A unified theory of zero power and power reactor noise via backward master equations

Traditionally, zero power noise, i.e. inherent neutronic fluctuations in a steady medium, and power reactor noise are treated as two separate phenomena. They dominate at different power levels and are described via different mathematical tools (master equations and the Langevin equation, respectively). Because of these differences, there has been known no joint or unified description, based on first principles rather than empirical analogies, that treats a case when both types of noise are present concurrently. The subject of the present paper is to develop a unified theory of zero power and power reactor noise by calculating the probability distribution of the neutrons in a core with fluctuating material properties. A backward type master equation formalism is used with point kinetics, and the fluctuating cross-sections are represented by a binary pseudorandom process. A closed form solution is obtained which is significantly more complicated than the cases of zero power noise or power reactor noise separately, which are also given in the paper. It is shown that the general solution contains both the zero power and power reactor noise in the sense that the two forms can be extracted individually as limiting cases of the general solution.