On the Boundary Perturbation Theory as Applied to Nuclear Reactors

The effects of boundary perturbations on eigenvalues are reviewed. The perturbation theory is developed for application to calculations of the buckling of reactors whose lateral surface is shaped like a right circular cylinder or a sphere. It is shown that with the perturbation approach applied, the zeroth-order approximation can be a circular cylinder or a sphere of such a radius that the first-order correction for the buckling is zero. A buckling formula for reactors with a cylindrical side surface has been obtained within the framework of the second-order perturbation theory. An elliptical cylinder and regular polygonal prisms are reviewed for illustration purposes.