On the kinetic response of a reactor with delayed neutrons II: spatial effects

In part I of this paper (Pázsit, 1996), the paradoxical phase behaviour of the point kinetic response of a reactor was discussed. Namely, the fact that for small, periodic reactivity perturbations, in the lower frequency part of the plateau region λ < ω < β/Λ, the phase delay decreases with increasing frequencies. In addition, the point kinetic phase delay of a “delayed systems” (i.e. one containing delayed neutrons) is smaller over the whole plateau region than the phase delay of a “prompt system” (one containing prompt neutrons only). In this paper it is shown that a similar paradoxical behaviour exists regarding the pure space dependence of the noise. Namely, the spatial increase of phase delay with increasing distance from a point source shows a behaviour which is contrary to expectations (it becomes smaller with increasing frequency) in the lower part of the plateau region. Besides, the spatial phase decay is smaller in a delayed system than in a prompt system for all frequencies within the plateau region. This fact has also the consequence that the deterioration of the point kinetic and adiabatic approximations is not monotonic with increasing frequency - the approximations are better in the middle of the plateau region than in the low frequency end of it.