Collection efficiencies of cylindrical and plane parallel ionization chambers: analytical and numerical results and implications for experimentally determined correction factors.

Objectives. To derive a collection efficiency formula,fGauss, for cylindrical ionization chambers in pulsed radiation beams from a volume recombination model of Boag et al (1996 Phys. Med. Biol. 41 885-97) including free electrons. To validatefGaussand a parallel plate chamber formulafexpusing an ion transport code and calculate changes in collection efficiencies caused by electric field charge screening at 0.1-100 mGy doses-per-pulse. And to determine collection efficienciesCE∞predicted at infinite voltage in the absence of avalanche effects by fitting scaled formulae to efficiencies computed for 100-400 V chamber voltages and 10 and 100 mGy doses-per-pulse. Approach. Calculations were performed for an idealized parallel plate chamber with 2 mm electrode separationd, and for an idealized cylindrical chamber with 0.5 and 2.333 mm inner and electrode radiirinandrout. Main results. fGaussandfexppredict the same collection efficiencies for cylindrical and parallel plate chambers satisfyingd2=(rout2-rin2)ln(rout/rin)/2, an equivalence condition met by the chambers studied. Without charge screening, efficiencies computed using the code equalledfGaussandfexp. With screening, efficiencies changed by ⩽0.03%, ⩽1.1% and ⩽21.3% at 1, 10 and 100 mGy doses-per-pulse, and differed between the chambers by ⩽0.9% and ⩽19.6% at ⩽10 and 100 mGy dose-per-pulse. For fits offexpandfGauss,CE∞values were ⩽1.2% and ⩽17.6% from unity at 10 and 100 mGy per pulse respectively, closer than for other formulae tested. Significance. Allowing for screening,fGaussandfexpdescribed computed collection efficiencies to within 0.03%, 1.1% and 21.3% at doses-per-pulse ⩽1, 10 and 100 mGy. Equivalence of the two chambers broke down at 100 mGy per pulse. Departures ofCE∞values from unity suggest that collection efficiencies determined experimentally by fittingfGaussorfexpto readings made at multiple voltages will be accurate to within 1.2% and 17.6% at 10 and 100 mGy per pulse respectively.
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