Prediction of statistical error in Monte Carlo transport calculations

Successive solutions to two coupled integral equations provide the expected statistical error of any Monte Carlo calculation in which the external source is specified and the score resulting from each collision has a known probability distribution. Each equation can be transformed into a differential-integro form that is adjoint to the transport equation. This result agrees with the stochastic theory of Bell for those special situations described by both theories. The coupled integral equations in the Monte Carlo theory of Coveyou et al. have other adjoint properties because they describe physically different quantities. In the presented theory, the first equation (for the expected value), but not the second (for the expected squared value), can readily be understood in terms of Selengut's general interpretation of adjoint solutions. The principal aim of this work is to provide a method for determining in advance whether or not development of a contemplated Monte Carlo program would be worthwhile. Any of the approximations commonly applied to the transport equation can be used. Some examples are worked out by diffusion theory, interpreted, and tested for accuracy