Stochastic theory of zero power nuclear reactors Part 3. Stochastic differential equations of zero_dimensional reactor kinetics. Weak external neutron source. analysis of the equivalent reactivity noise model

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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

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