Some comments in neutron noise theory

• The motion of the precursors is included in the noise equations.
• A modified perturbation formula (MPF) leads to more robust linearized noise eqs.
• The MPF equations are identical to the full diagonal noise equations.
• New source term for vibration-induced noise gives linear equations with noise O(∊∊).

We review the basic assumptions in traditional neutron noise theory regarding its application to vibration-generated noise. We include the description of precursor’s motion in the equations and introduce a different perturbation formula based on the time-averaged operator. Among other advantages, the latter results in a robust system of linearized equations that minimize the perturbation component of the flux by setting its time-averaged value to zero. This is in contrast to traditional noise theory whose linearized equations are not robust when the perturbation adds reactivity to the core, which is the case with vibrations. We also introduce a higher-order full diagonal approximation for the noise equations and show that our new perturbation formula yields the only linearized approximation which is equivalent to the full diagonal formulation. Finally, we introduce a new linear model which for vibration-generated noise is closer to the exact noise equations and has potential to give a better solution when the terms not included in the traditional linearized model are greater than O(∊2)O(∊2).