

ORIGINAL ARTICLE 

Year : 2022  Volume
: 45
 Issue : 1  Page : 4853 


Experimental investigation of ion recombination in a locally made lowvoltage ionization chamber
Mahsa NooriAsl, Hossein Afzal, Mohammad Hamdipour
Department of Physics, Faculty of Science, University of Mohaghegh Ardabili, Ardabil, Iran
Date of Submission  27Sep2021 
Date of Decision  22Mar2022 
Date of Acceptance  23Mar2022 
Date of Web Publication  28Jun2022 
Correspondence Address: Mahsa NooriAsl Department of Physics, Faculty of Science, University of Mohaghegh Ardabili, Ardabil Iran
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/rpe.rpe_36_21
In this study, the weak alpha radiation sources and the beta radiation by the effect of them on the electrical conductivity of air inside the ionization chamber are studied by measuring the produced current. The aim of this study is to make an ionization chamber to measure the ionization caused by weak radioactive sources which produce the electrical current at the order of femto to picoamperes and try to estimate the ion recombination coefficient at low ion densities. A parallelplate ionization chamber with proper shielding and noise reduction circuits are made which measure data and sent them to a personal computer by USB port. The currentvoltage characteristics of the ion chamber are measured when different radioactive sources are placed inside the chamber at the different separation of electrodes. The recombination constant obtained is estimated equal to 1.18 × 10^{−6} cm^{3}/s. It is shown that currentvoltage characteristic for ion chamber with different electrode separation lies on a unique curve by a proper normalization in the pico and femtoampere current range.
Keywords: Air electrical conduction, freeair ion chamber, ion current, ion recombination, natural ionization, nuclear radiation measurement
How to cite this article: NooriAsl M, Afzal H, Hamdipour M. Experimental investigation of ion recombination in a locally made lowvoltage ionization chamber. Radiat Prot Environ 2022;45:4853 
How to cite this URL: NooriAsl M, Afzal H, Hamdipour M. Experimental investigation of ion recombination in a locally made lowvoltage ionization chamber. Radiat Prot Environ [serial online] 2022 [cited 2022 Oct 6];45:4853. Available from: https://www.rpe.org.in/text.asp?2022/45/1/48/348728 
Introduction   
The study of the electric current in the ionization chamber has been started many years ago and many mathematical calculations, experimental measurements, and computer simulations have been done in this field.^{[1],[2],[3],[4]} In recent years also, many researchers have studied the issue and have tried to investigate it in different conditions using different approximations,^{[5],[6]} as well to find new applications for it.^{[7]} Nuclear radiation detectors usually detect ionizing radiation by the effect of radiation on some physical properties of the detecting material of the detector. Operation of the ionization detectors is based on the ionization of the filling gas of the detector, which in the open chamber detectors is the air, by the external ionizing radiation. Some other mechanisms could affect this process. Some of them are as follows:
 Recombination of positive and negative ions
 Attaching the free electrons to neutral atoms to create the negative ions
 The electrons recombine with the created positive ions and neutralize them.
In the open cadge ionization chambers, other factors such as the diffusion of created ions to outside of the chamber, diffusion of natural ions of environment and charged aerosols into the sensitive volume of the detector, and humidity may also influence on the detection process.
Measurements ever made were used strong sources that led to the saturation current in the range of nanoamps or even higher currents. In this article, we have made measurements for weak sources which create the saturation currents in the order of femtoamps to few picoamps, i.e., with an accuracy of at least 1000 times higher than the existing measurements, to our knowledge. Working in such low currents requires certain punctuality in the design of the detector system that we will explain them in the following.
Materials and Methods   
Thomson equations describe the dynamical motion of charges inside a gas ion chamber.^{[1]} Inside the chamber, there is an electrical field E. This electric field is due to the external electrical potential difference applied to the electrodes and it includes the effect of spatial charges. Since the exact mathematical solution for the Thomson equations is not found yet, many researchers have tried each with a series of approximations and in particular, conditions to solve these equations and found some results. Some of their most notable results are the current–voltage characteristic and spatial distribution of electric charge between electrodes and spatial variation of the electric field. Briefly, some of those results are explained here. Townsend ignoring the contribution of space charge in the electric field, and assuming constant velocity for positive and negative ions, solved the Thomson equations and found the following result for the ratio of passing electric current to the saturation electric current:^{[1]}
Where,
In equation 2, all the quantities related to the geometry of the system and the activity and the type of the radioactive source, are separated from the constant parameters.
Here, V_{eff} is the effective volume between the electrodes where the ionization occurs. Near the saturation current, this equation with secondorder approximations leads to the following equation:
Where n = 20. Boag and Wilson^{[2]} assuming a linear variation of charge density between the plates, obtained the same relation but with n = 18. In the Boag model,^{[3]} again the same relation was obtained but with n = 36. The Mie model^{[4]} also results to the same relation with,
In which λ is considered to be about 2 for the air. According to equation 3, if the ratio of current to saturation current is plotted versus the inverse of the voltage square, it will be a parabolic curve. This equation has two unknown coefficients, A and n.
These two unknowns are obtained by fitting a parabolic curve to the experimental points. Then, it can be determined that how well the measurements fit the theory and which theoretical model is most consistent with the experimental data. In addition, from A, the recombination coefficient of ions under experiments' environmental conditions is obtained. It should be noted that equation 3 is valid only near the saturation, so only the data points that are close to saturation, are used for fitting a parabola. Equation 2 after a straightforward calculation could be used to calculate the recombination constant.
If the current is normalized to saturation current and the voltage is normalized to the quantity appearing in the denominator of V, then all variables related to the system geometry and ionizing power of the radioactive source are removed from the equation. By this normalization, equation 1 turns to a universal equation which is valid for any distance d and with the radioactive source with any activity. That universal equation is:
Where f(x) is a function independent of the distanced and the ionization power of the radioactive source.
[Figure 1], schematically shows the experimental setup which is used for measuring the current flowing through the air between the parallelplate electrodes of the detector. The power supply which is pointed by number 8 in the figure is a variable, DC, switching mode power supply which can be adjusted from 0 to 60 V programmatically by a PIC microcontroller. Switchingmode power supplies operate by switching on and off the current of a transformer by a metal oxide semiconductor fieldeffect transistor, MOSFET, by the frequency at the range of tenth till few hundred kHz, so they intrinsically have highfrequency noise, which behaves like an AC electrical current component and easily passes through the detector as a displacement current and in the output shows a nonzero value even without any ionization radiation in the detector. Hence, to remove this noise a secondorder lowpass filter is used which removes highfrequency noises, with this technique the output set to zero when there was no ionization radiation and natural air inside the detector (this stage is tested in an evacuated closed box). Furthermore, metallic shielding is used to remove the environmental noise, which was mainly the 50 Hz mains noise and also the effect of any moving charged bodies in the laboratory, for example, the human body because of rubbing of clothes usually have big values of electrostatic charge which discharge by small sparks touching metallic things. By using suit metallic shielding, a stable output is reached.  Figure 1: This figure schematically shows the configuration of the experimental measurements setup. Number 1 is a metallic box that shield the system from environment electromagnetic waves which act as noises, number 2 is a lowdensity polyethylene box which is used to minimize any leakage current, number 3 is the radioactive source, number 4 is a plastic holder for the source, number 5, 6, and 7 show two parallel flat metallic electrodes, two plastic sheets which hold the electrodes and two polycarbonate holder respectively, number 8 is a programmatically adjustable power supply with additional low pass filter, number 9 is the femto/pico ammeter which sends data to the PC through the USB port
Click here to view 
In this article, the currentvoltage characteristics of an ionization chamber with flat parallelplate electrodes in different conditions using weak sources of alpha and beta particles are found. Then, results are compared with theoretical models and by fitting the theoretical curve to the experimentally measured data near the saturation region, it is determined which theoretical models are most consistent with the experimental measurements. Furthermore, by this way, the recombination coefficient of ions in laboratory conditions could be obtained.
In experiments, two cooper plate electrodes are used with area S = 150 cm^{2} (10 cm × 15 cm) which are parallel and separated by distance d from each other. Voltmeter shows the voltage applied to the electrodes, ammeter shows the electrical current passing through the air between the electrodes. For measuring the ionization created by radioactive sources, the desired radioactive source is placed in the middle of the plates (d/2) and increases the voltage across the plates step by step from 0 V to about 60 V. After reaching equilibrium at each step, the current flowing through the circuit (including the air between the plates) is recorded.
Results   
By the described method, the currentvoltage characteristic of the system under irradiation of the desired radioactive source is found. The first measurement is done without any radioactive source, to obtain the level of ionization under background irradiation. The result of this measurement which is done in the nuclear laboratory is shown in [Figure 2].  Figure 2: Currentvoltage characteristics of the system with electrode separation d = 3 cm for measuring the natural ions in the air inside the detector due to background radiation. Here, the radioactive source is not used
Click here to view 
This figure shows that some measurable ions are naturally present in the air and shows the magnitude of current flowing by that ions. These ions are created by the background radiation, especially radon gas, as well as some other factors. This figure shows that the designed system can measure currents in the order of 10 or 100 femto amps with acceptable accuracy and gives meaningful results. However, the saturation in this figure is detectable, but it is not perfect saturation behavior because ions that are naturally present in the air have a range of masses and motilities which cause, in a low voltage, in which the light ions are completely collected, the heavier ions (charged dust, smoke, or any other aerosols) may not be fully collected, which cause the system does not show an ideal saturation behavior. In the next stage, a betaemitting ^{90}Sr source with 74 kBq activity was inserted between the electrodes and again changed the voltage step by step to find the currentvoltage characteristic (CVC) of the system. Due to the low surface area of the electrodes, low separation of the electrodes, and low ionization power of beta particles, slightly more saturation current is expected. The result of this measurement is shown in [Figure 3]. From this figure, it can be seen that the current increased around 6–7 times and the measured data points are closer to the fitted curve with smaller relative fluctuations. The above two figures are presented to show the system's response to the background radiation as well as to show the system's sensitivity to beta particles and their detection. [Figure 4] shows the CVC when alphaemitting ^{241}Am source with 3.3 kBq activity placed between the electrodes. As it is seen, at the zero applied voltage, V = 0, the current between the electrodes is zero and all ions generated recombine and neutralize. With increasing the voltage, recombination rate decreases and at enough high voltages recombination does not occur in practice and all created ions are collected, so the current reach to a saturated value which is the maximum current. [Figure 5] shows measurements with the same source with an activity of 3.3 KBq for different electrode separations from 1 cm to 7 cm. From this figure, it is clear that saturation occurs for smaller distances in smaller currents and the saturation goes to higher voltages as the distance between the plates increases. The magnitude of the saturated current is less at short distances and increases with increasing the distance between electrodes, which is due to the collision of alpha particles with the electrodes and the loss of energy there at short distances. The measurement results, not shown here, show that the increase in saturation current does not last forever with increasing the distance between the electrodes, and from a distance onward the increase in the distance leads to an increase in recombination and decreases the saturation current. Hence, at the desired voltage, there is an optimum distance in which the saturation current has a maximum value. Now the experimental results are compared with the theoretical models, to obtain the recombination coefficient in the experiments' environmental conditions.  Figure 3: Currentvoltage characteristics when a 74 kBq betaemitting ^{90}Sr source is inserted between two electrodes. Here, the separation of electrodes is 3.5 cm
Click here to view 
 Figure 4: Currentvoltage characteristics when an alphaemitting source with 3.3 kBq activity is inserted between two electrodes. Here, the separation of electrodes, d is 3.75 cm
Click here to view 
 Figure 5: Currentvoltage characteristics when an alphaemitting source with 3.3 kBq activity is inserted between two electrodes, at the different separation of electrodes, d
Click here to view 
Discussion   
From [Figure 6], which shows the plot of equation 1 and a parabolic approximation of it, it is clear that how much error is made by using data points with a certain distance from saturation. Given this error, only the data points for which the ratio of current to saturation current is >0.85 are used.  Figure 6: Plot of equation 1 (principal) with a parabolic approximation of it, near the saturation state. It shows, to have certain accuracy, how far from saturation, the data points are allowed to be used for curve fitting
Click here to view 
[Figure 7] shows the result of this fit for different distances d. The values obtained from the fitting are marked in the figure. In the first four cases, in which the used data points are close to the saturation, the obtained n is consistent with the theoretical results, but in the last case, the obtained n is a large number, because the corresponding curve in [Figure 5] (green curve d = 7 cm) was not reached to saturated state. It experimentally confirms that the parabolic approximation works only in the near saturation region, as expected.  Figure 7: This figure fits a parabola to several points on each currentvoltage characteristics. Considering [Figure 6], the data points which have currently more than 0.85 times the saturation current are used
Click here to view 
In theoretical models, parabolic approximation was obtained only for the proximity of the saturation region. Hence, the last data leaved out and the rest of the data are averaged. Values of n = 23.47, 20.08, 16.7, and 17.51. The result of average is n = 19.44, which is more consistent with the Townsend model. By equation 2 the value of the recombination constant obtained equal to 1.18 × 10^{−6} cm^{3}/s, which of course, depends strongly on environmental conditions.
From equation 4 it is obvious that in the normalized form, all CVCs should coincide. In [Figure 8], the CVC of all separations, which are normalized as described, are plotted. It can be seen that unlike [Figure 5], the experimental data points are all on the same curve, regardless of the distance value, (A similar normalization is given in reference^{[8]} for higher currents).  Figure 8: This figure shows the normalized voltage versus the current. Normalization has caused all data points of different distances, d, to lie almost on the same curve. The vertical axis is dimensionless but on the horizontal axis, V is in volts, I_{sat} in picoamps, and d in cm, to avoid the appearance of powers of 10. V_{er} is also the relative effective volume which is normalized to the effective volume at d = 4cm
Click here to view 
Conclusions   
In this study, a current ionization chamber is designed that was suitable for measuring the radioactive sources with low ionization power, in which the current passing through the chamber is from the order of femtoamps to few picoamps. The measurements are done for weak sources by the built ionization chamber. The experimental results are compared with previously presented models. By comparing with theoretical models, it is determined which theoretical model is closest to the experimental results. The recombination constant of ions also is calculated from the experimental results. It is shown that all voltagecurrent curves with proper normalization lie on the same curve.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
References   
1.  Townsend JS. Electricity in Gases. London: Oxford University Press; 1915. 
2.  Boag JW, Wilson T. The saturation curve at high ionization intensity. Br J Appl Phys 1952;3:2229. 
3.  Boag JW. Ionization measurements at very high intensities. Pulsed radiation beams. Br J Radiol 1950;23:60111. 
4.  Mie G. The Electric Current in Ionized Air in a Planar Capacitor. Ann Phys 1904;318:85789. 
5.  Chabod SP. A perturbation method to examine the steadystate charge transport in the recombination and saturation regimes of ionization chambers. Nucl Instrum Methods Phys Res A 2008;595:41925. 
6.  Cabellos O, Fernández P, Rapisarda D, GarcíaHerranz N. Assessment of fissionable material behavior in fission chambers, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 2010;618:248259. (DOI: https://doi.org/10.1016/j.nima.2010.02.114). 
7.  Seran E, Godefroy M, Pili E, Michielsen N, Bondiguel S. What we can learn from measurements of air electric conductivity in 222Rn rich atmosphere, Earth and Space Science 2017;4:91106. (DOI: https://doi.org/10.1002/2016EA000241). 
8.  Bielajew AF. The effect of free electrons on ionization chamber saturation curves. Med Phys 1985;12:197200. 
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8]
