Detectors Based on Ionisation in Gases

Abstract

Charged subatomic particles can be detected by their electromagnetic interactions with matter. Neutral subatomic particles can only be detected if they first undergo an interaction. The charged particles produced in the interaction reveal that a neutral particle was present. Today there are three main methods for detecting charged subatomic particles that are important in nuclear science or in high-energy physics: detection based on gas ionisation, detection based on semiconductors and detection based on scintillation. All these methods are based on the detection of electron ionisation or electron excitation produced by the coulomb interaction of the charged particle with the medium.

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4.1 Introduction to Detectors for Subatomic Particles

Charged subatomic particles can be detected by their electromagnetic interactions with matter. Neutral subatomic particles can only be detected if they first undergo an interaction. The charged particles produced in the interaction reveal that a neutral particle was present.

Today there are three main methods for detecting charged subatomic particles that are important in nuclear science or in high-energy physics: detection based on gas ionisation, detection based on semiconductors and detection based on scintillation. All these methods are based on the detection of electron ionisation or electron excitation produced by the coulomb interaction of the charged particle with the medium.

Many years ago, there were several other useful detection methods, such as bubble chambers and cloud chambers, but these have all become obsolete because these methods did not allow advantage to be taken of the dramatic improvements in electronics.

One significant exception to this is the nuclear emulsion. A nuclear emulsion is essentially the same as a common black-and-white photographic emulsion. The very first observations of subatomic particles and ionising radiation were, in fact, made with photographic emulsions. In 1895, Wilhelm Conrad Roentgen discovered X-rays by observing that images could be obtained from the bones in a human body, by using what is now called a cathode ray tube and a photographic emulsion. One year later, Henri Becquerel observed that certain uranium salts emit a kind of penetrating radiation that can be detected with photographic emulsions. Ordinary photographic film consists of silver halide grains (mainly silver bromide) suspended in a gelatine matrix and supported with a backing of glass or cellulose acetate film. The action of ionising radiation in the emulsion is similar to that of visible light: some of the grains become sensitive through the excitation of electrons in the silver halide crystal. In the subsequent development process, the sensitive grains become metallic silver and are visible as black grains. The silver grains in emulsions can be made quite small, less than 1 μm, so that images of excellent resolution can be recorded. This excellent resolution is one of the main reasons why nuclear emulsions have not yet been abandoned as a detection technique.

Nuclear emulsions can be used for observing a radiation flux impinging on the emulsion, and the higher the radiation flux the darker the emulsion. This is the basis of the use of emulsions as film badge dosimeters. A long time ago, nuclear emulsions were also used to make X-ray images for medical applications, i.e. for clinical radiography. This method has long been abandoned because the probability of the X-ray interacting in the emulsion is small, typically only a few percent, resulting in the need of a large dose to obtain good images. For this application, emulsions have been replaced by methods that will briefly be described in Chap. 6. However, emulsions are still used for making X-ray images of objects, for example in non-destructive material testing, where dose is usually not important and advantage can be taken of the excellent spatial resolution of emulsions.

A limitation of the use of emulsions in radiography or in dosimetry is the limited dynamic range, i.e. the range in dose the emulsion can record. At higher or lower doses, the only information the emulsion provides is that the dose was above or below the range of sensitivity. Typically, emulsions have a dynamic range of ≈100.

Another application of emulsions is as a method to make trajectories of charged particles visible. If a charged particle travels in an emulsion, the silver halide crystals along its trajectory will become sensitive and after development the track of the particle becomes visible under a microscope. For a long time this was a very important method for the study of nuclear interactions. It is still used today, but only in cases where one wants to observe very short tracks that are difficult to observe by other methods. Figure 4.1 illustrates how emulsions can be used to observe tracks of subatomic particles.

Fig. 4.1

Alpha particles shoot out from a speck of uranium salt on the surface of a nuclear emulsion. The area shown corresponds approximately to 0.3 × 0.2 mm². Figure from [1]./Science Photo Library

If a charged particle penetrates in a medium, many atoms along the trajectory of the particle are ionised. If the medium is a gas, an electric field of the order of a few 100 V/cm will be sufficient to collect the charges and, in this way, detect the presence of charged particles. In a solid, it is usually not possible to collect the charges. This is because in a solid there are always a very large number of traps that will capture the charges and prevent the collection. Only for a small number of carefully engineered materials, such as silicon and germanium, is it possible for charges to move freely over distances of several millimetres with negligible loss. Semiconductor detectors are discussed in Chap. 5. In liquefied noble gases, it is also possible to collect the ionisation charges. This is because the noble gases have a very low affinity for electrons and the electrons move freely under the influence of an electric field if the material is extremely pure. This has a number of important applications in high-energy physics and this is briefly discussed in Sect. 6.6.

Observation of ionisation in gases is also one of the oldest ways of observing ionising radiation. In the very beginning of nuclear science, this was done with the help of an instrument called an electroscope (see Fig. 4.2).

Fig. 4.2

The gold leaf electroscope was one of the earliest instruments used in studying subatomic particles. It consists basically of a box with a window, or of a glass bottle. A metal rod, which passes through an insulating collar in the top of the box, has two thin sheets of gold foil attached. When the rod is electrically charged the two gold leaves acquire the same charge and repel each other. If the air in the box is ionised by radiation, the charge on the gold leaves leaks away to the walls of the box and the leaves collapse together

Today the use of ionisation in gases is one of the common methods used to detect the presence of high-energy subatomic particles. This is the subject of the rest of this chapter.

4.2 Ionisation and Charge Transport in Gases

Before we proceed with a discussion of detectors based on gas ionisation, it is useful to briefly review the main physical phenomena associated with the creation and the transport of charges in a gas. See Ref. [7] for a more in depth review of the subject.

When a charged particle travels in a gaseous medium, the coulomb interaction between this charged particle and the gas atoms will cause excitation or ionisation of the gas molecules. If the gas molecule is ionised, a free electron and a positive ion are produced. The ionisation energy for most gases is between 10 and 20 eV (see Table 4.1), but the average energy needed to produce an electron–ion pair is typically about two times larger. This is because the energy transferred to the electron is usually larger than what is needed to ionise the atom, and part of this kinetic energy will dissipate as heat. If this electron has acquired sufficient energy, it will itself cause further ionisation of gas molecules. Each primary electron will typically give rise to 3 electron–ion pairs.

Table 4.1 Energy loss characteristics in some commonly used gases. Energy loss, the number of electron–ion pairs and the number of primary electrons is for charged particles at minimum ionisation

If a charged track travels a fixed distance in a gas, the amount of energy deposited fluctuates from one event to the next. This is partly due to the fluctuation on the number of primary electrons ejected from the gas molecules and partly due to the fluctuation on the amount of energy received by each electron. This will give rise to a distribution of the number of charges produced that is wider than what can be expected for a Poisson distribution.

In the presence of an electric field, the electrons and ions created by the radiation are accelerated towards the anode and cathode, respectively. This acceleration is interrupted by collisions with the gas molecules. In these collisions, the electrons and ions will completely change direction. The collision resets the average drift velocity of the electron or ion in the direction of the field back to zero. After the collision, the charges will again be accelerated in the direction of the electric field. At the microscopic scale the movement is quite chaotic, but at the macroscopic level it appears as if the charges drift with constant velocity in the direction of the electric field and as if a diffusion component is superimposed on the otherwise uniform drift velocity. The cross section for the collision of ions with gas molecules is determined by the dimensions of the molecules involved and these cross sections are therefore of the order of a few 10⁻¹⁵ cm². The corresponding mean free path of the atoms or ions is about 100 nm. Moreover, these cross sections are independent of the kinetic energy of the ion. For the electric fields of interest the drift velocity is always much smaller than the thermal velocity of the particle. We can therefore derive an approximate expression for this drift velocity as follows.

The average thermal kinetic energy of the molecules, or ions, in a gas is 3kT/2. The average thermal velocity v _t of an ion is therefore given by

$$\begin{array}{l} E_{\rm{kinetic}} = \frac{1}{2}M\ \nu_t^2 = (3/2)\ kT \\ \\ \nu_t = \displaystyle\sqrt {\frac{{3kT}}{M}} \\ \end{array}$$

In this equation k is the Boltzmann constant, T the absolute temperature and M the mass of the molecule or ion. Applying this equation to nitrogen gas molecules, we find that the thermal velocity is ≈500 m/s. If λ represents the mean free path of the ion, the average time between two collisions is given by

$$ \Delta t = \frac{\lambda }{{\nu_t }} $$

If there is an electric field, the ion will be accelerated in the direction of the electric field. The acceleration is given by

$$ a = \frac{{eE}}{M} $$

The average velocity of the ion in the direction of the field is therefore given by

$$\nu_d = \frac{a}{2}\Delta t = \frac{{eE}}{{2\,M}}\frac{\lambda }{{\nu_t }} = \frac{{e\lambda }}{{\sqrt {12kT\ M} }} E $$

((4.1))

We see that the drift velocity is proportional to the electric field and it is therefore useful to introduce the mobility ‘’ defined by

$$\nu(E) = \mu E $$

Applying Eq. (4.1), we find that the drift velocity of charged nitrogen molecules in an electric field of 1000 V/cm is 34 m/s if we assume a mean free path of 100 nm. This is indeed much smaller than the thermal velocity of the molecules. The ion mobilities of a few ions are listed in Table 4.2.

Table 4.2 Ion mobility in a few gases. Data taken from Refs. [6] in Chap. 1 and [2]

For electrons, the drift velocity is not proportional to the electric field and the mobility therefore becomes a function of the electric field. This difference in behaviour is due to the fact that the cross section for collisions of the electrons on gas molecules is strongly dependent on the kinetic energy of the electrons, as is illustrated in Fig. 4.3. Moreover, electron–molecule cross sections are, on average, much smaller than ion–molecule cross sections. Figure 4.4 shows the drift velocity of electrons in an electric field, for a few gases of interest. Electron drift velocities are typically of the order of a few cm/μs for an electric field of 1 keV/cm. This is about 10,000 times faster than the typical ion drift velocities.

Fig. 4.3

Electron–argon cross section in argon gas as a function of the kinetic energy of the electron. The data for this figure were obtained from [2]

Fig. 4.4

Drift velocity of electrons as a function of the electric field in several gases. Figure from [3], copyright CERN

While drifting in an electric field, the electrons and ions can be involved in a number of interactions with the gas molecules of the medium:

• Several gases, e.g. oxygen, are strongly electronegative. This means that electrons will become attached to oxygen atoms and form a negative ion. After capture, the negative oxygen ion displays similar drift behaviour as positive ions.

• During a collision between different molecules, one charged and one neutral, the molecule with the largest ionisation energy will tend to capture the electron from another molecule, where the electron is less tightly bound. As a result the charge can be transferred from one molecule to another.

• Electrons and positive ions, or positive and negative ions can also recombine their charges to produce neutral atoms.

Diffusion causes the drifting charges to deviate from the direction given by the electric field. If the diffusion is perpendicular to the motion of the particle, this is called lateral diffusion. However, the diffusion will also cause some particles to move slightly faster or slower than others. This is called longitudinal diffusion. If a group of particles is created at the same moment in one point in the gas, the electric field will cause these particles to drift in the direction of the field. After some time these particles will no longer be at one point but will be spread over a certain volume. Since this dispersion is due to a large number of uncorrelated random collisions along the track, the positions of the particle will have a Gaussian distribution, and the dispersion is proportional to the square root of the drift distance. It can be shown [7] that this dispersion is related to the diffusion constant D by the relation

$$\sigma_x = \sqrt {(2D/\nu_d)l}$$

In this equation σ _x represents the dispersion of the projected distance on some direction x, ν _d represents the drift velocity, and l the path length of the particle.

If the electric field is increased, at some point the moving charges in the gas can acquire sufficient energy to ionise other atoms. In this way, the number of charges will increase. The mean free path of the electrons is much larger than the mean free path of ions; therefore, electrons can acquire a much larger energy than the ions, and electrons will start multiplying at a lower value of the electric field than the ions. As is discussed in Sect. 4.4, this charge multiplication effect is exploited to amplify the very small signals that are produced by ionisation in gases.

4.3 Ionisation Chambers

The amount of ionisation in a gas volume is a measure of the amount of radiation present. This provides a commonly used method to measure gamma ray exposure. The SI unit of X-ray or gamma ray exposure is defined as the amount of radiation producing one coulomb of charge per kilogram of air at standard temperature and pressure.

An ionisation chamber to measure gamma ray exposure is a very simple device and is illustrated schematically in Fig. 4.5. A certain volume of air is enclosed between two electrodes and a voltage difference of several 100 V is applied on these electrodes. If the voltage is too low, the electrostatic force on the charges is not sufficient to overcome the random thermal movement of the gas molecules, and we have incomplete collection of the ionisation in the gas. In addition, the charges have to be collected fast enough so that recombination of the charges remains negligible. A moderate field of the order of a few 100 V/cm is usually sufficient to obtain full charge collection. Increasing the voltage over the electrodes further will not lead to an increase in the collected current. If the voltage over the electrodes is increased to a value much larger than 1000 V/cm, at some point amplification of the charges will occur and the current will again increase. In that case, the amount of charge collected is no longer equal to the ionisation produced by the gamma rays. The voltage at which charge multiplication will occur depends strongly on the geometry of the ionisation chamber. In practice, it is fairly easy to find a working voltage where the charges are collected and no charge amplification occurs.

Fig. 4.5

Schematic representation of an ionisation chamber. (b) Current–voltage diagram in an ionisation chamber. A voltage of a few 100 V/cm is usually sufficient to collect all the charges

Implied in the definition of gamma ray exposure is the assumption that the sample air volume is taken in a sufficiently large volume of air. Sufficiently large here means large compared to the typical trajectories of the electrons produced by the gamma rays. These trajectories can be up to several metres long! Ideally, one should therefore make the gas enclosure and the electrodes sufficiently thin such as to produce a negligible perturbation of the radiation present. In a practical measurement set-up, the ionisation chamber and the electrodes are unavoidably made of some suitable solid material. This material will perturb the measurement because, on the one hand, it shields the gas in the ionisation chamber from electrons produced outside the sample air volume, and on the other hand, it adds electrons produced by interactions of the gamma rays in the walls of the ionisation chamber. This perturbation will be minimised if the walls are made of ‘air equivalent material’, i.e. of material with approximately the same atomic charge as nitrogen and oxygen. The electrodes should therefore preferably be made of aluminium and the detector walls of plastic.

The currents that need to be measured with ionisation chambers are usually extremely small. If we assume that there are 1000 electron tracks per second in the gas volume and that each track is 2 cm long. The corresponding current in the ionisation chamber will be 18 × 10⁻¹⁵ A. This is an extremely small current, and without adequate precautions, the leakage current in the system will be much larger that the ionisation currents one wants to measure. The solution that is universally adopted is the use of guard rings. The principle of guard rings is schematically illustrated in Fig. 4.6. The measurement electrode is completely surrounded by another electrode called the guard ring. This guard ring is at the same voltage as the measurement electrode. Because there is no voltage difference between the high-voltage electrode and the guard ring there is no leakage current.

Fig. 4.6

Cross-sectional view of an ionisation chamber with guard rings. The leakage current between the guard ring and the ground is not included in the measured ionisation current. The very small ionisation currents can be measured with a large series resistor and an electrometer to record the voltage over the resistor

The method used for the measurement of the small ionisation currents is illustrated in Fig. 4.6. The ionisation current causes a voltage difference over a resistor, and this voltage difference is measured with a sensitive voltmeter (DC electrometer). The values of the resistors used are typically between 10⁺⁹ Ω and 10⁺¹² Ω.

Battery-operated portable ionisation chambers are commonly used as radiation-monitoring instruments to measure gamma ray exposure. Figure 4.14 shows some commercially available systems. Because the walls of these detectors can never be made exactly equivalent to air, each instrument has to be calibrated for its sensitivity as a function of the gamma ray energy.

When an ionisation chamber is used to measure gamma ray exposure, the total charge pulse corresponding to one electron trajectory of a few centimetres long corresponds to only a few 100 electron charges. However, an ionisation chamber can also be used to measure the concentration of air-borne alpha emitters. An alpha particle of 3.38 MeV will produce about 100,000 electron–ion pairs in air. This is still a very small electrical pulse, but large enough to be observed with suitable low noise electronics.

It is always better to count individual pulses rather than measuring just a total current. The example at hand illustrates this. If one were to use the current to measure the number of alpha emitters present in a gas, it would be impossible to distinguish the current caused by the alpha particles from the current caused by electrons produced by gamma rays. If the individual pulses are observed, it is possible to distinguish the two types of events because of the very large difference in amplitude between the corresponding pulses. Another advantage of counting pulses is that this method is much less sensitive to changes in the collection efficiency of the charges, either variations over the volume of the detector or variations with time. On the other hand, counting pulses needs a more elaborated electronics and becomes impossible if the rate of events exceeds a few 10 MHz.

To understand the time development of the electrical pulse caused by ionisation in a gas, let us consider a detector consisting of two parallel plates enclosing a gas volume. These two plates form a capacitor with a capacitance denoted by C. A potential difference V ₀ between the plates causes a constant and parallel electric field between them (see Fig. 4.7). Let us assume that one electron–ion pair forms in the gas. Under the influence of the electric field the electron and the positive ion will drift towards the anode and cathode, respectively. After a certain time the electron and the positive ion will have reached their electrodes, and if the plates are not permanently connected to an external voltage source, the voltage difference over plates changes by

$$dV_0 = \frac{{ - e}}{C} $$

((4.2))

Fig. 4.7

Under the influence of the electric field an electron and a positive ion drift towards the electrodes delimiting the volume of an ionisation chamber. These two electrodes form a parallel plate capacitor

In this equation ‘–e’ represents the charge of the electron.

The drift of the electron and the ion in the gas to their respective electrodes is equivalent to a current source connected between the two plates and injecting a charge ‘–e’ and ‘e’ in the anode and cathode, respectively. However, it is not immediately obvious at what moment exactly this charge appears on the electrodes. Energy conservation will help us in answering this question.

In the interest of clarity let us only consider the motion of the electron. If the electron has only travelled a fraction of the distance between the plates, it will have crossed a potential difference ΔV and the energy it received in doing so, eΔV, has been dissipated as heat in the gas. Because of energy conservation, this energy must have been supplied by the energy stored in the capacitor 1/2CV ₀ ². The voltage over the capacitor has therefore changed by dV ₀ and we have the relation:

$$\begin{array}{l} d(\frac{1}{2}CV_0^2 ) = V_0 CdV_0 = - e\Delta V \\ dV_0 = - \displaystyle\frac{{e\Delta V}}{{CV_0 }} \\ \end{array}$$

The motion of the charge –e has injected an apparent charge in the electrode given by

$$\Delta Q = - \frac{{e\Delta V}}{{V_0 }}$$

The motion of a particle with charge ‘–e’ in the detector is therefore equivalent to a current source injecting a current in the anode given by the Eq. (4.3):

$$i = \frac{{dQ}}{{dt}} = \frac{{ - e}}{{V_0 }} \frac{{dV}}{{dt}} = \frac{{ - e}}{{V_0 }}\frac{{dV}}{{ds}}\frac{{ds}}{{dt}} $$

((4.3))

In this equation, s represents the trajectory of the electron. Notice that, if a current ‘i’ is injected on the anode, necessarily a current ‘–i’ is injected on the cathode. One is therefore free to choose either of the electrodes to read the signal. In fact, we can use both signals and this is often used in detectors.

We have seen in the above example that the signal in a detector is caused by the motion of the charges between the electrodes. This is completely general and applies to all detector types and all detector geometries. In the simple case, where the detector only has two electrodes, the signal can be found using energy conservation as we have done here. Later in this book we will see many examples of detectors where there are more than two electrodes. In that case, we need to use the Shockley–Ramo theorem to find the signal induced in one particular electrode. Assume that there are many electrodes in the detector and we want to know the current injected in one of these electrodes by the motion of a charge somewhere in the space between the electrodes. The Shockley–Ramo theorem [4, 5] states that the current injected in this electrode is also given by Eq. (4.3), but using the weighting potential field for this electrode in calculating dV/ds, not the true potential field in the detector. The weighting potential field is the potential field obtained when all other electrodes are set at zero potential and only the electrode under consideration is at the potential V ₀. If there are only two electrodes, the weighting potential field is the same as the true potential field in the detector. If there are more than two electrodes, the weighting potential field is, in general, different from the true potential field in the detector. In the calculation of the current, the trajectory ‘s’ used in Eq. (4.3) must of course be the true trajectory caused by the real potentials used when operating the detector.

The time development of the electrical pulse caused by one electron–ion pair produced in the electric field of an ionisation chamber with parallel plate electrodes is shown in Fig. 4.8. The electron travels much faster than the positive ion and therefore reaches the anode in a short time. The movement of the positive ion is much slower and the signal induced by the positive ion lasts much longer. The current pulse therefore also consists of two parts, one fast part corresponding to the electron movement and one slow part corresponding to the movement of the positive ions.

Fig. 4.8

Time development of the signal caused by the motion of the electron and the ion in a parallel plate ionisation chamber. In the interest of clarity, the figure is drawn as if the electron drift velocity were only ten times faster than the ion drift velocity. In reality, the difference in velocity is much larger. The top figure shows the change of voltage over the plates caused by the motion of the charges if the plates are disconnected from the power supply. The bottom figure shows the apparent current caused by this motion of the charges

The voltage difference caused by the creation of one electron–ion pair in a detector with a capacitance of 10 pF (a typical value) is 1.6 × 10⁻⁸ V. This is a very small signal and is not observable. An alpha particle of 3 MeV will give a signal of 15 × 10⁻⁴ V. This is still very small but is observable with suitable low noise electronics.

If a high-energy electron causes the ionisation in the detector, the signal will typically only be of the order of 100 electron charges and such a signal is unobservable using purely electronic methods. One therefore needs to use gas amplification as described in the next section.

4.4 Counters with Gas Amplification

The electrical signals produced by charged particles in a gas are often too small to be observable. In 1928, Geiger and Müller invented a detector that takes advantage of the phenomenon of charge amplification in gas to obtain much larger electrical signals. Counters based on the same principle are still in common use today. These counters are now usually of a type called ‘proportional counters’; the difference between a proportional counter and a Geiger counter will be explained later.

A proportional counter or a Geiger counter consists of a metal tube of radius R with a thin metallic wire of radius ‘r’ in its centre (see Fig. 4.9). The central wire is brought to a large positive voltage, i.e. it is used as an anode, while the tube itself is at ground potential and is used as a cathode.

Fig. 4.9

A Geiger tube or a proportional tube is a conductive cylinder with a thin wire in its centre. The dotted line shows an imaginary cylinder used in calculating the electric field in the tube

The electric field in the counter can be found by applying the Maxwell equations in the integral form over an imaginary cylindrical volume of radius $\rho$ shown as a dotted line in Fig. 4.9.

$$\int\limits_{\rm{surface}}{\vec D. \vec ds} = \int\limits_{\rm{volume}}{q. d\nu} $$

We assume the cylinder to be a finite section taken out of a very long cylinder. The electric field over the flanges at both ends therefore points radially outwards from the central wire and does not contribute to the surface integral. We therefore have

$$\begin{array}{l} \varepsilon E(\rho )2\pi \rho L = Q \\\noalign{}\\ E(\rho ) = \frac{Q}{{2\pi \varepsilon L}}\frac{1}{\rho } \\\end{array}$$

((4.4))

Equation (4.4) gives the expression for the electric field as a function of the electric charge present on the central anode wire. In practice, this wire is charged by connecting it to a voltage power supply. We therefore need to calculate this charge on the wire as a function of the externally applied voltage V ₀. This is the same as calculating the capacitance of the system. The electric field in the cylinder is given by

$$E = - \frac{{dV}}{{d\rho }}$$

Integrating this equation along a line pointing radially outwards from ‘r’ to R, we obtain

$$V(R) - V(r) = - \int\limits_r^R {E(\rho )d\rho }$$

The outer cylinder is at ground potential, therefore V(R) = 0 and the central wire is connected to the external powers supply, hence V(r) = V ₀. We hence have

$$V_0 = \int\limits_r^R {E(\rho )d\rho = \frac{Q}{{2\pi \varepsilon L}} \ln \left( {\frac{R}{r}} \right)}$$

By definition, the capacitance of a system is given by Q/V. Therefore, the capacitance C of the proportional tube is given by

$$C = \frac{Q}{{V_0 }} = \frac{{2\pi \varepsilon L}}{{\ln (R/r)}} $$

((4.5))

Eliminating Q from Eqs. (4.4) and (4.5), we readily find the expression for the electric field in the cylinder:

$$E(\rho ) = \frac{{V_0 }}{{\rho \ln (R/r)}}$$

We see that the electric field in the tube varies inversely proportional to the distance to the centre of the tube. For a central wire with a radius of 10 μm and a power supply of only 1000 V, the electric field close to the central wire is 1.5 × 10⁷ V/m. This is sufficient to cause electron multiplication.

Let us assume that a charged particle produces a number of electron–ion pairs in the gas inside the tube. Under the influence of the electric field, the electrons and the ions move towards the anode and cathode, respectively. As an electron comes closer to the anode, the electric field increases, and in the last few 10 μm, very close to the anode wire, the field is sufficiently strong to give rise to charge multiplication. This means that the electrons acquire enough energy that they can ionise other atoms and create additional free electrons. In this avalanche, the number of electrons increases exponentially. Because of charge diffusion, the electron avalanche spreads more or less evenly around the anode wire.

A large number of electrons and an equal number of positive ions are formed. These electrons move much faster than the positive ions; therefore, the electrons reach the anode in about 1 ns and leave the positive ions behind. The ions move slowly towards the cathode. In doing so, the ions do not cause any charge multiplication, because the onset of charge multiplication for ions is at much larger electric fields than for electrons. The ions need several 100 μs to reach the cathode; the exact value depends on the dimensions of the system and on the gas filling of the tube. This is illustrated in Fig. 4.10.

Fig. 4.10

Development of an electron avalanche in a proportional tube. An electron formed somewhere in the gas volume drifts towards the positive anode wire. In the intense electric field close to the anode, the electrons multiply. Because of diffusion, the avalanche more or less evenly surrounds the anode wire. The electrons created in the avalanche reach the anode in less than 1 ns. The positive ions drift slowly outwards towards the cathode

Pulse shape in counters with gas amplification. Let us first imagine that the charged particle has created only one electron–ion pair in the gas. The signal caused by this single electron–ion pair is negligible compared to the signal produced by the many electrons and ions produced in the avalanche. The electrons in the avalanche reach the anode wire in less than 1 ns, but these electrons only travel a few 10 μm, and therefore the fraction of the total potential difference travelled by the electrons is very small. As a result, the contribution of the electron motion to the total signal is, at most, a few percent. Most of the potential difference is travelled by the ions, and therefore the motion of the ions causes the largest part of the electrical pulse.

Let us consider a proportional tube with a signal readout as shown in Fig. 4.11(a). We assume that the current is measured with an ideal current meter with zero impedance. We, furthermore, suppose leakage currents are negligible. As long as no ionisation is produced in the gas, there is no current. If one electron–ion pair forms, the electron will quickly drift to the anode wire. Close to the anode wire this electron will give rise to the formation of an electrons’ avalanche and the number of charges is multiplied by a large factor. The motion of the positive ions determines the evolution of the signal. In the beginning, the ions are in a very large electric field, and both the velocity of these ions and the potential gradient are large. Therefore, in the beginning, the induced signal current is large. As the ions move away from the anode, the change in potential slows down and the current decreases. Eventually all the ions reach the cathode and the current stops.

Fig. 4.11

(a) Idealised electrical circuit for the readout of a proportional tube. The anode current I is read with an ideal current meter with zero internal resistance. (b) Realistic electrical circuit for the readout of a proportional tube. The capacitance of the anode wire C _a and the input impedance R _I of the amplifier are drawn as dotted lines to show that these are not actual components in the circuit. These are only drawn as a reminder that the anode wire has a certain capacitance and that the amplifier has a certain input impedance. (c) Pulse shape of a proportional tube for different values of the shaping time τ = C _a  R _I. (d) Simplified equivalent circuit allowing to derive the shape of the output pulse

A more realistic electrical readout scheme is shown in Fig. 4.11(b). The capacitance C _a, shown in dotted lines, represents the capacitance of the anode wire itself. The external resistor R _e and the external capacitance C _e represent external components. The triangle to the right of Fig. 4.11(b) represents an amplifier. This amplifier has an input impedance represented by the resistor R _I, also shown in dotted lines in the figure.

The value of the external resistor, R _e, should satisfy the condition R _e >> R _I. This condition guarantees that most of the signal goes to the amplifier instead of going to the voltage power supply. Indeed, a voltage power supply has negligible internal impedance. The external resistor R _e decouples the anode wire from the power supply for short pulses. This means that a short pulse will develop as if the anode were not connected to the external power supply. After the arrival of a pulse, the anode potential will slowly return to its nominal value V ₀ with a time constant given by R _e C _a. Obviously, this time constant should be large compared to the duration of the pulse. On the other hand, the resistor cannot be too large because at high rates, the voltage of the anode wire will not be restored to its normal value before the next pulse arrives, resulting in a drop of the average level of the anode voltage. This will introduce a rate dependence of the gain of the proportional tube. In practice, the value of the external resistor R _e will be a compromise between these conflicting requirements. The external capacitor C _e is necessary to isolate the amplifier from the high voltage of the anode wire. The value of this capacitor is not critical; the only condition is that C _e >> C _a. This will ensure that the charge is effectively transferred to the amplifier instead of staying on the capacitor formed by the anode wire.

Finding the exact output signal that will be produced by the circuit shown in Fig. 4.11(b) is rather involved and the tools allowing to do so will only be introduced in Chap. 8. However, if the capacitance C _e and the resistor R _e are sufficiently large, to a good approximation these components can be ignored and the circuit becomes equivalent to the much simpler circuit shown in Fig. 4.11(d). The current source in Fig. 4.11(d) delivers a current equal to the current signal shown in Fig. 4.11(a). The shape of the output pulse is completely determined by the shape of the current pulse and the value of the time constant $\tau= C_a R_I$. Figure 4.11(c) shows the influence of the value of this time constant on the output pulse of the proportional tube. If the time constant $\tau$ is much longer than the duration of the current pulse, the total current pulse is integrated and the signal amplitude is large. After the pulse, the voltage returns to zero with a time constant τ. The result is a pulse that is extremely long, leading to a severe limitation of the maximum pulse rate the detector can handle. If this time constant τ is made shorter, this will lead to pulses that are much shorter, but are also much smaller. If the time constant τ is made short compared to the physical formation time of the pulse, the output is directly proportional to the current. Depending on the application, different values for this time constant will be used. One often chooses a time constant τ of the order of 100 ns.

When using a time constant much shorter than this, one will see the individual avalanches caused by the individual electrons arriving at the anode wire. Indeed, these individual electrons will not arrive at the same time on the anode, giving rise to a pulse as shown in Fig. 4.12.

Fig. 4.12

Signal of a proportional tube as it would be seen if a very short shaping time were used. In this case, the individual pulses caused by each individual electron are visible

We have seen that the motion of the relatively slow ions causes the pulse in a proportional tube. As a result the rise time of the pulse is not very fast and the time resolution that can be achieved is not very good. A time resolution of a few 10 ns (r.m.s.) is typical.

Pulse amplitude and amplitude fluctuations. Charge multiplication occurs if the electron acquires sufficient energy between two collisions with gas molecules to ionise one of these molecules. The probability that an electron creates an additional electron in an infinitesimal path length dx is αdx and the quantity α is called the ‘first Townsend coefficient’. If n(x) represents the number of charges as a function of the distance travelled by an electron in a constant electric field, we have

$$\frac{{dn(x)}}{{dx}} = n(x)\ \alpha $$

The number of charges increases exponentially

$$n(x) = n_{0 }\ e^{\alpha x} $$

More generally, if the particle moves in a non-uniform electric field, the first Townsend coefficient becomes a function of x and the expression for the gas gain generalises to

$$n(x) = n_0\ e^{\int {\alpha (x)dx} } $$

This equation is only valid for moderate values of the gas gain. If the gas gain becomes too large, the space charge represented by the cloud of charges modifies the electric field and therefore the value of the first Townsend coefficient. If the gas gain exceeds the value of about 10⁸, the simple mechanism described breaks down and the charge multiplication ends in a discharge. This is called the Raether limit.

Until now we have only considered the average gain in an avalanche. The charge multiplication is a stochastic process, and obviously all primary electrons will not be multiplied by exactly the same gas gain factor. It can be shown that, if all electron multiplication is only dependent on the local electric field strength in the absence of an avalanche, and for large values of the multiplication, the number of electrons in an avalanche produced by one primary electron has an exponential distribution.

$$P(n) = \frac{1}{{\left\langle n \right\rangle }} e^{ - n/\left\langle n \right\rangle } $$

This expression is a fair approximation of the amplitude distribution for moderate values of the gas gain. However, the primary signal in a gas amplification detector consists of many electrons, and the fluctuations on the pulse height in the total pulse is often dominated by the fluctuation on this primary number of electrons.

Gas mixtures: The gas mixture used in a proportional tube is very important. The gas should not contain any electronegative component. An electronegative molecule tends to form negative ions by capturing the electrons. The result is that the positive and the negative charge carriers are both ions and gas multiplication will only begin at much larger voltages. Moreover, as soon as there is charge amplification, both the positive and the negative ions give rise to multiplication resulting in an avalanche that never stops growing, ending in a discharge. Since oxygen is electronegative, air is not a good working gas for proportional tubes.

An obvious choice for the gas filling of a proportional tube is a noble gas. A noble gas certainly is not electronegative; moreover noble gases can easily be purified avoiding impurities that give rise to complications. Finally, a noble gas has the advantage that the collisions of the electrons with the gas atoms are elastic below the ionisation threshold. Since noble gas molecules are single atoms, there are no rotation or vibration states that can absorb the electron energy during the collisions. As a result, avalanche multiplication occurs at a lower voltage in a noble gas than in other gases. Of all the noble gases, argon is the least expensive, therefore nearly all proportional tubes use a gas filling based on argon. However, with pure argon the gain of a proportional tube is limited to a few times 100. This is due to the following mechanisms. The ionisation potential of argon is 11.6 eV, while the ionisation potential of all metals is less than 11.6 eV. The ionisation potential of copper, for example, is 7.7 eV. Therefore, electron–ion recombination, or exited argon atoms, will give rise to VUV photons that will be able to extract electrons from the cathode. If the average number of such secondary electrons is larger than one, each avalanche will, on average, give rise to more than one new avalanche. The number of avalanches will grow exponentially until the tube is filled throughout with avalanches, and the voltage drops to a very low value due to the large current drawn by all these avalanches.

Another reason why pure argon is not suitable as a fill gas is the fact that the argon ions arriving at the cathode will form neutral argon atoms by extracting an electron from this cathode and can dissipate the energy liberated in doing so by extracting an additional electron from the cathode. Again, if for one avalanche the average number of electrons extracted from the cathode is larger than one, the number of avalanches keeps increasing until breakdown occurs.

To prevent these phenomena from occurring, a small amount (typically 10%) of a polyatomic gas is added. This is called a quenching gas and several polyatomic gases can be used for this purpose. Isobutane (C₄H₁₀) or methane (CH₄) is often used as quenching gas. Since these polyatomic gases have many rotation and vibration degrees of freedom, they will readily absorb these UV photons without being ionised. Moreover, in the collisions between the argon ions and quenching gas molecules, the charge will be transferred from the argon atom to the quenching gas molecule because the binding energy of the electron is lower in the quenching gas. When the charged quenching gas molecule arrives at the cathode, the likelihood of extracting an electron is much smaller, because this molecule has many other ways of dissipating the extra energy. In a gas mixture consisting of argon and ≈10% of a suitable quenching gas, stable operation with electron multiplication of 10⁶ is possible.

The choice of gas mixture is very important if the detector has to work at a high count rate for a long time. The avalanche produces a large number of excited molecules and in this way initiates complex chemical reactions. In particular, the quenching gas, usually a gas containing carbon, participates in the formation of more complex molecules. These complex molecules are deposited on the electrodes in the proportional tube and, in particular, on the anode. This forms a thin insulating layer on the surface of anode wires, and this prevents the normal operation of the proportional tube. Finding a gas mixture that minimises these problems is largely done empirically. It is found that not only the gas mixture, but also all other materials used in the construction of the detector have a very strong influence on the ageing effect. Trace amounts of impurities in the gas or in other construction materials can have a dramatic effect on the ageing properties of a wire chamber. With correct choice of materials and proper care, it is found that a wire chamber can cope with a total accumulated charge of more than 1 coulomb/cm of anode wire. This means that with a gas gain of 10⁴, and a rate of 10⁴/s minimum ionising tracks per mm of anode wire, the chamber will work for 10 years without problems.

Figure 4.13 shows the signal amplitude in a proportional tube as a function of the externally applied voltage. In this plot, it was assumed that the primary charged particles produce 100 electron–ion pairs in the gas. The following operational regimes of the chamber can be distinguished.

Fig. 4.13

Number of electrons in the signal caused by one minimum ionising particle in a counter with gas amplification. The different operating regimes of the counter as a function of the anode voltage V ₀ are shown

Ionisation chamber: at a voltage of a few 100 V, the device works as an ionisation chamber. All the charges are collected but there is no charge amplification. The amplitude of the pulse is therefore only 100 electron charges.

Proportional regime: As the voltage is increased, charge multiplication sets in. The charge amplification increases more or less exponentially with the voltage. As long as the gain is less than about 10⁵, each electron arriving at the anode receives the same amplification, regardless of how many electrons there are in total. In this case, the amplitude of the output pulse is proportional to the amount of primary ionisation in the gas. The names ‘proportional regime’ and ‘proportional counter’ refer to this property of the counter.

Non-proportional regime: As the voltage is increased further, the gain becomes very large and the proportionality property no longer holds. This is because the first electrons arriving at the anode undergo a very large amplification. After the electrons from this first avalanche have reached the anode, they leave behind a large number of positive ions that drift slowly towards the cathode. These positive ions will weaken the field close to the anode wire. Therefore, the electrons arriving later see a smaller field and are amplified less than the first electron.

The Geiger regime: If the voltage is increased further, at some point the Geiger regime is reached. A stable Geiger regime is only reached for suitable gas mixtures.

In this regime, the avalanche extends laterally along the anode wire and eventually fills the whole tube. The extension of the avalanche is due to UV photons formed in the process of avalanche multiplication. These UV photons will ionise molecules some distance away from the original avalanche, inducing further avalanches. Eventually, the anode wire is surrounded along its full length with avalanches.

The avalanche formation stops because the space charge of all these positive ions left behind reduces the electric field close to the wire to a point where there is no more avalanche formation. The voltage drop over the external resistor in series with the voltage power supply also contributes to stopping the avalanche multiplication process.

In the Geiger regime, the pulses are very large and can be several volts. The drawback is that the counter has a very large dead time because one must wait until all the positive ions have been evacuated, and this typically needs several 100 μs. In the proportional regime, the number of charges in each avalanche is much smaller and a new event at the same point is possible before all the charges have been evacuated. Moreover, the avalanche is localised at one point along the wire. The rest of the length of the wire is not affected at all and is ready to accept new events. The count rate achievable in proportional tubes is therefore about 10⁷ pulses per meter of wire, several orders of magnitude larger than what can be achieved with a Geiger counter.

Figure 4.14 shows a few, commercially available, gas based counters.

Fig. 4.14

Some commercial radiation monitoring devices based on ionisation in gas. Photograph by courtesy of IAEA, from Ref. [14] in Chap. 3

4.5 Applications of Counters with Gas Amplification

Detectors for subatomic particles based on gas amplification have found many applications. The main application is as a device for localising trajectories of high-energy charged particles, i.e. as ‘tracking’ detectors. However, proportional tubes also make excellent detectors for thermal neutrons, for low-energy X-rays and for beta electrons. In the present section, I will discuss the use of proportional tubes and detectors derived from them, such as multi-wire proportional chambers or drift chambers, as tracker detectors and as X-ray detectors. The discussion of their use as neutron detectors is deferred to Chap. 7.

Gas amplification-based detectors are usually relatively simple devices and therefore tend to be inexpensive. In particular, if a large detector area is needed, the lower cost of gas amplification systems makes this often the preferred solution. In a proportional tube, the signal is generated by the slow motion of the ions, the signal therefore has a slow rise-time and a long duration. This results in poor time resolution and large dead times. A number of different gas amplification-based devices have been developed to overcome these limitations, and these are briefly discussed in Sect. 4.6.

4.5.1 Proportional Counters for X-Ray Detection

Proportional counters are not very suitable for the detection of high-energy gamma rays, since the probability for the gamma ray to interact in the gas of the counter is small. The main sensitivity to high-energy gamma rays comes from interactions of the gamma rays in the walls of the detector. The interaction probability of X-rays in argon drops to a very low value above 20 keV. With krypton or xenon, sizeable detection efficiencies up to100 keV can be obtained. This is illustrated in Fig. 4.15.

Fig. 4.15

Probability to absorb X-rays in 5 cm of argon gas, krypton gas and xenon gas at standard temperature and pressure. The data for this figure were obtained from [9] in Chapter 1

For X-rays of the order of 10 keV, the photoelectron can be fully contained in the gas and the counter signal will be proportional to the energy of the X-ray. The energy resolution that can be obtained depends on the number of primary electron–ion pairs formed. However, the fluctuations on this number are not well described by Poisson statistics. The fact that the total energy used to create electron–ion pairs must equal the energy of the gamma reduces the fluctuations. It is customary to express this with the help of an empirical factor called the ‘Fano factor’. For a Poisson distribution we have F = 1. The r.m.s. dispersion σ on the number of charges can be written as

$$\sigma = \sqrt {F\,n} = \sqrt {\frac{{F\,E}}{W}} $$

where n is the number or electrons produced in the gas and W is the energy needed to produce one electron–ion pair given in Table 4.1. The relative energy resolution, expressed as ‘full width at half maximum’ (FWHM) is therefore given by

$$FWHM = 2 \times 2.35\frac{\sigma }{E} = 2 \times 2.35\sqrt {\frac{{FW}}{E}} $$

In deriving this expression we have used that the ‘full width at half maximum’ for a Gauss distribution is 2.35σ. The Fano factor F in gases is typically about 0.1. On the other hand, each electron is not amplified by the same amount. These fluctuations in gain degrade the energy resolution by about a factor of 2. This is the excess noise factor and this effect will be discussed more extensively in Sect. 6.4.

The energy resolution of X-rays of 5.89 keV in argon is about 11% FWHM.

4.5.2 Gas Counters for the Tracking of High-Energy Charged Particles

In high-energy physics experiments, one often wants to measure the direction and the energy of all the particles produced in a collision. In nearly all experiments, there is a magnetic field and the momentum of the charged particles can be obtained from the curvature of the trajectory. Determining the trajectory of charged particles is called tracking. This requires the measurement of the space coordinates of a sufficient number of points along the track. Measuring three points is sufficient to determine the trajectory, but there are usually many tracks in the same event, and with only three points per track it is impossible to know which points belong to the same track. For this reason one usually needs to measure many more points along each track.

The momentum resolution of the particle is related to the position resolution on the points along the track. In the simplest case, where only three equidistant points are measured along the trajectory, this momentum resolution is obtained as follows. Let P denote the projection of the momentum on the plane perpendicular to the magnetic field. If the multiple scattering and energy loss are negligible, the trajectory of the particle projected on this plane is a circle. The radius R and the momentum P are related by Eq. (http://3.1), Pc = 0.3 Z B R, where Pc is expressed in GeV, R in meter, B in tesla and Z in proton charges. The sagitta ‘s’ is related to the length of the track ‘L’and the curvature ‘R’ by (see Fig. 4.16(a)):

$$s = (1 - \cos \theta )R \approx \frac{{\theta ^2 }}{2}R \approx \frac{{L^2 }}{{8R}} $$

Fig. 4.16

(a) Relation between the curvature and the sagitta for an arc segment. (b) Effect of the presence of scattering material in the middle of the track. Full line, unscattered track, dotted line, scattered track

We therefore have

$$\begin{array}{l} \displaystyle\frac{{\sigma \{ s\} }}{s} = \frac{{\sigma \{ R\} }}{R} = \frac{{\sigma \{ P\} }}{P} \\ \\ \displaystyle\frac{{\sigma \{ P\} }}{P} = 8 \sigma \{ s\} \frac{{Pc}}{{0.3\ Z\ B\ L^2 }} \\ \\ \end{array}$$

In the case of only three equidistant points along the trajectory, the error on the sagitta is related to the error on the position measurement of the points σ by

$$\sigma \{ s\} = \sqrt {\sigma ^2 + \frac{{\sigma ^2 }}{2}} = \sqrt {\frac{3}{2}} \sigma $$

The momentum resolution due to the measurement error on the space points is therefore given by

$$\left[ {\frac{{\sigma \{ P\} }}{P}} \right]_{SP} = 8\sqrt {\frac{3}{2}} \frac{{\{ Pc\} [\rm{GeV}]}}{{0.3\ Z \;B[\rm{tesla}] \;L^2 [\rm{m}]}} \sigma $$

It can be shown that, if there are N equidistant points along the trajectory, this expression generalises to (see [6])

$$\left[ {\frac{{\sigma \{ P\} }}{P}} \right]_{SP} = \sqrt {\frac{{720(N - 1)^3 }}{{(N - 2)N(N + 1)(N + 2)}}} \frac{{\{ Pc\} [\rm{GeV}]}}{{0.3\ Z\ B[\rm{tesla}]\ L^2 [\rm{m}]}} \sigma $$

As expected, the momentum resolution improves as 1/ for large values of N.

The effect of multiple scattering is not always negligible. If only three equidistant points are measured along the track, an expression for the error on the momentum due to multiple scattering is obtained as follows. As a first step let us assume that all the scattering material is concentrated in the middle of the track. At this middle point the direction of the track is changed by an angle given by Eq. (http://2.5). We are only concerned about the angle projected on the plane perpendicular to the magnetic field and this projection gives rise to the additional factor $1/\sqrt{2}$ in the expression below.

$$\sqrt {\left\langle {\theta _p } \right\rangle ^2 } = \frac{1}{{\sqrt 2 }} \frac{Z}{{\beta Pc}} (0.02\,{\rm GeV}) \sqrt {\frac{L}{{X_0 }}} $$

In this equation Pc is the momentum in units GeV, L is the total thickness of scattering material in the tracker and X ₀ the radiation length of this material. If we assume that the scattering material is all concentrated in the middle of the track, the r.m.s distribution on the sagitta, caused by the presence of this scattering material, is given by (see Fig. 4.16(b)):

$$[\sigma \{ s\} ]_{MS} = \frac{L}{4}\sqrt {\left\langle {\theta _p } \right\rangle ^2 } $$

If the scattering material is not in the middle of the track but at a distance xL from one end, the dispersion σ{s} will depend on the value of x. From the geometry of the problem, one easily finds that the r.m.s on the sagitta caused by multiple scattering is given by

$$\begin{array}{*{20}c} {[\sigma \{ s\} ]_{MS}= \frac{L}{4}\sqrt {\left\langle {\theta _p } \right\rangle ^2 } } & {f(x)}\\ {f(x) = 2x} & {0< x < 0.5}\\ {f(x) = 2(1 - x)} & {0.5 >x > 1}\\\end{array}$$

If the scattering material is evenly distributed along the track, the total r.m.s. squared is the sum of the squares of the contributions of all sections along the track, and we have

$$[\sigma \{ s\} ]_{MS} = \frac{L}{4}\sqrt {\left\langle {\theta _p } \right\rangle ^2 } \sqrt {\int\limits_0^1 {\left( {f(x)} \right)^2 dx} } = \frac{L}{{4\sqrt 3 }}\sqrt {\left\langle {\theta _p } \right\rangle ^2 }$$

The contribution of the multiple scattering to the momentum resolution is hence given by

$$\left[ {\frac{{\sigma \left\{ P \right\}}}{P}} \right]_{MS} = \sqrt {\frac{2}{3}}\ \frac{{0.02}}{{0.3 }} \frac{1}{{ L[\rm{m}] B[\rm{tesla}]\ \beta }}\sqrt {\frac{L}{{X_0 }}} $$

The above derivation rests on the assumption that only three equidistant points were measured along the track. However, it can be shown that the error due to multiple scattering is almost independent of the number of points measured along the track [6]. In real detectors usually the scattering material does not consist of only one type of material, moreover this material is usually not distributed homogeneously over the total length of the track. The generalisation of the above expression to this more general case is straightforward.

The total error on the momentum of a particle is the square root of the sum of the squares of the multiple scattering and the space point measurement error contributions. Notice that the error due to multiple scattering is independent of the momentum, while the error due to the position measurement is proportional to the momentum of the track.

Detectors based on gas amplification can be used to determine the trajectories of charged particles. The most straightforward way to obtain position information with proportional tubes is by using a multi-wire proportional chamber (MWPC). This detector consists of two conductive cathodes planes with a series of anode wires stretched in the middle between the cathode planes (see Fig. 4.17). The distance between the anode wires is typically 2 mm. The corresponding electric field configuration is shown in Fig. 4.18. A charged particle traversing the counter perpendicularly to the detector plane leaves a trail of ionisation behind in the gas. The electrons drift along the electric field lines to the nearest anode wires. The electric field geometry close to the anode wires is very similar to the field in a proportional tube and each individual anode wire behaves as a proportional counter. Consider an avalanche produced near one particular anode wire. This avalanche will induce a negative signal on this particular wire, and a positive signal on the neighbouring wires. This positive signal on the neighbouring wires compensates the negative signal on the same wires caused by capacitive coupling between the wires. As a result, a strong signal is only induced on the wire where the avalanche is formed. Each wire is, therefore, working as an independent counter. If each wire is equipped with its own readout electronics, the MWPC behaves as a counter giving the position in one direction. Each anode wire can handle a rate of up to 10⁵ Hz/mm.

Fig. 4.17

Schematic representation of a multi-wire proportional chamber (MWPC). The cathode planes are at ground potential and the anode wires are at a large positive voltage, typically 3000 V. Each anode wire is equipped with its own amplifier and readout electronics. If a charged particle crosses perpendicularly to the plane of the detector, the wire nearest to the crossing point will have a signal

Fig. 4.18

Electric field geometry in a multi-wire proportional chamber. Figure from Ref. [6] in Chap. 1, with permission

For perpendicular incident tracks, the position resolution depends on the wire spacing Δ. If we assume that the MWPC always gives the position of the wire closest to the track, the r.m.s. position resolution is $\sigma = \frac{\Delta }{{\sqrt {12} }}$ (see Exercise 1). However, the spatial resolution depends on the readout electronics. If this electronics only lists the wires with a signal above some fixed threshold, the spatial resolution will be worse. If the electronics provides the amplitude for all the wires near to the trajectory, it is possible to calculate the centre of gravity of the signals and the spatial resolution can be significantly better than $\frac{\Delta }{{\sqrt {12} }}$.

Since a simple wire chamber as described above gives only one position coordinate, two superimposed chambers with crossed wire planes are needed to know both coordinates. This approach runs into trouble at high rates because, if several particles pass the two wire chambers at the same moment, it is impossible to know which x-coordinate is associated with which y-coordinate. To remove this ambiguity, more MWPC planes have to be added with the wires oriented in different directions. This is illustrated in Fig. 4.19. Another possible solution is to equip each wire with readout electronics on both sides and get an approximate position along the wire from the ratios of the signals at both ends. This method is called charge division and relies on the resistance of the wire itself.

Fig. 4.19

(a) Two superimposed MWPC chambers with perpendicular anode wires allow the determination of the x and y coordinates of the particle track; (b) with two simultaneous particle tracks there are ambiguities regarding the exact position; (c) adding more MWPC planes under different angles allows resolving these ambiguities

A MWPC, in addition to the negative signals on the anodes, also has positive signals on the cathodes. The sum of all the induced negative signals equals the sum of all the induced positive signals. If, for the cathode plane we take a printed circuit board with a strip pattern orientated perpendicularly to the anode wires, one chamber can give the two coordinates of a track. In this case, the cathode signals are spread over several cathode strips, and a more elaborate electronics reading the amplitude of the signals on the strips is needed to obtain a good spatial resolution.

If the event rate in the detectors is not very large, the cost of the electronics can be considerably reduced by using a drift chamber. The principle of a drift chamber is illustrated in Fig. 4.20. Assume that a charged particle traverses the detector as indicated in the figure. A number of field shaping electrodes create an electric field pushing the electrons towards the anode wires. Close to the anode wires the field is similar to the field in a proportional tube and each electron creates an avalanche. If the time when the particle passed through the chamber is known, we can derive the distance between the trajectory of the particle and the anode from the time difference between the passage of the particle and the arrival of the corresponding anode pulse.

Fig. 4.20

A drift chamber is a tube with a section as shown in this figure. The position of the track is derived from the time the charges need to drift to the anode. Typical voltages are anode +2000 V, cathode 0 V and field shaping electrodes, −1000 V, −2000 V and−3000 V

A few examples of applications of wire chambers are given below.

In high-energy physics collider experiments, beams of particles are made to collide at a given point in a beam pipe. A large number of particles are produced in each collision and the corresponding tracks radiate outwards from the collision point. One needs to observe all the particles emerging from the interaction point and determine the trajectories of these particles with the best possible accuracy. If there is a magnetic field, the momentum of the charged particles can be obtained from the curvature of the track. In e+ e− colliders, the rates are not very high and therefore this is often done with a large drift chamber called a time projection chamber (TPC). To explain the principle of a TPC, it is easier to consider first a simple TPC box as illustrated in Fig. 4.21(a). Assume we have a box with dimensions of the order of 1 m and we want to reconstruct the trajectories of all charged particles in this box. The box is filled with a typical wire chamber gas such as argon with 10% of isobutane. At the bottom of the box we have a plane of anode wires. The plane opposite the anode wires is brought to a large negative potential that will create a uniform electric field pushing all the electrons produced in the active volume towards the anode plane. In order to have a uniform electric field in the box, the sidewalls are covered with electrodes at intermediate potentials between the top and the bottom of the box. As the electrons reach the anode wires, the avalanches induce signals on the cathode pads next to them. If the cathode pads are equipped with amplifiers and readout electronics, we can reconstruct the trajectories of all charges particles in the volume of the box. The z-coordinate is given by the drift time and the pad identifies the x- and y-coordinates.

Fig. 4.21

(a) The principle of a TPC is explained with the help of this imaginary TPC box-shaped detector. The position of a charged track in the volume is obtained from the drifty time (z-coordinate) and from the signals induced in the cathode pads close to the anode wires (x and y coordinate). (b) Most TPC detectors are used at electron colliders. The TPC is a cylindrical detector surrounding the interaction region. The two halves of the cylinder form two independent detector chambers with the wire planes and readout pad planes forming the end flanges of the cylinder. Typical dimensions are given

In a collider experiment, owing to the overall geometry, the TPC should be a cylinder surrounding the beam pipe as shown in Fig. 4.21(b). The plane in the middle of the cylinder, just at the point of the collision, is an electrode brought to a large positive voltage. This plane divides the detector in two identical half chambers. At both ends of the cylinder there are planes of anode wires in the shape of a spider’s web. Outside of these anode wires we have planes with pads. Besides the cylindrical shape, a TPC works in the same way as the TPC box described before.

In hadron colliders, such as the recently built LHC accelerator at CERN, the particle flux is too high to use conventional wire chambers. Only in the muon detection part, after a considerable amount of shielding material, is the particle flux low enough to use MWPC or drift chambers. In the CMS experiment, the muon detection in the barrel part uses layers of drift chambers similar to the ones described in Fig. 4.20 and in the end caps, where the rates are larger, it uses MWPCs with cathode strip readout. The muon system also has resistive plate chambers. The principle of this type of gas detector will be explained later in this section.

4.5.3 Applications of Gas Counters in Homeland Security

A completely different example of the use of wire chambers in charged particle tracking is the installation that is planned for use in several major US ports and that is illustrated in Fig. 4.22. The aim of the equipment is to prevent terrorists from smuggling a nuclear warhead into the US. A nuclear warhead can easily be detected by the emission of gamma rays in the MeV range. To prevent the detection of these, the terrorists could place the warhead in a massive lead box with a wall thickness of 5 cm or more. This would, indeed, stop most of the gamma rays and therefore would avoid detection. However, such a massive lead shield would reveal itself by the multiple scattering it would cause for cosmic ray muons. A complete lorry can be placed between several large detector planes made from drift tubes, each several metres long. The position along the wire is obtained from charge division. With this system, in 1 min a sufficient number of muons to detect the presence of such a massive lead shield can be observed and measured.

Fig. 4.22

The multiple scattering on the trajectories of cosmic ray muons can be used to detect the presence of a massive piece of lead shielding inside a lorry

4.6 Recent Developments in Counters Based on Gas Amplification

An MWPC is a relatively simple and robust detector. It is most useful in a situation in which charged particle tracks have to be detected and localised over a large area. Its inherent limitations are due to the wire spacing and the ion mobility. It is difficult to build wire planes with a wire spacing of less than 1 mm. This limit is due, in part, to the practical difficulty of constructing wire planes with smaller wire spacing and also due to the electrostatic repulsive forces between the wires. These forces push the wires above and below the plane and make the chamber unstable. This problem can only be avoided by using short wires, which removes much of the advantages of the MWPC. The low mobility of the positive ions results in a long rise-time for the pulses and in the build-up of an ion cloud around the wires. This, in turn, results in a poor time resolution and limits the maximal count rate to approximately 10⁴ mm⁻¹s⁻¹.

To overcome these limitations, a number of variants of the standard MWPC or drift chamber have been developed. These devices take advantage of techniques to produce micro-patterns that have been developed over the last decades, mainly for the microelectronics industry. A few of these detectors are discussed below.

4.6.1 Micro-strip Gas Counters (MSGC)

A Micro-Strip Gas Counter (MSGC) is an ionisation chamber, where the anodes and cathodes consist of thin metallic electrodes deposited on an insulating substrate, usually a glass plate. Very narrow (≈7 μm) anode strips alternate with wider cathode strips (≈100 μm), making a periodic structure with a pitch of typically 200 μm (see Fig. 4.23). The anodes are at a positive potential relative to the neighbouring cathode strips.

Fig. 4.23

Geometry and typical operating voltages of a Micro-Strip Gas Counter ( MSGC). (a) The plane with the anodes and cathodes forms one wall of the gas gap; the other wall is a plane with a fully conductive surface. Both planes together create an electric field that pushes the electrons towards the cathode plane. The gas gap is typically 2 mm wide. Typical trajectories of electrons and positive ions are shown. (b) Structure of the plane with the anodes and cathodes. Typically, the anode strips are 7 μm wide, the cathode strips 100 μm wide and the periodicity of the structure is 200 μm

The construction of such a fine electrode pattern is only possible by using photolithography, a technique commonly used to make masks for integrated circuits. Using this technique, it is possible to produce very fine strip structures with dimensions in the micrometer range. The electrode geometry of a MSGC is illustrated in Fig. 4.23(b).

Some of the charges produced in the avalanche close to the anode will reach the surface of the insulating substrate; the surface of this substrate will become charged and this will modify the geometry of the electric field. To prevent the accumulation of positive charges on the surface of the insulator, a proper choice for the resistivity of the substrate is essential. This can be achieved either by using low-bulk resistivity glass, or by using a low-surface resistivity obtained by ion implantation or by applying diamond-like coatings. Typically, the value of the resistivity is 10¹⁵ or 10¹⁶Ω/square. Lower values must be avoided because this would give rise to an unacceptably large dark current in the detector. The surface resistivity of normal glass is of the order of 10¹⁸Ω/square or more.

The MSGC has several advantages over the MWPC. Owing to the short ion path between the anode strip and the neighbouring cathode strips, the time needed for evacuating the cloud of positive ions is considerably shorter. This results in a shorter rise-time of the pulses and in better count rate performance. Counting rates at least two orders of magnitude higher than those of a standard MWPC can be achieved. The position resolution depends, among other things, on the pitch of the structure, which in a MSGC is typically 5–10 times smaller than in a MWPC. A space resolution of 30 μm has been achieved with a structure with 200 μm pitch. Furthermore, in an MSGC, the periodicity of the structure can be maintained with very high accuracy over the entire detector surface, resulting in an identical distribution of the electric field lines and hence a homogeneous gas amplification. This means that the energy resolution of an MSGC when used as an X-ray detector will be very good.

One of the main limitations of the MSGC, compared to a MWPC, is the small value for maximum gas gain that can be achieved. This is due to the presence of a strong electric field parallel to the substrate surface. The highest gain that can be achieved is a few 10³. This is at the limit of what is required to detect the signals from minimum ionising particles. To overcome this limitation, other geometries such as the MICROMEGAS and the GEM have been proposed. These detectors are now discussed.

4.6.2 GEM and MICROMEGAS Counters

GEM stands for ‘gas electron multiplier’. In this structure, a completely different geometry is chosen to try and overcome the limitations of the proportional chambers. Figure 4.24(a) shows the structure of a GEM and typical values for the dimensions. The essential element of the GEM detector is a thin, self-supporting three-layer mesh consisting of a thin (50 μm) insulating polyimide (Kapton) foil, metal clad on both sides and with a regular pattern of small holes in it (see Fig. 4.24(b)). Typical dimensions are: holes of 70 μm diameter and a 120 μm pitch. Such a mesh can be made by conventional photolithographic methods used to produce multilayer PCBs. When applying a voltage across the metal sheets on both sides of the mesh, a very high electric field is generated in the centre of the channels (40 kV/cm is achieved with 200 V voltage difference) as shown in Fig. 4.24(b). A GEM counter has a conversion gas gap, a few mm thick, where the charged track ionises the gas. Over this conversion gap there is a voltage difference pushing the electrons towards the GEM foil. The top electrode typically is a thin metallised Mylar sheet. Electrons produced by ionisation in the gas-filled conversion gap drift into the channels and multiply in the high field present inside the channels. The electrons leave the channel and drift further towards a collecting electrode.

Fig. 4.24

(a) Schematic representation of a GEM detector with typical values for the electric field and dimensions. Electrons are liberated along the track of the charged particle and drift toward the GEM holes. Inside the holes, there is a large electric field multiplying the number of electrons. (b) Details of electric field lines (solid) and equipotential surfaces (dashed) in the region of the GEM holes. Electron transparencies are typically 100%. Most positive ions produced in the high-field region within a hole drift back to the GEM’s top side. Figure from Ref. [6] in Chap. 1, with permission

The ions produced during the avalanche tend to follow the field lines and are thus channelled towards the metal-clad top surface of the GEM. A stable and uniform amplification of over 2000 has been achieved with one GEM-electrode. This amplification is rather low, but it is possible to use several GEM foils with a small gap between them, resulting in an amplification that can exceed 10⁶. Sometimes one GEM foil is combined with a MSGC counter.

A MICROMEGAS also has a conversion gap similar to a GEM counter, but a different structure is used for the amplification. It consists of the following components (typical dimensions are given):

• anode strips on a printed circuit or similar substrate, with a width of 100 μm and a pitch of 200 μm. The accuracy needed for this structure is much less than that required for an MSGC. Standard commercial PCB production techniques can be used.

• quartz fibres, or other spacers, with a thickness of 100 μm glued on top of the anode strips and defining the amplification gap. These spacers are necessary because of the electrostatic attraction between the mesh and the anodes.

• the micromesh: a metallic grid with 3 μm thickness, 17 μm openings and a pitch of 25 μm. It is made of nickel using the electroforming technique. Precision is better than 1 μm and the transparency is 45%.

• 3 mm thick gas-filled conversion gap.

• a drift electrode to create a field pushing the electrons created by an ionising particle towards the micromesh.

• as gas filling a typical proportional tube gases such as Ar+10% isobutane are used.

The working principle of a MICROMEGAS detector is as follows: ionisation electrons created in the conversion gap drift towards the mesh and are transferred through the micromesh to the amplification gap. In this gap between the mesh and the anode strips, there is a large electric field of the order of 10 kV/cm and this is sufficient to cause electron multiplication. Notice that in this amplification gap we have a parallel and uniform electric field, hence the amplification takes place over the full length of the gap, not only close to the anode strips. The anode strips collect the electron cloud, while the positive ions drift in the opposite direction and are collected by the micromesh. However, with this electric field geometry, the average electrons drift over an important fraction of the potential difference, therefore the electron contribution to the signal formation is much larger than with a proportional tube. Owing to this and because of the much shorter drift time of the positive ions, the signal of the MICROMEGAS is much faster than the signal of an MWPC.

An important feature of the MICROMEGAS is the fact that the micromesh is almost transparent to the electrons coming from the conversion gap and stops most of the positive ions coming from the amplification gap. It can be shown that these transparencies depend mainly on the ratio of the field strengths in the amplification and in the conversion gap. Under typical operating conditions, this ratio is large; hence, almost all electrons are transmitted from the conversion gap to the amplification gap, while only a small fraction of the positive ions is transmitted from the amplification gap to the conversion gap. Charging of the substrate between the anode strips will have little effect on the operation of the detector. A gain of 10⁵ can be achieved in a MICROMEGAS chamber.

4.6.3 Resistive Plate Chambers

Another, and very different, type of detector based on the amplification in gases is the resistive plate chamber or RPC. This detector consists of a gas gap between two planar surfaces and a large voltage of 7–12 kV between the plates. The surfaces are resistive but the back side of the plates is made slightly conductive. If a charged particle traverses the gas gap an avalanche will form at this point. The avalanche will remain localised because the resistivity is very high and the voltage drops immediately to a very low value, preventing further development of the avalanche.

The plates are made of high resistivity (10⁹–10¹³ Ωcm) material, usually glass, phenol formaldehyde resin (Bakelite) or melamine laminate plates. The backside of the plates is made slightly conductive with a suitable coating to give it a surface resistivity of the order of 10⁵ Ω/square. The unit Ω/square is the usual unit to express surface conductivity. It is the resistivity between two conducting lines on the surface if the distance between the lines is equal to the length of the lines. It is easy to see that this resistivity is independent of the dimension of the square. The unit Ω/square is somewhat confusing because the actual dimension of the quantity simply is Ohms.

A typical layout for an RPC is shown in Fig. 4.25(a). To make sure that the gap between the plates remains the same over the whole surface of the detector there are spacers between the plates approximately every 10 cm. Without spacers the electrostatic attraction between the plates would cause the plates to come closer together in the middle. The signal readout is via the metallic pickup strips separated by a thin insolating foil from the slightly conductive coating. The coupling is through the capacitance formed by the pickup strip and the semi-conductive coating and is schematically represented in Fig. 4.25(b).

Fig. 4.25

(a) Typical structure of a resistive plate chamber (RPC). Figure from Ref. [6] in Chap. 1, with permission. (b) Equivalent electric circuit representing the readout of an RPC

RPC chambers typically have a surface of the order of 1 m² and are relatively inexpensive. They produce large signals, up to 300 mV, and allow good timing accuracy. The rate is limited by the time it takes to recharge the plates at the point where the discharge occurred. This time is quite long, of the order of 1 ms depending on the gain used, but this dead time is limited to the area of less than 1 cm² around the discharge point. The rest of the detector remains fully sensitive.

4.7 Exercises

• 1. Consider an MWPC with wire spacing Δ. Assume that for perpendicular tracks the signal is always on the nearest wire. Show that the r.m.s. position resolution obtainable with such a detector is given by $\sigma = \frac{\Delta }{{\sqrt {12} }}$.

• 2. You suspect that the gas in a cave is heavily contaminated by radon [²²² ₈₆Rn] gas. To determine the radon contamination you measure the current caused by the radon in an ionisation chamber containing one litre of air from the cave. You measure 0.1 pA. How much radiation expressed in pico Curie (pCi) per litre is there in the air of the cave? How many radon atoms per litre are there in the air of the cave?

  Radon has a half-life of 3.8 days and decays into alpha particles of 5.6 MeV nearly 100% of the time. To simplify the calculation, ignore the fact that radon decay products will also be present and will significantly contribute to the current. Also ignore the fact that often the alpha particle will hit the wall of the ionisation chamber and therefore will not use all its energy to ionise the air.

• 3. A GEM detector has a conversion gap of 2 mm. The gas filling is 90% Ar and 10% CH4. Cosmic ray muons are falling perpendicularly on this detector. What is the probability that a muon will be go undetected because there is no primary ionisation event in the conversion gap?

• 4. Calculate the mobility of nitrogen ions in nitrogen gas assuming that the cross section for the collision is 3.7 × 10⁻¹⁵ cm².