Overview Phys. 649: Nuclear Instrumentation Physics Department Yarmouk University Chapter 5: Gas-Filled Detectors Introduction Part I: Ionization Chambers Part II: Proportional Counters Part III: Geiger Mϋller Counters Dr. Nidal M. Ershaidat Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors Introduction Common Properties Gas-filled detectors operate by using the ionization produced by radiation as it passes through a gas. Ionization produces pairs of electron-positive ions which tend to recombine again and reform molecules. A gas-filled detector is designed to stop this recombination by imposing an electric field. All detectors of this type derive, in different ways, an electronic signal that originates with the ion pairs formed within the gas filling the detector Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 4 Main Gas-Filled Detectors Three detectors (or counters): A Schematic Gas-Filled Detector Fig. 1 shows schematically a gas-filled detector. Ionization Chambers Proportional Counters Geiger-Müller Counters (or Tubes) Figure 1 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 5 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 6 1
Region of Operation The differences between the various types of gas-filled counters operated in pulse mode are illustrated by the following figure. Recombination is there! At low values of the voltage, the field is insufficient to prevent recombination of the original ion pairs and the collected charge is less that that of the original ion pairs. Figure Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 7 Dr. Nidal M. Ershaidat 8 Ion Saturation Region As the voltage is raised, recombination is suppressed and the so-called ion saturation is reached! Proportional Region Increasing the voltage, the threshold field at which gas multiplication begins is reached. The collected charge begins then to multiply and the observed pulse amplitude will increase. Ionization Chambers are operated in this region! Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 9 Gas multiplication will be linear over some region and the collected charge will be proportional to the number of original ion pairs created by the incident radiation. This is the true region of proportionality and represents the mode of operation of proportional counters. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 1 Limited Proportionality While free electrons are collected, the positive ions barely move. They thus form a cloud of positive charge which is slow to disperse as it drifts toward the cathode. Increasing the voltage still further can introduce non linear effects. These effects are mainly due to positive ions which are also created in each secondary ionization process. If the concentration of these ions is sufficiently high, they represent a space charge which can alter the shape of the electric field within the detector. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 11 Geiger-Müller Region If the applied voltage is sufficiently high, the space charge created by the positive ions can become completely dominant in determining the subsequent history of the pulse. Under these conditions, the avalanche* proceeds until a sufficient number of sufficient positive ions have been created to reduce the electric field below the point at which additional gas multiplication can take place. * See Section III Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 1
Geiger-Müller Region The process is then self-limiting and will terminate when the same total number of positive ions have been formed regardless of the number of initial ion pairs created by the incident radiation. Now each pulse from the detector is of the same amplitude and no longer reflects any properties of the incident radiation. Part I. Ionization Chambers This is the Geiger-Muller region of operation. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 13 Knoll: Chapter 5 What is an Ionization Chamber? It is a type of detector in which ion pairs are collected from gases. 1- The Ionization Process in Gases A radiation passing in a gas interacts with the gas molecules and the result is excited or ionized atoms. The result is the production of pairs of ions and electrons. Regardless of the detailed mechanisms of interaction involved, the practical quantity of interest is the total number of pairs created along the track of the radiation. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 15 A. Number of Ion Pairs Formed The entering particle or radiation must transfer, at a minimum, an amount of energy equal to the ionization energy of the gas molecule to permit the ionization process to occur. The ionization energy for the least tightly bound electron shells for gases used in this type of detectors varies between 1 and 5 ev. (Table 1) Methane Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 16 Energy Dissipation by Ion Pairs The average energy lost by the incident particle per ion formed, called the W-value, is always substantially greater than ionization energy. A priori the W-value depends on the type of gas used, the type and energy of the incident radiation. Practically this value appears as constant and almost independent of the previous factors. Typical values are 5-35 ev Per ion pair. A simple calculation shows that an incident particle of 1 MeV energy will produce ~ 3 ion pairs. Energy deposited by the incident radiation will be proportional to the number of ion pairs produced> Thus measuring the number of ion pairs created gives the energy of the incident radiation (We still have to Diffusion - Kinetic Theory of Gases The neutral atoms or molecules of the gas are in constant thermal motion, characterized by a mean free path for typical gases under standard conditions of about.1µm to 1 µm. Positive ions or free electrons created within the gas also take part in the random thermal motion and therefore have some tendency to diffuse away from regions of high density. This diffusion process is more important for free electrons than for ions since their average thermal velocity is much greater. A point-like collection of free electrons will spread about the original point into a Gaussian spatial. Distribution whose width will increase with time. know the proportionality constant(s). 17 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 18 3
Diffusion - Kinetic Theory of Gases If σ is the standard deviation of this distribution as projected onto an arbitrary orthogonal axis (x, y, or z) at t the elapsed time, then we have: σ D t 1 Diffusion, Charge Transfer and Recombination Now we proceed to the stage where the ion pairs are created after the passage of radiation in the gas. These ion pairs will interact with the neutral gas molecules. Typical and significant types of collisions between the free electrons and neutral gas molecules are: Charge Transfer: The value of the diffusion coefficient D in simple cases can be predicted from kinetic gas theory, but in general, a more complex transport model is required to accurately model experimental observations. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 19 Charge transfer can occur when a positive ion encounters another neutral gas molecule. In such a collision, an electron is transferred from the neutral molecule to the ion. Thus the positive ion becomes neutral and the originally neutral molecule becomes a positive ion! Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors Diffusion In its diffusion the free electron suffers many collisions. Electron Attachment In some gases, a free electron attaches itself to a neutral molecule forming a negative ion. This negative ion behaves like the originally created positive ions. In air, oxygen has tendency to form negative ions when free electrons undergo diffusion in air. The other gases (nitrogen, hydrogen and hydrocarbon gases and noble gases) are all characterized by low electron attachment coefficients and therefore the electron continues its trajectory as free electrons under normal conditions. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 1 Recombination Here the electron is captured by a positive ion and returns to its state of charge neutrality. Another process is the collision between a positive ion and a newly formed negative ion. The extra electron is transferred to the negative ion and as a result both ions become neutral. In both cases, the charge produced by the passage of the radiation is lost! If n + is the number of positive ions n - is the number of negative ions α is the recombination coefficient then we have: + dn dn + α n n dt dt Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors Recombination Coefficient Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 3 A. Charge Mobility (µ) If an external field, E is applied to the region in which ions or electrons exist in the gas, electrostatic forces will tend to move the charges away from their point of origin. The net motion consists of a superposition of a random thermal velocity together with a net drift velocity in a given direction The drift velocity for positive ions in the direction of the conventional electric field, whereas free electrons and negative ions drift in the opposite direction. For ions in a gas (pressure p), the drift velocity v can be fairly accurately predicted from the relation: µe v 3 p Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 4 4
µ - Order of Magnitude The charge mobility (µ) tends to remain fairly constant over wide ranges of electric field and gas pressure and does not differ greatly for either positive or negative ions in the same gas Typical values are between 1. and 1.5 1-4 m atm/v.s for detector gases of medium atomic number Typically the electric field used in gas-filled detectors, operating at 1 atm pressure, is of the order of 1 V/m in which case the drift velocity is of the order of 1 m/s *. Corresponding drift times for detectors of 1 cm length is thus 1 ms, which is rather a long time. * 5 times larger than the drift velocity of electrons of a current of 1 A. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 5 The Free Electrons Case Free electrons behave quiet differently. Their much lower mass allows a great acceleration between encounters with neutral gas molecules and the value of the mobility is typically 1 times greater than for ions. Typical collection times are of the order of microseconds. Another different behavior is that is some gases a saturation value for the drift velocity of electrons is observed. See Fig. In argon-hydrocarbon mixtures (Argon+1% methane) v approaches a maximum for high values of E/p and may even decrease slightly if the field is further increased. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 6 Drift Velocity - Free Electrons Other Gas-Filled Detectors In many other gases, the electron drift velocity continues to increase for the largest E/p values likely to be used in gas-filled detector. Figure 3 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 7 Figure 4 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 8 Explanation Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 9 B. The Ionization Current The drift of the positive and negative charges, in the presence of an externally applied electric field constitutes a current. A steady state radiation sources irradiating a given volume of a gas the rate of formation of ions is constant A priori, this rate is exactly balanced by the rate at which ion pairs are lost from the volume, either through recombination or by diffusion or migration from the volume. Neglecting the recombination, the resulting collected current is an accurate measure of the rate at which ion pairs ate formed within the volume. Measurement of this ionization current is the basic principle of the dc ion chamber. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 3 5
Ion Chamber - Scheme A volume of gas is enclosed within a region in which an electric field is created by applying an external voltage At equilibrium, the current flowing in the external circuit, measured by a sensitive ammeter, will be equal to the ionization current collected at the electrodes. The figure shows the current measured. Figure 5 Ion Chamber Current The (collected) current-voltage characterizes the chamber shown in the previous figure. At low voltage, no net current flows. Recombination is predominant here. As we said before, increasing the voltage will progressively suppress the recombination and a steady linear current is observed. At a certain value of V, the current is entirely coming from the free electrons (ionization current) The (collected) current-voltage characterizes the chamber shown in the figure see next slide. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 31 Figure 6 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 3 Design and Operation of DC Ion Chambers A. General Considerations In current mode, a dc ion chamber collects negative charges, either they are free electrons or negative ions (resulting from electron attachment). Thus any gas can be used including those with high attachment coefficients (oxygen). Although recombination is more significant when negative ions are formed, diffusion losses are less important here. The dimensions of such chambers can be of the order of a few centimeters since the conditions of saturation can be achieved over small distances. The most common ionization chambers are those used for the measurement of gamma-ray exposure and they all use air. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 34 Geometry The main concern is choosing the geometry to obtain a uniform electric field. Parallel plate or Planar geometry can do the job. Cylindrical geometry is also used. See Fig. 7 The outer shell is operated at ground potential and an axial conducting rod carries the applied voltage. Note that the electric field here varies inversely with the radius (See EM course). Figure 7 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 35 B. Insulators and Guard Rings A supporting insulator (synthetic plastic) should be installed between the electrodes. This insulator should be chosen in a way that the leakage of the tiny ionization current ( pa) should be kept very small. Ideally, a simple calculation shows that for a chamber operating at 1 V giving an ionization current of 1-1 A, the leakage in an insulator of resistance 1-16 would be or the order of 1%. This is never the case, since moisture may alter the resistance of the insulator and we use the socalled guard rings to reduce the effects of insulator leakage. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 36 6
Reducing the leakage 1 The insulator is segmented into two parts (inner and outer) separated by the conducting guard ring (from each side of the central electrode (The one connected to the anode wire) Reducing the leakage Most of the voltage drop occurs across the outer segment in which the resulting leakage current does not pass through the measurement device. Figure 8 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 37 The voltage drop across the inner segment equals the voltage difference between the ammeter terminals and can be very small and neglected. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 38 C. Measurement of the Ion Current - Amplification The ion current being small, standard ammeters or galvanometers are not adequate. Picoammeters can be used, but the standard procedure is to carry out some active amplification of the current to allow its indirect measurement by an electrometer. An electrometer senses the voltage drop across a series of resistance placed in the measuring circuit. Measurement Circuit - Scheme The technique is to amplify the voltage drop across the resistor (typical values 1 9-1 1 ohms) This method has an important weakness! The dc coupling between the components may change the measured output readings. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 39 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 4 Alternative method An alternative approach is to convert the signal from dc to ac at an early stage which then allows more stable amplification to the signal in subsequent stages. This conversion is accomplished using a dynamiccapacitor (Fig. 9) or a vibrating reed electrometer by collecting the ion current across an RC circuit with long capacitive time constant. Figure 9 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 41 Converting the signal - dc to ac Simple electrokinetics If I is the steady state ionization current then the voltage across the resistor is simply V IR 4 A charge Q is stored in the capacitance and is given by: Q CV 5 If the capacitance is caused to change rapidly, i.e. in times less than τ, then a corresponding change will be induced in the voltage across C (V C ) Q C I R R V C C I C 6 C C C Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 4 7
Integration Method Now if the capacitance is varied sinusoidally about an average value C, the amplitude of the resulting ac voltage is therefore proportional to the ionization current Average ionization currents can also be measured over finite periods of time by integration methods. Integration Method - Advantage If the amount of natural leakage across C can be kept small this integration technique has the potential of being able to measure much smaller ionization currents than through direct dc current measurements. Here R is made infinite, forcing the current to be stored in the capacitance. The total integrated charge (and finally the current) is measured by measuring the voltage change across C, i.e. Q V C Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 43 7 See discussion page 139 and section D. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 44 Radiation Measurement with Ion Chambers Application of DC Ion Chambers Knoll: pages 14-144 Calibration of Gamma-Ray Sources The (portable) dc ion chambers are mainly used as survey radiation monitoring devices. Size of these chambers, filled with air, is hundreds of cubic centimeters and the measuring device is a battery-powered electrometer circuit. Walls are fabricated from plastic or aluminum. There also exist portable ionization chambers based on the charge integration principle and those are mainly used for dose measurement. Here we will detail the use of these chambers in the important procedure of calibrating gamma-ray sources. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 47 Portable Ion Chamber http://www.indiamart.com/sanlar-imex-services/nuclear-medicines.html Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 48 8
Calibration of Gamma-Ray Sources The long term stability of the ion currents, which mainly depends on the geometry of the source and the detector make them excellent tools for calibration purposes. Typical main characteristics can remain stable to within.1% for several years*. Here the active volume may be in thousands of cm 3 and the walls are made of brass or steel. The idea is to compare an unknown source with a well-known one under the same geometry conditions. * We shall see that other devices (GM Tubes for example) could become less stable with time. 49 Calibration of Gamma-Ray Sources Figure 1: Ionization chambers used for calibration of gamma-ray source. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 5 Calibration of Gamma-Ray Sources The curves below each configuration shows the behavior of ionization current for small displacements of the source position. (Knoll, Fig. 5.13) Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 51 9
DC Ion Chambers Pulse Mode Operation A. General Considerations Ion chambers can be used in pulse mode Reminder: In the pulse mode each separate radiation quantum gives rise to a distinguishable pulse. Pulse mode offers significant advantages in sensitivity or ability to measure the energy of the incident radiation. Ionization chambers operated in pulse mode remain the best option in certain specialized applications such as: alpha spectrometry Neutron detection Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors Pulse Mode Setup The basic electric signal in the measuring circuit is the voltage across the resistance (V R ) Figure 11 In the absence of any ionization charge (t) in the chamber, V R and all the applied voltage V appears across the ionization chamber itself Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 3 Pulse Mode Setup The passage of radiation will create ion pairs which will drift toward the electrodes of the chamber, thus reducing the voltage across the chamber. A voltage across the load resistance appears and is equivalent to the voltage drop in the chamber. V R reaches its maximum value when all the charges within the chamber have been collected. Depending on the time constant of the RC circuit, a slow return to the equilibrium takes place. Again if the collection time is small compared to τ, then a signal pulse is produced whose amplitude indicates the magnitude of the original charge generated within the ion chamber. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 4 Pulse Mode Setup Pulse-type ionization chambers are operated in the electron sensitive mode. (i.e. insensitive to positive or negative ions in the chamber see discussion Knoll page 149) The time constant is chosen to be intermediate between the electron collection time (a few microseconds) and the ion collection time (a few milliseconds) The amplitude of the pulse reflects only the drift of electrons and will have much faster rise and fall times. In this manner, shorter shaping time constants and much higher rates are tolerated. One last thing, the choice of a gas should be chosen with a little attachment coefficient in order for electrons to remain as free electrons (minimal Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 5 Electron Sensitive Mode formation of extra negative ions). Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 6 1
Derivation of the Pulse Shape Main assumptions: 1. Simple ion chamber with parallel plate electrodes.. The separation (d) between the plates is small compared to the dimensions of the plates, thus A - Edge effects are neglected. B- The analysis would involve one variable (x): the position of the charges in the dimension perpendicular to the plates. Figure 1 Technique Other assumptions: 1. The electric field is sufficient so one can neglect recombination of ions.. Negative charges remain as free electrons. Case τ >> Ion and electron Collection times. In this configuration, equipotential surfaces are uniformly spaces planes parallel to the electrode surfaces. Thus the electric field is simply: V E 8 d Now we shall assume that all ions pairs are formed at an equal distance x from the positive electrode (Potential surface Ex) Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 7 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 8 Conservation of Energy Because τ is large enough, no appreciable current can flow during the relatively short time required to collect the charges within the ion chamber. Therefore, the energy required to move the charges from their place of origin must come from the energy stored across the capacitance C, i.e. 1 CV 9 After a time t, the ions will have drifted a distance v + t toward the cathode and the electrons will have moved a distance v - t toward the anode. v + and v - are respectively the drift velocities of the ions and the electrons. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 9 Conservation of Energy Both ions and electrons move to a region of lower electric potential, and the difference of potential energy is absorbed in the gas through the multiple collisions between the charges and the gas molecules. If Q is the involved charge of n created ion pairs and ϕ is the change in electric potential, then the energy should be Q ϕ n e ϕ. The change in electric potential is simply E (v + t) for the ions and E (v - t) for the electrons. Conservation of energy gives: 1 + 1 C V n e E v t + n e E v t + CV ch 1 or 1 C ( V Vch ) n e E ( v + + v )t 11 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 1 Approximations Eq. 11 can be rewritten as: 1 V C ( V V )( V V ) n e ( v + ch ch + v ) t d 1 V R is almost always small compared to V, thus we can make the following approximations: V + Vch V and Vch V d d 13 Simple algebra gives: n e V R ( t) ( v v ) + t d C 14 This result describes the initial portion of the signal pulse and predicts a linear rise with time. The validity of this results is limited to the period of time that both the ions and electrons are drifting within the chamber. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 11 Induced Charge The concept of induced charge is used to describe the changes caused by the drifting charge carriers. By drifting a distance v + t, the ions cause the chamber voltage to drop by an amount equal to n ev + t/d C. The same effect would be caused by the reduction of the charge stored across the capacitance C by an amount n ev + t/d. Therefore, the ion motion can be thought of as inducing a charge of this magnitude A similar induced charge (n ev - t/d) is created by the electron motion. It should be emphasized that the induced charge results only from the motion of the charge carriers within the chamber volume and does not require their collection at either electrode! 1
Time t - to t + After a time t - x/v - the electrons reach the anode (The ions are still moving). Their drift has then contributed the maximum possible to the signal voltage and the nd term in the left-hand side term of eq. 14 becomes a constant, namely n e n e v t x d C d C For the next period (t > t -- ), only the ions are still drifting and eq. 14 takes the form: n e + V R ( t > t ) ( v t + x) 16 d C Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 13 15 V max The ions reach the cathode after a time t + (d-x)/v +. At this point, the signal voltage no longer increases and Eq. 14 becomes: n e n e V R (( d x) + x) 17 d C C Fig. 1 shows the shape of the signal pulse predicted by the three equations (for the three periods, equations 14, 16 and 17). Thus in the case RC >> t +, the maximum amplitude of the signal pulse is given by eq. 17. This value is independent of x. The maximum amplitude V max gives a direct indication of the original number of ion pairs n that contributed to the pulse. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 14 Case t - << RC << t + In electron sensitive operation (t - <<RC<<t + ), the first portion of the curve in Fig. 13 is preserved while the portion of the pulse derived in the case t - <t<t + is almost entirely lost. The pulse that remains reflects only the drift of the electrons and will have an amplitude given by eq. 16 (in which we neglect the ion drift) V elec n e x 18 d C Here the pulse amplitude is position-dependent. Fig. 13 also shows the shape of the signal pulse predicted in this case. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 15 V R (t) Figure 13 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 16 C. The Gridded Ion Chamber The dependence of the pulse amplitude in position of interaction in electron sensitive ion chamber can be removed through the use of a gridded ion chamber. Homework: Read this paragraph Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 17 D. Pulse Amplitude The typical amplitude of an ion chamber is relatively small. Here we will make a rough estimation of this amplitude. 6 E 1 4 n.86 1 W 35 For typical ion chambers and associated electronics the capacitance C will be of the order of 1-1 farads. Thus we have: n e 5 V max 4.58 1 V 45.8µ V C Actual electronics available can measure such a value with precision. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 18 3
E. Statistical Limit to Energy Resolution Let us assume alpha particles with energy of 5.5 MeV fully stopped in a gas with a W-value of 3 ev and a Fano Factor of.15 ( See chapter 4) The number of ion pairs is: 6 Ed 5.5 1 5 n 1.83 1 W 3 The variance in this number is given by: σ n F n Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 19 4.75 1 and the standard deviation is: σ n F n 166 The FWHM of the gaussian distribution describing n is FWHM.355σn 39 Energy Resolution The FWHM in units of particle energy FWHM.355 σ n. W 39 3 ev 11. 7 kev This figure (11.7 kev) would be considered as its energy resolution..355 σ R E d 3 W 11.7 1 ev 6 5.5 1 n.13% This (theoretical) resolution is never achieved because electronic noise dominates over the contribution of statistical noise. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors Principal features and advantages Charged Particle Spectroscopy Measurements of the energy of charged particles are achieved using semiconductor detectors. Nevertheless, ionization chambers offer attractive feature for these measurements. 1- They can be constructed with almost arbitrary size and geometry, - Their design is simple and can be fabricated in standard workshops, 3- More importantly, the pressure of the gas can be chosen to "tailor" the stopping power or the effective thickness of the active volume. 4- They are less subject to performance degradation due to radiation damage then are semiconductor detectors. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors Alpha Spectrometry Bragg Curve Spectroscopy Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 3 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 4 4
II. Proportional Counters Introduction Knoll: Chapter 6 Principal features and advantages In common with the Geiger-Müller tubes, the proportional counters (invented in the 194's) have the following features: 1-They are almost always operated in pulse mode, -They rely on the phenomenon of gas multiplication (avalanches). Output pulses are therefore much larger than those of an ionization chamber. The proportional counter (PC) is the most appropriate in the cases where the number of ion pairs created is very small. Gas multiplication plays the role of "an amplifier" and this reduces the electronics needed for the signal treatment. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 7 Use of Proportional Counters Detection and spectroscopy of low-energy X- radiation. Neutron detection, Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 8 I. Gas Multiplication A. Avalanche Formation We have seen that increasing the electric field applied between the electrodes suppresses the recombination of ion pairs. Increasing this field further will also accelerate the free electrons (and the positive ions). Free electron gain kinetic energy which can be enough for them to ionize other gas molecules on their way while drifting to the anode. Thus, secondary ion pairs are created following the collisions between the "original" free electrons (primary ionization) and the gas molecules. This process occurs above a threshold value of the electric field, which is of the order of 1 6 V/m for typical gases under atmospheric pressure. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 3 5
Townsend Avalanche This value is very large and the gas in the counter (and in the GM tube) is maintained under lower values of pressure. This process is called gas multiplication. It takes the form of a cascade, known as Townsend avalanche. Townsend Equation The fractional increase in the number of electrons per unit path length (n) is governed by the Townsend equation: dn αdx 19 n This equation expresses the proportionality between the number of secondary ion pairs dn created after a path length dx and (1) the original number of free electrons n and () dx. The proportionality constant in Eq. 19, α, is called the first Townsend coefficient for the gas. Figure 14: Townsend avalanche - Schematic 31 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 3 Townsend Coefficient (α) Fig. 15 shows the variation of this constant with the electric field (strength). α below the threshold and increases with increasing electric field. Figure 15 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 33 Townsend Equation Solution In a simple parallel plate geometry, α is a constant. The solution of the Townsend equation gives: α x n( x) n( ) e n() is nothing else but the number of the original free electrons. In a more sophisticated geometry (cylindrical counters) the electric field increases in the direction that the avalanche progresses and the growth of secondary ion pairs is even steeper! The total number of ions can be multiplied by a factor of many thousands. This "amplification" within the detector itself has the advantage to reduce the need for amplification, thus reducing the electronic noise. The so-called signal-to-noise (or S/N) ratio is much smaller in proportional counters than in ionization chambers. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 34 Major Disadvantage The formation of an avalanche involves many energetic electron-atom collisions which may create a variety of excited atomic or molecular states. The performance of a proportional counter (and a GM tube) is therefore much more sensitive to the composition of trace impurities in the fill gas than in the case for ion chambers. B. Choice of Geometry Typical proportional counter (and GM tubes) are constructed with cylindrical geometry. (Fig. 16) Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 35 Figure 16 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 36 6
Electric Field The anode consists of a fine wire (generally copper) that is positioned along the axis of a large hollow tube that serves as the cathode. The electric field in such a configuration, at distance r from the anode is given by: V E( r) 1 r ln b a ( ) where a and b are, respectively, the anode wire radius and the cathode inner radius. Large values of the electric field, required for the gas multiplication to occur, are obtained in the immediate vicinity near the anode (r is small) Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 37 Order of Magnitude For a cylindrical counter where a.8 cm and b 1. cm* with V1 V, the electric field at the anode surface is: E ( a) V a ln 1V 5 ( b a) 8 1 ln ( 1..8).6 1 V m In order to get an equivalent electric field in a parallel-plate type (d1. cm) one would need a voltage:.6 1 V cm V 6 V 1. which is an unworkable electric field.! 4 * The counter volume is: πb a.5 cm 3 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 38 6 Order of Magnitude If uniform multiplication is to be achieved for all ion pairs formed by the original radiation interaction, the region of gas multiplication must be confined to a very small volume compared with the total volume of the gas. See discussion in Knoll, pages 16-163 Monte-Carlo simulation Fig. 17 II. Design Features of Proportional Counters Figure 17 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 39 A. Sealed Tubes - Technical Details The following figure shows a sketch of a PC incorporating common design features. Figure 18 Cathode - Window For applications involving neutrons or gammarays, the cathode wall can be several millimeters thick to provide adequate structural rigidity. For low-energy γ-ray, X-rays or particulate radiation, a thin entrance "window" can be provided either on one end of the tube or at some point along the cathode wall. http://www.moxtek.com/x-ray-windows/sealed-proportional-counter-xray-windows.html The outer cathode is conventionally grounded, Anode: A thin axial wire supported at either end by insulators that provide a vacuum-tight electrical feedthrough for connection to the high voltage Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 41 The electric field becomes very distorted near the point at which the anode wire enters the insulator. See discussion about "end" effects. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 4 7
B. Windowless Flow Counters Here the source of radiation is a small sample of a radioisotope which can be introduced directly into the hemispherical volume of the detector. The pancake detector See details in Knoll Figure 19 Figure Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 43 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 44 The 4π Gas Flow PC Used to detect radiation that emerge from both surfaces of the sample. Figure 1 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 45 C. Fill Gases Gas multiplication is critically dependent on the migration of free electrons rather than negative ions. Thus gases with low "attachment coefficients" are the best choice for proportional counters. (Air is no good) Noble gases (Ar, Kr and Xe) are commonly used for beta measurements. These often require a quench gas however (See next paragraph) Ar is used for cost reasons. A mixture of 9% Ar with 1% methane, The so-called P-1 gas is generally the best choice. For γ measurements krypton or xenon are used if budget is OK. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 46 Quench Gas Collisions between primary electrons and the gas neutral molecule produce the secondary ionization and avalanches. These collisions may also only excite the molecules and the de-excitation is accompanied by the emission of visible or UV photons. These photons may be responsible of secondary ionization elsewhere in the fill gas through photoelectric interactions with less tightly bound electron shells or could produce electrons through interactions at the wall of the counter. Those photon-induced events are important in GM tubes but undesirable in PC's, because they create spurious pulses and/or loss of proportionality A polyatomic gas (generally methane) is added to the fill gas in order to "absorb" these photons preventing the photon-induced ionization. This added gas is called quench gas. 47 Thermal Neutrons Counters Thermal neutron counters use BF 3 or 3 He as the fill gases. The reactions are 1 B(n,α) 7 Li and 3 He(n,p) 3 H. Both these reactions have high cross-sections. The counters work by measuring the charge induced by the recoil of the ionized reaction products. BF 3 is slightly cheaper but 3 He has the advantage of being a slow neutron spectrometer because of recoil effects. Fast neutron counters use hydrogen, methane, helium or low Z gases and again, look at the charge induced by recoiling reaction products. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 48 8
Dosimetry Counters Some dosimetry counters use tissue equivalent gas. This gas is used to model tissue because the counters are intended to model the energy deposition in human tissue. A commonly used tissue equivalent mixtures are tissue-equivalent propane and tissue equivalent methane. III. PC Performances Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 49 A. Gas Multiplication Factor Gas multiplication requires migration of free electrons. If the original number of ion pairs is n then the total charge generated by these ion pairs is: Q n e M Where M is the average multiplication factor. Calculating M - Assumptions: 1- The only multiplication process is through electron collisions - photoelectric effects are neglected, - No electrons are lost to negative ion formation, 3- The space charge effects are neglected. In cylindrical geometry we must take into account the radial dependence of the Townsend coefficient caused by the radial variation of the electric field. 51 Diethorn Equation In general the mean gas amplification factor M can be written as: r c ln M α ( r)dr a r represents the radius from the center of the anode wire (of radius a). The integration runs over the entire range of radii over which gas multiplication is possible or from the anode radius a to arc. r c is the critical radius beyond which the field is too low to support further gas multiplication. 3 5 Diethorn Equation We rewrite the integral as: We get: E( r c ) ln M α E( a) Introducing: E( r) V r ln V ln M ln ( E) ( b a) ( b a) dr de de E( r c ) α E E( a ) ( E) de E 5 6 53 Diethorn Equation And assuming linearity between α and E, Diethorn derived a widely used expression for M: V ln V ln M ln ln 7 ln( b a) V ( ) pa ln b a K where V: potential difference through which an electron moves between successive ionization events, K: E/p value at the threshold of the multiplication. A priori V and K should be constants for any given gas. This is confirmed experimentally - see Table 1 54 9
Diethorn Parameters for Proportional Gases Table 1 shows the Diethorn parameters for several proportional gases M vs. V Table 1 55 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 56 M vs. V Fig. shows the variation of the gas multiplication factor M with voltage applied to various proportional counter. (See legend) Figure Diethorn Plot Fig. 3: Diethorn plot of the same data as in Fig. 1 V ln V ln M ln ln ln( b a) V ( ) pa ln b a K ln M ln( b a) ln V ln ln ln K V V pa ln( b a) V y a x + b Figure 3 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 57 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 58 B. Space Charge Effects The positive ions produced in the avalanche, in the area close to the anode finish by forming a space charge. This space charge may distort the applied electric field. It will particularly change the electric field at small radii (i.e. small values of (r)) and may reduce the amplitude of the output pulse. The distortion depends also on the geometry of the counter and thus the energy resolution is also affected. These effects were studied by Hendricks (1969) and some practical solutions are: - Choosing a small gas multiplication factor. - If the gas multiplication factor is linear, then one should be able to record the same pulse height spectrum by decreasing counter voltage and increasing the gain of the amplifier (to offset or cancel the corresponding drop in gas multiplication. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 59 Hendricks Paper Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 6 1
C. Energy Resolution 1. Statistical Considerations We shall assume here that the charge Q which is developed in a pulse from a PC is the sum of the charges created in each individual avalanche. In other words we shall assume the absence of nonlinearities (we neglect the space charge and the edge effects. If the number of ion pairs created by the passage of radiation is n then there will be n avalanches each triggered by a separate electron. If A represents the electron multiplication factor for any one single avalanche and M the average gas multiplication factor from all avalanches which contribute to a given pulse then statistically we have: 1 n A i A n i 1 M 8 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 61 (Relative) Variance of Q M is also related the charge contributed by the ith avalanche, i.e. ea i simply by: or Q M 9 e n Q e n M 3 The pulse amplitude, as we have seen, is proportional to Q. This amplitude is subject to (statistical) fluctuations due to the independent inherent variations in both n and M. The expected relative variance of Q in this case is: σ Q Q σn σ M 31 n + M Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 6 (Relative) Variance of Q Because each avalanche is assumed to be independent then according to the error propagation formula we can write: And we thus obtain n 1 1 σ M σ A σ i A n n i 1 σq σn 1 σ A + Q n n A Expected relative variance of the pulse amplitude Contribution of ion pair fluctuations Single-electron multiplication variation Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 63 3 33 a. Variation in n We have seen that: and σ n σ n F n n The Fano factor for proportional gases ranges from about.5 to. b. Variation in Single-Electron Avalanches Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 64 A simple theoretical model for the single-electron avalanche distribution is based on the assumption that the probability of ionization by an electron is dependent only on the electric field and is independent of its previous history! F n 34 35 Furry Distribution The expected distribution (the number of electrons produced in an avalanche) should be predicted by the Furry distribution: P ( A) 1 ( 1 1 A) ( 1 1 M ) If the avalanche multiplication or the number of electrons in the avalanche A is reasonably large (> 5 or 1) which is almost always the case then Eq. 36 reduces to the following exponential form: A A e P( A) 37 A Which predicts a relative variance A σ A 1 A A A 1 M 36 38 65 Case of strong electric fields The single-electron exponential distribution holds no more under strong electric fields (usually used in PC's). Experimental single-electron spectra shows a o- called Polya distribution, defined as θ A ( ) ( 1+ θ) A( 1+ θ) P A exp 39 A A θ is a parameter related to the fraction of electrons whose energy exceeds a threshold energy for ionization (<θ<1). The relative variance predicted by the Polya distribution is σ A 1 + b 4 A A b (1 + θ) -1 and is observed to have a value of about.5 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 67 11
c. Overall Statistical Limit For large values of the multiplication factor we have: σ A b A Eq. 33 can be thus rewritten as: σq Q F n b 1 n n [ F + b] The relative standard deviation is thus: + 1 σq 1 [ F + b] 43 Q n Typical values for Fano factor are.5 to. and those of b are.4 to.7, Thus one can conclude that the pulse amplitude variance is dominated by the fluctuations in avalanche size and that the fluctuations dues to the original number of ion pairs are typically a small contributing factor. 68 41 4 D. Time Characteristics of the Signal Pulse There are several major differences between the output pulse from an ionization chamber and a PC. 1. In a Proportional tube, time can be divided into two intervals The electron (from the ion pair formed anywhere in the chamber) drift time to the anode wire and the time during which an avalanche is produced. The contribution to the pulse during the drift time is negligible compared to the contribution of the much faster avalanche. The drift time (1 µs much larger than the "avalanche time") introduces a delay between the production of ion pair and the start of the corresponding pulse. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 71 General Behavior. Because most of the ions and electrons are created very close to the anode wire, the bulk of the output pulse is attributable to drift of the positive ions rather than the movement of the electrons (who already arrived!). At first the positive ions are in a region of higher electric field making them move rapidly toward the cathode but as soon as they become "far" from the anode their motion becomes slower (lower electric fields) and the effect, is a slow rise in the output pulse. The pulse "ends" when they finally arrive to the cathode. Still this part of the pulse is simply not observed because of the finite shaping times of the subsequent electronic circuit. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 7 A Simplified Analysis A simplified analysis is done in the same "spirit" used for the (parallel plate) ion chamber. Except that for obvious reasons here we have to take the cylindrical geometry into account. The energy absorbed de by a positive charge Q through a potential difference dϕ is given by: de Q dϕ 45 In terms of the electric field E(r) -dϕ(r)/dr de dr QE ( r) Q 46 r ln( b a) If n is the number of electrons and positive ions formed in an avalanche at a fixed distance r from the surface of the anode wire, then Q n e Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 73 V A Simplified Analysis The energy absorbed by the motion of the positive ions to the cathode is then: b b + de QV E dr dr ln a + ρ a + ρ dr QV b ln 47 ( b a) r ln( b a) a + ρ The energy absorbed by the negatively charged electrons inward to the anode is: a QV dr QV a + ρ E 48 ( b a) ln ln r ln( b a) a a + ρ The sum of the energy absorbed after both species have been collected is: + QV b a + ρ E E + E ln QV ln ( b a) a + ρ a Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 74 49 A Simplified Analysis As we have seen in the parallel plate geometry, this energy must come from at the expense of the energy stored on the detector capacitance, i.e. 1 1 CVch CVch E 5 1 C ( Vch + V )( Vch V ) E QV Q CV VR QV VR 5 C which is the same results we obtained in the case of the parallel plate geometry. This value is the maximum pulse amplitude that would be developed if the (capacitive) time constant RC is long compared to the ion collection time. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 75 51 1
Voltage-Time Profile In proportional counters this condition never holds. RC is always between t + and t -. In this case the shape of the pulse amplitude depends on the voltage-time profile. Most of the electrons and the ions created in an avalanche are formed close to the anode wire surface. The exponential growth (n(x) n e αx ) predicts that half will be formed within one mean free path of the anode, typically a few micrometers from the surface! Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 76 E - /E + Let's evaluate the ratio E - /E + for a 5 µm, b 1 cm and ρ 3 µm E ln[ ( a + ρ) a] ln[ 8 5].193 53 + 4 E ln[ b ( a + ρ) ] ln 1 ( 8) [ ] This calculation shows that the contribution of the avalanche electrons is less than % of the maximum signal, This allows us to neglect the electron contribution and to assume that the entire signal pulse develops from drift of the ions that are essentially created at the anode wire surface Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 77 Drift Velocity Collection Time The drift velocity of the ions varies with the position as: + ue ( ) ( r) µ V 1 v r 54 p p ln( b a) r Putting this expression in the law of motion (drvdt) r( t ) dr t + ( ) dt 55 a v r a Integrating we have: µ V 1 r( t) t + a p ln( b a) 56 The time required to collect the ions can be found by substituting r(t) b in eq. 55 µ V ( ) ( ) + b t + b a pln b a t p ln( b a) a µ V 57 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 78 Drift Velocity Using typical values for the parameters, this collection time is very long with a representative value of several hundred microseconds. A large fraction of the signal is developed during the very early phase of the ion drift. The energy absorbed by the motion of the ions as a function of time is: r( t ) + QV dr QV r ( ) ( t) E t ln 58 ln( b a) r ln( b a) a a Using Eq. 56 and setting V R (t) E + (t)/cv we find the time profile of the signal pulse to be: V R ( t) Q 1 µ V ln ln( ) t C b a a pln( b a) 1 + 1 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 79 59 Drift Velocity Eq. 59 predicts that the pulse will reach half its maximum amplitude within a time given by: Using eq. 57 we have: t half amplitude a a + b t + ( b a) pln( b a) t a half amplitude µ V At this point, the radial position of the ion is given by ab, where the value of the electric field has dropped to a fraction given by a b of its value at the anode wire surface. 6 61 t half amplitude Evaluating for standard values (a 5 µm and b 1 cm) we have: 5 + + t t.5% t half amplitude 4 5+ 1 which means that the half point is reached after only.5% of the full ion drift time, typically a fraction of a microsecond. At this instant t half amplidtude the ions have moved from the wire surface a distance: d v + t half amplitude 475µ m The electric field at this distance is down to 5% of its surface value. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 8 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 81 13
t half amplitude This fast leading edge of the pulse is followed by a much slower rise corresponding to the drift of the ions through the lower-field regions found at larger radial distance. If all original ion pairs are formed at a fixed radius, the electron drift times will all be identical and all avalanches will be synchronized. Then Eq. 59 will also describe the shape of the output pulse for these events Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 8 Real Situation Ion pairs are formed along the track of the incident radiation and thus cover a certain range of radii (different r). This introduces a spread in electron drift times and consequently an additional spread in the rise time of the output pulse. Fig. 3 shows the shape of the expected leading edge (discussed in the previous paragraph) under two conditions: 1- ion pairs formed at a constant radius - ion pairs uniformly distributed throughout the volume of the counter. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 83 Real Situation Figure 4 Minimizing the rise! To minimize the rise in the dashed pulse, a short electron drift time is helpful This can be done by keeping the electric field values as high as possible in the drift region and/or by choosing a gas with high electron drift velocities ion pairs formed at a constant radius ion pairs uniformly distributed throughout the volume of the counter. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 84 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 85 Slow and Fast Fill Gas Fig. 5 shows a variety of "slow" and Fast" fill gases Ballistic deficit See discussion in Knoll pages 18-183 Figure 5 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 86 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 87 14
E. Spurious Pulses In some circumstances, satellite pulses may be generated following the primary pulse from a PC. These secondary pulses have nothing to do with the incident radiation but are generated from secondary processes that arise from effects within the primary avalanches. Theses spurious pulses: 1. can lead to multiple counting where only one pulse should be recorded and. are a potential cause of counter instability! See discussion in Knoll pages 183-184 IV. Detection Efficiency ad Counting Curves Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 88 A. Selection of the Operating Voltage Lower values of the gas multiplication are typically used, which require that the pulse originate from a finite number of ion pairs in order to have an amplitude large enough to exceed the discrimination level of the counting system. B. Alpha Counting If almost all pulses from the detector are of the same size, the differential pulse height spectrum (DPHS) has a single isolated peak, Figure 5-a See Counting curves and plateaus! Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 9 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 91 Counting Curve - Plateaus The corresponding counting curve has a simple plateau. Such a curve is observed in a Geiger tube but this is a situation where it is observed using a proportional counter. Counting Curve - Plateaus Monoenergetic alpha particles produce such a situation and the PC detects (almost) each and every alpha entering the active volume of the counter Detection efficiency 1%. Figure 5-b Absolute measurements can be made using a windowless PC (solid angle π). Alpha selfabsorption and scattering in the source itself or in the source backing require corrections. (And we know how to do that) Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 9 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 93 15
C. Beta Counting The range of beta particles being larger than the dimensions of the counter, the number of ion pairs formed in the gas is then proportional to only that small fraction of the particle energy lost in the gas before reaching the opposite wall! The DPHS in the figure is that obtained with a mixed source (α and β) Figure 6-1 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 94 Counting Curve - Plateaus The counting curve will show two plateaus. The alpha plateau and a second plateau (shorter than the first plateau) where both α and β are counted. Notice the larger slope of the beta plateau due to the broadening of the pulse spectrum of the beta particles and to the fact that they are less separated from the lowamplitude noise. Absolute beta measurements are carried out in a 4π flow counter, The fact that the range of beta particles is relatively large allows the fabrication of sources on backings that are sufficiently thin to allow the particles to emerge and only small corrections are required to account for those particles that do not reach either half of the chamber active volume! Fig. 6-b Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 95 D. Mixed Sources See Knoll Pages: 185-186 E. X-Ray and Gamma-Ray Sources PC's can be used for the detection of soft X-rays or gamma-rays whose energy is low enough to interact with reasonable efficiency in the counter gas. Fig. 7 shows the interaction probability in a 5.8-cm thickness of the common high-z proportional gases at STP. Figure 7 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 96 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 97 Problems Problems 6.1 to 6.1 due by Next Wed. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 98 16
Part III. Geiger-Mϋller Knoll: Chapter 7 Counters Introduction - Secondary Avalanches Geiger-Müller counter (G-M counter or Geiger tube) is one of the oldest radiation detector types in existence (198). G-M counters employ gas multiplication, as PC's, to greatly increase (or amplify) the charge represented by the original ion pairs formed along the radiation track, but in a fundamentally different manner. In a G-M tube, substantially higher electric fields are created that enhance the intensity of each avalanche. Under proper conditions, an avalanche can itself trigger a second avalanche at a different position of the tube. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors The Geiger Discharge At a critical value of the electric field each avalanche can create, on the average, at least one more avalanche. A selfpropagating chain reaction results. At greater values of the electric field, the number of avalanches can grow exponentially within a very short period of time. This is called a Geiger discharge. Once this discharge reaches a certain size, however, collective effects of all the individual avalanches come into play and ultimately terminate the chain reaction! Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 3 Information on Energy is Lost This limiting point is always reached after the same number of avalanches have been created, all pulses from a Geiger tube are of the same amplitude regardless of the number of original ion pairs that initiated the process, Information on the amount of energy deposited by the incident radiation is thus lost!! A G-M counter can therefore function only as a simple counter of radiation-induced events and cannot be applied in direct radiation spectroscopy. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 4 Simple Amplification Needed A typical pulse from a G-M counter represents an unusually large amount of collected charge, about 1 9-1 1 ion pairs being formed in the discharge. Consequently, the output pulse amplitude is also large (typically of the order of volts). This signal allows considerable simplification of the associated electronics, often eliminating the need for external amplification. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 5 Advantages - Disadvantages Low cost and simple electronics make the Geiger- Müller counter the best choice for detecting radiation! Lack of information on energy is a major disadvantage. Another disadvantage of the G-M counters is their large dead time. This limits their use to low counting rates. For moderate counting rates (1 pulses/second) dead time corrections should be made! Another important disadvantage is that some of these counters have a limited lifetime and will begin to fail after a fixed number of total pulses have been recorded! Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 6 1
Photons In addition to the secondary ions created in a Townsend avalanche, many excited gas molecules are formed. I. The Geiger Discharge UV or visible photons are the result of the deexcitation of these molecules. The photons play a key role in the propagation of the chain reaction which makes the Geiger discharge. A photon can "create" a free electron either by: 1- photoelectric absorption by a less bound electron in another molecule elsewhere in the gas, or - simply by photoelectric effect absorption at the walls of the cathode. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 8 The case of Ar Excited states (~ 11.6 ev) that decay with the emission of photons of wavelength 14 ev nm λ 17 nm 11.6eV 6 New Avalanches In both cases, the created free electron will migrate toward the anode wire and create an avalanche as the original ion pair electrons! (Fig. 8) These are UV photons. Figure 8 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 9 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 1 Criticality Condition If the number of avalanches is n ' and p is the probability of photoelectric absorption to occur then the product n 'p, called the criticality condition, is a measure of the number of secondary avalanches created by the photons. In a PC, the multiplication factor M is of the order of 1 to 1 4. The probability p is also relatively low and we have: n ' p 1 (subcritical condition) Critical and Subcritical Situations In a Geiger discharge, the multiplication factor is of the order of 1 6 to 1 8 and here the criticality condition n ' p 1 can be achieved. An increasing number of avalanches may potentially be created throughout the Geiger tube. The time required for the spread of these avalanches is relatively short. Adding to that, the presence of quench gases in the PC which prevents the creation of such secondary avalanches by absorbing the deexcitation photons. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 11 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 1
Propagation Velocity Photons create free electrons close to the original avalanches These electrons must drift, within a few mean free paths, into the high field region near the anode wire to generate further avalanches. Secondary avalanches (from both sides of the anode) and the Geiger discharge propagates with a velocity typically of to 4 cm/µs, until the entire length of the wire is involved. The Geiger discharge will finish by surrounding the wire regardless of the position at which the primary initiating event occurred. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 13 End of the Geiger Discharge The mobility of positive ions is much less than the free electrons. The positive ions remain essentially motionless while the electrons are being collected from the multiplying region. When the concentration of these ions is sufficiently high their presence reduces the electric field below the value E( r) V r ln ( b a) in the absence of space charge! Another way of seeing this is to consider that the anode wire and because of the positive space charge "becomes" a new anode wire with larger radius! Which reduces the electric field. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 14 The Geiger Pulse For a fixed applied voltage, which we call the operating voltage of the tube, the point at which Geiger discharge is terminated will always be the same, independently from the radiation who has initiated it. Each Geiger discharge is terminated after developing (about) the same total charge regardless of the number of ion pairs created by the incident radiation. Rising the applied voltage will increase the Geiger discharge and consequently the size of the output pulse. http://hps.org/publicinformation/ate/q4338.html Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 15 Studies Continue! Figure 9 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 16 II. Fill Gases Best Choice: Noble Gases The choice of a fill gas in a G-M counter satisfies similar criteria as in a a proportional counter. Gases with high attachment coefficients (as oxygen) are to be avoided. Noble gases (He, Ar, Kr and Xe) are the best choice. Argon and helium are the most popular choice. The need of a quench gas is also present here. (See discussion in previous lectures) Sealed or windowless flow Geiger-Müller counters also exist. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 18 3
Gas Pressure n ' increase with the energy attained by a free electron between collisions with gas molecules which depends on the ratio E/p (v µe/p) Typical gases at several tens of 1 atm with operating voltages of about 5- V are required to reach the necessary value of the electric field using anode wires of about 1 microns. The development of a Geiger discharge requires a minimum value of the parameter E/p which depends on the gas mixture. Geiger-Müller counters can be also designed to operate at atmospheric pressure. In which case, the mechanical design is simplified because no pressure differential need be supported across the walls or window of the tube. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 19 III. Quenching Quench Gas External Quenching Quenching in G-M tubes is more critical than in PC's. Simply because of the difference in ion pairs involved. Mixtures of noble gases with methane are the most used. In commercial G-M tubes it is rather the ethyl alcohol and ethyl formate which are used. External quenching is also used in G-M tubes. This means reducing the external high voltage applied to the tube for a fixed time after each pulse, to a value that is enough low in order to prevent further gas multiplication. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 1 Degradation An organic quenched tube may typically have a limit of about 1 9 counts in its useful lifetime before multiple pulsing can no longer be prevented because of depletion of the quench gas. Mixtures of noble gases with methane are the most used. In commercial G-M tubes it is rather the ethyl alcohol and ethyl formate which are used. Halogens (Cl or Br) are used sometimes as quenching gases in order to avoid limited lifetime problems. The halogen molecules recombine at a later time after the "quenching" process making them have an "infinite" lifetime. Other mechanisms limiting the lifetime of Geiger tubes: Contamination of the gas by reaction products produced in the discharge and Changes on the anode surface due to the deposition of polymerized reaction products. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors IV. Time Behavior A. Pulse Profile The rise of the pulse we have seen in a PC is also present here except that the positive ions responsible of it are much larger in the case of a G-M tube In a Geiger discharge the pulse corresponds to the cumulative effects of many avalanches that have been formed along the entire length of the anode wire. The time required for secondary electrons to reach the multiplying region (near the anode wire) to trigger the secondary avalanches will be variable but differences will be limited by the relative rapid motion of the electrons The initial pulse rise (leading edge) will be slower than for a single avalanche (PC case). This rise will still develop over a time that is typically less than a few microseconds. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 4 4
Fast Rise followed by a Slow Rises The net effect is that the output pulse from a G-M tube still exhibits a fast rise (a microsecond or less), followed by a much slower rise due to the slow drift of the ions. In a Geiger discharge the pulse corresponds to the cumulative effects of many avalanches that have been formed along the entire length of the anode wire. The time constant RC is often chosen much less than 1 µs which largely eliminates the slow-rising portion of the pulse and leave only the fast leading edge (See figures 3 and 31). Collection circuit Figure 3 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 5 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 6 Output Pulse Shape Figure 31 General Features A significant fraction of the potential output pulse amplitude may be lost. The large amount of charge generated in the Geiger discharge produces a large pulse that some amplitude loss can easily be tolerated. All Geiger discharges are approximately uniform in size and time profile. All pulses will be attenuated by the same fraction in the shaping process and the output pulses will remain almost of one amplitude. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 7 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 8 B. Dead Time See Lab for the measurement of the dead time VI. Counting Efficiency Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 9 5
A. Charged Particles Because a single ion pair formed within the fill gas of the Geiger tube can trigger a full Geiger discharge, the counting efficiency for any charged particle that enters the active volume of the tube is essentially 1% The major concern for charged particles is the absorption or backscattering by the tube's window. A window as "thin" as 1.5 mg/cm are commercially available for the case of detection of alpha particles. Thicker windows can be used in the case of beta particles but here the backscattering is the problem! Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 31 B.1 Thermal Neutrons Geiger tubes are not suited for neutron detection For thermal neutron, the conventional Geiger gases have a low capture cross sections and consequently they have low detection efficiency. A detector filled with a gas which has high capture cross section ( 3 He for example) can be used. But then the detector is much more sensibly operated in the proportional region than in the Geiger region! In the proportional counter, neutrons are distinguishable because the neutron-induced events are of much larger amplitude than pulses generated by gamma-ray background. In a G-M counter, as we mentioned earlier, the pulses are of the same amplitude and no distinction between neutrons and gamma-rays is possible! Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 3 B. Fast Neutrons Fast neutrons can produce recoil nuclei in a Geiger gas that generate its ion pairs and a subsequent discharge, Geiger tubes (Helium filled in particular) will respond to a fast neutron flux. Still, gas-filled neutron detectors are operated as proportional counters rather than as Geiger tubes to take advantage of the spectroscopic information provided only in the proportional region! C. Gamma Rays In any gas counter, the response to gamma rays of normal energy comes about the way of gamma-ray interactions in the solid wall of the counter. If the interaction takes place in close enough to the inner wall surface so that the secondary electron created in the interaction can reach the gas and create ions, a pulse will result. Because only one single ion pair is required, the secondary electron need only barely emerge from the near end of its track in order to generate a pulse from a Geiger tube. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 33 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 34 Efficiency The efficiency for counting gamma rays depends on two factors: 1.The probability that the incident photon interacts in the wall and produces a secondary electron and.the probability that the secondary electron reaches the fill gas before the end of its track. Because only one single ion pair is required, the secondary electron need only barely emerge from the near end of its track in order to generate a pulse from a Geiger tube. Secondary Electrons Fig. 3 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 35 36 6
Thickness of the Wall The figure shows that only the innermost layer of the wall near the gas may contribute secondary electrons. This region has a thickness equal to the maximum range of the secondary electrons that are formed or typically 1 millimeter or two! Material of the Wall The probability of γ-ray interaction within the critical layer increases with the atomic number of the wall material. Making the thickness of the wall thicker would not change the efficiency because electrons formed in the regions of the wall farther from the gas have no chance to reach the gas before being stopped. Fig. 33 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 37 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 38 Material of the Wall G-M with cathodes of high Z (bismuth, Z83, for example) are more efficient. Still, the probability of interaction remains small even for high-z material and typical gamma-ray efficiencies are seldom higher than several percent! Low-Energy γ Rays and X-Rays The interaction low-energy photons ( γ or X- ray) in the fill gas may become non-negligible. The counting efficiency in this case can be enhanced by: Using gases of high atomic number (Xe or Kr) At a pressure as high as possible. For such G-M counters, counting efficiencies near 1% can be achieved (See Proportional Counters for low-energy photons). Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 39 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 5: Gas-Filled Detectors 4 Next Lecture Chapter 6 Scintillators Dr. Nidal M. Ershaidat 7