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Nuclear Instruments and Methods in Physics Research A 566 (2006) 706–712

www.elsevier.com/locate/nima

Characteristics of the saturation curve of the ionization chambers inoverlapping pulsed beams

S.H. Parka,�, Y.K. Kimb, H.S. Kima, S.M. Kanga, J.H. Haa

aAdvanced Radiation Detecting Instrument and Sensors Laboratory, Korea Atomic Energy Research Institute, Daejeon 305-600, Republic of KoreabDepartment of Nuclear Engineering, Hanyang University, Seoul 133-791, Republic of Korea

Received 9 March 2006; received in revised form 14 July 2006; accepted 15 July 2006

Available online 10 August 2006

Abstract

When a pulsed radiation is incident on an air-filled ionization chamber wherein the primary electrons are rapidly absorbed to become

negative ions, it is known that the reciprocal of the ionizing current is linearly proportional to the reciprocal of the polarization voltage in

the near saturation region. However, the relationship between the reciprocal of the ionizing current and the reciprocal of the polarization

voltage will deviate from a simple linearity when the ion transit time in the ionization chamber is longer than the interval between the

radiation pulses. Two thimble-type ionization chambers, one of which was designed and fabricated by us, were employed to measure the

saturation curves of the ionization chambers in a pulsed Bremsstrahlung X-ray, which was generated with an electron accelerator. A

model was developed to explain the shape of the measured saturation curves in the overlapping pulsed radiation, and the results of it

were compared with the measured ones. The dependency of the shape of the saturation curve on the geometrical design of the ionization

chambers in the pulsed radiation was discussed.

r 2006 Elsevier B.V. All rights reserved.

PACS: 29.40.Cs; 78.70.Ck; 87.53.Hv; 87.53.Bn

Keywords: Pulsed radiation; Ionization chamber; Ion transit time; Saturation curve; Bremsstrahlung X-ray; Electron accelerator

1. Introduction

Ionic losses in the sensitive volume of an ionizationchamber have to be considered carefully to determine theabsolute dose accurately with the ionization chamber. Theimportant ionic losses in the ionization chamber are initialrecombination, general recombination, and ionic diffusionagainst the electric field. The initial recombination is therecombination of positive and negative ions formed withinthe track of a single ionizing radiation, and the generalrecombination is the recombination of positive andnegative ions formed by different ionizing radiation. Theinitial recombination is independent of the incident doserate, but the general recombination increases as the averageconcentration of ions of both signs increases, that is, withincreasing dose rate [1].

e front matter r 2006 Elsevier B.V. All rights reserved.

ma.2006.07.028

ing author. Tel.: +8242 868 2546; fax: +82 42 868 4738.

ess: ex-spark@kaeri.re.kr (S.H. Park).

Procedures for determination of collection efficiency inionization chambers have been studied by numerousinvestigators. If continuous radiation is incident on anair-filled ionization chambers, the theoretical model, inwhich only the general recombination is included, showsthat 1/I(V) is linearly proportional to 1/V2 in the nearsaturation region, where I(V) is the current measured withthe ionization chamber at a given polarization voltage V.When the charge multiplication occurs in high voltageregion, the relation between 1/I(V) and 1/V2 will deviatefrom the simple linearity. For pulsed radiation beam, it isknown that linear relationship appears between 1/I(V) and1/V when the collection efficiency, f, is larger than 0.9 [1].Because of the assumption of the linear relationship of 1/I(V) with 1/V or 1/V2 in the near-saturation region, itbecomes simple to determine the saturation current, Isat,with the measurements [2].The above discussion of the collection efficiency of the

ionization chamber exposed to the pulsed radiation is valid

ARTICLE IN PRESSS.H. Park et al. / Nuclear Instruments and Methods in Physics Research A 566 (2006) 706–712 707

only if each pulse is cleared before the next one occurs. Thetransit times of the ions in the chamber must be shorterthan the time interval between the radiation pulses. Mostof the previous works concerning the characteristics of thesaturation curve of an ionization chamber in the pulsedbeam were done for the case where the transit times of theions were shorter than the interval between the radiationpulses [2–6].

Yamamoto derived the theoretical shape of the satura-tion curve when the pulse duration is nearly equal to theion transit time [7]. Boag discussed the extreme case, wherethe ion transit time in the chamber was much longer thanthe interval between the radiation pulses [1]. The saturationcurve behaved like a continuous radiation case even thoughthe pulsed beam entered the ionization chamber. However,the experimental data for the intermediate case, where theion transit time was comparable to the interval between theradiation pulses or the ion transit time was slightly longerthan the interval between the radiation pulses, were rare.

The saturation curves of the ionization chambers in thepulsed radiation were measured with the pulse-beamedelectron accelerator at the Korea Atomic Energy ResearchInstitute (KAERI), where the ion transit times in theionization chambers were longer than the time intervalbetween the radiation pulses. We used two ionizationchambers: one was a commercial thimble-type ionizationchamber, which was made by Exradin (Model A 12) andwill be referred to as small thimble-type ionization chamberhereafter, and the other was a home-made thimble-typeionization chamber. The ion transit time in the smallthimble-type ionization chamber was roughly estimated tobe 100 ms at V ¼ 500V, and that in the home-madethimble-type ionization chamber was 3ms. Since the timinginterval between the radiation pulses from the electronaccelerator was 43 ms for 2MeV, 30 mA electron beam, theshape of the saturation curve in the intermediate case couldbe studied experimentally in our work. A model wasdeveloped to explain the measured data, and the results ofit were compared with the measured ones.

2. Experiments

A CW electron accelerator is being operated at theKAERI. Electron beams with incident energies of 2 or10MeV can be produced with the accelerator. The

Fig. 1. Experimental setup to measure the Bremsstrah

accelerator is composed of a 300-keV electron gun, a RFbunching cavity, two RF accelerator cavities, and a beamdump. The duration of a bunching pulse is 350 ps, and therepetition rate of the beam pulse is 23 kHz for 2MeV,30 mA electron beam. The repetition rate is doubled whenthe beam current is doubled. The details about the electronaccelerator are discussed in Ref. [8]. The accelerator will beused as the injector for a high-power Free Electron Laser(FEL), and it can also be used for a tunable X-raygenerator. We designed a setup to generate the Brems-strahlung X-ray with the electron accelerator and theexperimental setup is shown in Fig. 1. In our experiment, 2-MeV electron beam hit the stainless-steel stopper, and theX-ray from the stopper was measured with the ionizationchambers.The optimum thickness of the stopper was determined

with the EGSnrc Monte-Carlo calculation code [9].TwoMeV electron was incident perpendicular to thestopper and the total deposited energies of the electronand the photon in the forward and the backward regionswere calculated. The number of simulation events was 105.The results of the calculation are shown in Fig. 2. As thestopper becomes thicker, the deposited photon andelectron energies in the forward region become smaller.The deposited energy of the electron in the forward regiondecreases faster than that of the photon as the stopperbecomes thicker, and most of the electrons cannotpenetrate the stopper when the stopper is thicker than2mm. The deposited photon and electron energies in thebackward region are increased and saturated as the stopperbecomes thicker.The currents from the ionization chamber were mea-

sured as a function of the stopper thickness, and they werecompared with the simulated ones. The small thimble-typeionization was used in the measurement, and the Keithley6517. A electrometer was employed to bias the high voltage(�500V) on the ionization chamber and measure thecurrent from the ionization chamber. The leakage currentof the ionization chamber was less than 10 fA. When theelectron beam hit the stopper, the ionizing current was�1 nA, and when the electron beam was stopped, theionizing current was reduced to �0.1 pA. Therefore, theionizing current, which was measured while the electronbeam was incident on the stopper, was mostly caused bythe Bremsstrahlung X-ray.

lung X-ray from the pulsed electron accelerator.

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Fig. 3. The current of the ionization chamber as function of the stopper

thickness. The closed circles are from the measurement, and the line is

from the simulation. The size of error of each measured point is generally

smaller than the size of the circle. The simulated data are only from the X-

ray contribution.

(a) (b)

Fig. 2. The deposited energies of the X-ray and the electron as a function of the stopper thickness. The data were obtained from the EGSnrc simulation.

S.H. Park et al. / Nuclear Instruments and Methods in Physics Research A 566 (2006) 706–712708

Because of a high dose near the stopper while theelectron beam hit the stopper, the electrometer wasremotely controlled with a computer via the IEEE 488.2General-Purpose Interface Bus (GPIB). A LabVIEWprogram, which was based on a Virtual Instrument (VI),was used to interface with the electrometer. We coded twoVIs, one was a voltage control VI and the other was asignal control VI. The voltage source control VI couldcontrol the voltage source of the electrometer from �999 to999V and displayed a voltage state. The signal control VIcould receive and store the signals automatically per ms bydefault. The receiving time and count number wereadjustable. In the measurement, the receiving time wasset as 0.5 s and 30 data were stored to obtain the averageionizing current at each polarization voltage.

The change of the measured ionizing current as afunction of the stopper thickness was consistent with thesimulated one, which is shown in Fig. 3. The validity of thesimulation to determine the stopper thickness was con-firmed with this comparison. The thickness of the stopperwas determined to be 4mm. Since the Bremsstrahlung X-ray was dominant in the forward region, the ionizationchambers were placed in the forward region to onlymeasure the response of the ionization chamber to theBremsstrahlung X-ray.

Fig. 4 is the cross-sectional view of the two ionizationchambers. We designed and fabricated a thimble-typeionization chamber. Electrodes were made of Shank air-equivalent conductive plastic C552. The electrodes werecomposed of the collector, which was to collect the ionizingcurrent from the chamber, the outside electrode, which wasbiased by a high voltage, and the guard electrode. Theguard electrode was placed between the collector and theoutside electrode to reduce the leakage current. Thecollector diameter and the diameter of the outside electrodewere 1.0 and 24.0mm, respectively, and the active volumeof the home-made ionization chamber was 14 cc. Air wasfilled in the ionization chamber. A low noise tri-axial cablewas connected between the ionization chamber and the

electrometer. The leakage current of the home-madeionization chamber is shown in Fig. 5. The collectordiameter and the diameter of the outside electrode of thesmall thimble type ionization chamber were 1.0 and6.1mm, respectively, and the active volume was 0.65 cc.The transit time of the ions across the space between the

electrodes of the ionization chamber, T, in a cylindricalgeometry is approximately

ða� bÞ2ðaþ bÞ

ða� bÞ

lnðaþ bÞ

2=V ðk1 þ k2Þ

where V is the applied voltage, ki the mobility of the ion, a

the outer radius, and b is the inner radius of the ionizationchamber [1]. From the above formula, the ion transit timeof the home-made ionization chamber is estimated to be 30times longer than that of the small thimble-type ionizationchamber.

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Guard Electrode

Guard ElectrodeCollector

Collector

Large Ionization chamber Small Ionization chamber

Outside Electrode

Outside Electrode39

�1

�24

�6.

1�1

(a) (b)

Fig. 4. The cross-sectional views of the ionization chambers used in this work.

Fig. 5. The leakage current of the home-made ionization chamber. Fig. 6. The saturation curve of the home-made ionization chamber. The

ionization chamber was placed in the forward region, and the currents

were normalized with another ionization chamber. The electron beam

current was 30mA. The size of error of each measured point is generally

smaller than the size of the circle.

S.H. Park et al. / Nuclear Instruments and Methods in Physics Research A 566 (2006) 706–712 709

A 2-MeV electron beam with a beam current of 30 or60 mA, which correspond to the gamma-ray exposure of99.9 and 196.3R/s, respectively, hit the stopper, and thecurrents from the ionization chambers were measured asthe polarization voltage on the ionization chamber wasvaried. While the saturation curve of an ionizationchamber was measured, the other ionization chamber witha fixed polarization voltage was also placed in the forwardregion to monitor the fluctuation of the incident beamcurrent. When the saturation curve of the home-madeionization chamber was measured, a parallel plate ioniza-tion chamber (Exradin Model A15) with an active volumeof 2.46 cc was used as the flux monitoring detector, andwhen the saturation curve of the small thimble-typeionization chamber was measured, the home-made ioniza-tion chamber was used as the monitoring detector. Theionization currents from the ionization chambers weremeasured 30 times to obtain the average current andestimate the error at each polarization voltage. Fig. 6 is one

of the measured saturation curves, in which the ionizingcurrents were normalized. The errors of the data areinserted in Fig. 6. The error of each data point isdetermined from the standard deviations of the ionizingcurrents from the ionization chambers. The size of theerror of each data point is smaller than the size of the circle.

3. Analysis

Figs. 7 and 8 show the plots of the reciprocal of theionizing current (I) against the reciprocal of the polariza-tion voltage (V) in f40.9. All the data showed deviationsfrom the linearity predictions. In the data with the smallthimble-type ionization chamber, the deviation from thelinearity appeared at high polarizing voltage region. Theexistence of the deviation from the linearity at the high

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Fig. 7. The plots of 1/I and 1/V at the polarization voltage region from 20

to 800V, which were obtained with the small thimble-type ionization

chamber. I is normalized current, in which the ionization current with the

small thimble-type ionization chamber is divided by the ionization current

with the monitoring ionization chamber. The circles are measured ones,

and the lines are from the model calculation. The size of error of each

measured point is generally smaller than the size of the circle.

Fig. 8. The plots of 1/I and 1/V in the polarization voltage region from

200 to 800V, which were obtained with the home-made ionization

chamber. I is normalized current, in which the ionization current with the

small thimble-type ionization chamber is divided by the ionization current

with the monitoring ionization chamber. The circles are measured ones,

and the lines are from the model calculation. The circles are measured

ones, and the lines are from the model calculation. The size of error of

each measured point is generally smaller than the size of the circle.

S.H. Park et al. / Nuclear Instruments and Methods in Physics Research A 566 (2006) 706–712710

polarizing voltage region had been reported previously.Piermattei measured the saturation curves of the parallelplate ionization chambers when the chambers were exposedto the pulsed electron beam, and the deviation from thelinear relation at high polarization voltage region wasmeasured [4]. They included the effect of free electroncollection in the recombination formula to explain thedeviation from the linearity prediction. DeBlois measured

the saturation curves in pulsed photon and electron beam,and the deviation from the predicted linearity was observed[2]. They explained the deviation with the onset of thecharge multiplication in the chamber. The charge multi-plication effect was included with an exponential term, elV,where l was a parameter,

1

I¼

1

I satþ

lpV

� �e�lV (1)

Also there were also deviations of the data points, whichwere measured with the small thimble-type ionizationchamber, from the linearity at the polarizing voltage of20V.A model calculation was done to explain the data.

Previously, many models have been developed to determinethe collection efficiency of the ionization chamber. Amongthese, Boag provided a model, which could calculate thecollection efficiency of the ionization chamber in pulsedradiation. His model can be used in the case where the totalionization per pulse occurs instantaneously and the ionsproduced by each pulse are collected before the next oneoccurs [1]. He considered the recombination processeswithin a single tube of force in the applied electric field. Inthe region of overlap containing ions of both signs, theconcentration of positive ions was assumed to be the sameas that of negative ions. The free-electron effect and thespace charge effect was not considered in his model. Boagshowed that

f ¼1

ulnð1þ uÞ (2)

where m ¼ Lp/V, with V the polarization voltage andLp ¼ mrd2. In the expression for Lp, m is constant, r theinitial charge density per pulse, and d the equivalentelectrode spacing of the chamber, which depends on thegeometry of the ionization chamber. For f40.9 and forsmall charge density r the quantity u becomes sufficientlysmall enough to allow for the following expansion ofEq (2):

f �1 ¼u

lnð1þ uÞ� 1þ

u

2� � � � (3)

or

1

IðV Þ�

1

I satþ

lpV

(4)

with lp ¼ Lp/2Isat. It predicts the linear relation between 1/I(V) and 1/V in the near saturation region. This assump-tion forms the basis of the two voltage method [2].Yamamoto studied the model of the collection efficiency

of the ionization chamber when the radiation pulseduration is of the same order as the ion transit time acrossthe chamber, or even longer [7]. He only considered thenegative and positive ion transit, and neglected the spacecharge effect and the diffusion term. The mobility of thepositive ion was assumed to be equal to that of the negativeion.

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There can be the effect of the free-electron componentand the space charge on the shape of the saturation curveof the ionization chamber in the pulsed radiation. Boagdiscussed the effect of the free-electron component on thesaturation curve for pulsed radiation [1]. He assumed thatthe free electron was collected instantaneously with 100%collection efficiency before the ions moved from the initialposition. Recombination was assumed to proceed inaccordance with the following equation:

dn=dt ¼ �anðn� pn0Þ, (5)

where a is the recombination coefficient, n0 is the initial iondensity, n is the positive ion concentration, and p is thefraction of the free electron. The collection efficiency wasdeduced based on the Eq. (5), and it was compared with thecollection efficiency from the two voltage estimate. The twovalues showed quite close results when the ionizationchambers with 1- and 3-mm air gap were employed. Thespace charge effect was also discussed previously, and thewhole saturation curve was found to be displaced slightlyby the space charge [1].

In our model, the following assumptions were included: thespace charge effect, which can be ignored in near-saturationcondition [1], and the diffusion term were neglected. At thelowest voltage of 20V at Fig. 7, the charge stored between thedetector electrodes and the charge stored in the gas werecompared to estimate the space charge effect. The chargestored in the gas was estimated by multiplying the ion transittime and the signal current, and it was 3� 10�12 1C at 20V.The charge stored between the detector electrodes wasestimated by multiplying the effective capacitance of theionization chamber and the polarization voltage, and it was10�11 1C at 20V. The charge stored in the gas became smallerthan the charge stored between the detector electrodes at thelowest voltage and the space charge effect would be smaller athigher polarization voltage.

We also did not consider the effect of the free electronfor simplicity. The mobility of the positive ions wasassumed to be equal to that of the negative ions. Sincethe radiation pulse duration was very short in our case, thedisappearance of the ionic charges due to recombinationduring charge production was neglected.

A single tube of force in the applied electric field wasassumed. The positive and negative ions were trappedwithin the tube following an instantaneous pulse ofradiation. They drifted toward opposite electrodes, andthe concentrations of the positive and the negative ionswere reduced by the recombination. Recombination couldonly take place in the region of overlap. Before the ionsreached the electrode, another pulsed radiation entered theionization chamber, and the positive and the negative iondensity would be increased with the same amount in thewhole region of the tube.

Thus, the decreasing charge concentration obeys thefollowing equation [1]:

dnþ=dt ¼ �anþn� (6)

dn�=dt ¼ �anþn�. (7)

The velocity of negative ions at s is

ds=dt ¼ k2V=As

Z d

0

ðAsÞ�1 ds (8)

where k2 is mobility of negative ions, and As

R d

0 ðAsÞ�1 ds is

the term, which depends on the geometry of the ionizationchamber [1].In the simulation, two one-dimensional columns of bins

were assumed. Each bin represented the position of theionization chamber, and it contained the density of ions atthe position. One column of bins contained the densities ofthe positive ions, and the other column of the binscontained the densities of the negative ions. At each loopof the simulation, the charge density at each bin wasdecreased according to Eqs. (6) and (7), and each decreasedcharge density was shifted to another bin, where the shiftdistance of each charge density was the same and the shiftdirections of the two columns of the charge density wereopposite. The a in Eqs. (6) and (7) was a parameter. Theshift distance at a given polarization voltage was propor-tional to the real velocity of ions in the ionization chamber,which depended linearly on the polarization voltage fromEq. (8). The charge density at each bin was increasedabruptly in a number of times while the charge was shifted,which simulated the radiation entrance during the iontransit. The number of the sudden increase of the chargedensities during the ion transit in the simulation was set tobe the same as the number of radiation pulses entering intothe ionization chamber during an ion transit in themeasurement. The number of the radiation pulses, enteringthe ionization chamber during an ion transit, could beestimated from the ion transit time in the ionizationchamber and the time interval between the electron-beampulse. To simulate the recombination process at eachpolarization voltage, the real drift velocity of the ions in theionization chamber was not used, but the number ofradiation pulses entering into the ionization chamberduring the ion transit was used in the simulation. Thedecreased charge densities, which were obtained at the endof the column after the transit through the ionizationchamber, were summed, and the summed charge densitywas divided by the total charge density, which wasproduced in the ionization chamber without recombina-tion, to compare with the measured data. The exponentialterm was included in fit of the data with the small thimble-type ionization chamber to explain the break down of thelinearity in the near-saturation region.The data, measured with the small thimble-type ioniza-

tion chamber for 30 and 60 mA electron beam, were fittedsimultaneously to the model calculation by minimizing thechi-square. Five parameters were varied, and MINUIT wasemployed in the fitting process [10]. The fitting parameterswere a, the recombination coefficient, n1, the normalizationconstant of 1/I for 30 mA electron beam data, n2, thenormalization constant of 1/I for 60 mA electron beam

ARTICLE IN PRESSS.H. Park et al. / Nuclear Instruments and Methods in Physics Research A 566 (2006) 706–712712

data, l1, the parameter of the exponential term for 30 mAelectron beam data, and l2, the parameter of theexponential term for 60 mA electron beam data. The resultsof the fit are shown in Fig. 7. The reduced chi-square of thefit was 1.17.

Fig. 8 shows the plot of 1/I and 1/V with the home-madeionization chamber. There was deviation of data pointsfrom the linearity. If we plotted the data in the form of 1/Ivs. 1/V2, the linearity of the data points were excellent. Itmeans the recombination process of the home-madeionization chamber in our measurement was more likethe recombination process in the continuous radiation. Itwas consistent with the previous estimation. As moreradiation pulses entered the active volume of the ionizationchamber during the ion collecting time, and the recombi-nation process became more like that in the continuousradiation.

We fitted the data, measured with the home-madeionization chamber, to the model calculation. The dataobtained with the home-made ionization chamber at 30and 60 mA were fitted simultaneously. We varied threeparameters, a, n1, and n2 in the fitting process. Theparameters of l1 and l2, which were to explain thedeviation from the linearity in high polarization voltageregion, were not included. The reduced chi-square of the fitwas 1.66, and the results of the fit are shown in Fig. 8.

4. Conclusion

When an absolute dose is determined with an ionizationchamber accurately, the saturation current of the ioniza-tion chamber has to be determined. It is known that if thecontinuous radiation is incident on the ionization chamber,the plot of 1/I and 1/V2 shows a linear relation in highcollection efficiency region, and if the pulsed radiation isincident on the ionization chamber, the plot of 1/I and 1/Vshows a linear relation. This fact makes it simple todetermine the absolute dose with the ionization chamber.Previously the characteristics of the saturation curves in thepulsed radiation had been measured by many groups. Inmost of the previous works, the ion transit time in theionization chamber was shorter than the interval betweenthe radiation pulses.

The characteristics of the saturation curve in the pulsedradiation were studied in our work, where the ion transit

times were longer than the interval between radiationpulses. We employed two different-sized ionization cham-bers, and the dependency of the shape of the saturationcurve on the distance between the electrodes of theionization chamber was measured. The saturation curvemeasured with the large-sized ionization chamber (home-made ionization chamber) showed the characteristics of thesaturation curve in the continuous radiation. The satura-tion curve measured with the small-sized ionizationchamber showed the characteristics of the saturation curvein the pulsed-radiation; however, there were deviations ofthe data points from the linearity at some voltage regions.A simulation code was developed and could explain themeasured saturation curve successfully.In our work, the breakdown of the linear relationship

between 1/I vs 1/V in the overlapping pulsed radiation wasmeasured. A more elaborate method is necessary todetermine the absolute dose with the ionization chamberin such cases, and our simulation method can help todetermine the absolute dose accurately.

Acknowledgement

This work has been carried out under the Nuclear R&Dprogram of the Ministry of Science and Technology(MOST) of Korea. We are also supported by the SRC/ERC program of MOST/KOSEF (Grant # R11-2000-067-02001-0).

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