Providing solid angle formalism for skyshine calculations

Michael S Gossman,Mary B Rising,A Jussi Pahikkala,Patton H Mcginley

doi:10.1120/jacmp.v11i4.3286

Abstract

We detail, derive and correct the technical use of the solid angle variable identified in formal guidance that relates skyshine calculations to dose‐equivalent rate. We further recommend it for use with all National Council on Radiation Protection and Measurements (NCRP), Institute of Physics and Engineering in Medicine (IPEM) and similar reports documented. In general, for beams of identical width which have different resulting areas, within ±1.0% maximum deviation the analytical pyramidal solution is 1.27 times greater than a misapplied analytical conical solution through all field sizes up to 40×40 cm2. Therefore, we recommend determining the exact results with the analytical pyramidal solution for square beams and the analytical conical solution for circular beams.PACS number(s): 87.52.‐g, 87.52.Df, 87.52.Tr, 87.53.‐j, 87.53.Bn, 87.53.Dq, 87.66.‐a, 89., 89.60.+x

Highlights

The determination of skyshine involves the calculation of the solid angle subtended by a linac radiation beam of known field size and square shape
279 Gossman et al.: Solid angle equation where (Gy/h) is the X-ray absorbed dose-rate at 1 m from the target, di (m) is the vertical distance from the target to a point 2 m above the roof, ds (m) is the lateral distance from the isocenter to a point outside the barrier where measurements are to be taken, Ω is the solid angle formed by the radiation beam in steradians and is given by Eq 2: [2]
Equation 2 represents the correct form of the solid angle equation, but only for circular fields such as from those formed by cerrobend blocks

Summary

Introduction

The determination of skyshine involves the calculation of the solid angle subtended by a linac radiation beam of known field size and square shape. Previous research has been documented where analytical conical expressions were used.[1,2,3] Cone-based equations are more appropriate for circular collimation such as from round apertures of cerrobend blocks.

Results

Conclusion