Author: Julien Bancheri, Jan P. Seuntjens 👨🔬
Affiliation: Medical Biophysics, University of Toronto, Princess Margaret Cancer Centre & University of Toronto 🌍
Purpose: To obtain an analytical expression for the charge collection efficiency of parallel-plate ionization chambers in high dose-per-pulse (DPP) beams that takes into account the square pulse time structure, space charge and the free electron collection. Such an expression has not yet been put forward in the literature but is critical for accurate dose measurements in high DPP beams, which are increasingly used in radiotherapy clinics.
Methods: Perturbation theory is employed with the partial differential equations (PDEs) that describe the drift-diffusion of the positive ion, negative ion and free electron concentrations. Positive ion - negative ion recombination, free electron attachment and space charge are considered. The variation of the electron attachment rate and electron velocity with electric field strength is also explicitly modelled in this method. The square pulse time structure is incorporated by solving the PDEs during and after the pulse. A series solution is obtained for the collection efficiency.
Results: In comparison to previously published experimental data, the resulting analytical expression is accurate up to 760 mGy DPP for a 1 mm and 0.5 mm plate separation at voltages of 300 V - 500 V. For a plate separation of 2 mm, the expression is accurate to 180 mGy DPP. The derived expression is also more accurate at DPPs above 100 mGy DPP in comparison to other current theories.
Conclusion: This work enables the determination of an analytical expression for the charge collection efficiency in high DPP beams. In comparison to previously published solution methods, this expression does not include any fit parameters. All constants considered in this method are either physical constants or determined by the chamber design and beam. In future work, the expression derived in this work will be used to develop a method to determine the ion recombination correction factor in a clinical setting.