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PURPOSE: The purpose of this work was to establish an empirical model of the ion recombination in the Advanced Markus ionization chamber for measurements in high dose rate/dose-per-pulse electron beams. In addition, we compared the observed ion recombination to calculations using the standard Boag two-voltage-analysis method, the more general theoretical Boag models, and the semiempirical general equation presented by Burns and McEwen. METHODS: Two independent methods were used to investigate the ion recombination: (a) Varying the grid tension of the linear accelerator (linac) gun (controls the linac output) and measuring the relative effect the grid tension has on the chamber response at different source-to-surface distances (SSD). (b) Performing simultaneous dose measurements and comparing the dose-response, in beams with varying dose rate/dose-per-pulse, with the chamber together with dose rate/dose-per-pulse independent Gafchromic™ EBT3 film. Three individual Advanced Markus chambers were used for the measurements with both methods. All measurements were performed in electron beams with varying mean dose rate, dose rate within pulse, and dose-per-pulse (10-2  ≤ mean dose rate ≤ 103 Gy/s, 102  ≤ mean dose rate within pulse ≤ 107  Gy/s, 10-4  ≤ dose-per-pulse ≤ 101  Gy), which was achieved by independently varying the linac gun grid tension, and the SSD. RESULTS: The results demonstrate how the ion collection efficiency of the chamber decreased as the dose-per-pulse increased, and that the ion recombination was dependent on the dose-per-pulse rather than the dose rate, a behavior predicted by Boag theory. The general theoretical Boag models agreed well with the data over the entire investigated dose-per-pulse range, but only for a low polarizing chamber voltage (50 V). However, the two-voltage-analysis method and the Burns & McEwen equation only agreed with the data at low dose-per-pulse values (≤ 10-2 and ≤ 10-1  Gy, respectively). An empirical model of the ion recombination in the chamber was found by fitting a logistic function to the data. CONCLUSIONS: The ion collection efficiency of the Advanced Markus ionization chamber decreases for measurements in electron beams with increasingly higher dose-per-pulse. However, this chamber is still functional for dose measurements in beams with dose-per-pulse values up toward and above 10 Gy, if the ion recombination is taken into account. Our results show that existing models give a less-than-accurate description of the observed ion recombination. This motivates the use of the presented empirical model for measurements with the Advanced Markus chamber in high dose-per-pulse electron beams, as it enables accurate absorbed dose measurements (uncertainty estimation: 2.8-4.0%, k = 1). The model depends on the dose-per-pulse in the beam, and it is also influenced by the polarizing chamber voltage, with increasing ion recombination with a lowering of the voltage.

Original publication




Journal article


Med Phys

Publication Date





1157 - 1167


flash, high dose rate, ion recombination, ionization chamber, Electrons, Models, Theoretical, Phantoms, Imaging, Radiation Equipment and Supplies, Radiometry, Water