Some Aspects of the Integral Transport Method for the Deep Penetration Problem

The integral transport method, which has been used in the early calculation of a beam hole tube in an experimental reactor and many reactor parameters of a power reactor; has been reviewed. The Generalized First-Flight Collision Probability (GFFCP) method, based on the integral transport equation, and the discrete ordinates method, based on the differential transport equation, are compared in the context of the deep penetration problem. The direct integral method derived from the partial integral transport equation, which eliminates many of the drawbacks of the GFFCP method, is discussed. A method similar to the GFFCP method, which needs spherical harmonics expansion instead of the discrete ordinates scheme, is presented. The future of these analytical methods is discussed in the comparison with the straight numerical method based on the differential transport calculation and the Monte Carlo calculation.