Fenwick, JD; Kumar, S; (2023) Collection efficiencies of ionization chambers in pulsed radiation beams: an exact solution of an ion recombination model including free electron effects. Physics in Medicine & Biology , 68 (1) , Article 015016. 10.1088/1361-6560/aca74e.

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Abstract

OBJECTIVE: Boag et 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. Boag et al (1996) therefore derived collection efficiency formulae f', f'' and f''' based on three approximate descriptions of the exponentially-varying negative ion cloud, each uniform within a region. Collection efficiencies calculated by Boag et 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 with f, f', f'' and f''' values and results from an ion transport code. MAIN RESULTS: fexp values agreed to 5 decimal places with ion transport code results. The maximum relative difference between fexp and f''', which was often closest to fexp, was 0.78% for the chamber properties and doses-per-pulse studied by Boag et al (1996), rising to 6.1% at 1 Gy dose-per-pulse and 2 mm electrode separation. SIGNIFICANCE: Use of fexp should reduce ambiguities in collection efficiencies calculated using the approximate formulae, although like them fexp does not account for electric field distortion, which becomes substantial at doses-per-pulse ≥100 mGy.

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