Spatial Eigenfunctions, Time Eigenvalues, and Leakage Currents of Two-Region (Grooved) Neutron Moderators

Grooved moderators provide greater neutron leakage currents from their channeled surfaces than flat moderators of the same volume. Operated in conjunction with pulsed sources to provide beams of slow neutrons, their pulse widths depend in a complicated way on the groove parameters, as does the leakage current. A one-speed diffusion theory treatment of the asymmetric grooved moderator is described, the eigenfunctions and eigenvalues are presented, and a simple graphical method for eigenvalue calculation is provided. The leakage from the bottoms of the grooves and from the tips of the fins are separately determined and the lowest order functions for a cold polyethylene moderator are calculated. The results for the lowest order time eigenvalue are in good agreement with a measurement obtained at the Intense Pulsed Neutron Source.