Evaluation of the two-voltage method for parallel-plate ionization chambers irradiated with pulsed beams

Air-vented ionization chambers exposed to clinical radiation beams may suffer from recombination during the drift of the charge carriers towards the electrodes. Thus, dosimetry protocols recommend the use of a correction factor, usually denominated saturation factor ( $k_{\mathrm{sat}}$ ), to correct the ionization chamber readout for the incomplete collection of charge. The two-voltage method (TVM) is the recommended methodology for the calculation of the saturation factor, however, it is based on the early Boag model, which only takes into account the presence of positive and negative ions in the ionization chamber and does not account for the electric field screening or the free electron contribution to the signal.

To evaluate the impact of a more realistic approach to the saturation problem that accounts for the free electron fraction.

The saturation factor of four ionization chambers (two Advanced Markus and two PPC05) was experimentally determined in the ultra-high dose per pulse reference beam of the German National Metrology Institute (Physikalisch-Technische Bundesanstalt [PTB]) for voltages ranging from 50 to 400 V and pulse durations between 0.5 and 2.9  $\mu s$ . Several analytical models and a recently developed numerical model are used to calculate the saturation factor as a function of the dose per pulse and compare it to the obtained experimental data. Parameterizations of the saturation factor against the ratio of charges at different voltages are given for parallel plate ionization chamber with a distance between electrodes of 0.6 and 1 mm in pulsed beams for different pulse durations.

The saturation factors calculated using the different Boag analytical models do not agree neither with each other nor with the numerical simulation even at the lowest dose per pulse of the investigated range (  30 mGy). A recently developed analytical model by Fenwick and Kumar agrees with the numerical simulation in the low dose per pulse regime but discrepancies are observed when the dose becomes larger (i.e., $>$  40 mGy for Advanced Markus) due to the electric field perturbation. The numerical simulation is in a good agreement with the experimentally determined charge collection efficiency (CCE) with an average discrepancy of 0.7% for the two PPC05 and 0.5% for the two Advanced Markus. The saturation factor obtained with the numerical simulation of the collected charge has been fitted to a third-order polynomial for different voltage ratios and pulse duration. This methodology provides a practical way for $k_{\mathrm{sat}}$ evaluation whenever .

The numerical simulation shows a better agreement with the experimental data than the current analytical theories in terms of CCE. The classical TVM, systematically overestimates the saturation factor, with differences increasing with dose per pulse but also present at low dose per pulse. These results may have implications for the dosimetry with ionization chambers in therapy modalities that use a dose per pulse higher than conventional radiotherapy such as intraoperative radiotherapy but also in conventional dose per pulse for ionization chambers that suffer from significant charge recombination.