Ionisation cavity theory: a formal derivation of perturbation factors for thick-walled ion chambers in photon beams

Abstract

Ionisation cavity theory for thick-walled chambers in photon beams is considered. Mathematically rigorous expressions based upon energy conservation are derived that equate the dose to the cavity to the product of the collision kerma, Bragg-Gray or Spencer-Attix stopping power ratios evaluated with idealised equilibrium spectra and correction factors. These correction factors account for photon attenuation and scatter and centre of electron production. They appear naturally in the derivation and differ only slightly from those used in the cavity-gas calibration factor, N_gas, in the AAPM 'Protocol for the Determination of Absorbed from High-Energy Photon and Electron Beams'. Additionally, a factor that corrects for the perturbation of the electron fluence by the cavity is derived. The expressions derived are formal only in the sense that analytical methods for calculating the fluences involved are not given. However, they may be evaluated in Monte Carlo calculations and they provide for analytical calculations.