Generalized Off-Axis Distributions from Disk Sources of Radiation
- 1 April 1954
- journal article
- research article
- Published by AIP Publishing in Journal of Applied Physics
- Vol. 25 (4), 519-527
- https://doi.org/10.1063/1.1721675
Abstract
In the field of shielding it is frequently necessary to calculate biological radiation doses at any point in space due to disk sources of radiation. Such a source is the leakage radiation from an end of a cylindrical reactor. If G(R) is the dose at distance R from a unit point source (e.g., G∼e−σR/R2) then the dose due to a disk source of radius ``a'' with source strength S(ρ) is given by , where (z,ρ,θ) are the usual cylindrical coordinates, z=0 is the source plane, and (z,ε,0) locates the dose point. This integral is quite general, arising in many physical problems. In counter measurements, use of G=z/(4πR3), S=1 yields the solid angle subtended by the counter. In neutron physics the slowing down density of neturons from a circular source of finite radius can be calculated in the age approximation with G∼exp(−R2/τ). Since for most G's the integral cannot be evaluated in closed form, there are derived three alternative series for D(z,a,ε) each of which has a direct physical interpretation and a different region of convergence. The results are obtained for a class of analytic functions G(R), the possible singularities of which occur only at R=0 for finite R; and for S(ρ) of the form ΣpSpρ2p. The approach in each case is to expand either the double integral or one of the two repeated integrals in a power series in cosθ, ε, or ρ prior to performing the detailed integrations. Numerical results are given for the case of a typical shielding function.