Impact of space charges on the saturation curves of ionization chambers

Chabod, S.

doi:10.1016/j.nima.2009.01.018

Cited by 10 publications

(17 citation statements)

References 10 publications

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“…Note also that, as we demonstrated in [6], the perturbations induced by space charges on the calibration curves can be neglected only when the Langevin factor, , of the filling gas is close to 1. Consequently, if (9) overestimates , then it follows that the space charges must be accounted for in fission chambers operated in current mode, thus, justifying the introduction of the Maxwell-Gauss equation in (2).…”

Section: B Modeling Parametersmentioning

confidence: 64%

“…The parameters involved in the integral satisfy a system of nonlinear differential equations [6] (2)…”

Section: A Key Equationsmentioning

confidence: 99%

“…Using (1) and (5), we obtain the saturation current, , of the detector, given in [8], [10], and [11] when (6) where the function is the complete elliptic integral of the second kind [9].…”

Section: B Modeling Parametersmentioning

confidence: 99%

“…It obeys the equation ). Using formulae (3.19) and (3.20) of [5] and results of [6], can be approached by (12) Coefficients and are the electronic and ionic Langevin factors of the filling gas, introduced in [6]. The factor represents the impact of the space charges on the current delivered by the detector.…”

Section: B Lower Limit Of the Saturation Regimementioning

confidence: 99%

“…The factor represents the impact of the space charges on the current delivered by the detector. Values of are listed in [6].…”

Section: B Lower Limit Of the Saturation Regimementioning

confidence: 99%

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Improvements in the Modeling of Sub-Miniature Fission Chambers Operated in Current Mode

Chabod

Letourneau

Gourdon

et al. 2010

IEEE Trans. Nucl. Sci.

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We review the theoretical basis necessary to model sub-miniature fission chambers operated in current mode. For these detectors, we propose formulae for the lower and upper limits of the saturation zone, obtained through analytical and numerical solutions of the charge transport equations. Using these results, we calculate the voltage width of the saturation plateau, as a function of parameters such as the electrode geometries or the characteristics of the filling gas.

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Section: B Modeling Parametersmentioning

confidence: 64%

“…The parameters involved in the integral satisfy a system of nonlinear differential equations [6] (2)…”

Section: A Key Equationsmentioning

confidence: 99%

“…Using (1) and (5), we obtain the saturation current, , of the detector, given in [8], [10], and [11] when (6) where the function is the complete elliptic integral of the second kind [9].…”

Section: B Modeling Parametersmentioning

confidence: 99%

Section: B Lower Limit Of the Saturation Regimementioning

confidence: 99%

“…The factor represents the impact of the space charges on the current delivered by the detector. Values of are listed in [6].…”

Section: B Lower Limit Of the Saturation Regimementioning

confidence: 99%

See 3 more Smart Citations

Improvements in the Modeling of Sub-Miniature Fission Chambers Operated in Current Mode

Chabod

Letourneau

Gourdon

et al. 2010

IEEE Trans. Nucl. Sci.

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A semi‐analytical procedure to determine the ion recombination correction factor in high dose‐per‐pulse beams

Bancheri,

Seuntjens

2024

Medical Physics

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BackgroundThe conventional theories and methods of determining the ion recombination correction factor, such as Boag theory and the related two voltage method and Jaffé plot extrapolation, do not seem to yield accurate results in FLASH /high dose per pulse (DPP) beams (10 mGy DPP). This is due to the presence of a large free electron fraction that distorts the electric field inside the chamber sensitive volume. To understand the influence of these effects on the ion recombination correction factor and to develop new expressions for it, it is necessary to re‐visit the underlying physics.PurposeTo present a mathematical procedure to develop an analytical expression for the ion recombination correction factor. The expression is the basis for an extrapolation method so the correction factor can be determined in a clinical setting.MethodsA semi‐analytical solution method, the homotopy perturbation method (HPM), is used to solve the partial differential equations (PDEs) describing the charge carrier physics, including space charge and free electrons. The electron velocity and attachment rate are modeled as functions of the electric field strength. An expression for the charge collection efficiency and ion recombination correction factor are developed. A fit procedure based on this expression is used to compare it to measured data from previously published articles. Another fit procedure using a general equation is also proposed and compared to the data.ResultsThe series obtained for the charge collection efficiency and the ion recombination correction factor are determined to be asymptotic series and the optimal truncation established. The ion recombination correction factor exhibits a dependency due to the free electron presence. The fit using this expression agrees well with measured data as long as (1) the DPP is below 1 Gy for chambers with a 1 mm plate separation and (2) when the DPP is below 3 Gy for chambers with a 0.5 mm plate separation. In these DPP ranges, the deviation between measured and fit value did not exceed 6%. In both chamber cases the voltage range where the fit applies decreases as DPP increases. The general equation yielded comparable results.ConclusionsThe HPM was shown to be applicable to a complex system of PDEs and generate meaningful and novel solutions, as they include both space charge and free electrons. The HPM also lends itself to other chamber geometries. The fit procedure was also shown to yield accurate results for the ion recombination correction up to the 1 Gy DPP level.

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On the empirical success of Boag’s box model in describing cluster and columnar recombination

Chabod

2010

Nuclear Instruments and Methods in Physics Research Section A:

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Impact of space charges on the saturation curves of ionization chambers

Cited by 10 publications

References 10 publications

Improvements in the Modeling of Sub-Miniature Fission Chambers Operated in Current Mode

Improvements in the Modeling of Sub-Miniature Fission Chambers Operated in Current Mode

A semi‐analytical procedure to determine the ion recombination correction factor in high dose‐per‐pulse beams

On the empirical success of Boag’s box model in describing cluster and columnar recombination

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