

References:

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