A CORRELATION OF INTERACTION DATA WITH CALCULATIONS USING THE GELLER MODEL
J. Fox · 1965
This report describes a simple model for calculating the critical separation of regular arrays of identical fissile units.The units must be separated mainly by air.The model used i s one f i r s t derived by L. Geller.Use i s made of the fact that for a critical system the material buckling is equal to the geometric buckling.The model assumes that the total interaction probability, @, is simply related to the ratio of the geometric buckling, B ; , of the critical isolated unit to that of one unit in the array: ~g = B? (1 -$).where ~f is the geometric buckling of a single unit in the array.The ,total interaction probability depends mainly upon the solid angle between two units,'.and the total number of units in the array.Normalization to experiment is used.'$odetermine the pr6p6rti6naiity constant relating the solid angle to the interacti& probability.Thus, the calculation i s reduced to a simple geometrical.'problem.To determine the total interaction probability a s a function ..of. number of units in an array a determinant i s set up based on symmetry.A major difficulty with this method is in how to treat shadow effects.~h e s e become important for large arrays.Hence, extrapolations ' a r e used to estimate the coupling coefficients of large arrays.