Asymptotic Reactor Theory

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Abstract
It is first shown that the results of “asymptotic reactor theory” may be derived simply from the condition that an infinite medium rather than the correct finite medium diffusion equation be used to describe the thermal neutron flux in a reactor. In an asymptotic (bare, homogeneous, thermal) reactor, it is possible to describe the thermal flux through such an equation if the kernel of the infinite medium equation is defined properly, even when the reactor is not “large.” The relation between the kernels of the two equations is explicitly derived, and the conditions examined under which the kernel of the infinite medium equation can be interpreted physically as the Green's function of the infinite medium slowing-down problem. It is found that this interpretation is not restricted to the case in which the finite medium, slowing-down problem can be treated accurately by diffusion theory. Rather, the restriction is that the “asymptotic” portion of the flux give a reasonably accurate description of the finite medium Green's function. Thus, the use of transport kernels in asymptotic reactor theory is meaningful, a result which has been observed, but not explained, by a number of authors.

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