A perturbation method to examine the steady-state charge transport in the recombination and saturation regimes of ionization chambers

Chabod, S.

doi:10.1016/j.nima.2008.07.115

Cited by 14 publications

(15 citation statements)

References 10 publications

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“…Apart from the least-squares fitting based on the exact solution of the Thomson problem, experimental data was also fitted using the Boag-Wilson formula [4], which is the first order approximation to the exact solution [19] and yields a estimate of the saturation current that will be referred as I ð0Þ sat . In this case, some care must be taken, since the fitting is expected to yield reliable values if only points satisfying the condition I=I sat 4 95% are taken into account.…”

Section: Resultsmentioning

confidence: 99%

“…From Eq. (6) and the expression relating N and I sat , N ¼ I sat =eV eff , the k=μ e ratio may be expressed as…”

Section: Resultsmentioning

confidence: 99%

“…The spacial distribution of electrons, for instance, is given by the following formula, which will be useful later when computing the space charge effects [6] n e ðxÞ ¼ kI ÀK tan ðK=2eSν e ν a Þðx þ CÞ…”

Section: The Thomson Problemmentioning

confidence: 99%

“…No additional assumption is made as (5) may be derived only by simplification and rearrangement of the expression of the electron spacial distribution [6]. As it will be shown later, expression (5) may be set as the model function in the least squares procedure.…”

Section: The Thomson Problemmentioning

confidence: 99%

“…FðI; ΔVÞ ¼ 0), which makes the procedure of data fitting by the least squares method infeasible. Recently, Chabod [6] found a way to write ΔV explicitly as a function of I (i.e. ΔV ¼ f ðIÞ).…”

Section: Introductionmentioning

confidence: 99%

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On the interpretation of current–voltage curves in ionization chambers using the exact solution of the Thomson problem

Ridenti

Pascholati

Gonçalves

et al. 2015

Nuclear Instruments and Methods in Physics Research Section A:

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a b s t r a c tThe I À ΔV characteristic curve of a well type ionization chamber irradiated with 192 Ir sources (0.75 Ci-120 Ci) was fitted using the exact solution of the Thomson problem. The recombination coefficient and saturation current were estimated using this new approach. The saturation current was compared with the results of the conventional method based on Boag-Wilson formula. It was verified that differences larger than 1% between both methods only occurred at activities higher than 55 Ci. We concluded that this new approach is recommended for a more accurate estimate of the saturation current when it is not possible to measure currents satisfying the condition I=I sat 4 0:95. From the calibration curve the average value of pairs of carriers created per unit volume was estimated to be equal to η ¼ 8:1 Â 10 À 3 cm À 3 s À 1 Bq À 1 and from that value it was estimated that $ 17 pairs were created on average per second for each decay of the source.

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Section: Resultsmentioning

confidence: 99%

“…From Eq. (6) and the expression relating N and I sat , N ¼ I sat =eV eff , the k=μ e ratio may be expressed as…”

Section: Resultsmentioning

confidence: 99%

Section: The Thomson Problemmentioning

confidence: 99%

Section: The Thomson Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the interpretation of current–voltage curves in ionization chambers using the exact solution of the Thomson problem

Ridenti

Pascholati

Gonçalves

et al. 2015

Nuclear Instruments and Methods in Physics Research Section A:

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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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Impact of space charges on the saturation curves of ionization chambers

Chabod

2009

Nuclear Instruments and Methods in Physics Research Section A:

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A perturbation method to examine the steady-state charge transport in the recombination and saturation regimes of ionization chambers

Cited by 14 publications

References 10 publications

On the interpretation of current–voltage curves in ionization chambers using the exact solution of the Thomson problem

On the interpretation of current–voltage curves in ionization chambers using the exact solution of the Thomson problem

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

Impact of space charges on the saturation curves of ionization chambers

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