Derivation of a formula describing the saturation correction of plane-parallel ionization chambers in pulsed fields with arbitrary repetition rate

Abstract

Gas-filled ionization chambers are widely used radiation detectors in radiotherapy. A quantitative description and correction of the recombination effects exists for two cases, for continuous radiation exposure and for pulsed radiation fields with short single pulses. This work gives a derivation of a formula for pulsed beams with arbitrary pulse rate for which the prerequisites of the two existing descriptions are not fulfilled. Furthermore, an extension of the validity of the two known cases is investigated. The temporal evolution of idealized charge density distributions within a plane parallel chamber volume is described for pulsed beams of vanishing pulse duration and arbitrary pulse repetition rate. First, the radiation induced release, movement and collection of the charge carriers without recombination are considered. Then, charge recombination is calculated basing on these simplified charge distributions and the time dependent spatial overlap of positive and negative charge carrier distributions. Finally, a formula for the calculation of the saturation correction factor is derived by calculation and simplification of the first two terms of a Taylor expansion for small recombination. The new formula of saturation correction contains the two existing cases, descriptions for exposure by single pulses and continuous irradiation, as limiting cases. Furthermore, it is possible to determine the pulse rate range for which each of the three descriptions is applicable by comparing the dependencies of the new formula with the two existing cases. As long as the time between two pulses is lower than one third of the collection time of the chamber, the formalism for a continuous exposure can be used. The known description for single pulse irradiation is only valid if the repetition rate is less than 1.2 times the inverse collection time. For all other repetition rates in between the new formula should be used. The experimental determination by Jaffe diagrams can be applied for all repetition rates which are not single pulse irradiation but will result in a small deviation from the correct saturation correction value.

Feasibility of proton FLASH effect tested by zebrafish embryo irradiation

“…Both chambers were crosscalibrated against a capped Markus IC (M-IC, model 34045, PTW; cap: plastic, 1 mm water equivalent thickness) and EBT3 films at sample position. Recombination inside the ICs can be treated with the formalism of continuous irradiation [11], since the pulse duration (>100 ms) is much longer than the IC collection time ($10 ms). For the M-IC (electrode distance of 1 mm, applied voltage of 300 V) used for absolute dosimetry the recombination correction is according to the chamber data sheet 0.5% at a dose rate of 200 Gy/s and is therefore less and negligible for the mean dose rate of max.…”

Ion collection efficiency of ionization chambers in ultra‐high dose‐per‐pulse electron beams

“…The approach presented included improvements to the numerical solution first presented by Karsch. 16 Gotz et al 15 demonstrated that none of the Boags's models could provide good agreement with data experimentally determined with the Advanced Markus chamber for chamber voltages > 100 V in the range of ultra-high DPP values (up to 1 Gy/pulse). Their results agree to a more recent study conducted by Petersson et al, 17 who have also investigated the Advanced Markus ionization chamber from high to ultra-high DPP electron beam range (10 mGy/pulse -10 Gy/pulse).…”

“…Gotz et al 15 have proposed a numerical solution to account for the ion collection efficiency of plane‐parallel ion chambers due to volume recombination taking into account the space charge effect when irradiated with high DPP beams. The approach presented included improvements to the numerical solution first presented by Karsch 16 . Gotz et al 15 demonstrated that none of the Boags’s models could provide good agreement with data experimentally determined with the Advanced Markus chamber for chamber voltages > 100 V in the range of ultra‐high DPP values (up to 1 Gy/pulse).…”

Ion recombination and polarity correction factors for a plane–parallel ionization chamber in a proton scanning beam

“…Notably, there has recently been an increased interest in studying ion recombination effects in ionization chambers exposed to beams of protons or heavier ions. At the time of this work, several new publications devoted to ion recombination correction in ionization chambers have appeared in the literature …”

“…At the time of this work, several new publications devoted to ion recombination correction in ionization chambers have appeared in the literature. [21][22][23][24][25][26] In the case of an active scanning beam, the dose rate in single proton pencil beams may be much higher than that in clinical photon and electron beams, or that observed in typical continuous dose rate proton beams used in ocular radiotherapy (0.43 Gy/s). 19 Since a single beamlet can within a few milliseconds deposit a dose of 2 Gy over its Bragg peak region, the maximum local dose rate may exceed hundreds of Gy/s.…”