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Empirical study of the spatial variation of recombination, polarity and polarization effects in ionization chambers
Nuclear Inst. and Methods in Physics Research, A 914 (2019) 15–24
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Nuclear Inst. and Methods in Physics Research, A journal homepage: www.elsevier.com/locate/nima
Empirical study of the spatial variation of recombination, polarity and polarization effects in ionization chambers Duncan J. Butler a ,∗, Toby Beveridge a , Joerg Lehmann b,c,d , Chris P. Oliver a , Tracy E. Bailey a , Andrew W. Stevenson e,f , Jayde Livingstone e a
Australian Radiation Protection and Nuclear Safety Agency (ARPANSA), Yallambie, Victoria 3085, Australia Institute of Medical Physics, University of Sydney, Physics Road A28, Sydney, NSW 2006, Australia c School of Mathematical and Physical Sciences, The University of Newcastle, Newcastle, NSW 2308, Australia d Radiation Oncology Department, Calvary Mater Newcastle, Newcastle NSW 2300, Australia e Australian Synchrotron, 800 Blackburn Road, Clayton, Victoria 3168, Australia f CSIRO, Future Industries, Clayton, Victoria 3168, Australia b
ARTICLE Keywords: Dosimetry Kilovoltage Synchrotron Ionization chamber High resolution
INFO
ABSTRACT We present measurements of the spatial response of two ionization chambers obtained by scanning them through a 0.1 mm diameter beam of synchrotron radiation (weighted-average energy 95 keV). The technique was used to investigate the spatial variation of effects associated with recombination, bias voltage and beam polarization on the signal. The chamber types investigated were the PTW model 30013 0.6 cm3 Farmer-type chamber and the Exradin model A5 100 cm3 spherical chamber. Recombination was found to vary according to the local electric field strength inside the chamber and the volume of air presented to the beam. The bias polarity effect was found to be small and relatively uniform across the chamber. Within the accuracy of the measurements, no difference could be determined between response scans with the electric field vector of the incident beam aligned parallel and orthogonal to the chamber axis.
1. Introduction Ionization chambers are frequently used for dosimetry in beams of radiation that cover the whole chamber. The response of the chamber is the sum of the response of the individual parts of the chamber, but these are usually difficult to study in isolation. Most theories used to describe the chamber response do not include the electric field inside the chamber, nor do they model the charge migration in the cavity, or extra-cameral response when determining chamber response to radiation, or whether beam polarization is consequential. These effects are nevertheless known to be important in explaining the behaviour of ionization chambers [1–4]. In this work we use a proven technique whereby collimated synchrotron radiation is used to map the spatial response of radiation detectors [5,6]. In these papers we showed that the response of the chamber varies strongly according to where the 0.1 mm2 beam was located on the chamber, and increased where the beam grazed internal surfaces. The synchrotron-based technique was able to identify regions where the chamber response was low due, for example, to reduced electric field (at the base of a thimble chamber cavity) or guarding (such as at the edge of a Roos chamber cavity). Here we extend this work to investigate four properties of the ionization chamber response: (a)
recombination, (b) the low-bias response, (c) bias polarity effect and (d) polarization dependence, as a function of the position of the beam. We present spatial maps for these quantities for a typical Farmertype chamber (PTW model 30013). We also present recombination and polarity maps for a much larger Exradin A5 spherical chamber. While the Farmer-type chamber represents the type of chamber we wish to investigate, the effects are more easily observed in the larger chamber. Specifications for these chambers are given in Table 1. While these effects are well known when the chamber is fully irradiated, little is known about their spatial variation inside the chamber itself. The spatial variation may lead to a better understanding of the chamber operation and improved Monte Carlo models of the response. It may also suggest new ways to design chambers to reduce those effects which compromise the accuracy with which the chambers can be used. 2. Methods 2.1. Pinhole collimator The experimental arrangement is shown in Fig. 1 and a more detailed description can be found in Ref. [5]. Three concentric pinholes, each in
∗ Corresponding author. E-mail address: [email protected] (D.J. Butler).
https://doi.org/10.1016/j.nima.2018.10.095 Received 28 June 2018; Received in revised form 14 September 2018; Accepted 14 October 2018 Available online 25 October 2018 0168-9002/Crown Copyright © 2018 Published by Elsevier B.V. All rights reserved.
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Table 1 Ionization chamber specifications. Make and model Shape Short name/type Nominal collecting volume/cm3 Internal radius/mm Internal length/mm Wall material Collecting electrode material Collecting electrode diameter Collecting electrode length/mm Bias voltagec Build-up cap Nominal response/(nC/Gy)
PTWa 30013 Thimble Farmer-type 0.6 3.05 23 Graphite/PMMA Aluminium 1.15 mm 22 400 V Removed 20
Exradinb A5 Sphere Spherical 100 28.6 – C552 C552 6.5 37.3 400 V Removedd 3000
a
PTW-Freiburg GmbH, 79115 Freiburg, Germany. chambers are now manufactured by Standard Imaging, Inc., Middleton, USA. c Collecting electrode negative. b Exradin
d
The modern version of the A5 chamber has an integral build-up cap.
Fig. 1. Experimental setup: the ionization chamber was scanned through the beam and the current measured at each point to map the response.
2 mm thick tungsten, were used to collimate the synchrotron beam to around 0.1 mm in diameter, and stepper-motor driven stages were used to position the ionization chamber under test.
larger scans required for the spherical chamber, 70 mm was scanned with the motor speed at 0.875 mm/s resulting in 0.1 mm between measurement points. Two dimensional scans were taken with faster motor speeds, resulting in lower resolution. The speed was chosen so as to complete a scan in 1–2 h. Radiographs of the Farmer-type chamber were performed as described in Ref. [5], with a Feinfocus FXE-225.20 microfocus X-ray source (cylindrical reflection-type W target; 30 kVp, 200 μA; 6 μm spot size) and CCD. Radiographs of the spherical chamber were performed with a Siemens Luminos dRF X-ray system at 60 kVp.
2.2. Scanning technique Computer code running on the synchrotron control computers using the EPICs system [7] was used to control the positioning motors, open the shutter, and collect readings from the Keithley 6517A electrometer. Two dimensional raster scans were performed by moving one motor in a continuous line, while stepping the second motor in between these scans. The electrometer was programmed to read the current during the line scans, and this data was sent to the computer while the motor returned to the start of the scan. For 1D scans of the Farmer-type chamber, a 10 mm distance was scanned with the motor speed at 0.2 mm/s resulting in 0.015 mm between measurement points. For the
2.3. Beam quality The beam in the experimental hutch on the Imaging and Medical Beamline is produced by a superconducting multipole wiggler operating
Fig. 2. Radiograph (left) and photograph (right) of the Farmer-type chamber (PTW model 30013) used in this study. The base of the stem (scanned at high resolution in Fig. 3) is shown as a rectangle and the path of the 1D scans is shown as a line. The cylindrical cavity has an internal diameter 6.1 mm in diameter and is 23 mm long.
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achieve. On the synchrotron the ring current can be reduced, but this interferes with other experimental beamlines and was not possible during our experiment. Alternatively, the dose rate can be lowered by attenuators, but this would change the beam spectrum and compromise the experiment. Instead we used the more common approach of change in bias voltage to estimate the recombination losses. Since no theory of recombination was specifically developed for the geometry used, we can only use these theories to indicate regions of higher or lower recombination, and cannot quantify the recombination losses this way. The Farmer-type chamber experiences a relatively large recombination loss when the entire thimble is irradiated by a 1 mm ×20 mm synchrotron beam. With an air kerma rate of 270 Gy/s the recombination loss was of order 15%. However when the beam is collimated to 0.1 mm in diameter, the recombination losses are much smaller. As a result, we found that very low bias voltages were required to be able to see any difference in charge collection. We performed 1D and 2D scans with polarizing voltages of 400 V (central electrode positive, the normal operating voltage), 80 V, 10 V and 2 V. The recombination was estimated from the two-voltage formula for continuous radiation: [ ] 𝑘∗𝑠 = [1 − (𝑉1 ∕𝑉2 )2 ]∕ (𝐼1 ∕𝐼2 ) − (𝑉1 ∕𝑉2 )2 , (1)
Fig. 3. Two dimensional response scan of the base of the Farmer-type chamber cavity.
at 3 T inserted into the electron storage ring. The ring current was 200 mA. The beam emerging from the wiggler is polarized such that the electric field vector is horizontal [8]. The filtration and beam quality are described in Table 2.
where 𝑉1 is the normal operating voltage at which there is a relatively small amount of recombination loss, 𝑉2 is the reduced voltage and 𝐼1 and 𝐼2 are the ionization currents measured at each voltage. We have used the symbol 𝑘∗𝑠 instead of 𝑘𝑠 as a reminder that the formula may not be applicable in our geometry. Note that the synchrotron beam is pulsed (pulses of 25 ps duration, at 500 MHz), but the frequency is much faster than the transit time of ions in a gas (of order milliseconds [8]), so the response of an ionization chamber is expected to behave as for continuous radiation.
2.4. Investigation of recombination loss Most ionization chamber theories describe the behaviour of the whole chamber under uniform irradiation of the entire cavity. Mie and Boag provided theories of recombination in ionization chambers of various geometries in pulsed and continuous radiation. A review of these theories is provided in [9]. Ionization chambers experience recombination loss when charges liberated by radiation in the gas recombine with other charges before they reach the electrodes. It is possible for charges created by a single secondary electron track to recombine (‘‘initial recombination’’), or charges created by different tracks to recombine (‘‘volume recombination’’). Ideally, volume recombination is investigated by changing the dose rate in the beam. However in practice this is difficult to
2.5. Investigation of low bias charge collection When the bias voltage on an ionization chamber is reduced to a very low level, the relative effect of charge deposited in the guarded regions may change compared to the overall signal from the cavity. We performed scans of the Farmer-type with a polarizing bias of only 2 V
Fig. 4. 2D response scans of the Farmer-type chamber at bias voltages of (a) 80 V and (b) 10 V (central electrode positive) and the corresponding spatial plot of 𝑘∗𝑠 (c) as calculated by the two-voltage method for continuous radiation (limitations on the use of this formula in this situation are noted in the text).
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Nuclear Inst. and Methods in Physics Research, A 914 (2019) 15–24 Table 2 Nominal IMBL central-axis air kerma rate for a wiggler magnetic field of 3T in Hutch 1B. Beam ID
Filter 1 (at ∼45◦ )a
Filter 2 (at ∼45◦ )a
HVL (mm Cu)
Energy-weighted average (keV)
Approximate air kerma rate (Gy/s)
F1
1 mm Cu
1 mm Cu
1.44
95
300
a In
addition to beryllium and aluminium windows, a diamond filter, a short helium path, a 1.2 m air path and added in-vacuo filtration of 0.45 mm of graphene at 0◦ (i.e. the normal is parallel to the beam), 5 mm of high-density (HD) graphite at ∼45◦ and 10 mm of HD graphite at ∼45◦ .
to see if the relative response of the chamber changed. As with all the effects studied here, the signal from entire active volume was measured as a function of the position of the beam on the detector. 2.6. Investigation of bias polarity The change in the magnitude of ionization chamber response when the polarity of polarizing voltages is reversed has been detailed in several publications [2]. Recently, Miller et al. showed that for micro chambers the effect is predominantly due to a potential difference between the guard and central electrode [3]. The polarity effect was observed by taking two identical scans with the polarity of the polarizing voltage reversed. If 𝑉1 is the voltage of the normal operating voltage, resulting in current 𝐼1 , then the opposite voltage is 𝑉2 = −𝑉1 and 𝐼2 is the current at the opposite voltage. The polarity correction is given by: 𝑘𝑝𝑜𝑙 = (||𝐼1 || + ||𝐼2 ||)∕(2𝐼1 ).
(2)
Both 2D and 1D scans were taken at operating voltages of ±400 V, and 𝑘𝑝𝑜𝑙 was calculated as a function of beam position on the chamber. 2.7. Investigation of polarization orientation Nearly all conventional sources of ionization produce beams which are unpolarized, and there has been little work concerning the possibility of a sensitivity to beam polarization for typical radiotherapy ionization chambers. Nariyama et al. [10,11] showed that polarization was important for the collection efficiency of free-air chambers in kilovoltage synchrotron radiation. Secondary electrons are emitted preferentially in the plane containing the electric field, which leads to a polarization dependence of the electron loss correction. The synchrotron beam is polarized with the electric field vector horizontal (in the 𝑦-direction in Fig. 1). In order to map the chamber response using the orthogonal polarization, the chamber was rotated so that its axis was horizontal, and the scanning motors were interchanged so that the raster scanning took place in the vertical direction, with small steps between the raster lines taking place in the 𝑦-direction. The two scans were aligned and the difference plotted. Unfortunately, there was only time to scan the Farmer-type chamber at the orthogonal polarization. 2.8. Summary of measurements A list of all the measurements made during the investigation is given in Table 3. Unfortunately, due to time constraints, not all the scans could be repeated for both chambers. Instead, we prioritized measurements according to the time they would take and our estimate as to the likelihood of seeing a measurable effect. Fig. 5. The current I during 1D scans of the Farmer-type chamber, through the centre of the cavity at the location marked in Fig. 2, for five bias voltages (a). The current has been normalized in (b) to a point just outside the central electrode (where the electric field is strongest). In (c) the quantity 𝑘∗𝑠 , indicative of the recombination loss, as calculated by the two-voltage method using the 80 V and 10 V scans, is plotted as a function of beam position.
3. Results 3.1. High resolution scan A photograph and radiograph of the Farmer-type chamber are shown in Fig. 2. Two regions of interest have been marked on the radiograph: a line shows the region where the 1D scans were performed,
and a rectangle shows the region where the 2D scan in Fig. 3 was
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Nuclear Inst. and Methods in Physics Research, A 914 (2019) 15–24 Table 3 List of measurements made during the investigations, showing the bias voltage used for each scan. Investigation
Recombination Low bias Polarity Polarization
Section
3.2 3.3 3.4 3.5
Farmer-type (PTW 30013)
Spherical (Exradin A5)
1D
2D
1D
2D
2, 10, 80, 400 V 2V −400, 400 V 400 V
2, 10, 80, 400 V 2V −400, 400 V 400 V
10, 60, 200, 300, 400 V – −400, 400 V –
200, 400 V – −400, 400 V –
Fig. 6. Radiograph (a) and photograph (b) of the spherical chamber (Exradin model A5), with its build-up cap removed. The cavity has an internal diameter of 57.2 mm.
A radiograph and photograph of the spherical chamber are shown in Fig. 6. Two dimensional scans of the chamber at two bias voltages (400 V and 200 V) are shown in Fig. 7, and 1D scans at a series of voltages are shown in Fig. 8.
performed. The two dimensional scan of the base of the cavity of the Farmer-type chamber (Fig. 3) took some 3 h, and there was not enough time to perform this scan for the different effects we were investigating. A further confounding factor was the positional stability of the pinhole, which was found to cause the intensity in the beam to vary by several percent over 3 h, and would have affected results from consecutive scans of this resolution. Instead, we were forced to perform lower resolution 2D scans and high resolution 1D line scans.
3.3. Low bias response A 2D scan of the Farmer-type chamber with 2 V bias voltage applied is shown in Fig. 9. Note that the maximum ionization current is an order of magnitude lower than in the 80 V scan shown in Fig. 4(a). While this scan was performed as a part of the investigation of recombination, another interesting effect is apparent: a negative current was measured from the stem at the base of the chamber. The magnitude of current here (−7 × 10−11 A) was much greater than that of the background current (−1 × 10−11 A). Note that the background current is caused by radiation reaching the chamber when the beam is outside the cavity, but also includes chamber leakage and electrometer offset currents. Unfortunately a similar scan was not performed on the spherical chamber due to time restrictions.
3.2. Recombination The dependence of recombination on position was investigated by performing 2D scans with different polarizing voltages applied to the chamber. The normal operating voltage of 400 V (central electrode positive) was used and then the scan repeated at 80 V, 10 V and 2 V. Results for 80 V and 10 V are shown in Fig. 4, where a reduction in signal is clearly seen for the lower voltage. The recombination effect is more easily studied using 1D scans. Although these contain much less information, they take a couple of minutes instead of the 50 min required for each 2D scan as performed for Fig. 4. Scans were performed through the centre of the chamber cavity, orthogonal to the cylindrical axis of the chamber, using bias voltages of 400, 80, 10, 5 and 2 V (central electrode positive). The results are shown in Fig. 5(a) and (b) where in (b) they have been normalized to the point immediately outside the central electrode, so that the shape of the curves can be compared.
3.4. Polarity Response scans at opposite polarities are shown for the Farmer-type chamber in Fig. 10 (in 2D) and 11 (in 1D). So that the scans can be compared, the current has been multiplied by −1 for the −400 V case. The polarity correction has been calculated at each point according to 19
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Fig. 7. Response scan of the spherical chamber for (a) 400 V and (b) 200 V (central electrode negative), and (c) the map of the quantity 𝑘∗𝑠 , as calculated by the two-voltage method, as an indication of where recombination is greatest.
Eq. (2) and plotted in Fig. 11(c). The equivalent plot for the spherical chamber is shown in Fig. 12, and a 1D scan through this chamber is shown in Fig. 13. 3.5. Polarization The results of scanning the Farmer-type chamber using orthogonal beam polarizations are shown in Fig. 14. Fig. 14(a) is with the electric field vector perpendicular to the chamber axis, and (b) is parallel. The difference map (c) was created from the two measurements using the same formula as for the polarity correction, Eq. (2), after a rotation of 1 degree in software was applied to the second image to align it with the first. Regions where the current was less than 5 × 10−11 A (outside the chamber) were ignored, and thresholds of −7% and +7% were applied to the remaining pixels so that small changes are visible in the colour maps. The threshold limits the size of the large relative changes which occur in regions of steep response gradients (i.e. next to the wall and central electrode) as a result of jitter in the motor positions.
Fig. 8. 1D scans (a) through the centre of the spherical chamber, in the direction orthogonal to the central electrode, for 5 bias voltages, (b) the scans normalized to the point immediately outside the central electrode and (c) the quantity 𝑘∗𝑠 , indicative of the recombination correction, calculated from the 400 V and 200 V cases.
4.2. Recombination Plots of the recombination as a function of beam position for the Farmer-type chamber in Fig. 4(c) shows a weak dependence of the recombination on position. Near the internal surfaces, the data are inconclusive, because any differences between the 80 V and 10 V scans are mixed with variations caused by positional instabilities (of order 1 pixel), which are exacerbated at surfaces where the response gradients are very high. Throughout the thimble region however the recombination can be seen to be lower near the central electrode and increase towards the outer electrode. We postulate that this trend follows the magnitude of the bias voltage, which is radial in form and strongest near the central electrode. We note that recombination calculated by the two-voltage formula is not expected to be accurate. This formula (Eq. (1)) was developed
4. Discussion 4.1. High resolution scan The high-resolution scan of the base of the Farmer-type chamber (Fig. 3) reproduces and confirms the lower resolution scan published from our initial synchrotron beam time [5]. In particular, the enhanced signal when the beam is parallel (grazing incidence) to any of the internal chamber surfaces is clearly seen. The region close to the base of the cavity where the signal is reduced is also clear. We postulate that this corresponds to the reduction in electric field in the cavity expected near the stem [5]. 20
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Fig. 11. Polarity correction as a function of beam position for a 1D scan through the centre of the Farmer-type chamber, orthogonal to the central electrode. (a) The results for 400 V and −400 V bias voltages (with the negative of the −400 V current shown, to allow comparison) and (b) the polarity correction as a function of position.
Fig. 9. Response map of the Farmer-type chamber for a bias voltage of 2 V, presented on a different scale to Fig. 4(a) and (b). Note the region of negative current where the beam strikes the central electrode at the base of the chamber.
ionization chamber, and migrates to the electrodes through largely unirradiated volume. Nevertheless we believe that this formula gives a qualitative representation of where recombination losses occur.
for fully irradiated chambers, and this condition is not satisfied for our measurements, where charge is created in a small volume of the
Fig. 10. Response scans of the Farmer-type chamber for opposite bias voltages (a) 400 V and (b) −400 V (multiplied by −1 for comparison with 400 V) and (c) the polarity correction 𝑘𝑝𝑜𝑙 .
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Fig. 12. Response scans of the spherical chamber at (a) 400 V, (b) −400 V, and (c) the polarity correction calculated from (a) and (b). Fig. 13. Polarity correction as a function of beam position for a 1D scan through the centre of the spherical chamber, orthogonal to the central electrode. (a) The results for 400 V and −400 V bias voltages (with the negative of the −400 V current shown, to allow comparison) and (b) the polarity correction as a function of position.
The 1D scans shown in Fig. 5 show the radial variation of the recombination loss in more detail. In Fig. 5(b) the collection efficiency inside the thimble can be seen to be more uniform for the higher bias voltages. Fig. 5(c) shows the quantity calculated from Eq. (1) as a function of position, indicating that the recombination is higher in the outer region of the thimble. The recombination results for the A5 chamber show these effects much more clearly (Fig. 7). This is because the chamber volume is so much larger (100 cm3 compared to 0.6 cm3 for the Farmer-type) that there is significantly more opportunity for ions to recombine before they reach the electrodes, and the electric field strength is lower, since both chambers were operated at similar voltages. Fig. 7(a) and (b) show that the collection efficiency is lower at 200 V than at 400 V, as expected. The 1D and 2D A5 scans confirm that as the voltage is lowered, collection efficiency is reduced, and this occurs more strongly in the region away from the central electrode. As for the Farmer-type chamber, we postulate that this effect is produced by a combination of the mean distance to the electrodes that the ions must traverse (which is itself a complicated function of the opposition of the beam on the chamber and the geometry of the central electrode and walls), and the electric field strength, which reduces radially with distance from the central electrode. A quantitative analysis is however beyond the scope of this article.
were 1.86 × 10−9 A (80 V) and 2.00 × 10−10 A (2 V) and the minimum currents were 1.40 × 10−13 A (80 V) and −7.96 × 10−11 A (2 V). We do not have an explanation for this behaviour. Ionization chambers with zero applied external bias may produce a measurable signal, possibly due to a small residual electric field in the cavity caused by the biasing electrometer (even if set to zero volts). There could also be a response due to secondary electrons being deposited directly into electrodes. The effect was only discovered during the data analysis after the experiment, when it was too late to perform the same measurement on the spherical chamber. However we note that there is at least the suggestion of a difference in the response of the stem at different voltages apparent in Fig. 12, which contains the difference plot at opposite bias voltages. The stem response and its relationship to bias voltage will be the subject of future work. 4.4. Polarity The 2D plot for the Farmer-type chamber polarity effect (Fig. 10(c)) shows that the charge collection difference is relatively independent of the position of the beam in the air cavity. The 1D result in Fig. 11 suggests that the difference in this region is of order 1%. The 2D scan suggests that there is a signal arising at the base of the chamber which may not be symmetric with regard to the bias polarity. This result is consistent with the hypothesis that this region has a role in the polarity effect in thimble chambers. The spherical chamber scan (Fig. 12) and the accompanying 1D scan (Fig. 13) show that there is a difference when the ions are created near the chamber wall. The polarity difference rises from nearly zero near
4.3. Low bias collection efficiency Fig. 9 shows the current from a Farmer-type chamber measured with a very low bias voltage (2V). This image can be compared to Fig. 4(a) in which the collection efficiency is high (bias voltage 80 V). While the current is much lower everywhere at 2 V, of particular interest is the region at the base of the chamber were the current is of the opposite sign. This region does not appear in the 80 V scan. The maximum currents 22
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Fig. 14. Polarization: electric field vector of incident photons (a) perpendicular to chamber axis and (b) aligned with chamber axis. The difference plot is shown in (c) where the relative difference has been expressed following Eq. (2) and thresholds applied (see text). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
the central electrode to some 2% in the outer region. We postulate that this difference is caused by difference in the average path length of the negative and positive ions, for a given beam position, as they make their way to the electrodes, in combination with the different electric field strengths that occur throughout the spherical volume. However we were unable to explain the shape of the curve in Fig. 13(b). We note that, as for the recombination analysis, when two scans are subtracted or divided, the noise in the resulting data depends not only on the noise of the two signals, but also on the positional stability from scan to scan. This is particularly so in regions of high response gradients, where a shift of a single point can produce a large change in the result. These effects can be seen in Fig. 13(b) for example. The standard deviation of the current is around 8 × 10−12 A and this results in a relative uncertainty that is larger (0.4%) at the edges of the cavity (where the signal is smaller) than towards the middle (0.2%). Very close to the boundary regions, however, the noise is very large (>3%) due to the positional error of the stages. We estimate that the positional accuracy is around 0.05 mm based on the agreement between repeated scans. This is a function of the accuracy of the stepper motors, the timing of our dynamic method of data acquisition during a continuous scan, and the mechanical stability of the ionization chamber and its mount.
repeated with greater precision. At the wall and central electrode boundaries, where differences might be expected to be more pronounced, the technique fails due to noise in the motor positions.
4.5. Polarization
Acknowledgement
The results for the Farmer-type chamber scanned with chamber axis perpendicular and parallel to the electric field are shown in Fig. 14. Fig. 14(c) contains a difference plot, again using Eq. (2), to evaluate the magnitude of the change at each point. Due to the change of orientation, the images were aligned to within the nearest pixel by shifting the second image pixel by pixel in each direction. There appears to be a very small variation of signal polarization direction inside the cavity volume, as the majority of pixels are blue rather than red. However the difference in current is only about 1 percent. In order to confirm this effect, the experiment would have to be
This work was undertaken on the IMBL beamline at the Australian Synchrotron, Victoria, Australia.
5. Conclusion We have investigated several properties of ionization chambers using a 0.1 mm diameter beam of kilovoltage photons. The spatial distribution of recombination, polarity, low bias collection efficiency and polarization has been observed, for a PTW model 30013 Farmertype chamber and an Exradin model A5 spherical chamber. In several cases the effects have a qualitative explanation, although in others, more information about the operation of the chambers is required. Nevertheless, this is the first time that such measurements have been reported with such high spatial resolution. We note that our technique cannot be used to investigate differences close to the air/wall boundaries because the chamber response has a strong position dependence. In areas of large response gradients, the effect of motor position error is greatly enhanced, making the comparison of repeated scans inaccurate. Finally, we would like to stress that the results are only valid for the beam quality used, and for the chamber models measured, in air.
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Nuclear Inst. and Methods in Physics Research, A 914 (2019) 15–24 [7] The Experimental Physics and Industrial Control System (EPICS) is an open source software environment used by devices such as synchrotrons to control equipment using distributed user interfaces: http://www.aps.anl.gov/epics/. (Accessed 3 November 2017). [8] A.W. Stevenson, J.C. Crosbie, C.J. Hall, D. Hausermann, J. Livingstone, J.E. Lye, Quantitative characterization of the X-ray beam at the Australian Synchrotron Imaging and Medical Beamline (IMBL), J. Synchrotron. Radiat. 24 (2017) 110–141. [9] J.W. Boag, T. Wilson, The saturation curve at high ionization intensity, Br. J. Appl. Phys. 3 (1952) 222–229. [10] N. Nariyama, N. Kishib, S. Ohnishi, Development of a portable free-air ionization chamber as an absolute intensity monitor for high-energy synchrotron radiation up to 150 keV, Nucl. Instrum. Methods Phys. Res. A 524 (2004) 324–331. [11] N. Nariyama, Characteristics of a miniature parallel-plate free-air ionization chamber for measuring the intensity of synchrotron radiation from an undulator, Rev. Sci. Instrum. 75 (2004) 2860, http://dx.doi.org/10.1063/1.1784566.
[3] J.R. Miller, B.D. Hooten, J.A. Micka, L.A. DeWerd, Polarity effects and apparent ion recombination in microionization chambers, Med. Phys. 43 (2016) 2141–2152, http://dx.doi.org/10.1118/1.4944872. [4] M. Le Roy, L. de Carlan, F. Delaunay, M. Donois, P. Fournier, A. Ostrowsky, A. Vouillaume, J.M. Bordy, Assessment of small volume ionization chambers as reference dosimeters in high-energy photon beams, Phys. Med. Biol. 56 (2011) 5637–5650, http://dx.doi.org/10.1088/0031-9155/56/17/011. [5] D.J. Butler, A.W. Stevenson, T.E. Wright, P.D. Harty, J. Lehmann, J. Livingstone, J.C. Crosbie, High spatial resolution dosimetric response maps for radiotherapy ionization chambers measured using kilovoltage synchrotron radiation, Phys. Med. Biol. 60 (2015) 8625–8641. [6] D.J. Butler, T. Beveridge, J. Lehmann, C.P. Oliver, A.W. Stevenson, J. Livingstone, Spatial response of synthetic microdiamond and diode detectors measured with kilovoltage synchrotron radiation, Med. Phys. 45 (2017) 943–952, http://dx.doi. org/10.1002/mp.12733.
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Nuclear Inst. and Methods in Physics Research, A journal homepage: www.elsevier.com/locate/nima
Empirical study of the spatial variation of recombination, polarity and polarization effects in ionization chambers Duncan J. Butler a ,∗, Toby Beveridge a , Joerg Lehmann b,c,d , Chris P. Oliver a , Tracy E. Bailey a , Andrew W. Stevenson e,f , Jayde Livingstone e a
Australian Radiation Protection and Nuclear Safety Agency (ARPANSA), Yallambie, Victoria 3085, Australia Institute of Medical Physics, University of Sydney, Physics Road A28, Sydney, NSW 2006, Australia c School of Mathematical and Physical Sciences, The University of Newcastle, Newcastle, NSW 2308, Australia d Radiation Oncology Department, Calvary Mater Newcastle, Newcastle NSW 2300, Australia e Australian Synchrotron, 800 Blackburn Road, Clayton, Victoria 3168, Australia f CSIRO, Future Industries, Clayton, Victoria 3168, Australia b
ARTICLE Keywords: Dosimetry Kilovoltage Synchrotron Ionization chamber High resolution
INFO
ABSTRACT We present measurements of the spatial response of two ionization chambers obtained by scanning them through a 0.1 mm diameter beam of synchrotron radiation (weighted-average energy 95 keV). The technique was used to investigate the spatial variation of effects associated with recombination, bias voltage and beam polarization on the signal. The chamber types investigated were the PTW model 30013 0.6 cm3 Farmer-type chamber and the Exradin model A5 100 cm3 spherical chamber. Recombination was found to vary according to the local electric field strength inside the chamber and the volume of air presented to the beam. The bias polarity effect was found to be small and relatively uniform across the chamber. Within the accuracy of the measurements, no difference could be determined between response scans with the electric field vector of the incident beam aligned parallel and orthogonal to the chamber axis.
1. Introduction Ionization chambers are frequently used for dosimetry in beams of radiation that cover the whole chamber. The response of the chamber is the sum of the response of the individual parts of the chamber, but these are usually difficult to study in isolation. Most theories used to describe the chamber response do not include the electric field inside the chamber, nor do they model the charge migration in the cavity, or extra-cameral response when determining chamber response to radiation, or whether beam polarization is consequential. These effects are nevertheless known to be important in explaining the behaviour of ionization chambers [1–4]. In this work we use a proven technique whereby collimated synchrotron radiation is used to map the spatial response of radiation detectors [5,6]. In these papers we showed that the response of the chamber varies strongly according to where the 0.1 mm2 beam was located on the chamber, and increased where the beam grazed internal surfaces. The synchrotron-based technique was able to identify regions where the chamber response was low due, for example, to reduced electric field (at the base of a thimble chamber cavity) or guarding (such as at the edge of a Roos chamber cavity). Here we extend this work to investigate four properties of the ionization chamber response: (a)
recombination, (b) the low-bias response, (c) bias polarity effect and (d) polarization dependence, as a function of the position of the beam. We present spatial maps for these quantities for a typical Farmertype chamber (PTW model 30013). We also present recombination and polarity maps for a much larger Exradin A5 spherical chamber. While the Farmer-type chamber represents the type of chamber we wish to investigate, the effects are more easily observed in the larger chamber. Specifications for these chambers are given in Table 1. While these effects are well known when the chamber is fully irradiated, little is known about their spatial variation inside the chamber itself. The spatial variation may lead to a better understanding of the chamber operation and improved Monte Carlo models of the response. It may also suggest new ways to design chambers to reduce those effects which compromise the accuracy with which the chambers can be used. 2. Methods 2.1. Pinhole collimator The experimental arrangement is shown in Fig. 1 and a more detailed description can be found in Ref. [5]. Three concentric pinholes, each in
∗ Corresponding author. E-mail address: [email protected] (D.J. Butler).
https://doi.org/10.1016/j.nima.2018.10.095 Received 28 June 2018; Received in revised form 14 September 2018; Accepted 14 October 2018 Available online 25 October 2018 0168-9002/Crown Copyright © 2018 Published by Elsevier B.V. All rights reserved.
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Table 1 Ionization chamber specifications. Make and model Shape Short name/type Nominal collecting volume/cm3 Internal radius/mm Internal length/mm Wall material Collecting electrode material Collecting electrode diameter Collecting electrode length/mm Bias voltagec Build-up cap Nominal response/(nC/Gy)
PTWa 30013 Thimble Farmer-type 0.6 3.05 23 Graphite/PMMA Aluminium 1.15 mm 22 400 V Removed 20
Exradinb A5 Sphere Spherical 100 28.6 – C552 C552 6.5 37.3 400 V Removedd 3000
a
PTW-Freiburg GmbH, 79115 Freiburg, Germany. chambers are now manufactured by Standard Imaging, Inc., Middleton, USA. c Collecting electrode negative. b Exradin
d
The modern version of the A5 chamber has an integral build-up cap.
Fig. 1. Experimental setup: the ionization chamber was scanned through the beam and the current measured at each point to map the response.
2 mm thick tungsten, were used to collimate the synchrotron beam to around 0.1 mm in diameter, and stepper-motor driven stages were used to position the ionization chamber under test.
larger scans required for the spherical chamber, 70 mm was scanned with the motor speed at 0.875 mm/s resulting in 0.1 mm between measurement points. Two dimensional scans were taken with faster motor speeds, resulting in lower resolution. The speed was chosen so as to complete a scan in 1–2 h. Radiographs of the Farmer-type chamber were performed as described in Ref. [5], with a Feinfocus FXE-225.20 microfocus X-ray source (cylindrical reflection-type W target; 30 kVp, 200 μA; 6 μm spot size) and CCD. Radiographs of the spherical chamber were performed with a Siemens Luminos dRF X-ray system at 60 kVp.
2.2. Scanning technique Computer code running on the synchrotron control computers using the EPICs system [7] was used to control the positioning motors, open the shutter, and collect readings from the Keithley 6517A electrometer. Two dimensional raster scans were performed by moving one motor in a continuous line, while stepping the second motor in between these scans. The electrometer was programmed to read the current during the line scans, and this data was sent to the computer while the motor returned to the start of the scan. For 1D scans of the Farmer-type chamber, a 10 mm distance was scanned with the motor speed at 0.2 mm/s resulting in 0.015 mm between measurement points. For the
2.3. Beam quality The beam in the experimental hutch on the Imaging and Medical Beamline is produced by a superconducting multipole wiggler operating
Fig. 2. Radiograph (left) and photograph (right) of the Farmer-type chamber (PTW model 30013) used in this study. The base of the stem (scanned at high resolution in Fig. 3) is shown as a rectangle and the path of the 1D scans is shown as a line. The cylindrical cavity has an internal diameter 6.1 mm in diameter and is 23 mm long.
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achieve. On the synchrotron the ring current can be reduced, but this interferes with other experimental beamlines and was not possible during our experiment. Alternatively, the dose rate can be lowered by attenuators, but this would change the beam spectrum and compromise the experiment. Instead we used the more common approach of change in bias voltage to estimate the recombination losses. Since no theory of recombination was specifically developed for the geometry used, we can only use these theories to indicate regions of higher or lower recombination, and cannot quantify the recombination losses this way. The Farmer-type chamber experiences a relatively large recombination loss when the entire thimble is irradiated by a 1 mm ×20 mm synchrotron beam. With an air kerma rate of 270 Gy/s the recombination loss was of order 15%. However when the beam is collimated to 0.1 mm in diameter, the recombination losses are much smaller. As a result, we found that very low bias voltages were required to be able to see any difference in charge collection. We performed 1D and 2D scans with polarizing voltages of 400 V (central electrode positive, the normal operating voltage), 80 V, 10 V and 2 V. The recombination was estimated from the two-voltage formula for continuous radiation: [ ] 𝑘∗𝑠 = [1 − (𝑉1 ∕𝑉2 )2 ]∕ (𝐼1 ∕𝐼2 ) − (𝑉1 ∕𝑉2 )2 , (1)
Fig. 3. Two dimensional response scan of the base of the Farmer-type chamber cavity.
at 3 T inserted into the electron storage ring. The ring current was 200 mA. The beam emerging from the wiggler is polarized such that the electric field vector is horizontal [8]. The filtration and beam quality are described in Table 2.
where 𝑉1 is the normal operating voltage at which there is a relatively small amount of recombination loss, 𝑉2 is the reduced voltage and 𝐼1 and 𝐼2 are the ionization currents measured at each voltage. We have used the symbol 𝑘∗𝑠 instead of 𝑘𝑠 as a reminder that the formula may not be applicable in our geometry. Note that the synchrotron beam is pulsed (pulses of 25 ps duration, at 500 MHz), but the frequency is much faster than the transit time of ions in a gas (of order milliseconds [8]), so the response of an ionization chamber is expected to behave as for continuous radiation.
2.4. Investigation of recombination loss Most ionization chamber theories describe the behaviour of the whole chamber under uniform irradiation of the entire cavity. Mie and Boag provided theories of recombination in ionization chambers of various geometries in pulsed and continuous radiation. A review of these theories is provided in [9]. Ionization chambers experience recombination loss when charges liberated by radiation in the gas recombine with other charges before they reach the electrodes. It is possible for charges created by a single secondary electron track to recombine (‘‘initial recombination’’), or charges created by different tracks to recombine (‘‘volume recombination’’). Ideally, volume recombination is investigated by changing the dose rate in the beam. However in practice this is difficult to
2.5. Investigation of low bias charge collection When the bias voltage on an ionization chamber is reduced to a very low level, the relative effect of charge deposited in the guarded regions may change compared to the overall signal from the cavity. We performed scans of the Farmer-type with a polarizing bias of only 2 V
Fig. 4. 2D response scans of the Farmer-type chamber at bias voltages of (a) 80 V and (b) 10 V (central electrode positive) and the corresponding spatial plot of 𝑘∗𝑠 (c) as calculated by the two-voltage method for continuous radiation (limitations on the use of this formula in this situation are noted in the text).
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Nuclear Inst. and Methods in Physics Research, A 914 (2019) 15–24 Table 2 Nominal IMBL central-axis air kerma rate for a wiggler magnetic field of 3T in Hutch 1B. Beam ID
Filter 1 (at ∼45◦ )a
Filter 2 (at ∼45◦ )a
HVL (mm Cu)
Energy-weighted average (keV)
Approximate air kerma rate (Gy/s)
F1
1 mm Cu
1 mm Cu
1.44
95
300
a In
addition to beryllium and aluminium windows, a diamond filter, a short helium path, a 1.2 m air path and added in-vacuo filtration of 0.45 mm of graphene at 0◦ (i.e. the normal is parallel to the beam), 5 mm of high-density (HD) graphite at ∼45◦ and 10 mm of HD graphite at ∼45◦ .
to see if the relative response of the chamber changed. As with all the effects studied here, the signal from entire active volume was measured as a function of the position of the beam on the detector. 2.6. Investigation of bias polarity The change in the magnitude of ionization chamber response when the polarity of polarizing voltages is reversed has been detailed in several publications [2]. Recently, Miller et al. showed that for micro chambers the effect is predominantly due to a potential difference between the guard and central electrode [3]. The polarity effect was observed by taking two identical scans with the polarity of the polarizing voltage reversed. If 𝑉1 is the voltage of the normal operating voltage, resulting in current 𝐼1 , then the opposite voltage is 𝑉2 = −𝑉1 and 𝐼2 is the current at the opposite voltage. The polarity correction is given by: 𝑘𝑝𝑜𝑙 = (||𝐼1 || + ||𝐼2 ||)∕(2𝐼1 ).
(2)
Both 2D and 1D scans were taken at operating voltages of ±400 V, and 𝑘𝑝𝑜𝑙 was calculated as a function of beam position on the chamber. 2.7. Investigation of polarization orientation Nearly all conventional sources of ionization produce beams which are unpolarized, and there has been little work concerning the possibility of a sensitivity to beam polarization for typical radiotherapy ionization chambers. Nariyama et al. [10,11] showed that polarization was important for the collection efficiency of free-air chambers in kilovoltage synchrotron radiation. Secondary electrons are emitted preferentially in the plane containing the electric field, which leads to a polarization dependence of the electron loss correction. The synchrotron beam is polarized with the electric field vector horizontal (in the 𝑦-direction in Fig. 1). In order to map the chamber response using the orthogonal polarization, the chamber was rotated so that its axis was horizontal, and the scanning motors were interchanged so that the raster scanning took place in the vertical direction, with small steps between the raster lines taking place in the 𝑦-direction. The two scans were aligned and the difference plotted. Unfortunately, there was only time to scan the Farmer-type chamber at the orthogonal polarization. 2.8. Summary of measurements A list of all the measurements made during the investigation is given in Table 3. Unfortunately, due to time constraints, not all the scans could be repeated for both chambers. Instead, we prioritized measurements according to the time they would take and our estimate as to the likelihood of seeing a measurable effect. Fig. 5. The current I during 1D scans of the Farmer-type chamber, through the centre of the cavity at the location marked in Fig. 2, for five bias voltages (a). The current has been normalized in (b) to a point just outside the central electrode (where the electric field is strongest). In (c) the quantity 𝑘∗𝑠 , indicative of the recombination loss, as calculated by the two-voltage method using the 80 V and 10 V scans, is plotted as a function of beam position.
3. Results 3.1. High resolution scan A photograph and radiograph of the Farmer-type chamber are shown in Fig. 2. Two regions of interest have been marked on the radiograph: a line shows the region where the 1D scans were performed,
and a rectangle shows the region where the 2D scan in Fig. 3 was
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Nuclear Inst. and Methods in Physics Research, A 914 (2019) 15–24 Table 3 List of measurements made during the investigations, showing the bias voltage used for each scan. Investigation
Recombination Low bias Polarity Polarization
Section
3.2 3.3 3.4 3.5
Farmer-type (PTW 30013)
Spherical (Exradin A5)
1D
2D
1D
2D
2, 10, 80, 400 V 2V −400, 400 V 400 V
2, 10, 80, 400 V 2V −400, 400 V 400 V
10, 60, 200, 300, 400 V – −400, 400 V –
200, 400 V – −400, 400 V –
Fig. 6. Radiograph (a) and photograph (b) of the spherical chamber (Exradin model A5), with its build-up cap removed. The cavity has an internal diameter of 57.2 mm.
A radiograph and photograph of the spherical chamber are shown in Fig. 6. Two dimensional scans of the chamber at two bias voltages (400 V and 200 V) are shown in Fig. 7, and 1D scans at a series of voltages are shown in Fig. 8.
performed. The two dimensional scan of the base of the cavity of the Farmer-type chamber (Fig. 3) took some 3 h, and there was not enough time to perform this scan for the different effects we were investigating. A further confounding factor was the positional stability of the pinhole, which was found to cause the intensity in the beam to vary by several percent over 3 h, and would have affected results from consecutive scans of this resolution. Instead, we were forced to perform lower resolution 2D scans and high resolution 1D line scans.
3.3. Low bias response A 2D scan of the Farmer-type chamber with 2 V bias voltage applied is shown in Fig. 9. Note that the maximum ionization current is an order of magnitude lower than in the 80 V scan shown in Fig. 4(a). While this scan was performed as a part of the investigation of recombination, another interesting effect is apparent: a negative current was measured from the stem at the base of the chamber. The magnitude of current here (−7 × 10−11 A) was much greater than that of the background current (−1 × 10−11 A). Note that the background current is caused by radiation reaching the chamber when the beam is outside the cavity, but also includes chamber leakage and electrometer offset currents. Unfortunately a similar scan was not performed on the spherical chamber due to time restrictions.
3.2. Recombination The dependence of recombination on position was investigated by performing 2D scans with different polarizing voltages applied to the chamber. The normal operating voltage of 400 V (central electrode positive) was used and then the scan repeated at 80 V, 10 V and 2 V. Results for 80 V and 10 V are shown in Fig. 4, where a reduction in signal is clearly seen for the lower voltage. The recombination effect is more easily studied using 1D scans. Although these contain much less information, they take a couple of minutes instead of the 50 min required for each 2D scan as performed for Fig. 4. Scans were performed through the centre of the chamber cavity, orthogonal to the cylindrical axis of the chamber, using bias voltages of 400, 80, 10, 5 and 2 V (central electrode positive). The results are shown in Fig. 5(a) and (b) where in (b) they have been normalized to the point immediately outside the central electrode, so that the shape of the curves can be compared.
3.4. Polarity Response scans at opposite polarities are shown for the Farmer-type chamber in Fig. 10 (in 2D) and 11 (in 1D). So that the scans can be compared, the current has been multiplied by −1 for the −400 V case. The polarity correction has been calculated at each point according to 19
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Fig. 7. Response scan of the spherical chamber for (a) 400 V and (b) 200 V (central electrode negative), and (c) the map of the quantity 𝑘∗𝑠 , as calculated by the two-voltage method, as an indication of where recombination is greatest.
Eq. (2) and plotted in Fig. 11(c). The equivalent plot for the spherical chamber is shown in Fig. 12, and a 1D scan through this chamber is shown in Fig. 13. 3.5. Polarization The results of scanning the Farmer-type chamber using orthogonal beam polarizations are shown in Fig. 14. Fig. 14(a) is with the electric field vector perpendicular to the chamber axis, and (b) is parallel. The difference map (c) was created from the two measurements using the same formula as for the polarity correction, Eq. (2), after a rotation of 1 degree in software was applied to the second image to align it with the first. Regions where the current was less than 5 × 10−11 A (outside the chamber) were ignored, and thresholds of −7% and +7% were applied to the remaining pixels so that small changes are visible in the colour maps. The threshold limits the size of the large relative changes which occur in regions of steep response gradients (i.e. next to the wall and central electrode) as a result of jitter in the motor positions.
Fig. 8. 1D scans (a) through the centre of the spherical chamber, in the direction orthogonal to the central electrode, for 5 bias voltages, (b) the scans normalized to the point immediately outside the central electrode and (c) the quantity 𝑘∗𝑠 , indicative of the recombination correction, calculated from the 400 V and 200 V cases.
4.2. Recombination Plots of the recombination as a function of beam position for the Farmer-type chamber in Fig. 4(c) shows a weak dependence of the recombination on position. Near the internal surfaces, the data are inconclusive, because any differences between the 80 V and 10 V scans are mixed with variations caused by positional instabilities (of order 1 pixel), which are exacerbated at surfaces where the response gradients are very high. Throughout the thimble region however the recombination can be seen to be lower near the central electrode and increase towards the outer electrode. We postulate that this trend follows the magnitude of the bias voltage, which is radial in form and strongest near the central electrode. We note that recombination calculated by the two-voltage formula is not expected to be accurate. This formula (Eq. (1)) was developed
4. Discussion 4.1. High resolution scan The high-resolution scan of the base of the Farmer-type chamber (Fig. 3) reproduces and confirms the lower resolution scan published from our initial synchrotron beam time [5]. In particular, the enhanced signal when the beam is parallel (grazing incidence) to any of the internal chamber surfaces is clearly seen. The region close to the base of the cavity where the signal is reduced is also clear. We postulate that this corresponds to the reduction in electric field in the cavity expected near the stem [5]. 20
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Fig. 11. Polarity correction as a function of beam position for a 1D scan through the centre of the Farmer-type chamber, orthogonal to the central electrode. (a) The results for 400 V and −400 V bias voltages (with the negative of the −400 V current shown, to allow comparison) and (b) the polarity correction as a function of position.
Fig. 9. Response map of the Farmer-type chamber for a bias voltage of 2 V, presented on a different scale to Fig. 4(a) and (b). Note the region of negative current where the beam strikes the central electrode at the base of the chamber.
ionization chamber, and migrates to the electrodes through largely unirradiated volume. Nevertheless we believe that this formula gives a qualitative representation of where recombination losses occur.
for fully irradiated chambers, and this condition is not satisfied for our measurements, where charge is created in a small volume of the
Fig. 10. Response scans of the Farmer-type chamber for opposite bias voltages (a) 400 V and (b) −400 V (multiplied by −1 for comparison with 400 V) and (c) the polarity correction 𝑘𝑝𝑜𝑙 .
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Fig. 12. Response scans of the spherical chamber at (a) 400 V, (b) −400 V, and (c) the polarity correction calculated from (a) and (b). Fig. 13. Polarity correction as a function of beam position for a 1D scan through the centre of the spherical chamber, orthogonal to the central electrode. (a) The results for 400 V and −400 V bias voltages (with the negative of the −400 V current shown, to allow comparison) and (b) the polarity correction as a function of position.
The 1D scans shown in Fig. 5 show the radial variation of the recombination loss in more detail. In Fig. 5(b) the collection efficiency inside the thimble can be seen to be more uniform for the higher bias voltages. Fig. 5(c) shows the quantity calculated from Eq. (1) as a function of position, indicating that the recombination is higher in the outer region of the thimble. The recombination results for the A5 chamber show these effects much more clearly (Fig. 7). This is because the chamber volume is so much larger (100 cm3 compared to 0.6 cm3 for the Farmer-type) that there is significantly more opportunity for ions to recombine before they reach the electrodes, and the electric field strength is lower, since both chambers were operated at similar voltages. Fig. 7(a) and (b) show that the collection efficiency is lower at 200 V than at 400 V, as expected. The 1D and 2D A5 scans confirm that as the voltage is lowered, collection efficiency is reduced, and this occurs more strongly in the region away from the central electrode. As for the Farmer-type chamber, we postulate that this effect is produced by a combination of the mean distance to the electrodes that the ions must traverse (which is itself a complicated function of the opposition of the beam on the chamber and the geometry of the central electrode and walls), and the electric field strength, which reduces radially with distance from the central electrode. A quantitative analysis is however beyond the scope of this article.
were 1.86 × 10−9 A (80 V) and 2.00 × 10−10 A (2 V) and the minimum currents were 1.40 × 10−13 A (80 V) and −7.96 × 10−11 A (2 V). We do not have an explanation for this behaviour. Ionization chambers with zero applied external bias may produce a measurable signal, possibly due to a small residual electric field in the cavity caused by the biasing electrometer (even if set to zero volts). There could also be a response due to secondary electrons being deposited directly into electrodes. The effect was only discovered during the data analysis after the experiment, when it was too late to perform the same measurement on the spherical chamber. However we note that there is at least the suggestion of a difference in the response of the stem at different voltages apparent in Fig. 12, which contains the difference plot at opposite bias voltages. The stem response and its relationship to bias voltage will be the subject of future work. 4.4. Polarity The 2D plot for the Farmer-type chamber polarity effect (Fig. 10(c)) shows that the charge collection difference is relatively independent of the position of the beam in the air cavity. The 1D result in Fig. 11 suggests that the difference in this region is of order 1%. The 2D scan suggests that there is a signal arising at the base of the chamber which may not be symmetric with regard to the bias polarity. This result is consistent with the hypothesis that this region has a role in the polarity effect in thimble chambers. The spherical chamber scan (Fig. 12) and the accompanying 1D scan (Fig. 13) show that there is a difference when the ions are created near the chamber wall. The polarity difference rises from nearly zero near
4.3. Low bias collection efficiency Fig. 9 shows the current from a Farmer-type chamber measured with a very low bias voltage (2V). This image can be compared to Fig. 4(a) in which the collection efficiency is high (bias voltage 80 V). While the current is much lower everywhere at 2 V, of particular interest is the region at the base of the chamber were the current is of the opposite sign. This region does not appear in the 80 V scan. The maximum currents 22
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Fig. 14. Polarization: electric field vector of incident photons (a) perpendicular to chamber axis and (b) aligned with chamber axis. The difference plot is shown in (c) where the relative difference has been expressed following Eq. (2) and thresholds applied (see text). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
the central electrode to some 2% in the outer region. We postulate that this difference is caused by difference in the average path length of the negative and positive ions, for a given beam position, as they make their way to the electrodes, in combination with the different electric field strengths that occur throughout the spherical volume. However we were unable to explain the shape of the curve in Fig. 13(b). We note that, as for the recombination analysis, when two scans are subtracted or divided, the noise in the resulting data depends not only on the noise of the two signals, but also on the positional stability from scan to scan. This is particularly so in regions of high response gradients, where a shift of a single point can produce a large change in the result. These effects can be seen in Fig. 13(b) for example. The standard deviation of the current is around 8 × 10−12 A and this results in a relative uncertainty that is larger (0.4%) at the edges of the cavity (where the signal is smaller) than towards the middle (0.2%). Very close to the boundary regions, however, the noise is very large (>3%) due to the positional error of the stages. We estimate that the positional accuracy is around 0.05 mm based on the agreement between repeated scans. This is a function of the accuracy of the stepper motors, the timing of our dynamic method of data acquisition during a continuous scan, and the mechanical stability of the ionization chamber and its mount.
repeated with greater precision. At the wall and central electrode boundaries, where differences might be expected to be more pronounced, the technique fails due to noise in the motor positions.
4.5. Polarization
Acknowledgement
The results for the Farmer-type chamber scanned with chamber axis perpendicular and parallel to the electric field are shown in Fig. 14. Fig. 14(c) contains a difference plot, again using Eq. (2), to evaluate the magnitude of the change at each point. Due to the change of orientation, the images were aligned to within the nearest pixel by shifting the second image pixel by pixel in each direction. There appears to be a very small variation of signal polarization direction inside the cavity volume, as the majority of pixels are blue rather than red. However the difference in current is only about 1 percent. In order to confirm this effect, the experiment would have to be
This work was undertaken on the IMBL beamline at the Australian Synchrotron, Victoria, Australia.
5. Conclusion We have investigated several properties of ionization chambers using a 0.1 mm diameter beam of kilovoltage photons. The spatial distribution of recombination, polarity, low bias collection efficiency and polarization has been observed, for a PTW model 30013 Farmertype chamber and an Exradin model A5 spherical chamber. In several cases the effects have a qualitative explanation, although in others, more information about the operation of the chambers is required. Nevertheless, this is the first time that such measurements have been reported with such high spatial resolution. We note that our technique cannot be used to investigate differences close to the air/wall boundaries because the chamber response has a strong position dependence. In areas of large response gradients, the effect of motor position error is greatly enhanced, making the comparison of repeated scans inaccurate. Finally, we would like to stress that the results are only valid for the beam quality used, and for the chamber models measured, in air.
References [1] C.K. Ross, Comments on ‘Ionization chamber volume determination and quality assurance using micro-CT imaging’, Phys. Med. Biol. 54 (2009) L23–L27, http: //dx.doi.org/10.1088/0031-9155/54/6/l01. [2] Y.K. Kim, S.H. Park, H.S. Kim, S.M. Kang, J.H. Ha, C.E. Chung, S.Y. Cho, J.K. Kim, Polarity effect of the thimble-type ionization chamber at a low dose rate, Phys. Med. Biol. 50 (2005) 4995–5003.
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