Collection efficiencies of cylindrical and plane parallel ionization chambers: analytical and numerical results and...

Objectives.To derive a collection efficiency formula,fGauss, for cylindrical ionization chambers in pulsed radiation beams from a volume recombination model of Boaget al(1996Phys. Med. Biol.41885-97) 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.