Derivation of formulas to calculate the saturation correction of ionization chambers in pulsed beams of short, nonvanishing pulse durations.

Purpose: Gas-filled ionization chambers are the most important radiation detectors in radiotherapy. The collected charge at the electrodes does not represent the total released charge due to the unavoidable recombination processes. This needs to be considered for precise dose measurements. A quantitative description and correction of the recombination effects is established for two cases: continuous radiation exposure and pulsed radiation fields of single pulses with vanishing pulse duration. This work derives formulas for calculating the saturation correction for pulsed beams of nonvanishing pulse duration.

Methods: Recursive formulas are derived describing the spatio-temporal development of the charge density distributions in plane-parallel ionization chambers starting at neglected recombination. Pulse duration dependent effective chamber parameters are calculated, by comparing the coefficients of a series expansion for small recombination effects. These parameters are used afterward in the known formula for the saturation correction factor for pulsed irradiation with increased recombination effects which was established with the assumption of vanishing pulse duration.

Results: The formulas should be valid for pulse durations shorter than half the collection time of the chamber. They allow calculating the saturation correction factor for pulsed beams of nonvanishing pulse duration and arbitrary pulse dose, if chamber, beam, and filling gas parameters are known. The filling gas parameters could be determined from experimental data. The calculation results are in good agreement with already published experimental and simulated results for a Roos chamber.

Conclusions: The new formulas can be applied to determine the expected saturation correction for pulsed beams of different pulse duration and pulse dose including new beams at accelerators of new technologies. More experimental validation by using other chambers and an extension of the new formalism to pulse durations longer than half the collection time of the chamber is desired.