Fenwick, John D and Kumar, Sudhir
(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 AND BIOLOGY, 68 (1).
015016-015016.
Abstract
<i>Objective.</i>Boag<i>et al</i>(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,<i>f</i>, was straightforwardly obtained assuming a uniform negative ion cloud. Boag<i>et al</i>(1996) therefore derived collection efficiency formulae<i>f</i>',<i>f</i>″ and<i>f</i>'″ based on three approximate descriptions of the exponentially-varying negative ion cloud, each uniform within a region. Collection efficiencies calculated by Boag<i>et al</i>(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.<i>Approach.</i>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,<i>f</i><sub>exp</sub>, collection efficiencies were calculated for a range of ionization chamber properties and doses-per-pulse, and compared with<i>f</i>,<i>f</i>',<i>f</i>″ and<i>f</i>″' values and results from an ion transport code.<i>Main results</i>.<i>f</i><sub>exp</sub>values agreed to 5 decimal places with ion transport code results. The maximum relative difference between<i>f</i><sub>exp</sub>and<i>f</i>″', which was often closest to<i>f</i><sub>exp</sub>, was 0.78% for the chamber properties and doses-per-pulse studied by Boag<i>et al</i>(1996), rising to 6.1% at 1 Gy dose-per-pulse and 2 mm electrode separation.<i>Significance.</i>Use of<i>f</i><sub>exp</sub>should reduce ambiguities in collection efficiencies calculated using the approximate formulae, although like them<i>f</i><sub>exp</sub>does not account for electric field distortion, which becomes substantial at doses-per-pulse ≥100 mGy.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ionisation chamber, ion recombination, dose-per-pulse, collection efficiency, free electrons |
| Divisions: | Faculty of Health and Life Sciences Faculty of Health and Life Sciences > Institute of Systems, Molecular and Integrative Biology |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 06 Jan 2023 12:17 |
| Last Modified: | 11 Jan 2023 22:53 |
| DOI: | 10.1088/1361-6560/aca74e |
| Open Access URL: | https://doi.org/10.1088/1361-6560/aca74e |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3166918 |
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