^{1,a)}, M. R. McEwen

^{2,b)}and D. W. O. Rogers

^{3,c)}

### Abstract

**Purpose:**

To investigate the behavior of plane-parallel ion chambers in high-energy photon beams through measurements and Monte Carlo simulations.

**Methods:**

Ten plane-parallel ion chamber types were obtained from the major ion chamber manufacturers. Absorbed dose-to-water calibration coefficients are measured for these chambers and factors are determined. In the process, the behaviors of the chambers are characterized through measurements of leakage currents, chamber settling in cobalt-60, polarity and ion recombination behavior, and long-term stability. Monte Carlo calculations of the absorbed dose to the air in the ion chamber and absorbed dose to water are obtained to calculate factors. Systematic uncertainties in Monte Carlo calculated factors are investigated by varying material properties and chamber dimensions.

**Results:**

Chamber behavior was variable in MV photon beams, especially with regard to chamber leakage and ion recombination. The plane-parallel chambers did not perform as well as cylindrical chambers. Significant differences up to 1.5% were observed in calibration coefficients after a period of eight months although factors were consistent on average within 0.17%. Chamber-to-chamber variations in factors for chambers of the same type were at the 0.2% level. Systematic uncertainties in Monte Carlo calculated factors ranged between 0.34% and 0.50% depending on the chamber type. Average percent differences between measured and calculated factors were − 0.02%, 0.18%, and − 0.16% for 6, 10, and 25 MV beams, respectively.

**Conclusions:**

Excellent agreement is observed on average at the 0.2% level between measured and Monte Carlo calculated factors. Measurements indicate that the behavior of these chambers is not adequate for their use for reference dosimetry of high-energy photon beams without a more extensive QA program than currently used for cylindrical reference-class ion chambers.

The authors thank Igor Gomola and Frantisek Gabris of IBA, Mark Szczepanski and Christian Pychlau of PTW, and Eric DeWerd and Brian Hooten of Standard Imaging for supplying the chambers and chamber drawings used for this work. The authors thank Ben Spencer of Carleton University for assistance imaging the ion chambers. Work was supported by an OGSST held by B.R. Muir, by NSERC, the CRC program, CFI, and OIT.

I. INTRODUCTION

II. METHODS

II.A. Measurements: Chamber performance and factors

II.B. Monte Carlo calculations: factors and uncertainties

III. RESULTS AND DISCUSSION

III.A. Chamber stabilization

III.B. Leakage currents

III.C. Polarity correction

III.D. Ion recombination

III.D.1. Ion recombination in pulsed beams

III.D.2. Comparison with literature values

III.D.3. Ion recombination in cobalt-60

III.E. Measured and calculated factors

III.F. Chamber-to-chamber variation of measured factors

III.G. Long-term stability

III.H. Systematic uncertainties in calculated factors

III.I. Comparison of measured and calculated values

IV. CONCLUSIONS

### Key Topics

- Calibration
- 50.0
- Ionization chambers
- 30.0
- Photons
- 28.0
- Error analysis
- 14.0
- Electric measurements
- 13.0

## Figures

The IBA NACP-02 geometry. Figure 1(a) is the Monte Carlo model of the chamber while Fig. 1(b) is a radiograph of the chamber taken for aid with modeling and to ensure no significant differences between design and manufacture. Major components of the ion chamber are labeled in the radiograph of Fig. 1(b).

The IBA NACP-02 geometry. Figure 1(a) is the Monte Carlo model of the chamber while Fig. 1(b) is a radiograph of the chamber taken for aid with modeling and to ensure no significant differences between design and manufacture. Major components of the ion chamber are labeled in the radiograph of Fig. 1(b).

Ion recombination correction factors as a function of dose per pulse for all chamber types collecting positive charge at an operating voltage of 100 V. Linear fits to the data are shown by lines. Most chambers use a plate separation of 2 mm and have very similar gradients in this figure except for the Exradin P11TW (3 mm), the PTW Advanced Markus (1 mm) and the IBA PPC-05 (0.5 mm). In cases where more than one chamber of each type was investigated, a chamber is used that is representative of the chamber type. Error bars representing systematic uncertainties are shown for the Roos chamber.

Ion recombination correction factors as a function of dose per pulse for all chamber types collecting positive charge at an operating voltage of 100 V. Linear fits to the data are shown by lines. Most chambers use a plate separation of 2 mm and have very similar gradients in this figure except for the Exradin P11TW (3 mm), the PTW Advanced Markus (1 mm) and the IBA PPC-05 (0.5 mm). In cases where more than one chamber of each type was investigated, a chamber is used that is representative of the chamber type. Error bars representing systematic uncertainties are shown for the Roos chamber.

Ion recombination correction factors as a function of dose per pulse showing the difference in recombination behavior depending on the polarity of the charge collected for some chambers. Solid symbols (solid lines) are data (linear fits) obtained when positive charge is collected while open symbols (dashed lines) are for negative charge collection. Error bars representing the systematic uncertainty in values are shown for the IBA NACP-02 chamber. Values of at Gy are obtained in cobalt-60 but are not used for the linear fits.

Ion recombination correction factors as a function of dose per pulse showing the difference in recombination behavior depending on the polarity of the charge collected for some chambers. Solid symbols (solid lines) are data (linear fits) obtained when positive charge is collected while open symbols (dashed lines) are for negative charge collection. Error bars representing the systematic uncertainty in values are shown for the IBA NACP-02 chamber. Values of at Gy are obtained in cobalt-60 but are not used for the linear fits.

Beam quality conversion factors with comparison to literature values and Monte Carlo calculations for the subset of chambers for which literature values are available. Filled symbols are calculated factors with a fit [Eq. (5)] to the values shown by the lightly colored line. Present measurements, shifted so that the inside of the chamber window is at the measurement depth and corrected for recombination in cobalt-60, are open circles with error bars representing combined systematic uncertainties. Measured literature values are shown by open squares, connected with straight lines. The dashed lines represent our measurements modified for comparison to literature values as described in the text. In the upper two panels, values are compared to measurements from McEwen *et al.* (Ref. 1). In the lower two panels, values are compared to factors measured by Kapsch and Gomola (Ref. 2).

Beam quality conversion factors with comparison to literature values and Monte Carlo calculations for the subset of chambers for which literature values are available. Filled symbols are calculated factors with a fit [Eq. (5)] to the values shown by the lightly colored line. Present measurements, shifted so that the inside of the chamber window is at the measurement depth and corrected for recombination in cobalt-60, are open circles with error bars representing combined systematic uncertainties. Measured literature values are shown by open squares, connected with straight lines. The dashed lines represent our measurements modified for comparison to literature values as described in the text. In the upper two panels, values are compared to measurements from McEwen *et al.* (Ref. 1). In the lower two panels, values are compared to factors measured by Kapsch and Gomola (Ref. 2).

Radiographs of Exradin A11 chambers showing major differences in body construction. Figure 1(a) is the older chamber model (S/N 145) which is no longer available for purchase while Fig. 1(b) shows the new chamber (S/N 81624) which is currently available from Standard Imaging.

Radiographs of Exradin A11 chambers showing major differences in body construction. Figure 1(a) is the older chamber model (S/N 145) which is no longer available for purchase while Fig. 1(b) shows the new chamber (S/N 81624) which is currently available from Standard Imaging.

Histograms showing the percent difference between measured and calculated factors for the 6, 10, and 25 MV beams.

Histograms showing the percent difference between measured and calculated factors for the 6, 10, and 25 MV beams.

## Tables

Combined uncertainty in measured coefficients and factors for plane-parallel ion chambers.

Combined uncertainty in measured coefficients and factors for plane-parallel ion chambers.

Major dimensions and materials for the plane-parallel ion chambers investigated. The radius of the active region of the chamber is indicated with the total radius (active and guard region) in parentheses. Unless otherwise indicated, the density of graphite used for the Monte Carlo calculations is 1.7 g/cm^{3}. Materials are MYLAR, graphite (Gr), rexolite (cross-linked polystyrene, Rex), polyetheretherketone (PEEK), air-equivalent plastic (C552), polyoxymethylene (POM, trade name Delrin), polystyrene-equivalent plastic (D400), Kapton, and polyethylene (PE). The abbreviation Gr’d refers to a graphited material where a thin layer of graphite is applied to the material in question. Chambers indicated by an asterisk require a water-proofing cap.

Major dimensions and materials for the plane-parallel ion chambers investigated. The radius of the active region of the chamber is indicated with the total radius (active and guard region) in parentheses. Unless otherwise indicated, the density of graphite used for the Monte Carlo calculations is 1.7 g/cm^{3}. Materials are MYLAR, graphite (Gr), rexolite (cross-linked polystyrene, Rex), polyetheretherketone (PEEK), air-equivalent plastic (C552), polyoxymethylene (POM, trade name Delrin), polystyrene-equivalent plastic (D400), Kapton, and polyethylene (PE). The abbreviation Gr’d refers to a graphited material where a thin layer of graphite is applied to the material in question. Chambers indicated by an asterisk require a water-proofing cap.

Measured polarity corrections in linac beams and standard deviation.

Measured polarity corrections in linac beams and standard deviation.

Measured recombination parameters with comparison to literature values. Uncertainties on and are estimated to be 17% and 8%, respectively.

Measured recombination parameters with comparison to literature values. Uncertainties on and are estimated to be 17% and 8%, respectively.

Fitting parameters for Eq. (5) for in terms of %*dd*(10)_{ x } and the rms deviation of the calculated data to the fit. The fit is valid for values of %*dd*(10)_{ x } between 62.7% and 86.1%.

Fitting parameters for Eq. (5) for in terms of %*dd*(10)_{ x } and the rms deviation of the calculated data to the fit. The fit is valid for values of %*dd*(10)_{ x } between 62.7% and 86.1%.

Measured factors and percent difference between measured and calculated factors. These measured values are those shifted for comparison to Monte Carlo values such that the inside of the front face of the chamber is at the reference depth. Combined uncertainties on measured factors are 0.4%.

Measured factors and percent difference between measured and calculated factors. These measured values are those shifted for comparison to Monte Carlo values such that the inside of the front face of the chamber is at the reference depth. Combined uncertainties on measured factors are 0.4%.

Sample uncertainty budget for Monte Carlo calculated factors for the IBA NACP-02 chamber. Photon cross-sections are assumed to be correlated and contribute a negligible component to the uncertainty in calculated factors.

Sample uncertainty budget for Monte Carlo calculated factors for the IBA NACP-02 chamber. Photon cross-sections are assumed to be correlated and contribute a negligible component to the uncertainty in calculated factors.

Combined uncertainty in Monte Carlo calculated factors. Uncertainty in calculated factors from possible variation in W/e is assumed to be 0.25% as estimated in Sec. III I.

Combined uncertainty in Monte Carlo calculated factors. Uncertainty in calculated factors from possible variation in W/e is assumed to be 0.25% as estimated in Sec. III I.

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