A Modal Analysis of Neutron-Flux Spatial Oscillation

The stability of flux-shaped spatial modes is studied in a Calder Hall type reactor in three dimensions using the homogeneous boundary condition of the reactivity with the following three results: 1) the modal interaction due to coolant flow is also a second-order term in the three-dimensional modal analysis and can be ignored as the first approximation; 2) the Nyquist criterion should be applied to the expression containing the involved transcendental function in the transfer function of the thermal system; and 3) the simple thermal model, which treats only the fuel, moderator, and coolant, is adequate to judge the stability of the mode. The effects of flattening the radius on the threshold value of the moderator reactivity temperature coefficient and on the period of the sustained oscillation have been studied by this method as a function of the eigenvalue, and it has been shown that: 1) the modes with the same order in axial and radial direction form a group; and 2) the modes with the second order in axial direction are more stable than the modes with the first order in axial direction.