Collection efficiencies of ionization chambers in pulsed radiation beams: an exact solution of an ion recombination model including free electron effects.

ABSTRACT

Objective.Boaget al(1996) formulated a key model of collection efficiency for ionization chambers in pulsed radiation beams, in which some free electrons form negatively charged ions with a density that initially varies exponentially across the chamber. This non-uniform density complicates ion recombination calculations, in comparison with Boag's 1950 work in which a collection efficiency formula,f, was straightforwardly obtained assuming a uniform negative ion cloud. Boaget al(1996) therefore derived collection efficiency formulaef',f″ andf'″ based on three approximate descriptions of the exponentially-varying negative ion cloud, each uniform within a region. Collection efficiencies calculated by Boaget al(1996) using these formulae differed by a maximum of 5.1% relative (at 144 mGy dose-per-pulse with 212 V applied over a 1 mm electrode separation) and all three formulae are often used together. Here an exact solution of the exponentially-varying model is obtained.Approach.The exact solution was derived from a differential equation relating the number of negative ions collected from within some distance of the anode to numbers of ions initially located within that region. Using the resulting formula,fexp, collection efficiencies were calculated for a range of ionization chamber properties and doses-per-pulse, and compared withf,f',f″ andf″' values and results from an ion transport code.Main results.fexpvalues agreed to 5 decimal places with ion transport code results. The maximum relative difference betweenfexpandf″', which was often closest tofexp, was 0.78% for the chamber properties and doses-per-pulse studied by Boaget al(1996), rising to 6.1% at 1 Gy dose-per-pulse and 2 mm electrode separation.Significance.Use offexpshould reduce ambiguities in collection efficiencies calculated using the approximate formulae, although like themfexpdoes not account for electric field distortion, which becomes substantial at doses-per-pulse ≥100 mGy.