Initial recombination in the track of heavy charged particles: numerical solution for air filled ionization chambers

Acta Oncol. 2012 Mar;51(3):368-75. doi: 10.3109/0284186X.2011.626452. Epub 2011 Nov 2.


Introduction: Modern particle therapy facilities enable sub-millimeter precision in dose deposition. Here, also ionization chambers (ICs) are used, which requires knowledge of the recombination effects. Up to now, recombination is corrected using phenomenological approaches for practical reasons. In this study the effect of the underlying dose distribution on columnar recombination, a quantitative model for initial recombination, is investigated.

Material and methods: Jaffé's theory, formulated in 1913 quantifies initial recombination by elemental processes, providing an analytical (closed) solution. Here, we investigate the effect of the underlying charged carrier distribution around a carbon ion track. The fundamental partial differential equation, formulated by Jaffé, is solved numerically taking into account more realistic charge carrier distributions by the use of a computer program (Gascoigne 3D). The investigated charge carrier distributions are based on track structure models, which follow a 1/r(2) behavior at larger radii and show a constant value at small radii. The results of the calculations are compared to the initial formulation and to data obtained in experiments using carbon ion beams.

Results: The comparison between the experimental data and the calculations shows that the initial approach made by Jaffé is able to reproduce the effects of initial recombination. The amorphous track structure based charge carrier distribution does not reproduce the experimental data well. A small additional correction in the assessment of the saturation current or charge is suggested by the data.

Conclusion: The established model of columnar recombination reproduces the experimental data well, whereas the extensions using track structure models do not show such an agreement. Additionally, the effect of initial recombination on the saturation curve (i.e. Jaffé plot) does not follow a linear behavior as suggested by current dosimetry protocols, therefore higher order corrections (such as the investigated ones) might be necessary.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Air Ionization*
  • Carbon / chemistry*
  • Heavy Ions*
  • Humans
  • Models, Theoretical*
  • Radiometry / instrumentation*
  • Radiotherapy Dosage
  • Radiotherapy, High-Energy / instrumentation*


  • Carbon