On the evaluation of rectangular plane-extended sources and their associated radiation fields

Abstract

The objective of this paper is to provide an efficient and reliable analytical procedure for the evaluation of rectangular plane-extended sources and their associated radiation fields. Integrals with integer and non-integer values appear in the evaluation of the radiation field distribution. The latter results from a homogeneous rectangular plane target bombarded by hollow-cylindrical ion beams, the elementary areas anisotropically emitting in non-dispersive media, and fast neutrons produced in non-dispersive media by sealed-off neutron generating tubes (NGT) in an axi-symmetric situation [Hubbell, J.H., Bach, R.L., Lamkin, J.C., 1960. Radiation from a rectangular source. J. Res. NBS 64C (2), 121–137; Hubbell, J.H., 1963a. A power series buildup factor formulation. Application to rectangular and offaxis disk source problems. J. Res. NBS 67C, 291–306, Hubbell, J.H., 1963b. Dose fields from plane sources using point-source data. Nucleonics 21 (8), 144–148; Timus et al., 2005a. Plane rectengular tritium target response to excitation by uniform distributed normal accelerated deuteron beam. Appl. Radiat. Isot. 63, 823–839; Timus et al., 2005b. Analytical characterization of radiation fields generated by certain witch-type distributed axi-symmetrical ion beams. Arab J. Nucl. Sci. Appl. 38(I) 253–264]. In these references, the resulting expressions are represented as infinite linear combinations of basic J q ( a, b, z) integrals. With the help of relation for J q ( a, b, z), we can evaluate the high terms of energy expressions, which have been proposed in the above-mentioned references. The extensive test calculations show that the proposed algorithm in this work is the most efficient one in practical computations.