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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.

Figure 1. Photons Compton-scatter in the cavity gas; the recoil electrons create ion pairs at one pair per W = 33.97 eV; the pairs drift to the electrodes under the collecting voltage, where recombination at low voltage reduces the collected charge (the Boag saturation curve). The dose follows from D = (Q/m)(W/e), converted to medium dose by the Bragg-Gray stopping-power ratio. Method: seeded Monte Carlo recoil sampling plus the Boag and Bragg-Gray relations; Canvas2D, deterministic.
photon energy (keV)100
collecting voltage (V)300
dose rate (rel.)1

WHAT TO TRY

  • Raise the collecting voltage: the Boag efficiency f = 1/(1 + xi^2/6) climbs toward 1 along the saturation curve as fewer ion pairs recombine before reaching the electrodes.
  • Raise the dose rate: recombination losses grow (xi scales with sqrt(dose rate)), so the same chamber under-collects more at high intensity and needs a higher voltage to saturate.
  • Follow the charge-to-dose chain: energy deposited divided by W gives ion pairs, times electron charge gives collected charge, times the Bragg-Gray stopping-power ratio gives the dose to medium.