^{1,a)}, Malcolm McEwen

^{2}and D. W. O. Rogers

^{3,b)}

### Abstract

For ion chambers with cavities open to the surrounding atmosphere, the response measured at a given temperature and pressure must be corrected using the standard temperature-pressure correction factor . A previous paper based solely on Monte Carlo simulations [D. J. La Russa and D. W. O. Rogers, Med. Phys.33, 4590–4599 (2006)] pointed out the shortcomings of the correction factor when used to correct the response of non-air-equivalent chambers for low-energy x-ray beams. This work presents the results of several experiments that corroborate these calculations for a number of ion chambers.Monte Carlo simulations of the experimental setup revealed additional insight into the various factors affecting the extent of the breakdown of , including the effect of impurities and the sensitivity to chamber dimensions. For an unfiltered 60 kV beam, the -corrected response of an NE 2571 ion chamber measured at 0.7 atm was below the response measured at reference conditions. In general, Monte Carlo simulations of the experimental setup using EGSnrc were within of measured values. EGSnrc-calculated values of air kerma calibration coefficients at low x-ray energies are also provided as a means of estimating the level of impurities in the chambers investigated. Calculated values of normalized to the value measured for a 250 kV beam were obtained for three chambers and were within of experiment with one exception, the Exradin A12 in a 50 kV beam.

The authors wish to thank J.E. Burns for alerting us to earlier experimental results, and Steve Davis for pointing out our use of the wrong value of in our previous paper. The authors would also like to thank Vincent Clancy for carrying out the XRF measurements, Brian Hooten for providing us with details about the Exradin A2 and Exradin A19 chambers, and Elsayed Ali for his assistance with the calculations of x-ray spectra and associated parameters. Special appreciation goes to Hong Shen for his assistance with measurements, and for providing us with measured values of . Comments from the reviewers of this manuscript were also very helpful and appreciated. This research was enabled by support from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canada Research Chairs program.

I. INTRODUCTION

II. METHODS AND PROCEDURES

II.A. Ion chambers

II.B. X-ray spectra and Monte Carlo simulations of the NRC x-ray tube

II.C. Experimental measurements

II.D. Monte Carlo calculations of ion chamber response

III. RESULTS

III.A. NE 2571-type chambers

III.B. Modified Exradin A2 chambers

III.C. Exradin A12 chamber and calculations of

IV. DISCUSSION

IV.A. Detection of impurities and influence on chamber response

IV.B. Sensitivity of Monte Carlo results to chamber geometry

V. CONCLUSIONS

### Key Topics

- Ionization chambers
- 22.0
- Monte Carlo methods
- 12.0
- Photons
- 11.0
- X-ray effects
- 10.0
- X-ray spectra
- 9.0

## Figures

Schematic of the experimental setup. The ion chambers were supported by an aluminum stand within a cylindrical PMMA vessel (0.65 cm thick walls) and laser-aligned in the center of the field. The field size was collimated to a diameter of 9 cm at a distance of 100 cm. Note that the diagram is not drawn to scale, and the x-ray tube and monitor chamber are only shown for perspective.

Schematic of the experimental setup. The ion chambers were supported by an aluminum stand within a cylindrical PMMA vessel (0.65 cm thick walls) and laser-aligned in the center of the field. The field size was collimated to a diameter of 9 cm at a distance of 100 cm. Note that the diagram is not drawn to scale, and the x-ray tube and monitor chamber are only shown for perspective.

Measured and calculated responses due to the unfiltered 60 kV beam as a function of air density for the NE 2571, Exradin A19, and NE 2505/3 chambers enclosed in the PMMA vessel (Fig. 1). -corrected measurements (closed symbols) were fit to second-order polynomials which were then normalized to unity at the reference air density . Calculated values of chamber response (open symbols) were normalized to the fit line for each chamber using the method of least squares. The NE 2505/3 chambers were modeled using the composition of the wall measured with x-ray fluorescence spectroscopy (Table II). The NE 2571 and Exradin A19 were modeled with no impurities. All statistical uncertainties on the calculations are or less.

Measured and calculated responses due to the unfiltered 60 kV beam as a function of air density for the NE 2571, Exradin A19, and NE 2505/3 chambers enclosed in the PMMA vessel (Fig. 1). -corrected measurements (closed symbols) were fit to second-order polynomials which were then normalized to unity at the reference air density . Calculated values of chamber response (open symbols) were normalized to the fit line for each chamber using the method of least squares. The NE 2505/3 chambers were modeled using the composition of the wall measured with x-ray fluorescence spectroscopy (Table II). The NE 2571 and Exradin A19 were modeled with no impurities. All statistical uncertainties on the calculations are or less.

As in Fig. 2 except for the 150 kV beam, with the range of the ordinate significantly reduced. The more softly filtered 150 kV beam was used with the NE 2571 chamber (Table III). Statistical uncertainties on the calculations are approximately .

As in Fig. 2 except for the 150 kV beam, with the range of the ordinate significantly reduced. The more softly filtered 150 kV beam was used with the NE 2571 chamber (Table III). Statistical uncertainties on the calculations are approximately .

As in Fig. 2 but for the modified Exradin A2 chambers. Experimental results are indicated by closed symbols, and the corresponding EGSnrc calculations by open symbols. The dashed line shows results for an Exradin A2 made with C-552 air-equivalent plastic walls and electrode. The dotted line shows results for an otherwise identical chamber with an aluminum electrode of the same thickness (1 mm). Results for these same two chambers with an aluminum thimble replacing the C-552 plastic walls are shown in the solid lines and dotted-dashed lines, respectively. Statistical uncertainties on the calculations are or less.

As in Fig. 2 but for the modified Exradin A2 chambers. Experimental results are indicated by closed symbols, and the corresponding EGSnrc calculations by open symbols. The dashed line shows results for an Exradin A2 made with C-552 air-equivalent plastic walls and electrode. The dotted line shows results for an otherwise identical chamber with an aluminum electrode of the same thickness (1 mm). Results for these same two chambers with an aluminum thimble replacing the C-552 plastic walls are shown in the solid lines and dotted-dashed lines, respectively. Statistical uncertainties on the calculations are or less.

As in Fig. 2 for the modified Exradin A2 chambers and the 150 kV beam. As is the case for the NE type chambers, the scale of the ordinate is significantly reduced relative to the corresponding data for the unfiltered 60 kV beam (Fig. 4). Statistical uncertainties on the calculations are approximately .

As in Fig. 2 for the modified Exradin A2 chambers and the 150 kV beam. As is the case for the NE type chambers, the scale of the ordinate is significantly reduced relative to the corresponding data for the unfiltered 60 kV beam (Fig. 4). Statistical uncertainties on the calculations are approximately .

As in Fig. 2 for the 100 kV and unfiltered 60 kV beams incident on Exradin A12 chamber enclosed in the PMMA vessel. -corrected responses were calculated with (dotted line) and without (dashed line) the addition of high- impurities in the C-552 plastic. Since calculations of response for the 60 kV beam case did not reflect the variation observed experimentally, the data were collectively normalized to unity in order to make differences in the respective trends easier to visualize. The calculated responses for the 100 kV beam were normalized to the experimental data as in Fig. 2. All statistical uncertainties on the calculations are or less.

As in Fig. 2 for the 100 kV and unfiltered 60 kV beams incident on Exradin A12 chamber enclosed in the PMMA vessel. -corrected responses were calculated with (dotted line) and without (dashed line) the addition of high- impurities in the C-552 plastic. Since calculations of response for the 60 kV beam case did not reflect the variation observed experimentally, the data were collectively normalized to unity in order to make differences in the respective trends easier to visualize. The calculated responses for the 100 kV beam were normalized to the experimental data as in Fig. 2. All statistical uncertainties on the calculations are or less.

Measured and EGSnrc-calculated air kerma calibration coefficients as a function of beam effective energy for the Exradin A12 chamber used in this study. values were calculated for the chamber simulated with (dotted line) and without (dashed lines) high- impurities in the C-552 plastic walls, and normalized to the experimental value corresponding to the 250 kV beam (, Table III). The composition of C-552 with impurities (463 ppm) was taken from a chemical analysis published in a previous study (Ref. 25). All statistical uncertainties on the calculations are or less, and the uncertainties on the experimental values with the correlations removed are approximately .

Measured and EGSnrc-calculated air kerma calibration coefficients as a function of beam effective energy for the Exradin A12 chamber used in this study. values were calculated for the chamber simulated with (dotted line) and without (dashed lines) high- impurities in the C-552 plastic walls, and normalized to the experimental value corresponding to the 250 kV beam (, Table III). The composition of C-552 with impurities (463 ppm) was taken from a chemical analysis published in a previous study (Ref. 25). All statistical uncertainties on the calculations are or less, and the uncertainties on the experimental values with the correlations removed are approximately .

As in Fig. 7 but for the NE 2571 and Exradin A19 chambers with no impurities. Statistical uncertainties on the calculations are or less, and the uncertainties on the experimental values with the correlations removed are approximately .

As in Fig. 7 but for the NE 2571 and Exradin A19 chambers with no impurities. Statistical uncertainties on the calculations are or less, and the uncertainties on the experimental values with the correlations removed are approximately .

Calculations of the -corrected response of the NE 2571 chamber *free in air* (no PMMA vessel) as a function of air density for two different geometrical configurations: the one used in this study, and the cylindrical one shown in Fig. 1 of our preceding paper (Ref. 3). A 40 kV PTB spectrum was used as the incident beam (see Table II of La Russa and Rogers, Ref. 3), and the solid line shows data from Fig. 3 of our preceding paper using the EGSnrc CAVRZnrc user-code (Ref. 26). The dotted line shows the same calculations using the “cavity” user code and the identical chamber geometry as that defined by CAVRZnrc. The dashed line shows the calculations of the cavity user code using a more accurate model of the chamber which includes the cone-shaped top. This latter geometry is the same as that used throughout the rest of this study for that chamber.

Calculations of the -corrected response of the NE 2571 chamber *free in air* (no PMMA vessel) as a function of air density for two different geometrical configurations: the one used in this study, and the cylindrical one shown in Fig. 1 of our preceding paper (Ref. 3). A 40 kV PTB spectrum was used as the incident beam (see Table II of La Russa and Rogers, Ref. 3), and the solid line shows data from Fig. 3 of our preceding paper using the EGSnrc CAVRZnrc user-code (Ref. 26). The dotted line shows the same calculations using the “cavity” user code and the identical chamber geometry as that defined by CAVRZnrc. The dashed line shows the calculations of the cavity user code using a more accurate model of the chamber which includes the cone-shaped top. This latter geometry is the same as that used throughout the rest of this study for that chamber.

## Tables

Physical characteristics of the Farmer-type thimble ionization chambers as modeled in this investigation. The diameter of the electrodes are all 1.0 mm, including the Exradin A2 chambers which normally come with a 4.6 mm diameter electrode. In all cases, the wall thickness was sufficient to provide full buildup for each beam quality used in this investigation. The mean chord length, , represents the average distance an electron must travel to cross the cavity, given by , where is the volume of the cavity and is the surface area. Radiographs and schematic diagrams of the NE 2571 and Exradin A12 chambers are given in Ref. 9, and the NE 2505/3 chambers were used in previous studies (Ref. 7).

Physical characteristics of the Farmer-type thimble ionization chambers as modeled in this investigation. The diameter of the electrodes are all 1.0 mm, including the Exradin A2 chambers which normally come with a 4.6 mm diameter electrode. In all cases, the wall thickness was sufficient to provide full buildup for each beam quality used in this investigation. The mean chord length, , represents the average distance an electron must travel to cross the cavity, given by , where is the volume of the cavity and is the surface area. Radiographs and schematic diagrams of the NE 2571 and Exradin A12 chambers are given in Ref. 9, and the NE 2505/3 chambers were used in previous studies (Ref. 7).

Results of the x-ray fluorescence spectroscopy analysis of the graphite and dural thimbles for the NE 2505/3 chamber listed in Table I. The total of the respective fractions for dural did not equal so the balance of the composition was taken as aluminum in our EGSnrc model.

Results of the x-ray fluorescence spectroscopy analysis of the graphite and dural thimbles for the NE 2505/3 chamber listed in Table I. The total of the respective fractions for dural did not equal so the balance of the composition was taken as aluminum in our EGSnrc model.

X-ray beams used in the investigation. The half-value layer (HVL) is defined as the thickness of material (Al or Cu) required to reduce the measured air kerma to one-half of the original value at 1 m distance from the source. The calculated HVLs for the simulated spectra were determined using Eq. 12 of Ref. 11. The effective energies in this case are defined as the energy of a monoenergetic photon beam having the same HVL as the corresponding spectrum.

X-ray beams used in the investigation. The half-value layer (HVL) is defined as the thickness of material (Al or Cu) required to reduce the measured air kerma to one-half of the original value at 1 m distance from the source. The calculated HVLs for the simulated spectra were determined using Eq. 12 of Ref. 11. The effective energies in this case are defined as the energy of a monoenergetic photon beam having the same HVL as the corresponding spectrum.

Estimated uncertainties associated with the experimentally measured chamber response per unit response of the monitor chamber.

Estimated uncertainties associated with the experimentally measured chamber response per unit response of the monitor chamber.

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