Investigation of Stochastic Reactor Noise Models—A One-Variable Space-Time-Dependent Model

Using the Markovian description of stochastic processes, the fluctuations in pressurized water reactor cores (for example, temperature and bubble population fluctuations) are modeled. The model includes one-dimensional space and time dependence. Fluctuations are described with the help of a single stochastic variable N(z, t). Generally this approach is not satisfactory in practical problems, but in this way spatial effects can be investigated by a simple model. For this case, connections between moments of N(z, t) are derived. These moments are calculated both for transient and steady-state processes. Introducing spectral density functions in frequency and wave-number domains, a condition is given for the validity of the point model approach.