Key Issues in the Application of Radioactive Radiation in Measurement Technology

N. I. Shteinbok

Contents

I. Basic Principles

§ 1. Introduction . . . 232

§ 2. Principal ways of using radioactive radiation in measurement technology . . . 233

§ 3. Basic scheme of ionization instruments with a radioactive ionizer . . . 234

§ 4. Volt-ampere characteristic of ionization chambers . . . 235

§ 5. Regularities in the action of α-ionization chambers . . . 238

§ 6. Fluctuations of ionization current and determination of the necessary amount of radioactive substance . . . 239

§ 7. Main types of ionization chambers . . . 244

§ 8. Efficiency of ionization chambers . . . 246

§ 9. High-ohmic resistances . . . 248

§ 10. Measurement and amplification of ionization currents . . . 250

§ 11. Basic circuits for connecting ionization chambers, their features and field of application . . . 252

§ 12. Terminology . . . 257

II. Application of Radioactive Radiation in Measurement Technology

§ 1. Introductory remarks . . . 258

§ 2. Group of instruments based on changes in the properties of a gaseous medium . . . 260
a) Instruments based on changes in absorbability, recombination, and radiation intensity . . . 260
b) Instruments based on changes in radiation intensity with variable composition or variable density of the medium . . . 267

§ 3. Group of instruments based on changes in the dimensions of ionization chambers or the position of a source of radioactive radiation with constant composition and constant density of the medium . . . 270
a) Instruments based on changes in the dimensions of ionization chambers . . . 272
b) Instruments based on changes in the position of the radiation source relative to the ionization chamber . . . 274

§ 4. Group of instruments based on changes in the properties of radioactive radiation . . . 275
a) Instruments based on absorption of β- and γ-rays . . . 277
b) Instruments based on scattering of β- and γ-rays . . . 281

N. I. SHTEINBOK

I. BASIC PRINCIPLES

§ 1. Introduction

The use of radioactive substances for solving various scientific and technical problems has at the present time acquired important significance for the national economy in connection with the considerable development of the atomic industry, which produces radioactive substances in ever-increasing quantities.

It should be borne in mind that in the production of plutonium large quantities of by-product radioactive products and their isotopes remain, awaiting their industrial use.^5

Radioelements, apart from their known applications in medicine, and also for the production of luminous compositions and flaw detection, are at present used mainly in two directions:

1) As “labeled atoms” in chemical, physical, biological, and scientific-technical investigations. In this field considerable successes have already been achieved, as a result of which the method of “labeled atoms” in a number of cases substantially surpasses other research methods both in sensitivity and in accuracy.^1,2,3,4,5,7,9,11,22,77,78,81 The application of the method of “labeled atoms” has led Soviet scientists to a number of important discoveries in the fields of biology, agrobiology, and chemistry.^4

2) As permanently operating portable sources of radioactive radiation of high energies in various kinds of new automatic instruments for the investigation and control of production and technological processes.^5,6,7,8,13,14,77

Owing to the natural properties of radioactive substances, radioactive ionizers, unlike other ionizers, require no special maintenance and no expenditure of additional energy. For the manufacture of one instrument only from 1 to 100 microcuries of radioactive substance are required.

The successes of physics in the field of research into and use of intra-atomic energy could not fail to affect the interest of engineers in this question. This is also promoted by the rapid development of such branches of technology as electrovacuum technology, electrical measuring technology, insulating materials, and others. If before 1941 the possibilities of applying radioactive radiation in measuring technology were little known, then at the present time the situation has changed, and many instruments based on the use of α-, β-, and γ-radiation of radioactive substances are already known.

In the present article the basic questions of the application of radioactive radiation in measuring technology are considered.

§ 2. Principal ways of using radioactive radiation in measuring technology

The principal ways of using radioactive radiation in measuring technology are determined by the ability of this radiation to ionize gas; moreover, typical dependences occur of the number of ions formed on the nature and density of the gaseous medium, and also on the range, absorption, and scattering of the ionizing radiations ^18,19.

There are a number of methods for investigating and measuring the intensity of ionizing radiation, based on its ionization ^20,21, photographic ^42, and scintillation ^40,41 effects, absorption ^18, the occurrence of discharge under the action of radiation ^20,23,24,25, measurement of the conductivity of certain semiconductors, and, finally, condensation of vapor on ions ^26,80.

The simplest, most accurate, and most convenient of these, suitable for the design and manufacture of various series-produced instruments, is the ionization method. In the case of sufficiently intense ionization, measurement of ionization currents is carried out with the aid of ionization chambers; in the case of weak ionization, with the aid of ionization and scintillation counters.

It should be noted, however, that it usually proves considerably more advantageous to proceed by increasing the quantity of radioactive substances used in instruments and to use ionization chambers, rather than expensive and bulky counting apparatus employed when the quantities of radioactive substances are small.

Taking into account the existing tendency in instrument design toward reducing the dimensions and weight of instruments, and in view of this the desirability of designing sensitive systems (sensors) of small dimensions, it is most expedient in many cases to use α-radiation, which possesses the highest ionizing power per 1 cm of range. However, in designing a number of instruments—for example, instruments for measuring gas pressures of the order of tens or thousands of atmospheres, liquid levels of the order of meters, material thicknesses, etc.—it is necessary to use β- and γ-rays.

These considerations form the basis for choosing the type of radioactive radiation. In choosing the radioactive substance it is also necessary to be guided by the lifetime of the radioactive element.

Among the approximately 800 radioactive elements and their isotopes known at the present time ^15,16,17, only a small part satisfies the conditions indicated above.

§ 3. Basic circuit of ionization instruments with a radioactive ionizer

A typical circuit of an ionization instrument with a radioactive ionizer placed inside the chamber is shown in Fig. 1, which depicts an ionization chamber for measuring gas pressure. In this circuit, connected in series with the ionization chamber are a source of e.m.f. \(E\) and a high-ohmic resistance \(R\), across which the ionization current produces a voltage drop proportional to the gas pressure being measured; by the capacitance \(C\) is meant the distributed capacitance of the entire circuit, composed of the capacitances of the chamber, the tube, and the connecting wires. The voltage drop across the resistance \(R\) is fed to the input of an electrometric amplifier. If further amplification in voltage and power is necessary, the output of the electrometric amplifier is connected to subsequent amplification stages. The scale of the meter is calibrated directly in units of the pressure being measured. For measuring other non-electrical quantities, the design of the ionization chamber is modified accordingly.

Fig. 1. Basic circuit of an ionization instrument with a radioactive ionizer located inside the ionization chamber.

To eliminate the influence of all possible external pickups and to facilitate shielding of the instruments, ionization chambers are often mounted in the same housing as the amplifier or, in any case, as the first amplification stage. The potentials of the housing and of individual points of the circuit are chosen so as to reduce to a minimum the parasitic ionization currents that may arise inside the housing owing to ionization produced by radioactive contamination and cosmic rays. Another important precaution for accurate operation of ionization instru-

...devices is the drying of the air inside the ionization chamber and in the area where the electrometer tube is located.

The most important elements of any ionization instrument are: the ionization chamber with a radioactive ionizer, a high-resistance element, and an ionization-current amplifier.

§ 4. Volt-ampere characteristic of ionization chambers

Of primary importance for the use of radioactive radiation in measurement technology are questions concerning the passage of current through a gas located in the zone of radioactive radiation.

If one or both electrodes, insulated from one another by a gas gap, are coated with a thin layer of radioactive substance, and a certain potential difference is applied to them, an ionic current arises in the circuit; its magnitude is a complex function of the amount of radioactive substance, the applied voltage, and the density and composition of the medium filling the ionization chamber.

Fig. 2. Volt-ampere characteristics of ionization chambers at two values of radiation intensity \(N_0\) and \(N'_0\).

With constant composition and constant density of the gas filling the ionization chamber, the dependences of the ionization currents on the applied voltage for different radiation intensities \(N_0\) and \(N'_0\) have the form shown in Fig. 2. Several regions are characteristic of these graphs: a linear region...

section \(I\), the saturation region \(II\), and the regions of non-self-sustained and continuous discharge \(III—VI\). Regions \(I\) and \(II\) are the most stable and have found application in the technique of measuring nonelectrical quantities; regions \(III—V\) are used for designing ionization counters. In region \(I\) the ion current depends on the mobility, recombination, and number of ions, as well as on the applied voltage. In region \(II\) the current is determined exclusively by the total number of ions created in the volume of the chamber by the ionizing agent.

The dependence of the ionization current \(I\) on the voltage \(U\) is a complicated function of many variables and cannot be expressed simply.

The balance equations for the concentrations of ions (positive \(n_1\) and negative \(n_2\)) for a stationary state in the case of a plane chamber have the form:

\[ \begin{aligned} N_0 &= \alpha n_1 n_2 + k_1 \frac{d}{dx}(n_1 E) - D_1 \frac{d^2 n_1}{dx^2},\\ N_0 &= \alpha n_1 n_2 - k_2 \frac{d}{dx}(n_2 E) - D_2 \frac{d^2 n_2}{dx^2}. \end{aligned} \tag{1} \]

Equations (1) express the equilibrium of ion concentrations as a result of the simultaneous processes of ionization \((N_0)\) and disappearance of ions due to recombination \((\alpha n_1 n_2)\), transport by the electric field \(\left(k \frac{d}{dx}(nE)\right)\), and diffusion \(\left(-D \frac{d^2 n}{dx^2}\right)\).

The true field inside the ionization chamber in the presence of a volume charge is determined by Poisson’s equation

\[ -\frac{dE}{dx} = 4\pi e (n_1 - n_2). \tag{2} \]

The ionization current, taking into account ion diffusion, is found from the equation

\[ I = eS \left[(k_1 n_1 + k_2 n_2)E + D_1 \frac{dn_1}{dx} - D_2 \frac{dn_2}{dx}\right]. \tag{3} \]

Here \(k_1\) and \(k_2\), \(D_1\) and \(D_2\) are the mobilities and diffusion coefficients of the ions, \(e\) is their charge, \(E\) is the electric-field strength, and \(S\) is the area of the electrodes of the ionization chamber.

Equations (1)—(3) have no rigorous solution. Some authors (see, for example, \(^{20,21,25}\)) have solved this problem approximately for the case in which ion diffusion is absent. Below is given one of these solutions for an infinitely large plane capacitor and uniform ionization:

\[ U = IR_0 \left(1 + C_1 \frac{I}{I_\infty}\right) \quad \text{for } \frac{I}{I_\infty} < 0.6 \tag{4} \]

and

\[ U=\frac{IR_0}{\sqrt{1-\dfrac{I}{I_\infty}}} \quad \text{for} \quad \frac{I}{I_\infty}>0.94, \tag{5} \]

where \(C_1\) is a constant, equal for air to 1.05, \(I_\infty\) is the saturation current, and \(R_0\) is the resistance of the ionization chamber at \(I \to 0\). The solution given by Seeliger, as well as the similar solution of Mie \(^{20,21}\), describes the current–voltage characteristic not completely, but by sections, for limiting cases.

Neglecting, in addition to ion diffusion, also the space charge, which is permissible for low radiation intensity, we have obtained a rigorous solution of equations (1) for an infinitely large plane capacitor and homogeneous ionization, which completely describes the current–voltage characteristic between the points \(O J_2\) (Fig. 2):

\[ \frac{I}{I_\infty} = \frac{ \sqrt{\dfrac{R^2}{R_0^2}-1} }{ \dfrac{R}{R_0^2}\operatorname{arcctg} \sqrt{\dfrac{R^2}{R_0^2}-1} }, \tag{6} \]

Here \(R\) is the resistance of the ionization chamber, equal to \(\dfrac{U}{I}\), and \(R_0\) is the resistance of the ionization chamber on the linear portion of the current–voltage characteristic at \(I \to 0\):

\[ R_0=\frac{h}{2eS}\sqrt{\frac{\alpha}{k_1k_2N_0}}, \tag{7} \]

where \(h\) is the distance between the electrodes, \(S\) is the electrode area, \(\alpha\) is the ion recombination coefficient, \(k_1\) and \(k_2\) are the ion mobilities, \(N_0\) is the number of ion pairs created by the ionizer per unit volume per unit time, and \(e\) is the ion charge.

Taking, in weak fields,

\[ \operatorname{arcctg}\sqrt{\frac{R^2}{R_0^2}-1} \]

to be equal to \(\dfrac{\pi}{2}\), and in strong fields to be equal to \(\dfrac{R}{R_0}\), we obtain from (6) the approximate solutions:

\[ U=IR_0\left(1+C_2\frac{I^2}{I_\infty^2}\right) \quad \text{for} \quad \frac{I}{I_\infty}<0.6, \tag{8} \]

where \(C_2\) is a constant equal to unity, and

\[ U=\frac{IR_0}{\sqrt{1-\dfrac{I^2}{I_\infty^2}}} \quad \text{for} \quad \frac{I}{I_\infty}>0.94. \tag{9} \]

Expressions (8) and (9), similar in form to (4) and (5), differ from them by the square of \(I\) and are in better agreement with experiment, at least for radiation intensities below 100 microcuries.

§ 5. Regularities in the operation of \(\alpha\)-ionization chambers

Familiarity with the question of the influence of radiation intensity, medium density, gas composition, chamber dimensions, gas-flow velocity, etc., on the course of the volt-ampere characteristics is of great importance for assessing the possibilities of applying the ionization method in measurement technology. Until recently, each case was considered separately on the basis of experimentally observed volt-ampere characteristics, as a result of which the connection between them was not evident and, naturally, the necessary generalizations could not be made.

Starting from expression (7), we have established a general regularity, which may be formulated as follows: the product of the saturation current \(I_\infty\) by the square of the initial resistance \(R_0\) of the ionization chamber is a constant quantity for given dimensions of the ionization chamber and of the gas filling the chamber.

Indeed, carrying out simple transformations of (7), we obtain:

\[ R_0=\sqrt{\frac{ah^3}{4ek_1k_2S}}\cdot \sqrt{\frac{1}{ehSN_0}}. \]

Taking further into account that \(ehSN_0\) is the saturation current \(I_\infty\), after further transformations we obtain:

\[ I_\infty R_0^2=\Omega, \tag{10} \]

where

\[ \Omega=\frac{a}{4ek_1k_2}\cdot\frac{h^3}{S}. \tag{11} \]

Regularity (10) does not depend on the radiation intensity and establishes the simple relation that exists between the initial resistance \(R_0\) and the saturation current \(I_\infty\). The indicated regularity has been verified on the basis of extensive experimental data\(^{76}\) and is well confirmed for ionization currents produced by \(\alpha\)-radiation, at least within the range from 10 to 1000 CGSE. This shows that regularity (10) also holds beyond the limits of validity of its derivation, i.e., under nonuniform ionization produced by \(\alpha\)-rays. However, in this case, when calculating the constant \(\Omega\), it is necessary to take into account the angular distribution of the emitted \(\alpha\)-particles.

In studying α-ionization chambers, for example when changing the distance between the electrodes or when producing high pressures in the chamber, cases are possible in which the range of the α-particles \(L\) becomes smaller than the dimension \(h\), while the saturation current remains constant despite the change in \(R_0\). Other cases are also possible, for example when producing gas pressures in chambers lower than atmospheric, when \(R_0\) remains constant while the saturation current changes. All these anomalies can be well explained by analysis of relation (10).

Starting from (7) and (10), and taking into account the above-mentioned features of α-ionization chambers, as well as experimental data, we have compiled Table I, in which the laws governing the operation of α-ionization chambers are summarized and, in a visual form, the changes in the form of the volt-ampere characteristics, the initial resistance \(R_0\), and the saturation current are shown as functions of changes in various factors. The same table also indicates the field of application of the α-ionization method in measuring technology. The laws governing the operation of α-ionization chambers, with the exception of Nos. 4 and 8, prove, with some approximation, to be applicable also when using β-rays, but, naturally, within different limits.

§ 6. Fluctuations of the ionization current and determination of the required amount of radioactive substance

The number of α- and β-particles or γ-quanta emitted by radioactive substances is not the same in equal intervals of time and is subject to statistical fluctuations about a certain mean value. When the mean number of particles emitted in one second is small, individual values may differ noticeably from the mean, causing fluctuations of the ionization current visible on the instrument. With high sensitivity of the electrical circuit and when measuring small changes in the ionization current, fluctuations of the order of tenths of a percent, occurring with low frequency, already make the reading of indications almost impossible. Therefore, reducing fluctuations of the ionization current to a value determined by the accuracy of measurement is an absolutely necessary element in the calculation of instruments.

The question of the influence of fluctuations in the number of ionizing particles on the readings of ionization instruments has been considered by many authors. We present, in a somewhat modified form, the solution given by I. Ya. Barit and M. I. Podgoretskii\(^{20,27}\) for the case of ionization by α-particles emerging from the wall of a plane chamber, when the ion-collection time is small in comparison with the \(RC\) of the circuit.

Table 1

Regularities in the operation of α-ionization chambers

	Variable quantity $\vartheta$	$R_0 = f_1(\vartheta)$	$I_\infty = f_2(\vartheta)$	Form of $I = f(U)$	Form of $R_0 = f(\vartheta)$, $I_\infty = f_2(\vartheta)$	Field of application in measurement technology
1	Radiation intensity $N_0$	$C_1 \sqrt{\dfrac{1}{N_0}}$	$K_1 N_0$	Graph of $I$ versus $U$: saturation curves; upper curve labeled $N_{02} > N_{01}$, lower curve labeled $N_{01}$; axes labeled $I$, $U$, origin $0$.	Graph versus $N_0$: $R_0$ decreases, $I_\infty$ increases; axes labeled $0$, $N_0$; curves labeled $R_0$, $I_\infty$.	Dosimetry of ionizing radiations; measurement of high gas pressures, thicknesses of sheet materials
2	Electrode area $S$ at $N_0 = \mathrm{const}$	$C_2 \dfrac{1}{S}$	$K_2 S$	Graph of $I$ versus $U$: saturation curves; upper curve labeled $S_2 > S_1$, lower curve labeled $S_1$; axes labeled $I$, $U$, origin $0$.	Graph versus $S$: $R_0$ decreases, $I_\infty$ increases; axes labeled $0$, $S$; curves labeled $R_0$, $I_\infty$.	Measurement of areas of complex configuration, angular and linear displacements
3	Distance between electrodes $h$ at $h > L$	$C_3 h$	$K_3 h$	Graph of $I$ versus $U$: curves labeled $h_2 > h_1$ and $h_1$; axes labeled $I$, $U$, origin $0$.	Graph versus $h$: both $R_0$ and $I_\infty$ increase; axes labeled $0$, $h$; curves labeled $R_0$, $I_\infty$.	Measurement of small angular and linear displacements, accelerations and vibrations

Continuation of Table 1

No.	Measured quantity \(\delta\)	\(R_0=f_1(\delta)\)	\(I_\infty=f_2(\delta)\)	Form of \(I=f(U)\)	Form of \(R_0=f_1(\delta)\), \(I_\infty=f_2(\delta)\)	Field of application in measuring technique
4	Distance between electrodes \(h\) for \(h>L\)	\(C_4 h^{\frac{3}{2}}\)	const	Graph of \(I\) versus \(U\): two rising saturation curves labeled \(h_1\) and \(h_2>h_1\).	Graph versus \(h\): \(I_\infty\) is constant; \(R_0\) increases with \(h\).	Measurement of large linear displacements
5	Gas density \(\rho\) for \(h<L\), \(p>1\,atm\)	\(C_5\rho\)	\(K_5\rho\)	Graph of \(I\) versus \(U\): saturation curves labeled \(\rho_2>\rho_1\) and \(\rho_1\).	Graph versus \(\rho\): \(I_\infty\) increases linearly with \(\rho\); \(R_0\) also increases with \(\rho\).	Measurement of gas pressures
6	Gas density \(\rho\) for \(h<L\), \(p<1\,atm\)	const	\(K_6\rho\)	Graph of \(I\) versus \(U\): saturation curves labeled \(\rho_2>\rho_1\) and \(\rho_1\).	Graph versus \(\rho\): \(I_\infty\) increases linearly with \(\rho\); \(R_0\) is constant.	Measurement of pressure, density, velocity, and composition of gases

Continuation of Table 1

No.	Variable quantity \(\delta\)	\(R_0=f_1(\delta)\)	\(f_\infty=f_2(\delta)\)	Form of \(I=f(U)\)	Form of \(R_0=f_1(\delta)\), \(I_\infty=f_2(\delta)\)	Field of application in measurement technology
7	Gas density \(\rho\) at \(h \ll L\), \(p < 100\) mm Hg	\(C_7\dfrac{1}{\rho}\)	\(K_7\rho\)	Plot of \(I\) versus \(U\): two rising curves from the origin; the upper curve is labeled \(\rho_2>\rho_1\), the lower \(\rho_1\).	Plot versus \(\rho\): \(R_0\) decreases, \(I_\infty\) increases.	Measurement of small gas pressures
8	Gas density \(\rho\) at \(h>L\), \(p>1\) atm	\(C_8\rho\)	const	Plot of \(I\) versus \(U\): two rising curves from the origin; the upper curve is labeled \(\rho_1\), the lower \(\rho_2>\rho_1\).	Plot versus \(\rho\): \(I_\infty\) is constant, \(R_0\) increases.	Measurement of large gas pressures
9	Dielectric constant of a gas \(\varepsilon\) at \(p=\mathrm{const}\)	\(C_9\sqrt{\varepsilon-1}\)	const	Plot of \(I\) versus \(U\): two rising curves from the origin; the upper curve is labeled \(\varepsilon_1\), the lower \(\varepsilon_2>\varepsilon_1\).	Plot versus \(\varepsilon\): \(I_\infty\) is constant, \(R_0\) increases.	Measurement of small concentrations of gas impurities, vapors, and fumes in air and other gases
10	Velocity of gas flow \(v\) at \(p=\mathrm{const}\)	\(C_{10}v\)	const	Plot of \(I\) versus \(U\): two rising curves from the origin; the upper curve is labeled \(v\), the lower \(v_2>v_1\).	Plot versus \(v\): \(I_\infty\) is constant, \(R_0\) increases.	Measurement of gas-flow velocity

The relative fluctuation is equal to

\[ \delta=\sqrt{\frac{1}{2\bar nRC}}\sqrt{1-\frac{7}{3}\frac{h}{kERC}}. \tag{12} \]

Here \(\bar n\) is the average number of particles emitted per unit time by the radioactive substance deposited on the chamber electrodes, \(h\) is the distance between the electrodes, \(k\) is the average mobility of the ions, and \(E\) is the electric-field strength.

In the case where the ion-collection time \(\frac{h}{kE}\) is negligibly small in comparison with \(RC\), which closely corresponds to the operating conditions of \(\alpha\)-ionization instruments in the saturation region, the relative fluctuation increases, and its expression assumes the simpler form:

\[ \delta=\frac{1}{\sqrt{2\bar nRC}}. \tag{13} \]

If the time constant of the instrument \(RC\) is specified and must not exceed a certain value, then the only remaining possibility for reducing fluctuations is by increasing the emission of ionizing particles, i.e., the number \(\bar n\). Conversely, if \(\alpha\)-ionization instruments are used to measure slowly varying quantities, the time constant \(RC\) may be not very small, and then, in order to reduce fluctuations, it is advantageous to increase the capacitance \(C\).

Since, in calculating the amount of radioactive substance to be deposited on the chamber electrodes, it is necessary to take into account the permissible magnitude of the fluctuation on the basis of the prescribed measurement accuracy, we transform (13) with respect to \(\bar n\):

\[ \bar n=\frac{1}{2\delta^2RC}. \tag{14} \]

The amount of radioactive substance required for the emission per unit time of \(\bar n\) ionizing particles, determined by the permissible fluctuation, can be found as follows. The number of atoms \(N_p\) decaying with the emission of \(\alpha\)- or \(\beta\)-particles in \(1\) g of radioactive substance per unit time is equal to

\[ N_p=\lambda\frac{N_a}{M}, \tag{15} \]

where \(\lambda\) is the decay constant of the radioactive substance, \(N_a\) is the total number of atoms present, and \(M\) is the molecular weight. From (15) it follows that \(\bar n\) ionizing particles will be emitted by \(p\) grams of radioactive substance, or

\[ \bar n=\lambda\frac{N_a}{M}p. \tag{16} \]

Equating (16) to the quantity \(\bar n\), determined by the fluctuation (14), we find the required amount of radioactive substance:

\[ p=\frac{M}{\lambda N_a}\frac{1}{2\varepsilon^2 RC}. \tag{17} \]

For a known radioactive substance, \(N_a\), \(M\), and \(\lambda\) are constant tabulated quantities.

§ 7. Principal types of ionization chambers

At the present time a rather large number of different types and designs of ionization chambers are known, and they have found wide application in nuclear physics. In principle, these chambers can also be used in the practice of designing instruments for measuring nonelectrical quantities. It should be noted that, generally speaking, any form of chamber electrodes, at any distance between them, can give satisfactory measurement results if the corresponding intensity of radiation of the radioactive substance and the voltage between the electrodes are selected. However, preference should be given to those electrode forms in which saturation current is achieved at a lower voltage.

The designs of ionization chambers differ somewhat depending on the kind of radiation used (\(\alpha\)-, \(\beta\)-, or \(\gamma\)-rays) and on the conditions under which the radiation penetrates into the chamber\(^{20,25}\). It is necessary, however, to note that ionization chambers intended for operation with \(\alpha\)- and \(\beta\)-radiations can in many cases be of one and the same design. The designs of \(\gamma\)-ionization chambers, however, differ substantially from \(\alpha\)- and \(\beta\)-chambers because of the great penetrating power of \(\gamma\)-rays and the different mechanism of interaction of the rays with matter.

Fig. 3. Typical designs of plane ionization chambers. The radioactive layer is shown by a dashed line.

According to the forms of the electrodes, all ionization chambers may be divided into the following principal types: plane, cylindrical, hemispherical, spherical, and multielectrode chambers. Plane and cylindrical chambers have become most widespread because of the simplicity of their manufacture.

Plane chambers. Figure 3 shows two typical designs of plane ionization chambers. The dashed line conventionally indicates a thin layer of radioactive substance producing \(\alpha\)- or \(\beta\)-radiation in the ionization chamber. In the first design

(fig. 3, a) plate \(A\) is connected to the control grid of an electrometer tube or to the filament of an electrometer. Plate \(B\) is connected to a pole of the battery, and a certain potential difference is established between the plates. The metal body of the chamber shields it from electrostatic fields. The second construction of the chamber (fig. 3, b) has only one separate electrode \(A\); the other electrode is the body of the chamber itself. Electrode \(A\) is insulated from the body by means of a double insulator with a guard ring. A plate with radioactive material previously deposited on it is usually placed on the bottom of the chamber body.

The advantage of the flat chamber is the possibility, under certain conditions, of obtaining a uniform electric field.

Cylindrical chambers. Typical designs of cylindrical ionization chambers are shown in fig. 4. Here the central electrode \(A\) and the body \(B\) have a cylindrical shape. With a large difference in the diameters of electrodes \(A\) and \(B\), the electric-field strength increases sharply as one approaches electrode \(A\). In view of this, the saturation current, at the same radiation intensity of the preparation, is reached in a cylindrical chamber somewhat later than in a flat chamber. In cylindrical chambers, depending on the conditions of use, the radioactive substance is deposited on the inner surface of the cylinder or on the central electrode, and in some cases on the bottom of the chamber, as shown in fig. 4, a.

Fig. 4. Typical designs of cylindrical ionization chambers: a—without a guard ring, b—with a guard ring.

Conditions for reliable operation. A guard ring plays a very important role for the stable operation of an ionization chamber; it diverts from the grid electrode*) leakage currents, variable in magnitude, over the surface and through the volume of the insulator. These leakages inevitably occur even in the best insulators through surface films and through the volume of the insulator when the latter is polarized. The instability of surface leakages is explained by the unstable

*) In the literature this electrode is usually called the collecting or capturing electrode. This name seems to us not entirely apt, since in the case of integrating ionization chambers both electrodes remove ions from the field and, thus, both of them are “collecting.”

condition of the surface films, in which the direction of the leakage paths changes continuously. To reduce leakages significantly, or to eliminate them almost completely, the guard ring must be kept at a constant potential, as close as possible to the potential of the grid electrode. Usually the guard ring is connected to the grounded point of the circuit. As insulators for the grid electrode it is necessary to use high-quality insulators: amber, polystyrene, polyethylene, escapone, quartz, and special grades of plastics and ceramics. The surface of the insulator must be carefully polished and degreased.

Incorrect
a

Correct
b

Fig. 5. Correct and incorrect designs of ionization chambers.

Of great importance for the reliable operation of ionization instruments is the correctly chosen design of the chamber. In Fig. 5 correct and incorrect designs of ionization chambers are shown.

In a correctly designed chamber the surface of the grid insulator must not be too large, in order to avoid the occurrence of a stray surface charge. The diameter, for example, of a flat grid electrode should be somewhat larger than the diameter of the insulator; by this means the insulator is shielded from the action of radiation, which worsens the properties of insulators \(^{18,43}\). The grid electrode must not adjoin the insulator directly with its surface, as shown in Fig. 5, a, since in this case the surface resistance of the insulator is reduced.

These precautionary measures, verified in practice, are absolutely necessary when measuring small values of ionization currents of the order of \(10^{-15}—10^{-11}\) a. However, in designing ionization chambers intended to operate with currents of the order of \(10^{-10}—10^{-8}\) a at voltages not above 400 v, it is possible to dispense with guard rings, which considerably complicate the design of the chambers.

§ 8. Efficiency of ionization chambers

By the efficiency of an ionization chamber with a radioactive ionizer we shall understand the ratio of the saturation current, or the number of ion pairs created by the radioactive substance in a chamber of given dimensions, to the total number of ion pairs created by the ionizer when the entire range of the ionizing particles is used. Let us consider the most difficult case of the efficiency of \(\alpha\)-ionization chambers.

To find the number of ion pairs \(m\) formed by \(\alpha\)-radiation inside an ionization chamber bounded by walls, we proceed from the assumption that the number of ion pairs formed in an elementary volume enclosed within the solid angle \(d\omega=\sin\theta\,d\theta\,d\varphi\) and a sphere of radius \(r\) (Fig. 6) is proportional to the angle \(d\omega\), to some function \(F(\theta)\) of the angle \(\theta\), and to some function \(f(r)\) of the radius of the sphere \(r\)*).

Fig. 6.

According to experimental determinations, the intensity of the \(\alpha\)-radiation of a plate coated with a radioactive substance varies according to the cosine law:

\[ F(\theta)=K_1\cos\theta, \]

where \(\theta\) is the angle between the direction of flight of the \(\alpha\)-particles and the normal to the emitting plate. The number of ion pairs created by \(\alpha\)-particles (as a function of their range \(L\)) is well approximated, according to the data of M. Curie \({}^{18}\), by the function

\[ f(r)=K_2L^{2/3}. \]

Fig. 7.

Since below the ratio of two quantities of ions of the same dimension is calculated, we take the proportionality coefficients equal to unity and obtain, for the number of ions formed per unit time in the elementary volume specified above, the expression

\[ dm=\sin\theta\cos\theta L^{2/3}\,d\theta\,d\varphi. \]

Denoting the number of ions formed by \(\alpha\)-particles under the condition that the entire range is used by \(M\), we find:

\[ M=L^{2/3}\int_0^{2\pi}d\varphi\cdot\int_0^{\frac{\pi}{2}}\sin\theta\cdot\cos\theta\,d\theta =\pi L^{2/3}. \tag{18} \]

To find the number of ions \(m=m_1+m_2\) formed per unit time inside a cylindrical chamber with the dimensions shown in Fig. 7, we denote by \(m_1\) the number of ions formed per unit time inside the cone with its vertex at the center of the disk and its base coinciding with the upper bottom of the chamber, and by che-

*) The derivation given below was made by N. I. Shteinbok jointly with T. A. Rozet.

— \(m_2\) is the number of ions formed in the remaining part of the chamber. Since \(r_1 = \dfrac{h}{\cos \theta}\), with the angle \(\theta\) varying from 0 to \(\theta_0 = \operatorname{arctg}\dfrac{a}{h}\), while \(r_2 = \dfrac{a}{\sin \theta}\) and \(\theta_0 \leq \theta \leq \dfrac{\pi}{2}\) (Fig. 7), we have

\[ m_1 = h^{2/3} \int_{0}^{2\pi} d\varphi \int_{0}^{\operatorname{arctg}\frac{a}{h}} \sin \theta \cos \theta \sec^{2/3}\theta\, d\theta = \]

\[ = \frac{3}{2}\pi h^{2/3} \left[ 1 - \frac{h^{4/3}}{(h^2+a^2)^{2/3}} \right]; \]

\[ m_2 = a^{2/3} \int_{0}^{2\pi} d\varphi \int_{\operatorname{arctg}\frac{a}{h}}^{\frac{\pi}{2}} \sin \theta \cos \theta \cosec^{2/3}\theta\, d\theta = \]

\[ = \frac{3}{2}\pi a^{2/3} \left[ 1 - \frac{a^{4/3}}{(h^2+a^2)^{2/3}} \right]; \]

\[ m = m_1 + m_2 = \frac{3}{2}\pi \left[a^{2/3}+h^{2/3}-(a^2+h^2)^{1/3}\right]. \tag{19} \]

To determine what part of the total number of ions formed is concentrated within the cylindrical chamber (Fig. 7), we find the ratio of (19) to (18):

\[ q = \frac{m}{M} = \frac{3}{2}\, \frac{a^{2/3}+h^{2/3}-(a^2+h^2)^{1/3}}{L^{2/3}} . \tag{20} \]

The ratio (20), which we have called the efficiency of the ionization chamber, characterizes the usefully utilized part of the \(\alpha\)-radiation in an ionization chamber of the given dimensions.

From (20) there follows the important conclusion that, since \(q\) grows not proportionally to the volume of the chamber but much more weakly, the rational course is to use ionization chambers of small dimensions.

§ 9. High-resistance resistors

The choice of appropriate high-resistance resistors, by means of which ionization currents are measured, is of great importance for the stable and accurate operation of ionization instruments. In most cases, when ionization currents have values of the order \(10^{-12}\)—\(10^{-9}\) a, high-resistance resistors must have values of the order \(10^{12}\)—\(10^9\) ohms. The manufacture of such stable resistors presents considerable difficulties.

At present two types of high-ohmic resistances are known: a) volume and b) surface.

Volume resistances. Volume resistances, in turn, are divided into liquid, solid, and ionization resistances.

Liquid resistances of the order of \(10^8\)—\(10^{10}\) ohms are readily made, for example, from a mixture of anhydrous alcohol, benzene, and picric acid. Depending on the percentage content of alcohol, the value of the resistance changes. Owing to polarization, liquid resistances cannot be made greater than \(\sim 10^{10}\) ohms.

The disadvantages of liquid resistances include a high temperature coefficient (about \(2\%\) per \(1^\circ\)C) and a change in resistance with time because of the gradual evaporation of alcohol and benzene.

Solid volume resistances of the “defar” type are made by impregnating porous porcelain tubes with an aqueous solution of dextrin, followed by firing in a reducing medium. These resistances are distinguished by great constancy and a small temperature coefficient, but, unfortunately, cannot be made above \(10^9\) ohms.

Very stable resistances up to \(10^9\) ohms can be made from black light-tight paper used for wrapping photographic materials. The temperature coefficient of these resistances in the range \(10\)—\(30^\circ\)C is \(0.03\%\) per \(1^\circ\)C.

Ionization resistances are essentially also volume resistances, except that their conductivity is determined by the ionized volume of gas. Radioactive substances emitting \(\alpha\)- or soft \(\beta\)-rays are used as the ionizer. The working region of ionization resistances is the linear portion of the current-voltage characteristic, on which the resistance is approximately constant up to limits of \(0.6\, \dfrac{I}{I_\infty}\). Ionization resistances are advantageously made, using small amounts of radioactive substance, for nominal values of the order of \(10^9\)—\(10^{13}\) ohms. The constructions of ionization resistances may be basically the same as those of ionization chambers (Figs. 3 and 4), but of smaller dimensions. By applying a special technology for the manufacture of ionization resistances, it is possible to obtain stable resistances of various magnitudes and temperature coefficients\({}^{30}\).

Surface resistances. Surface resistances are made by depositing an extremely thin film of conducting material on an insulating substrate. It is generally considered that high values of resistance are achieved not as a result of an increase in the resistance of the film itself, but as a consequence of its discontinuities.

Resistors of the order of \(10^8\)—\(10^{10}\) ohms, made on the basis of carbon black, India ink, or graphite, have an impermissibly large temperature coefficient: 5–6% per \(1^\circ\)C. In addition, they age over a long period of time.

Surface resistors on a metallic base are manufactured by cathodic sputtering of platinum onto cylinders of quartz, amber, or porcelain \(^{32}\). Silicon resistors are also known, obtained by the decomposition of silane on heated glass, porcelain, or quartz tubes \(^{32}\). Recently a method has been described \(^{81}\) for making high-ohmic resistors by rubbing the surface of glass or quartz cylinders with a metal (it is immaterial which), followed by sealing these resistors in glass bulbs. All these resistors have a considerable temperature coefficient (of the order of 2–3% per \(1^\circ\)C) and tend to change their value with time.

In the present state of the question under consideration, apparently the best solution is the use of ionization resistors.

§ 10. Measurement and amplification of ionization currents

When ionization chambers are used to create ionization instruments, one usually has to deal with measurements of ionization currents of the order of \(10^{-12}\)—\(10^{-8}\) A. Such currents can be measured under laboratory conditions with the aid of magnetoelectric galvanometers, string, dynamic, and vacuum-tube electrometers \(^{21,32}\). Under operating conditions the use of galvanometers and string electrometers is inconvenient, and in some cases impossible. Ionization currents are measured most simply, rapidly, and with sufficient accuracy by an indirect method. For this purpose, using vacuum-tube amplifiers that have recently become very widespread (vacuum-tube voltmeters, galvanometers, or electrometers), the voltage drop produced by the ionization current across a known resistance is measured.

The intrinsic noise of the tubes has practically no effect on the measurement results, since it reaches values of the order of microvolts, whereas the signal magnitude usually reaches values of the order of tenths of a volt and higher.

As the first, input electronic tubes in various circuits of ionization-current amplifiers, miniature tubes of the “Acorn” type 6Zh1Zh (954), produced in mass production, or special tubes EM-1, EM-2, EM-3 \(^{21,34,35}\), produced in small series, may be used. When using 6Zh1Zh tubes for measuring ionization currents, the role of the control grid is usually performed by the third grid, to which is applied

negative with respect to the cathode potential. The second grid dissipates the space charge, and its potential must be close to or equal to the anode potential, which in the electrometric regime lies within the range 5–10 V. The potential of the first grid, nearest to the cathode, is usually maintained at \(+1\) V. The filament voltage of the 6Zh1Zh tube in the electrometric regime must be considerably less than the nominal value and equal to 4 V. This greatly increases the service life of the tubes and reduces the grid current. The 6Zh1Zh tubes in the electrometric regime \((U_a = +6\text{ V},\ U_{c_2} = +6\text{ V},\ U_{c_1} = +1\text{ V},\ U_H = 4\text{ V})\) have a small grid current, on the order of \(10^{-13}\)—\(10^{-12}\) A, and a slope on the linear portion of the anode characteristic of 100–200 \(\mu\text{A}/\text{V}\).

The values of the grid currents can be reduced by lowering the voltages: anode, first and second grids, and filament \((U_a,\ U_{c_1},\ U_{c_2}\ \text{and}\ U_H)\); however, this also reduces the slope of the anode characteristic.

When a simple single-tube circuit is used for measuring ionization currents, a considerable error arises because of instability (drift) of the zero point of the circuit[^31][^32][^34]. There are three causes of instability (drift) of the zero point of amplifiers, namely: a) change in anode voltage; b) change in the contact potential difference; and c) variations in the resistances of the anode circuit.

A change in anode voltage can be compensated comparatively easily by selecting an appropriate operating mode of the tube, in which the anode current changes in proportion to the change in voltage of the power supply.

The other two causes of drift are produced by changes in the temperature and emission of the cathode and are equivalent in their effect to the appearance of an additional and nonconstant bias on the control grid[^32][^34], which cannot be compensated in a simple single-tube circuit.

In view of the foregoing, the choice of a proper amplifier circuit is of very great importance for the accurate and stable operation of ionization instruments.

The known types and varieties of circuits of direct-current tube amplifiers may be subdivided into cascade, bridge or balanced, compensation, modulation, combined, and amplifiers with choppers and transformation of circuit parameters. Each of the circuits listed has its own advantages and disadvantages, but in the present review it is not possible to subject them to the necessary comparison and critical analysis. Therefore, referring the reader to the extensive literature on this question[^29][^31][^32][^33][^34][^35][^75], we shall indicate only the absolute necessity of using deep negative feedback for stable operation and for reducing the time constant of the circuit of almost all direct-current amplifiers.

Very promising, from our point of view, are modulation amplifiers and amplifiers with mechanical interrupters and conversion of circuit parameters[^34][^36][^37][^38][^39][^75]. These amplifiers, although more complex, prove indispensable when significant power amplification is required at a small voltage.

§ 11. Basic circuits for connecting ionization chambers, their features and field of application

At the present time, basically three circuits are used for connecting ionization chambers that serve to measure ionization currents, which are a function of the measured electrical or nonelectrical quantity. In all circuits the input voltage \(U_{\text{in}}\) is taken to be constant during the measurement process, and the grid current of the input tube of the amplifier is negligibly small. Therefore the ionization chamber may be regarded as a variable ionization resistance which, depending on the portion of the current-voltage characteristic, may be linear or nonlinear.

In the circuits considered below the following conventional designations are adopted: closed ionization resistances are denoted by rectangles with two small strokes—the electrodes inside them, while open resistances are denoted by a break in the contour of such a rectangle, indicating communication with the medium being measured; \(R_0\) and \(R_I\) are, respectively, the linear and nonlinear resistances.

First circuit. The ionization chamber operates on the linear portion of the current-voltage characteristic as an ohmic resistance that changes its value under the action of the measured nonelectrical quantity. The comparison constant resistance is connected in series and may be the ionization resistance \(R_0\) or a simple ohmic resistance \(R\). The ionization current is measured by a tube galvanometer or by an amplifier of one type or another from the voltage drop across the resistance \(R\) (Fig. 8, a). The output voltage of the circuit \(U_{\text{out}}\), equal in magnitude to the voltage of the control grid of the electrometer tube, is determined graphically or analytically.

Figure 8, a gives a graphical method for determining \(U_{\text{out}}\). When the measured quantity changes, the current-voltage characteristic of the ionization resistance changes (the new characteristic is shown by a dashed line). Since

\[ U_{\text{in}} = U_1 + U_2 = U'_1 + U'_2 = \text{const}, \]

then

\[ U_{\text{out}} = U'_1 - U_1 = U'_2 - U_2. \]

Analytically, \(U_{\text{out}}\) is determined from the condition of equality of the currents flowing through the resistances \(R_0\) and \(R\). Denoting by \(R_0\)

Fig. 8. Basic connection circuits of ionization chambers and the graphical method for finding \(U_{\mathrm{out}}\); \(R_0\) is a linear ionization resistance, \(R\) is an ohmic resistance, \(R_1\) is a nonlinear ionization resistance.

the resistance of the ionization chamber on the initial current–voltage characteristic and by \(R_0'\) on the changed characteristic, after simple transformations we find the output voltage \(U_{\text{out}}\) and its change:

\[ \Delta U_{\text{out}} = U_{\text{out}} - U'_{\text{out}}; \]

\[ U_{\text{out}}=\frac{R}{R_0+R}, \qquad U'_{\text{out}}=\frac{R}{R_0'+R}; \]

\[ \Delta U_{\text{out}}= \frac{R_0'-R_0}{(R_0'+R_0)(1+R_0/R)}\,U_{\text{in}}. \tag{21} \]

The denominator of expression (21) changes little; therefore, for simplicity, we shall assume it constant and equal to \(R_a\); we denote the reciprocal quantity \(\frac{1}{R_a}\) by \(g_1\). The ionization resistance \(R_0\) is equal to

\[ R_0=\frac{h}{2eS}\sqrt{\frac{a}{k_1 k_2 N_0}}. \tag{7} \]

Substituting (7) into (21) and introducing primes for the quantities in expression (7), we find:

\[ \Delta U_{\text{out}}= \frac{g_1}{2e} \left[ \frac{h'}{S'}\sqrt{\frac{a'}{k_1'k_2'N_0'}} - \frac{h}{S}\sqrt{\frac{a}{k_1k_2N_0}} \right]U_{\text{in}}. \tag{22} \]

This expression is considerably simplified when particular cases of measurement are considered. The greatest sensitivity of the circuit is observed when measuring \(h\), \(S\), and the density \(\rho\), on which \(a\), \(k_1\), \(k_2\), and \(N_0\) depend. This circuit is, in principle, suitable for measuring angular and linear displacements, the density and composition of gases.

As follows from (22), \(\Delta U_{\text{out}}\) is directly proportional to \(U_{\text{in}}\), and therefore, in order to increase the sensitivity of the circuit, it is advantageous to increase \(U_{\text{in}}\). However, one cannot go far in this direction, since the linear portion of the current–voltage characteristic extends only up to \(0.65\,\frac{I}{I_\infty}\), and therefore the overall sensitivity of the circuit is low.

Second circuit. The ionization chamber operates on the saturation portion of the current–voltage characteristic and represents a nonlinear resistance \(R_I\), depending on the voltage and on the measured nonelectrical quantity. The comparison resistance \(R_0\), or \(R\), is connected in series. The electrical circuit and the graphical method of calculation, which remains the same as before, are shown in Fig. 8, б. The change in the output voltage of the circuit \(\Delta U_{\text{out}}\) is equal to

\[ \Delta U_{\text{out}}= \frac{R_I'-R_I}{(R_I'+R)\left(1+\frac{R_I}{R}\right)}. \tag{23} \]

The ionization resistance \(R_I\), according to (9), is approximately equal to

\[ R_I \approx \frac{R_0}{\sqrt{1-\nu^2}}, \qquad \text{where} \qquad \nu=\frac{I}{I_\infty}. \tag{24} \]

Substituting (7) into (24) and (24) into (23), and also denoting by \(R_I\) the resistance of the ionization chamber on the basic current-voltage characteristic and by \(R'_I\) that on the modified characteristic (dotted curve in Fig. 8, б), we find \(\Delta U_{\text{out}}\) in expanded form (taking the denominator of (23) to be the constant quantity \(R_b\) and denoting the reciprocal quantity \(\dfrac{1}{R_b}\) by \(g_2\)):

\[ \Delta U_{\text{out}} = \frac{g_2}{2e} \left[ \frac{h'}{S'} \sqrt{ \frac{a'}{k'_1 k'_2 N'_0(1-\nu_1^2)} } - \frac{h}{S} \sqrt{ \frac{a}{k_1 k_2 N_0(1-\nu^2)} } \right] U_{\text{in}}. \tag{25} \]

The circuit under consideration permits the application of a considerably larger input voltage than the circuit of Fig. 8, а. However, despite this, for the same relative change in the ionization current the circuit of Fig. 8, б has the same sensitivity as circuit 8, а. This is explained by the fact that the change in voltage \(\Delta U_{\text{out}}\) is limited by the voltage drop across the constant resistance \(R\).

The circuit of Fig. 8, б is widely used in measuring, in the saturation region, the intensity of radioactive radiations, the density of gases, and other quantities.

Third circuit. Both ionization chambers (the comparison chamber and the measuring chamber) operate in the saturation region and are nonlinear resistances. Since the resistances \(R_{I_1}\) and \(R_{I_2}\) are usually close in magnitude (of the order of \(10^{11}\)–\(10^{14}\ \Omega\)) and permit the application of high voltages, the circuits of Fig. 8, а and 8, б cannot be used for measuring large resistances; in the present case it is more expedient to use a bridge circuit. This circuit and the graphical method for finding it are given in Fig. 8, в.

It is evident from the graph that in the saturation region the ionization current asymptotically approaches \(I_\infty\). Therefore the greatest sensitivity of the circuit is obtained for a relatively small change in ionization current—of the order of a few percent of \(I_\infty\). For large changes in the current, \(\Delta U_{\text{out}}\) changes little, and in its properties the circuit approaches the circuit of Fig. 8, б.

For constant and equal values of \(R_3\) and \(R_4\), we have:

\[ \Delta U_{\text{out}} = \frac{R_{I_1}-R_{I_2}}{R_{I_1}+R_{I_2}} \frac{U_{\text{in}}}{2}. \tag{26} \]

The denominator of expression (26) changes only slightly, since, to the extent that \(R_{I_1}\) increases, \(R_{I_2}\) decreases by approximately the same amount. Therefore we take the denominator to be a constant quantity, and denote the reciprocal quantity by \(g_3\).

Substituting into (26) the value of \(R_I\) from (24) and taking into account, further, that the same current \(I\) flows through both chambers, we obtain, after simple transformations, an expression similar to (25):

\[ \Delta U_{\text{out}} = g_3 \left[ \frac{R_{01}}{\sqrt{1-\nu_1^2}} - \frac{R_{02}}{\sqrt{1-\nu_2^2}} \right] \frac{U_{\text{in}}}{2}. \tag{27} \]

The circuit of Fig. 8, c has no restrictions with respect to the values of \(\Delta U_{\text{out}}\) and \(U_{\text{in}}\), in any case up to \(\nu = 0.999\), and therefore has high sensitivity. The advantages of the circuit are used for measuring small changes in density, gas composition, and angular and linear displacements.

In the case of small changes in density and gas composition,

\[ k_1 \sim \frac{1}{\rho},\quad k_2 \sim \frac{1}{\rho},\quad a \sim \rho,\quad N_0 \sim \rho,\quad h_1=h_2=h,\quad S_1=S_2=S. \]

Then

\[ \Delta U_{\text{out}} = (\rho_2-\rho_1)\,g_3\,\frac{h}{4eS} \left[ \sqrt{ \frac{a'}{k_1' k_2' N_0'(1-\nu_2^2)} } - \sqrt{ \frac{a}{k_1 k_2 N_0(1-\nu_1^2)} } \right] U_{\text{in}}. \tag{28} \]

In the case of measuring small angular and linear displacements, \(k_1, k_2, a\), and \(\rho\) are constant, and \(\Delta U_{\text{out}}\) depends only on the dimensions \(h\) and \(S\), the radiation intensity \(N_0\), and the degree of saturation \(\nu = I/I_\infty\):

\[ \Delta U_{\text{out}} = \sqrt{\frac{a}{k_1 k_2}}\, \frac{g_3}{4e} \left[ \frac{h'}{S'\sqrt{(1-\nu_2^2)N_0'}} - \frac{h}{S\sqrt{(1-\nu_1^2)N_0}} \right] U_{\text{in}}. \tag{28′} \]

For a slight change in \(h\), the radiation intensity \(N_0\) may be taken as varying proportionally to \(h\). Despite the fact that \(N_0\) changes little, the degree of saturation \(\nu\), and therefore \(\Delta U_{\text{out}}\), change very considerably, ensuring high sensitivity of the circuit.

In all the circuits considered, the measured and comparison resistances are connected in series. In principle, when using a bridge circuit, parallel connection of ionization resistances is also possible (Fig. 8, d); however, single-tube circuits cannot be used for this purpose because of the difficulty of insulating

of both nodal points of the bridge diagonal. The circuit of Fig. 8, g, with two tubes, proposed by us, makes it possible to connect the ionization chambers in parallel, which in some cases has advantages over series connection, since in this case almost half the input voltage is required.

In the circuit of Fig. 8, v only one chamber is the measuring chamber, while the other is the one being compared. If, however, the chamber being compared is also placed in communication with the medium being measured (Fig. 8, d), then the output voltage of the circuit becomes proportional to the difference between the two media—for example, the difference in densities, the difference in gas compositions, the difference in angular and linear dimensions, etc.

If, by one means or another, the bridge circuit is brought into balance with the aid of one of the resistances, for example \(R_4\), the latter becomes proportional to the ratio of the two measured quantities—for example, the ratio of densities, the ratio of gas compositions, etc.

In many cases, in order to increase the accuracy of measurement, compensation of the output voltage is employed. An example is the circuit of Fig. 8, e.

§ 12. Terminology

In connection with the rapid development of the use of radioactive radiations in measurement technology, and the absence in the technical literature of suitable terms, the need has arisen to develop correct scientific terminology in this field. This is all the more necessary because Soviet literature is beginning to become cluttered with incorrect and unfortunate terms borrowed from foreign literature, such as “radioactive semimicrobalances” (see [7], Fig. 9), “radioactive galvanometers,” and the like. It is true that in all these instruments radioactive substances are used as ionizers; however, this still gives no grounds for calling these instruments radioactive. Moreover, such a term as, for example, “radioactive semimicrobalances” does not reflect the essentially most important features of the instrument: neither the type of radiation used nor the specific method of measuring the radiation.

One cannot agree, either, with such terms as, for example, “ionization manometer,” “ionization gas analyzer,” and the like, which are sometimes applied to instruments based on the use of radioactive radiations. This terminology also suffers from one-sidedness and indicates only the use of the ionization method of measurement. Meanwhile, a number of other ionization instruments are known which are likewise based on the general ionization principle of measurement, but have, for example, heated cathodes and, by virtue of this, possess different properties and have a different design than ionization instruments using radioactive radiation.

It seems to us that the terminology proposed below, including an indication of the type of radiation used and the method of measurement, more accurately reflects the specific character of these new instruments.

Taking into account that in instrument design all types of primary and secondary radiation of radioactive substances may find application—α-, β-, γ-rays, neutrons, etc.—and that, depending on the type of radiation used and the method of measurement, the properties and design of the instruments change, it is proposed to call these methods alpha-ionization, beta-ionization, gamma-ionization, neutron-ionization, etc.; or, for example, when a scintillation method of measurement is used, to call these methods alpha-scintillation, beta-scintillation, gamma-scintillation, etc. Instruments based on the methods listed are proposed to be called, respectively: alpha-ionization, alpha-scintillation, beta-ionization, beta-scintillation, etc.; for example: alpha-ionization thickness gauges, beta-ionization manometer, gamma-ionization level meter, etc., or, for example: beta-scintillation thickness gauge, gamma-scintillation level meter, etc., etc. It is easy to see that the proposed terminology can also be extended to other instruments based on the use of radioactive substances but on other methods of measurement.

In what follows in our review we shall use this terminology. The terms “radioactive instruments,” “ionization instruments,” and “scintillation instruments,” however, we consider it useful to retain as general abbreviated names for all alpha-, beta-, and gamma-ionization, alpha-, beta-, and gamma-scintillation, and other instruments taken together.

II. APPLICATION OF RADIOACTIVE RADIATIONS IN MEASUREMENT TECHNOLOGY

§ 1. Introductory Remarks

The regularities of operation of α-ionization chambers, summarized in Table 1, make it possible to outline the main areas of application of radioactive radiations in measurement technology. It should be noted that descriptions of various instruments based on the use of radioactive radiations have repeatedly appeared in the literature, but there have been no generalizing works that would make it possible to discern, in individual attempts to use radioactive isotopes, a large, new, and rapidly developing field of measurement technology capable in many cases of solving a number of problems by a simpler method. The entire aggregate of a large number of instruments,

which can be created using radioactive radiation, we divide into three main groups of instruments based on measurement of:

1) the properties of the gaseous medium;
2) the dimensions of ionization chambers or the position of the source of radioactive radiation, and
3) the properties of radioactive radiation.

In instruments of the first group, use is made of the fact that a change in the properties of the gaseous medium is accompanied by changes in the mobility and recombination of ions or in the intensity of the radiation of the ionizer \(N_0\). They make it possible to solve problems connected with measuring the density of gases, their composition, the velocity of a gas flow, etc. In considering this extensive group of instruments, it is advisable to introduce a further differentiation according to the measured quantity, leading to two subgroups:

a) instruments based on changes in mobility, recombination, and radiation intensity with a variable composition or density of the medium;

b) instruments based only on changes in radiation intensity with a variable composition or density of the medium.

Instruments of the first subgroup operate on the linear portion of the current-voltage characteristic, instruments of the second subgroup on the saturation portion. It is significant that the designs of instruments belonging to both subgroups may be identical, but a simple change in the voltage applied to the ionization chamber changes the properties of the instruments, transferring them from one subgroup to the other. For example, in the first case the instruments are sensitive to small admixtures of foreign gases and vapors, while in the second case they are sensitive only to large admixtures of gases and vapors.

In instruments of the second group, a change in the measured quantity entails a change in the distance between the electrodes, the area of overlap of the electrodes of ionization chambers, or the position of the radioactive-radiation source relative to ionization chambers and counters. This group of instruments makes it possible to solve problems connected with measuring angular and linear displacements.

In instruments of the third group, a change in the measured quantity is connected with changes in scattering (reflection), intensity, or the spectral composition of the radiation. This group of instruments is intended for solving such problems as measuring the thickness of materials, liquid levels, high gas pressures, etc. These instruments may also be subdivided into subgroups based on: a) absorption and b) scattering of radiation.

The examples given below of the practical application of radioactive radiation in measurement technology, as well as the most interesting proposals in this area, have been taken from various works published over the last 10 years; however, in some cases examples from earlier works are also given.

§ 2. Group of instruments based on changes in the properties of a gaseous medium

A) Instruments based on changes in mobility, recombination, and radiation intensity

Starting from (7), the ionization current on the linear portion of the volt-ampere characteristic of a plane ionization chamber, under the condition of a homogeneous electric field and the absence of space charge and ion diffusion, can be determined by the expression

\[ I_0=\frac{U_0}{R_0}=\frac{2eS}{h}\sqrt{\frac{k_1k_2N_0}{a}}\,U_0. \tag{29} \]

For constant dimensions \(h\) and \(S\) of the chamber and voltage \(U_0\), expression (29) is simplified and takes the form

\[ I_0=C_0\sqrt{\frac{k_1k_2N_0}{a}}, \tag{30} \]

where \(C_0\) is a constant equal to \(\dfrac{2eS}{h}U_0\).

Expression (30) shows that, on the linear portion of the volt-ampere characteristic, the current depends on the mobilities \(k_1\) and \(k_2\), the recombination coefficient \(a\), and the radiation intensity \(N_0\).

Since these quantities in turn depend on the density and composition of the gaseous medium, the use of this method is possible for measuring the composition of gases only when the gas density is constant, and for measuring the density of gases only when their composition is constant. In principle it is also possible to carry out measurements based on changes in radiation intensity at constant density and gas composition; however, this method has not found application in the technique of measuring nonelectrical quantities because of the weak dependence of \(I_0\) on \(N_0\).

It is much more expedient in this case to use not the linear portion but the saturation portion of the volt-ampere characteristic, where there is direct proportionality between \(I_\infty\) and \(N_0\).

Let us consider the possibilities of using the initial portion of the volt-ampere characteristic at constant density and constant gas composition.

Constant gas density. At constant gas density \(\rho\), the current on the linear portion of the volt-ampere characteristic (30) depends on the mobility and recombination coefficient of the ions, as well as on the radiation intensity. The mobility of ions \(k\) located in a gas of the same nature is most satisfactorily

but is determined by Langevin’s well-known expression (see, for example, \(^{44,45}\)):

\[ k=\frac{0.334}{\frac{\rho}{\rho_0}\sqrt{(\varepsilon-1)_0 M_0}} . \tag{31} \]

For a constant gas density, taking into account that \(N_0\) is proportional to \(M_0\), after substituting (31) into (30) we obtain:

\[ I_0=\frac{C'_0}{\sqrt{(\varepsilon-1)_0 a}} . \tag{32} \]

The recombination coefficients of ions \(\alpha\) for different gases differ very little from one another \(^{46}\) and depend on the gas density; therefore, at constant \(\rho\), \(\alpha\) may be taken to be independent of the gas composition.

From the foregoing we obtain that, on the linear portion of the current–voltage characteristic, the current depends only on the dielectric constant of the gas \(\varepsilon\), i.e., on the composition of the gas:

\[ I_0=\frac{C'_0}{\sqrt{(\varepsilon-1)_0}} . \tag{33} \]

This dependence is the basis of \(\alpha\)-ionization gas analyzers for determining very small contents of certain impurities of gases, vapors, and smokes in air, for which it may be assumed that, with the introduction of an impurity, the density of the air and the volume density of the ions remain practically constant. Typical current–voltage characteristics for this case are given in Table 1 (No. 9).

Constant gas composition. With a constant composition of the gaseous medium, the ion current on the linear portion of the current–voltage characteristic depends on the density of the medium. The ion mobilities \(k_1\) and \(k_2\) entering into (30), and the ion recombination coefficient \(a\), depend in a complicated way on the density of the medium; therefore it does not appear possible to write a general expression for the dependence of the ionization current on pressure. Table 1 gives the dependences of the initial resistance \(R_0\) on the air pressure \(p\) for various pressure ranges under ionization by \(\alpha\)-rays. Changes in the form of the current–voltage characteristics with changing pressure are also shown there. Using the indicated dependences of \(R_0\) on pressure, on the basis of Ohm’s law one can write the following relations for different pressure ranges, assuming here that the voltage \(U_0\) and the temperature \(t\) are constant, and that the distance between the electrodes \(h\) is less than the range of the \(\alpha\)-particles \(L\) at the given pressure, i.e. \(h<L\).

N. I. SHTEINBOK

The dependence of \(I_0\) on pressure is realized in measurement equipment for measuring vacuum in the range \(0\text{–}100\) mm Hg.\(^{55,58,59,74}\)

\(P\), mm Hg	\(I_0(p)\)
\(0\text{–}100\)	\(I_0 = A_1 p\)
\(100\text{–}760\)	\(I_0 = \mathrm{const}\)
\(760\text{–}2500\)	\(I_0 = A_2 \dfrac{1}{p}\)

Description of the Instruments

1. In Fig. 9, illustrating the circuit of an \(\alpha\)-ionization gas analyzer,\(^{47,48,51}\) two cylindrical ionization chambers are visible, coated on the inside with a thin layer of radioactive material. The gas being analyzed is drawn through measuring chamber 1. Chamber 2 is filled with clean air and serves to compensate for changes in the ambient temperature. Both chambers are connected in a bridge circuit, in the diagonal of which an electrometric tube is included. Initially the bridge is in equilibrium, and the microammeter, connected into the anode circuit of the tube, indicates conditionally zero.

Fig. 9. Schematic diagram of an \(\alpha\)-ionization gas analyzer. 1 and 2 — measuring and reference chambers.

When a small admixture of the analyzed gas appears in the measuring chamber, of the order of \(0.01\text{–}0.001\) percent by volume, the bridge goes out of equilibrium, and the microammeter indicates the impurity content.

The high sensitivity of the instrument is explained by the anomalously large change in the mobility of negative air ions when small admixtures of certain gases and vapors are added, such as, for example, chlorine and its compounds, sulfurous gas, ammonia, alcohols, fatty acids, organic solvents, etc. The same effect is also observed when small admixtures of electronegative gases are added to inert and noble gases.\(^{44}\)

The distinctive features of \(\alpha\)-ionization gas analyzers (besides high sensitivity) should also include:

low inertia of the readings, of the order of tenths of a second. A drawback of the instrument is the absence of selectivity with respect to various impurities and the need to maintain a constant pressure at the inlet of the instrument.

1. The high sensitivity of $\alpha$-ionization gas analyzers to extraneous impurities in the air makes it possible to use them to give warning of the appearance of a fire source even before a flame appears, by the products of the distillation of combustible materials that appear in the air. The idea of using radioactive radiation to create a fire alarm has been put forward repeatedly by many authors (for example, 47, 50); however, the practical implementation of this idea encountered the difficulty of creating an electrostatic relay that would operate when the voltage changed by 10–30 V. The various electronic relays proposed for this purpose did not find application because of the exceptionally stringent requirements imposed on the alarm device, namely: the alarm device must be ready for operation for an indefinitely long time without consuming electrical energy. Recently^49 this problem has been solved by using a highly sensitive cold-cathode thyratron. The circuit of such a fire alarm is shown in Fig. 10.

Fig. 10. Schematic diagram of an $\alpha$-ionization fire alarm. 1 and 2—measuring and reference chambers.

The alarm device consists of a hemispherical $\alpha$-ionization chamber 1 with openings in the chamber housing for air exchange. In series with chamber 1 there is connected a sealed flat chamber 2 filled with pure air. A constant voltage of 220 V is applied to chambers 1 and 2. The control grid of thyratron 3 is connected between chambers 1 and 2, and anode 4 and cathode 5 to the corresponding terminals of the DC voltage. In the absence of combustion products in the air, a potential difference of 80 V is established across chamber 1. When a fire breaks out, the ionization resistance of chamber 1 increases and the potential difference rises to 100–110 V, as a result of which the thyratron ignites, the electromagnetic relay and the audible signal are switched on. According to the data of^49, testing of the fire alarm gave satisfactory results.

1. In 1947 S. Ya. Samoilov52 proposed a method for measuring the velocity and direction of an air flow by means of radioactive radiation. It should be noted, however, that the scheme he proposed is far from the possibility of practical use. A modified and improved scheme of the instrument is shown in Fig. 11.

Fig. 11. Schematic circuit of an $\alpha$-ionization meter of the velocity of a gas flow, based on the entrainment of ions by the flow.

A certain potential difference $U$ is applied between the electrodes of a plane ionization chamber coated with a thin layer of radioactive substance. The ions formed in the chamber tend, under the action of the applied voltage, to move in the direction of the electric field. The measured velocity of the gas flow $v$ is directed perpendicular to the direction of motion of the ions in the electric field. If the velocity of the gas flow is somewhat greater than the velocity of the ions, then part of the ions will be carried away by the gas flow, reducing the ion current measured by the instrument. As the velocity of the gas flow increases, and with the voltage $U$ unchanged, an ever larger part of the ions will be carried out of the field. The scale of the measuring instrument can be graduated directly in units of gas-flow velocity.

We have obtained expression (34), relating the ionization current $I_0$ on the linear portion of the volt-ampere characteristic of a plane ionization chamber to the gas-flow velocity $v$, the chamber length $l$, the electric-field strength $E$, the ion mobility $k$, the ion recombination coefficient $a$, the radiation intensity $N_0$, the number of ions per unit volume $n_0$ in the absence of $E$ and $v$, and the distance from the electrode under consideration $x$:

$$ I_0 = 2 e n_0 \left[ kE - \frac{2 v k E}{\sqrt{v^2 + 4l^2 a N_0}\,\operatorname{cth}\omega x + 2 l a n_0 + v} \right], \tag{34} $$

where

$$ \omega = \frac{\sqrt{v^2 + 4l^2 a N_0}}{2 k E l}. $$

Considering expression (34), into the denominator of which $\operatorname{cth}\omega x$ enters, one can draw a conclusion concerning the magnitude of the argu-

APPLICATION OF RADIOACTIVE RADIATION

...ment. For a small value of \(E \ll \dfrac{\sqrt{v^{2}+4l^{2}aN_{0}}}{2\alpha l}\), if the argument of the hyperbolic cotangent exceeds \(0.7 \div 0.8\), then \(I_{0}\) does not depend on \(E\). In order for the influence of the gas-flow velocity to be appreciable, it is necessary to choose the argument lying within the limits \(0.1 \div 0.7\).

On the basis of the principle set forth, an instrument for measuring wind velocity (for a range of wind velocities within \(0 \div 100\ \text{m/min}\)) was constructed and tested on a ship during a voyage in Arctic waters. The instrument includes a device allowing the ionization chamber to be set along the direction of the wind. According to the authors’ report\({}^{53}\), the instrument worked quite satisfactorily during the voyage and provided sufficient measurement accuracy.

1. \(\alpha\)-ionization instruments, very closely resembling in construction the instruments described above, have found an interesting application in medicine. A description of these instruments is given by way of exception, owing to their great importance and their being little known among physicists and engineers.

At the beginning of the 1930s A. B. Verigo and V. A. Poderni designed a radium ionizer, used in some clinics of the Soviet Union for the treatment of a number of diseases (bronchial asthma, ozena, hypertension, etc.\({}^{54,55}\)). The treatment is based on the patient’s inhalation of a large quantity of negative aeroions produced by an \(\alpha\)-ionizer.

Fig. 12. Schematic of A. B. Verigo’s radium aeroionizer for negative ions.

The schematic arrangement of the radium aeroionizer is shown in Fig. 12. The aeroionizer consists of a metallic cylinder \(20 \div 25\ \text{cm}\) in diameter and \(30\ \text{cm}\) long, and a metallic rod coaxial with it, \(1 \div 3\ \text{cm}\) in diameter and \(15\ \text{cm}\) long. On the rod or along the generatrix of the cylinder there is applied, in a thin layer, about \(0.2\ \text{mg}\) of radium sulfate. A direct voltage of the order of several hundred volts is applied between the electrodes, creating a radial electric field whose strength increases as the rod is approached. If the rod is coated with radium, a region of bipolar ionization is formed near the rod (with a radius of \(5\)—\(7\ \text{cm}\)), and near the cylinder a region of unipolar ionization. With the adopted polarity of the electrodes, positive ions move toward the rod, and negative ions toward the cylinder. At a small distance from the instrument there is installed a winged venti-

lator driving air through the cylinder at a speed of 0.3–0.5 m/sec. Owing to the fact that the velocity of the air jet is somewhat greater than the velocity of the negative ions in the electric field, a considerable portion of them, without reaching the cylinder, is blown out together with the air jet, reaching the patient at a concentration of \(1\text{–}3 \cdot 10^6\) ions per \(1\ \mathrm{cm}^3\) of air. The disadvantages of the apparatus include its large dimensions, the need to use large quantities of radioactive substances, and the fact that, together with the useful negative ions, a small portion of positive ions, which have an adverse effect on human health, is also carried out.

Fig. 13. Diagram of the portable radium aeroionizer of negative ions by N. I. Shteinbok.

A substantial advantage over the apparatus described above is possessed by the portable aeroionizer developed by us. The schematic diagram of the apparatus is shown in Fig. 13. The apparatus consists of a plastic cup \(1\), inside which is located an electrode \(2\), coated with a thin layer of sulfurous radium or a radioisotope emitting \(\alpha\)- or soft \(\beta\)-rays. In the plastic tube \(3\) there is another electrode \(4\). A constant voltage of about 100 V, obtained from a miniature selenium rectifier located in the apparatus, is applied between the electrodes. Cup \(1\) has a height slightly exceeding the range of \(\alpha\)-particles in air. Electrode \(4\), having positive polarity, extracts negative ions from the bipolar region. A fan of the “hair-dryer” type is inserted into tube \(3\), creating an air stream directed perpendicular to the direction of motion of the negative ions. When the air-flow velocity is greater than the velocity of the negative ions in the direction of the field, all the negative ions are carried out of the field and reach the patient. In some cases one can dispense with the fan as well, inhaling the air through the nose or mouth.

Among the merits of the apparatus should be counted the production of 100% unipolar ionization with small dimensions of the apparatus and with quantities of radioactive substance 10 times smaller than in A. B. Verigo’s apparatus. Owing to the simplicity of its design and its low cost, the apparatus may become available to every patient for treatment at home, as well as for improving the air in living quarters.

b) Instruments Based on Measuring the Intensity of Radiation with Variable Composition or Variable Density of the Medium

The principle of operation of this group of instruments is easily understood from the diagram in Fig. 14. Between the electrodes of a plane $\alpha$-ionization chamber there is applied a certain potential difference $U$, sufficient to attain saturation current. The lower electrode is covered with a thin layer of radioactive substance emitting $\alpha$-rays. For greater clarity, Fig. 14 shows the path of a single $\alpha$-particle, which in air at normal pressure and temperature has a range $L$. The distance between the electrodes is equal to $h$. With the indicated relation $h<L$, the $\alpha$-particles produce a current $I$ smaller than that which they could produce if the distance between the electrodes were $L$, since only part of the kinetic energy of the $\alpha$-particle is expended on ionization.

Fig. 14. Schematic diagram of an $\alpha$-ionization manometer. $L$ is the range of the $\alpha$-particle in the gas, $h$ is the range of the $\alpha$-particle inside the chamber.

When the density of the gas changes as a result of a change in pressure, and with constant chamber dimensions, the range of the $\alpha$-particles changes inversely proportionally, while the saturation current is directly proportional to the density:

$$ I_{\infty}=ehSN_{0}=C\rho . \tag{35} $$

An analogous picture is also observed when the composition of the gas changes, or the percentage content of one of its components changes, since the density of the gas is proportional to the molecular weight of the gas, i.e. $I_{\infty}\sim M_{0}$.

The foregoing remains valid also for other ionizing particles. On the basis of the indicated principle, manometers, density meters$^{57}$, vacuum gauges$^{56,57}$, gas-flow meters with a Pitot tube$^{57}$, and also gas analyzers$^{47,48,51}$ have been proposed for determining the content of impurities (of the order of percent) in air and other gases.

The current–voltage characteristics at various values of the gas density are given in Table I (Nos. 5, 6, 7, 8).

N. I. LITEINBOK

Description of the instruments

1. The basic circuit of an instrument for measuring the density and pressure of gases is shown in Fig. 15^17. The instrument consists of $\alpha$-ionization chambers 1 and 2, connected in series. Of these, chamber 1 communicates with the medium being measured, while chamber 2 is hermetically sealed. Instead of chamber 2, a stable high-ohmic resistance may be connected. The ionization-current amplifier consists of electrometer tubes 3 and 4. As indicators, depending on the required accuracy and the conditions of application, millivoltmeters, logometers, automatic potentiometers, etc., may be used.

Fig. 15. Circuit of an $\alpha$-ionization meter for the density and pressure of gases.
1 and 2—open and closed ionization chambers.

The readings of the instrument, strictly speaking, are proportional to the density of the gas; for pressure measurement it is necessary to provide temperature compensation in the circuit.

If chamber 2 is also made to communicate with the medium being measured, then readings of the instrument proportional to the difference or ratio of pressures can be obtained.

A substantial advantage of $\alpha$-ionization manometers in comparison with manometers based on the use of aneroid boxes is the small inertia of the readings (on the order of tenths of a second), high overload capacity, absence of aftereffect, a natural electrical output, ease of transmitting readings over a distance and of changing to different measurement ranges. By using $\alpha$-radiation, it is possible to create manometers and instruments derived from them with a wide range of scales within the limits from 0.01 to 5000 mm Hg. The total error of $\alpha$-ioni-

tional manometers is ±1.5–2%, but it can be reduced with further improvement of the elements of the instrument.

1. The α-ionization vacuum gauge, called the “alphatron” (Fig. 16)58, 59, 74, consists of an ionization chamber inside which there is an α-emitter containing approximately 0.2 mg of radium. One of the chamber electrodes has a cylindrical shape, while the other is made in the form of four bent rods. The electrodes are insulated by porcelain insulators. The ionization current

Fig. 16. Diagram of the “alphatron” vacuum gauge.

is measured by means of an electrometer tube microammeter. The alphatron has three measurement ranges: 0–0.1, 0–1, and 0–10 mm Hg. The readings of the instrument depend on the kind of gas, but for each gas the proportionality of the reading to the pressure is preserved.

1. α-ionization gas analyzers15 are based on the dependence of radiation intensity on the composition of gases. In terms of design, the gas analyzer remains the same as before (Fig. 9), with the only difference that here a considerably higher voltage is applied to ionization chamber 1 than in the preceding case.

Thanks to this, the transition from the linear portion of the current–voltage characteristic to the saturation region is ensured. As a first approximation, it may be assumed that the change in the saturation current is directly proportional to the change in the density of the gas being analyzed. The gas analyzer is characterized by the low inertia of its readings (of the order of fractions of a second) and can be used to determine the content (of the order of percent) of hydrogen, methane, carbon dioxide, chlorine, and other gases in air. The disadvantages of the instrument include the need to maintain the pressure at the inlet of the measuring chamber with an accuracy of \(\pm 1\) mm Hg.

§ 3. Group of instruments based on changes in the dimensions of ionization chambers or in the position of the radioactive-radiation source at constant composition and constant density of the medium

Changes in the distance between the electrodes, in the area of overlap of the electrodes, or in the position of the radioactive-radiation source relative to ionization chambers or counters substantially affect the magnitude of the ionization current and may be made the basis for creating various kinds of instruments measuring electrical and non-electrical quantities. By using this effect, it is possible to construct very sensitive systems of galvanometers, electrometers, relays, manometers, micromanometers, follow-up systems, contactless regulators, amplifiers of small direct-current voltages, gravimeters, vibrographs, strain gauges, accelerometers, minimeters, and many other instruments in which, in one way or another, angular or linear displacement of a sensitive element is effected. We apparently were the first to propose\(^{60, 61}\) this method for measuring angular and linear displacements and to indicate its applications for creating the instruments listed above.

The various instruments based on this principle may, by their construction, be assigned to two main subgroups, in which the following change in one way or another:

a) the dimensions of the ionization chambers (Fig. 17, \(a, b, c, d\));
b) the position of the radioactive-radiation source relative to the ionization chambers or counters (Fig. 17, \(d, e\)).

In Fig. 17, \(a, b, c, d\) are shown the principal design variants of ionization chambers belonging to the first subgroup, which are used or can be used in instrument design. In this subgroup of instruments, when the distance between the electrodes changes or when the position of the electrodes relative to one another changes, the ionization current changes as a result of a change in the volume or area of overlap of the electrodes of the ionization chamber.

In another subgroup (Fig. 17, d, e), when the pointer, frame, or other parts of the controlled object coated with a radioactive substance are turned, the ionization current changes as a result of a change in the number or intensity of radioactive particles entering the ionization chamber or counter.

As a rule, in all instruments based on the principle described above, the distance between the electrodes of the ionization chambers is less than the range of the ionizing particles in the given medium. Measurement—

Fig. 17. Variants of a method for measuring angular and linear displacements by means of radioactive radiation.

—of ionization currents is carried out on the linear portion or on the saturation portion of the current–voltage characteristics.

When γ-rays are used as the ionizing agent, the measurement limits are increased many times over; however, in this case one can no longer be guided by the above-described method of considering the question, since the ionization current in this case depends not only on the gas gap but also on transition effects at the chamber walls and on scattering of the γ-rays.

Table I gives the current–voltage characteristics (Nos. 1, 2, and 3) for various values of the radiation intensity \(N_0\) and the chamber dimensions \(h\) and \(S\). It is noteworthy that the current–voltage characteristics at different distances between the electrodes (Table I, Nos. 3 and 4) are similar to the characteristics when meas—

change in density (Table I, Nos. 5 and 8). This result is not accidental and is in complete agreement with the theory of the ionization method.

Below are described some typical designs of ionization instruments based on the measurement of angular and linear displacements by means of radioactive radiation. Comparing ionization instruments with instruments based on other methods (capacitive, inductive, photoelectric, etc.), it should be noted that ionization instruments in a number of cases possess higher sensitivity, compactness, and simplicity of construction.

A) Instruments Based on Changing the Dimensions of Ionization Chambers

1. For measuring the pressures of gases and liquids, an $\alpha$-ionization manometer with a membrane has been proposed62 (Fig. 18, a). Here 1 is a membrane with an $\alpha$-emitter, 2 is a fixed electrode insulated from 1 by the material of the chamber housing. A potential difference is applied between electrodes 1 and 2, ensuring that the saturation current is reached. When the pressure $p$ changes, membrane 1 bends, changing the distance between the electrodes and the ionization current. The ionization current is then amplified and measured in the usual way. Manometers of the indicated type are expedient to use in cases where recording and remote transmission of pressure readings are required.

Fig. 18. $\alpha$-ionization membrane manometers for measuring: a — the pressure of gases and liquids, b — the difference of gas pressures.

1. A modification of the scheme in Fig. 18, a is the differential $\alpha$-ionization membrane chamber (Fig. 18, b) for measuring the difference or ratio of gas pressures64. By selecting a sufficiently sensitive membrane, pressure differences on the order of fractions of a millimeter of water column can be measured.

2. The examples cited above illustrate the use of radioactive radiation for measuring various nonelectrical quantities. It will be shown below that the use of radioactive radiation also gives a substantial effect in constructing instruments for measuring electrical quantities, significantly increasing the sensitivity and simplifying the design of highly sensitive instruments.

In Fig. 17, d, a device that increases the sensitivity of galvanometers is shown schematically\(^{7,60,61}\). Instead of the mirror fixed to the suspension of an ordinary mirror galvanometer, and instead of the rather complex and bulky optical reading arrangement, in this galvanometer a thin aluminum or mica platelet, coated on both sides with a radioactive substance, is fixed to the suspension. When the moving part of the galvanometer is deflected from the equilibrium position (the mean position), the platelet enters between electrodes insulated from one another, forming a flat ionization chamber. The resulting change in the ionization current is amplified and then measured by a technical electrical measuring instrument, which may be installed at any distance from the galvanometer. Thanks to the greater amplification of the electronic circuit and of the ionization chamber itself, galvanometers and electrometers of very high sensitivity can be constructed on the principle described. A rotation of the galvanometer suspension by one angular minute produces a change in the current at the amplifier output of the order of \(10\ \mu\mathrm{a}\).

1. In Fig. 19 another circuit of an \(\alpha\)-ionization pointer galvanometer is shown\(^{60}\). Here the mica pointer enters between

Fig. 19. \(\alpha\)-ionization pointer galvanometer and relay. 1 and 2—ionization chambers.

the electrodes of flat ionization chambers 1 and 2. In this version the electrodes of the ionization chamber are coated with radioactive substance, but the pointer may also be coated. Tubes 3 and 4 are connected in a bridge circuit. To stabilize the operation of the circuit, negative feedback is provided by means of the cathode resistance \(R_k\). When the position of the pointer changes in the dia-

... of the tube bridge, a potential difference arises between terminals 5 and 6, measured by a millivoltmeter. Relays that close the circuit of the actuating mechanism when the galvanometer pointer is deflected through a definite angle may also be connected into this same diagonal, or into the anode circuit of the tubes.

b) INSTRUMENTS BASED ON CHANGING THE POSITION OF THE RADIATION SOURCE RELATIVE TO THE IONIZATION CHAMBERS

1. For the regulation and recording of various processes, the circuit (Fig. 20) of an α-ionization follow-up system may be used.^61 As an example, a circuit is given for temperature control

Fig. 20. Circuit of an α-ionization follow-up system for recording and regulating various processes.

by means of a resistance thermometer \(T\), connected into the bridge \(M\).

In contrast to the circuits of Fig. 17, d and Fig. 19, in this circuit the radioactive substance coats the lower end of pointer 2. As can be seen from the drawing, the pointer moves over plate 7 with two openings. Beneath plate 7 are located miniature ionization chambers 3 and 4, connected in a differential circuit. In the equilibrium position of the upper bridge circuit, the pointer is located between the openings or, in another variant, partially covers the openings of the ionization chambers. When the pointer is displaced in one ...

or the other side, an ionization current appears in one of the ionization chambers; this current is then amplified by tubes 5 or 6. The ionization current increases in proportion to the rotation of the pointer within the limits of its width. When the pointer covers one of the holes in plate 7, the contacts of relay 8 or 9 are closed, causing the reversible motor 10, connected with the slider of rheostat 11, to rotate. The motor rotates until the circuit again comes into equilibrium.

In another version of the circuit, when the pointer simultaneously covers both ionization chambers and the bridge \(M\) goes out of balance, the potential of the grids of tubes 5 or 6 changes and a differential relay connected in the diagonal of tubes 5 and 6 is actuated.

1. On the principle of measuring small angular displacements with the aid of radioactive radiations, semi-microbalances have been constructed which make it possible to weigh samples of the order of micrograms with high accuracy \(^{7,60}\).

§ 4. Group of instruments based on changes in the properties of radioactive radiations

Unlike \(\alpha\)-rays, which are completely absorbed by a thin layer of matter, \(\beta\)- and \(\gamma\)-rays possess a considerably greater penetrating power. They are absorbed by matter according to an exponential law \(^{18,21}\)

\[ N = N_0 e^{-\mu x}, \tag{36} \]

where \(N_0\) is the intensity of the \(\beta\)- or \(\gamma\)-radiation emerging from the emitter, \(N\) is the intensity of the radiation after passing through a substance of thickness \(x\), and \(\mu\) is the linear attenuation coefficient of \(\beta\)- or \(\gamma\)-rays, depending on the type and energy of the radiation, and also on the properties of the material being penetrated. Usually \(\mu\) is expressed in \(\text{cm}^{-1}\) of substance or in \(\text{mg}^{-1}\,\text{cm}^2\). Hard \(\beta\)-rays are absorbed, for example, by a layer of lead \(1 \div 2\) mm thick, while \(\gamma\)-rays are absorbed by a thickness of 100 mm or more.

This ability of \(\beta\)- and \(\gamma\)-rays to pass through fairly thick layers of substances, undergoing gradual attenuation depending on the thickness of the layer, forms the basis for designing thickness gauges. It should be noted that, along with absorption of \(\beta\)- and \(\gamma\)-rays by matter, their scattering is always present. This effect can also be used for measuring the thickness of various materials and coatings.

The intensity of rays that have passed through a substance or have been scattered (reflected) by the substance can be measured with an ionization chamber, a Geiger–Müller counter, a scintillation counter with a photocell, or a scintillation counter with a photoelec-

multiple amplifier40, 41. Depending on the intensity of the attenuated radiation, one or another measurement scheme is used (Fig. 21).

At present, various long-lived radioactive isotopes, obtained artificially, are used as emitters of β- and γ-rays. The principal characteristics of some of these isotopes are given in Table II.15, 16, 17, 65

Fig. 21. Variants of methods for measuring the thickness of sheet materials, based on the absorption of β- and γ-rays (a, b, c, d) and on the scattering of β- and γ-rays (e, f).

Table II

Atomic number	Radioactive nucleus	Half-life period in years	Energy of β-rays in MeV	Energy of γ-rays in MeV
1	H3	12.5	0.02	—
6	C14	5700	0.16	—
27	Co60	5	0.31	1.17
38	Sr90	30	0.61—2.2	—
55	Cs137	33	0.52	—
56	Ba133	>20	—	0.35 (mean)
57	La140	3	0.90	0.79
60	Nd150	1.7	0.74	—
81	Tl204	2.7	0.78	—
95	Am243	400	0.5	—

The accuracy of thickness measurement depends substantially on the quantity of the radioactive isotope used, on the thickness and density

of the material under investigation, and also on the time constant of the electrical circuit, \(\tau = RC\).

In the case of applying the ionization method of measurement (Fig. 21, \(a\)), the relative accuracy of measuring the thickness is determined by the relation \(^{63,65}\)

\[ \frac{\Delta x}{x} = \frac{e^{-\frac{1}{2}\mu x}}{\mu x \sqrt{2N_0RC}} . \tag{37} \]

If we take \(\mu x = 2\), which for lead corresponds to a thickness of \(4\ \text{cm}\), \(N_0 = 10^4\) quanta of \(\gamma\)-rays per second, and \(\tau = 10\ \text{sec}\), then, substituting these values in (37), we obtain \(\frac{\Delta x}{x} = 0.003\). Hence it is seen that the thickness \(x\) can be measured with fairly high accuracy. The relative accuracy of measuring thin sheets, less than \(0.5\ \text{cm}\), for the same values of \(\mu\), \(N_0\), and \(\tau\), is about \(1\%\). To obtain greater measurement accuracy it is necessary, according to (37), to increase \(N_0\) or \(\tau\).

Table III

Material	Thickness in cm when measured with accuracy up to 1%, \(\tau = 0.2\ \text{sec}\)	Thickness in cm when measured with accuracy up to 1%, \(\tau = 2\ \text{sec}\)	Thickness in cm when measured with accuracy up to 1%, \(\tau = 20\ \text{sec}\)
Paper or plastic	0.02—0.4	0.01—0.4	0.0025—0.4
Aluminum	0.007—0.2	0.005—0.2	0.001—0.2
Steel	0.002—0.05	0.0015—0.05	0.0005—0.05
Bronze	0.002—0.05	0.0015—0.05	0.0005—0.05
Copper	0.002—0.05	0.0015—0.05	0.0005—0.05
Zinc	0.002—0.05	0.0015—0.05	0.0005—0.05

Table III gives values, achieved under laboratory conditions \(^{64}\), of the limits for measuring the thickness of various materials as a function of the time constant of the circuit. From this same table it is seen that, with increasing density of the material under investigation, the sensitivity of the method increases.

a) Instruments based on absorption of \(\beta\)- and \(\gamma\)-rays

A very important problem in various fields of technology is the precise measurement of the thickness of metallic and nonmetallic materials (and coatings) used in the form of sheets, tubes, hollow castings, etc. In some cases the task is complicated by the fact that access to the products is available only from one side—

...as, for example, in the case of measuring the thickness of the plating of ships, the walls of pipes, boilers, gas holders, and the like. In other cases it becomes necessary to measure the variation in wall thickness of pipes, cylinders, and other products.

For measuring thickness, various instruments have been proposed, based on electrical, magnetic, electromagnetic, and other methods of measurement. It has turned out that the highest accuracy of these instruments, according to data of K. M. Polivanov and other authors63, is \(\pm(5 \div 10)\%\), which in many cases is insufficient.

Fig. 22. Schematic diagram of the ionization method for measuring the variation in wall thickness of pipes: 1 and 2—ionization chambers, 3—\(\gamma\)-emitter, 4—the pipe under investigation.

1. In 1943, O. N. Vavilov, N. A. Dobrotin, I. M. Frank, A. I. Avdeenko, and V. A. Tsukerman63 developed a new method for measuring the variation in wall thickness of pipes, based on the different absorption of \(\gamma\)-rays by the material of the walls as a function of their thickness. Figure 22 shows the schematic diagram of a device for measuring the variation in wall thickness of pipes. Source 3, emitting \(\gamma\)-rays, is placed inside the pipe being irradiated. The weakened \(\gamma\)-radiation emerging from the pipe is measured by ionization chambers 1 and 2, connected differentially. If the pipe has unequal wall thickness, a difference current appears, measured by a microammeter.

This method of measurement has a number of advantages over other methods with respect to the possibility of measuring the variation in wall thickness not only of straight pipes, but also of bent and shaped pipes; moreover, it has been found that the measurement accuracy in this case does not depend on the thickness or on the quality of the surface treatment of the pipes.

1. In the production of paper, rubber, fabrics, nonferrous metals, alloy steels, photographic, motion-picture, and other materials, it becomes necessary continuously and without contact to monitor the thickness of tapes, films, and sheets. Such monitoring can be organized with the aid of radioactive radiations.

The first instruments for monitoring the thickness of tapes and films were built13 according to the schemes of Figs. 21a and 21b. It is easy to see that, with the indicated measurement schemes, the ionization current is proportional to the total intensity of the \(\beta\)- or \(\gamma\)-rays emerging from the material under investigation. Therefore, naturally, the measurement accuracy cannot be sufficiently high. In addition, when instruments built according to these schemes are used, an error arises because of insufficient stability of the setup.

The differential circuit (Fig. 23), which measures the difference in thickness between the material under investigation and the standard material, is free from these shortcomings and provides considerably greater measurement accuracy[^63][^67].

Fig. 23. Differential circuit for measuring the thickness of sheet materials by means of β- or γ-rays.

The disadvantages of the latter circuit include the presence of visual monitoring and the need to regulate the production process manually. The circuit in Fig. 24[^11] represents a step forward in this respect, since here automatic

Fig. 24. Circuit for automatic regulation of the production process of sheet materials by means of β- or γ-rays.

regulation of sheet thickness is carried out with the aid of movable rollers receiving a signal from an ionization chamber. However, since this circuit is based on the direct method of measuring the radiation intensity, the accuracy and stability of the installation cannot be sufficiently high. Probably the best solution to the problem will be a combination of the circuits in Fig. 23 and Fig. 24.

3. Automatic monitoring of the levels of liquids, molten salts and metals, or bulk materials in closed vessels is carried out by means of penetrating γ-radiation. Three principal schemes for measuring liquid level are known11, 12, 13, 70, 71. Schemes a and b in Fig. 25 are used when access to the vessel is impossible. The principle of operation of the scheme is clear from Fig. 25, a; this scheme is used for indicating and signaling the attainment of the maximum or minimum liquid level. When continuous measurement of the liquid level is necessary, the following system is implemented with the aid of a γ-ray source and a detector.

Fig. 25. Variants of γ-ionization instruments for measuring the level of liquid and molten metals: a and b—when there is no access to the vessel, c—when access to the vessel is available.

The scheme of Fig. 25, b, based on absorption of γ-rays by a column of liquid, is used when the height of the liquid column is small. In measuring the levels of liquids with low specific gravity (gasoline, kerosene, oil), the height of the measured liquid column may reach up to 1 m. Counters or ionization chambers are used as γ-ray detectors.

The scheme of Fig. 25, c is used when it is possible to place a float with a γ-emitter in the vessel. As the liquid level changes, the intensity of the γ-rays reaching the detector changes in a ratio inversely proportional to the square of the distance from the emitter to the detector. In addition, scattering of γ-rays also plays a certain role here.

On the same principle of γ-ray absorption, an instrument has been designed for determining the mercury level in mercury manometers made of steel tubes. The accuracy of level measurement with this instrument is ±0.5 mm72.

4. For measuring gas pressures on the order of tens or thousands of atmospheres, we have proposed β- and γ-ionization manometers73. The known designs of α-ionization manometers already prove unsuitable for measuring gas pressures above 50 atm because of significant ion recombination and the difficulty of sealing chambers with insulators.

In β- and γ-ionization manometers these shortcomings are eliminated by the use of an essentially different operating principle and by the fact that the receiving and measuring parts of the manometer are separated by a metal wall, which protects the insulator from destruction.

The schematic diagram of such manometers is shown in Fig. 26. In the manometer, between the rod coated with radioactive substance,

emitting β- or γ-rays and the walls of the pressure receiver, there is a gap filled with the compressed gas being measured.

When pressure is supplied to the metallic receiver, part of the radiation energy is absorbed by the compressed volume of gas, as a result of which the intensity of the rays emerging from the walls of the receiver becomes smaller, approximately in proportion to the pressure being measured.

Fig. 26. Schematic diagram of β- and γ-ionization manometers for measuring high gas pressures.

Around the pressure receiver there is arranged a cylindrical ionization chamber or counter, by means of which the pressures are measured. The limits of pressure measurement are established by choosing the appropriate dimensions of the pressure receiver and the energies of the β- and γ-radiation. With the proper time constant of the electrical circuit selected, these manometers can be used to measure not only static pressures, but also pressures and gas densities that change rather rapidly.

1. For measuring areas of complex configuration, an instrument has been proposed\(^{7,13}\), based on the absorption of α-rays by thin layers of substances. As the ionizing agent, the α-radiation of polonium is used, which is deposited in a uniform layer on the lower electrode of a flat ionization chamber. Between the upper and lower electrodes an insulated wire mesh is installed. The plate to be measured is placed on the mesh. In this case, part of the α-radiation, proportional to the area of the plate, is absorbed and does not participate in the production of the ionization current. The ionization current is measured by a tube voltmeter graduated in units of area.

b. Instruments Based on the Scattering of β- and γ-Rays

Recently, radioactive methods of thickness measurement have also begun to be used for measuring the thickness of sheet materials and coatings accessible from one side. These thickness gauges are based on the principle of scattering of β- and γ-rays.

It is known that fast electrons ($\beta$-rays), when incident on a metallic surface, are partially scattered by the electron shells of the atoms of the irradiated substance; moreover, the scattering is the greater, the larger the atomic number of the substance and the lower the energy of the electrons.

The schematic diagrams of this method of measuring thickness are shown in Figs. 21, d and 21, e. For a constant chemical composition of the substance being measured, the value of the ion current arising in the ionization chamber or counter depends on the thickness of the substance only up to a certain limit, tending toward a constant value. This is explained by the fact that the deeper layers of the substance take less part in the scattering of electrons.

When measuring the thickness of coatings on some substrate, it is necessary that the substrate and the coating being measured differ considerably in atomic weights, and that the range of the $\beta$-rays in the coating being measured amount to no less than 30% of the total range.

When $\beta$-rays are used, it is possible to measure the thickness of metallic coatings of the order of hundredths of a millimeter[^77].

On the principle of scattering of $\gamma$-quanta, thickness gauges have been constructed for measuring, with an accuracy of $\pm 5\%$, the wall thicknesses of steel pipes and sheet materials with thicknesses from several millimeters up to 20 mm[^7],[^69],[^77],[^79].

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