Ionization-Chamber Dosimetry: Charge, W and Bragg-Gray

An ionization-chamber dosimetry playground. Photons Compton-scatter in the cavity gas (Klein-Nishina recoil sampling); the recoil electrons ionize the gas at one ion pair per $W = 33.97 \, \mathrm{eV}$; the pairs drift to the electrodes, where the Boag collection efficiency $f = 1/(1 + \xi^2/6)$ ($\xi$ proportional to $d^2 \sqrt{\mathrm{dose\ rate}}/V$) reduces the collected charge by recombination at low voltage and saturates to one at high voltage. The cavity dose is $D = (Q/m)(W/e)$ and the medium dose follows from the Bragg-Gray stopping-power ratio. Panel A shows the cavity with recoil electrons and drifting ion pairs (some recombining), Panel B the saturation curve, Panel C the full charge-to-dose chain. The cavity dose $D = (Q/m)(W/e)$ is linear in collected charge and in $W$ and inverse in mass, the Bragg-Gray ratio carries it to the medium, and the Boag efficiency saturates to full collection at high voltage.