THE U N I V E R S I T Y OF M I C H I G A N COLLEGE OF ENGINEERING Department of Electrical Engineering Space Physics Research Laboratory Scientific Report No. HS-1 THEORETICAL AND EXPERIMENTAL INVESTIGATION OF RADIOACTIVE IONIZATION GAUGES Prepared on behalf of the project by: Mohammad A. El-Moslimany UMRI Projects 2096, 2406, 2597, 03554 The research reported in this document has been sponsored by the Geophysics Research Directorate of the Air Force Cambridge Research Center.,. Air Research and Development Command, under Contracts Nos. AF 19(604)-545, 1511, 1948, 6162. administered by: THE UNIVERSITY OF MICHIGAN RESEARCH INSTITUTE ANN ARBOR May 1960

This report has also been submitted as a dissertation in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan, 1960o

TABLE OF CONTENTS Page LIST OF FIGURES v LIST OF SYLBOLS x ABSTRACT xvii CHAPTER I. INTRODUCTION AND STATEMENT OF THE PROBLEM 1 1.1 Introduction 1 1o2. Description of a Simple Radioactive Gauge 1 1.3. Merits and Drawbacks of Radioactive Gauges 3 1.4. Objectives 8 1o 5. Procedure 8 II. SURVEY OF IONIC PROCESSES ENCOUNTERED IN A RADIOACTIVE IONIZATION GAUGE 9 2. 1. Introduction 9 2.2. Production of Ions 10 2.2.1. General Considerations 10 2.2.2. Ionization by Alpha Particles 10 2,2.3. Ionization by Beta Particles 14 2.2.4. Columnar Ionization 15 2.3. Ionic Mobility 16 2.3.1. Definitions 16 2,3.2. Langevin's Theory of Ionic Mobility 17 2.4. Electron Mobility 27 2.5. Recombination of Ions 28 2.5.1. Definitions 28 2.5.2, Columnar Ion-Ion Recombination 29 2.5.3. Volume Ion-Ion Recombination 32 2.5.4. Electron-Ion Recombination 35 2.6. Electron-Attachment and Formation of Negative Ions 35 2.6.1. General Considerations 35 2.602. Basic Theory of Attachment 40 2.6.3. Attachment in a Mixture of Gases 46 2 6.4. Attachment Properties of Oxygen and Water Vapor 47 III. THEORY OF RADIOACTIVE IONIZATION GAUGE 54 3.1. Introduction 54 3.2. Approximate Method 54 3113. General Method 60 3.4. Theory of Planar Gauge-Complete Attachment 68 3.4.1o Statement of Assumptions and Basic Equations 68 3.4.2, Derivation of Current-Pressure Relation 71 iii

TABLE OF CONTENTS (Concluded) Page 3o5 t Computation. of Currennt-Pressure Characteristics 79 350oo1 Variation of Output Current with Plate Voltage 80 3,5 2 TEffecrt of T'mne ra"t.re on the CGauslge Oultpuat 82 3o 3 5 The Effective Volumne and, Output Current 85 3o5o49> Correlatioar of Theoretical and Some of the Exper im.en1t.tal Results 85 3o 6 Planar-Gauge Theory —Vari able Attachment 3 W 6o. i As sumputions 89 3o6.2o Derivation of i-P Relation 90 3 6 3. Determination of the Negative-Ion-FormationL Factor 100 3 6 I- Int erpretation of Some Numerical Examples 102 IVo ENiEIRIEANTAI COBNSIDEIRATIONS 107 4,1 Introduction 107 4,t2 Characteristics of NPRC Radioactive Ionization Gauge 108 4~3o Dark Current 112 4o4o The Hysteresis Phenomenon 11_5 4.4.1o Possible Causes of Hysteresis 115 4.4o2. Verificatio:nr of the Constancy of Source Activity 116 4,4~j~ Effect of Electric Field on Hysteresis 123 4o5o Experimental Radioactive Ionization Gauge 126 4.5olo Constructional Details 126 4o5o.2. Effect of Plate Voltages on Output Current L29 4 o5o3o Determination of a/P vs E/P Curves 134 4K5.4. Effect of Temperature on Gauge Output 136 45o5 o Variation of Primary Ionization with Temperature 1.4 4 o5o 6 The i-P Characteristic in Mixture of Gases 143 4o6. Description of Two Protototype Radioactive Ionization Gauges 14 8 4o6olo Radium Prototype Gauge 149 4.6~2~ Tritium Prototype Gauge 152 46.o -The Amplifier.63 4.o 7 The Vacuum System. 165 Vo CONCLUSIONS 170 APPEhDIX. ANALYTI1CAL INVTESGATIAON OF SOURCE STABILITrY 172 REFERENCES i80 iv

LIST OF FIGURES Noo Page 1.1 Schematic diagram of a planar radioactive ionization gauge 2 1l2 Ideal current-pressure characteristic of radioactive ionization gauge 4 1.3 Typical current-pressure curve of radioactive iohization gauge 5 1.4 Actual i-P characteristic showing the hysteresis and dark current regions 7 2,o A plot of the calculated alpha-particle activity for a source that is initially radium alone and retains all of its decay products~ 12 2.2 Path of a negative ion under the influence of an induced electric dipole~ 18 2o5 Plot of Langevin's quantity 3/16Y as a function of the parameter _= 2r1 Lo g 22 2o4 Limiting values of E/P at which mobility of N2 ions in N2 gas ceases to be independent of E/P. 24 2.5 Mass-dispersion curve of Langevin s theory and experimental values for various ions in. N2 gase 25 2.6 Effect of temperature on mobility of N2 in N2 gas. 26 2 7 Calculated theoretical saturation currents compared to experimental points 31 2.8 Sayer!s data of pi in air as a function of pressure. 36 2~9 Gardner's data of Pi in 02 as a function of temperature at constant density, compared with calculations from Thomson's theoryo 57 v~ ~ ~~~3

LIST OF FIGURES (Continued) No. Page 2.10 A possible potential energy curve for 02, compared with the known ground state of 02~ 39 2.11 Theoretical potential energy curve for H2, compared with ground state of H12. 41 20.2 Probability of electron attachment in oxygen as a function of E/P. 48 2.13 Plot of be as a function of E/P as given by Bloch and Bradbury' s theory. 50 2.14 Bradbury's values for 6e as a function of E/P in air. 51 2.15 Bradbury's values for 6e in H20 as a function of E/P. 53 3.1 Ionic density distribution between the two parallel plates -simple theory. 56 3.2 Generalized saturation curve —simple theory. 61 5.3 The effect of plate voltage on the i-P characteristicsimple theory. 62 3.4 The potential distribution in planar configuration. 69 535 Variation of the electric field E across the gap as modified by space-charge effects near the plates. 74 3.6 Calculated current-pressure characteristics for different plate voltages-modified theory. 81 357 Variation of i-P characteristics with plate voltage for an experimental planar gauge. 83 3.8 Calculated i-P characteristics for different gas temperatures -modified theory. 84 3.9 Calculated i-P characteristics for different ionization volum es-modified theory. 86 3o10 Experimental i-P characteristics of a planar gauge using different plate spacings. 87 vi

LIST OF FIGURES (Continued) No. Page 3.11 Correlation between experimental and theoretical i-P curves. 88 3.12 Distribution of net ion density in a planar gauge. 94 3.13 Correlation between experimental and modified theoretical curves, assuming variable electron attachment. 101 3.14 Theoretical i-P curves for several mixtures of nitrogen and oxygen —variable attachment. 106 4.1 Diagram of NRC Type No. 510 radioactive ionization gauge. 109 4.2 Typical i-P characteristic of NRC No. 510 radioactive ionization gauge —room temperature 270C. 111 4.3 Change of dark current value with collector shape. 114 4.4 Variation of output current with time at given constant pressure and temperature. 117 4o5 Scintillation apparatus. 119 4.6 Photomultiplier circuit diagram, 121 4.7 Observed scintillation data for radium source activity. 122 4.8 Electric field map of NRC 510 gauge. 124 4.9 Potential distribution in an NRC 510 gauge. 125 4.10 Reduction of recombination loss and hysteresis by using higher collector voltage. 127 4.11 Experimental radioactive ionization pressure gauge. 128 4.12 Observed collected currents as function of plate voltage for different constant pressures at room temperature (27~C) -planar gauge. 130 4.13 Variation of collected ion current with pressure at room temperature (25~C) for different electrode voltages in a planar radioactive ionization gauge. 131 vii

LIST OF FIGURES (Continued) No. Page 4.14 Variation of dark current with plate voltage. 135 4.15 Ionization coefficient (a/P) as a function of the electric field (E/P) in air as derived from Fig. 4.13. 137 4.16 Change of output current and gas temperature with time for various pumping speeds. 139 4.17 Effect of gas temperature on i-P characteristics under different plate voltages. 141 4,18 Variation of ionization with temperature under constant density. 142 4.19 Experimental i-P cLrves for different mixtures of nitrogen. and oxygen at room temperature —planar gauge. 145 4.20 Variation of recombination dip with plate voltage. 146 4.21 Theoretical i-P curves for several mixtures of nitrogen and oxygen using Bradbury s experimental values of 6e. 147 4.22 Radium prototype gauge. 150 4.23 Typical i-P curves for radium prototype gauge. 151 4.24 Assembled ionization chamber with attached low-leakage wafer and high-megohm resistors. 153 4.25 End plate of ionization chamber showing titanium tritide source. 155 4.26 Ionization-chamber elements. 156 4.27 Ionization-chamber polarizing electrode. 157 4.28 Ionization-chamber collector assembly. 158 4.29 Ionization-chamber element assembly. 159 4.30 i-P curve of typical ionization chamber showing lowpressure and. high-pressure characteristics. 161 4.31 Typical composite i-P curve for ionization chamber showing corresponding load resistanceso 162 vaiii

LIST OF FIGURES (Concluded) No. Page 4.32 Amplifier schematic diagram. 164 4.33 System schematic diagram. 165 4.34 Complete system out of enclosing tubing. 166 4.35 Vacuum system layout. 167 4.36 Vacuum system used for calibrating pressure-measurement system. 168 A.1 Radioactive transformationof radium and its decay products. 173 A.2 Calculated alpha activity of a poorly sealed source. 179,,~ ~ ~~i

LIST OF SYMBOLS a rate of electron attachment. al coefficient used in Eq. (3.97). A coefficient in current polynomial, Eq. (3 63)~ A' coefficient in current polynomial, Eq. 13.102). b dimensionless parameter, Eq. (3e65)o bl coefficient used in Eq. (3097). b, effective radius of collisions for gas particles at T = oo B coefficient in current polynomial, Eq. (3 63) BI coefficient in current polynomial, Eq. (3.102). ce random velocity of electrons. c g random velocity of gas particles. ci random velocity of io:ns. cn random velocity of negative ions. cp random velocity of positive ions. cl coefficient used in Eq. (3-97). C constant of integration, Eq. (3.42). C1 constant of integration, Eq. (3.56). C2 constant of integration, Eq. (3 92)o C3 constant of integration, Eq. (3o95). do radius of sphere of active attraction, Eqo (2.20). D diffusion coefficient, De diffusion coeffi@cient of electrons.

Dn diffusion coefficient of negative ions. Dp diffusion coefficient of positive ions. electric field intensity. E electric field intensity, a vector quantity. Ex component of electric field intensity. f collection efficiency, Eq. (3.1). Ad molar fraction of the kth gas component. F attractive force between an ion and a molecule, Eq. (2.5). Fi effective molar fraction of ith component gas, Eq. (3.118). g average rate of volume ionization. go average rate of initial volume ionization, Eq. (2.1). g' average rate of volume ionization defined by Eq. (3. 81). G mobility constant, Eq. (2.3). i total current. io total saturation current. J total current density. J' net ionic current density, Eq. (3 82). Jm saturation current density, Eq. (3.4). total current density, a vector quantity. Se current density due to flow of electrons, a vector quantity. Jn current density due to flow of negative ions, a vector quantity. Jp current density due to flow of positive ions, a vector quantity. k Boltzmann's constant, value 1.38 x 10-23 joules/~K. Be electron mean free path. ~e~~~~~~~~x

Oea average random free path for electron attachment. Ie~o standard-of -comparison electron mean free path. 242eR Ramsauer electroun mean free path. Og mean free path of gas particles. g Oi mean free path of ith type of ions. i Qn mean free path of negative ions. mean free path of positive ions. p me mass of an electron. mg mass of a gas particle. mi mass of an ion. Mo molecular weight. ne concentration of free electrons. nn concentration of negative ions. np concentration of positive ions. No number of ion pairs initially produced per unit length, Eq. (2,1). NOO number of ions, per unit length, escaping columnar ionization, Eq. (2.17). NA Avogadro's number, value 6.025 x 10 2 Nq Loschmidt s number, value 2.687 x 1025 molecules per cubic meter. p total electric dipole moment. Pi induced electric dipole moment. pp permanent electr-ic dipole moment. P gas pressure in millibars. q ionic charge. qe electronic charge, value 1.6 x 10 coulomb. xii

r distance between ions and gas particles,Eq. (2.4). re rate of electron-ion recombination, Eqo (3o19), ri rate of ion-ion recombination, Eq. (3519). rm radius of deflecting cross sections of an electron in a gas. rl9r2 inner and outer diameter of two coaxial cylinders. s random distance in gaso so spacing between parallel plates. t time elapsed in seconds. T gas temperature on Kelvin scale. T' temperature constan.t, Eqo (2,23). u velocity of ionizing particles. ve electron drift velocity. Vi ion drift velocity. V total voltage between electrodes. VnVo,Vp regional potential differences between electrodes, Eqs. (3.60), (3.61), and (3559). VT kinetic temperature, Eq. (3.27). Vo,V1,V2 regional potential differences, Eqs. (30101), (3.99), and (3.100). w total probability that one of two ions will collide with a gas molecule within the sphere of their active attraction. wn probability of collision of a negative ion with a gas molecule within the sphere of active attraction of a positive ion. wp probability of collision of a positive ion with a gas molecule within the sphere of active attraction of a negative ion. W slope of the squared value of the field x-component, Eq. (3.41). Wi energy required to produce an ion pair in the ith gas. xi ii

X distance variable. x dimensionless parameter, Eq. (2.18). y arbitrary substitutior for Ex-, Eq.q (3.41). function of a variable, as illustrated in Fig. 2.3. 16Y z ratio of distance of active attraction to mean free path of an ion, Eq. (2.21)o ze collision frequency between electrons and gas molecules. first Townsend coefficient. escape constant for radon, Appendix. dimensionless parameter, Eqo (3.47). P1 dimensionless paramieter, Eq. (35 92).:2 dimensionless parameter, Eq. (3,95). total molecular polarizability, Eq6 (2 8). y dimensionless parameter, Eq. (3.112). 6 gas density. 60 gas density at normal temperature and pressure.,e probability of electron attachment. Er relative permittivity of a gas. E0 permittivity of free space, value 1 farad/meter. 36 JT ratio of K.E. to PoE. of polarized molecule at ion-molecule impact. negative-ion-formation factor, Eq. (3.81). rate of electron attachment per unit length, Eq. (4.1). G angle between ionizing-particle track and direction of electric field. XAX1,?i2 thickness of space charge layerso xiv

decay constant of the ith radioactive isotope. n, k1i ionic mobility. lie electron mobility. mobility of negative ions. Ilp mobility of positive ions. dimensionless parameter, Eq. (3e14). dimensionless parameter, Eq. (3.16). cyl p recombination coefficient. ie coefficient of electron-ion recombination. ~Pi coefficient of ion-ion recombination. Ga cross section of electron attachment. Og solid elastic collision cross section for gas molecules. am collision cross section, in a gas, for electron deflection~ Ta mean lifetime of a free electron, Eq. (2.40). a ~ ~ ~ ~ ~~~~x

ABSTRACT in measuring densities and temperatures at high altitudes, rocketborne radioactive ionization gauges have several merits. This type of gauge is characterized by its physical ruggedness, good response to density change, and freedom from damage when exposed to higher densities. Its usable range, however, is limited by several factors. At low densities, the linear gauge characteristic is marred by the relatively high residual (dark) current, and at higher densities, by a decrease in the collected current due to the loss of ions by recombination. This dissertation is intended to be a contribution towards a systematic study of the properties and behavior of radioactive ionization gauges. The chief ionic and electronic processes encountered are briefly reviewed. Then a relationship between the collected ion current and the gas pressure is analytically developed for a planar configuration, considering -the probability of electron attachment as a function of the electric field intensity and the gas pressure~ In calculating the theoretical current-pressure curves, the numerical values used for ionic mobilities and the recombination coefficient are those derived from kinetic theory; Bloch and Bradbury's theoretical values of electron attachment are used for different mixtures of nitrogen and oxygen. Experimental current-pressure curves are found to be in fair agreement with the theoretical results. It is indicated that the hysteresis phenomenon, sometimes exhibited by ionization gauges, may be caused by: a. Temperature dependence of the main electronic processes inside the gauge. b. Variation in the environmental conditions which may result in a change in the composition of one or more of the present electronegative gases. It is shown that the primary ionization by alpha particles, in a gas of constant density, increases as the temperature decreases. The results led to the design of two radioactive ionization gauges; one uses alpha particles emitted from a radium source as the ionizing agent and the other employs beta particles from a tritium source~ The general agreement of the theoretical and experimental currentpressure curves also points to the validity of Bloch and Bradbury's theory of electron attachment in diatomic moleculeso This agreement co nfirms the steep rise of attachment probability as well as the peak value predicted by them at low electron energies. In carrying out the experimental investigations, it is found that the planar gauge used would be a useful tool in the study of ionization of gases by electron collisions. onr e

CHAPTER I INTRODUCTION AND STATEMENT OF THE PROBLEM 1.1. INTRODUCTION For a number of years, a research program in the Department of Electrical Engineering of The University of Michigan has been aimed at determining upper-atmosphere ambient pressures and temperatures through the use of sounding rockets.1' The research has been concerned chiefly with measurements at altitudes above those readily attainable with balloons, and thus has been concentrated on the development of techniques and instruments which can perform reliably in a high-velocity rocket. The general measurement procedure is to determine the air pressures at selected points on the surface of the rocket nose cone- from which the flow Mach number may be determined. Subsequent interpretation of the Mach number with knowledge of rocket trajectory, combined with certain reasonable assumptions, permits calculation of ambient air temperature. The pressure measurements there have been made mostly by radioactive ionization gauges. 1.2. DESCRIPTION OF A SIMPLE RADIOACTIVE GAUGE In a simple radioactive ionization gauge, shown in Fig. 1.1, the gap between two parallel plane electrodes is irradiated by X-rays or alphaparticles emitted from a radioactive source such as radium. The number of ion pairs generated in a unit volume of the gas per second, i.e., rate

+ IONIZING f POLARIZING RADIATION FIELD I HI -MEGOHM ELECTROMETER RESISTOR Fig. 1.1. Schematic diagram of a planar radioactive ionization gauge.

of ionization, is characteristic of the type of gas used, its density, and the initial intensity of the ionizing radiation.3 If the applied field is strong enough, all ions produced in the gap will be swept toward their respective electrodes, thereby setting up a current, known as the saturation current, in the outer circuit. The magnitude of this current, however minute it may be, is found to be directly proportional to the gas density and hence to pressure, provided the temperature remains constant. Therefore, the value of the ionization current may be related graphically to the pressure at a known and constant temperature, as indicated in Fig. 1.2. In weak fields, however, only a portion of the ions produced can reach the electrodes because a large number of ions of unlike sign will recombine, that is, neutralize their charges in the gas, before having reached an electrode. For this reason the pressure-current characteristic becomes nonlinear at the high end of the pressure range. This is illustrated in Fig. 1.3. Throughout this study, the word "pressure" is often used in place of "density" for convenience. This is permissible only if the temperature is maintained constant. The gas temperature is therefore always assumed to be standard (273~K), unless stated otherwise. 1.3. MERITS AND DRAWBACKS OF RADIOACTIVE GAUGES Although several types of ionization gauges can be employed over portions or all of the pressure range concerned in the rocket-sounding investigations, the radioactive ionization gauge is often used for many reasons,

z. / D 0 PRESSURE P AT A GIVEN TEMPERATURE Fig. 1.2. Ideal current-pressure characteristic of radioactive ionization gauge.

5 Strong fie/d Current loss due to recombination w z Weak field Z.L) w w -J Dark Current O PRESSURE P (LINEAR) Fig. 1.3. Typical current-pressure curve of radioactive ionization gauge.

6 including the following:2 (1) It is physically rugged. (2) It responds adequately over the desired pressure range. (3) It can be operated without damage at atmospheric pressures. (4) It responds without delay to density change. (5) Its current-density characteristic is linear over a considerable range. However, it has certain drawbacks: (1) The presence of a radioactive source constitutes a potential health hazard, especially if gamma radiation is present. (2) The signal level is quite low, requiring appreciable electronic circuitry. (3) In a certain portion of the operating range, the output current appears not entirely dependent on the gas density, in that the curve for a rising pressure is not always retraced during the lowering of the pressure. This is designated by the broken line in Fig. 1.4. This phenomenon will be referred to in the course of this work as hysteresis. However, a word of caution about such nomenclature is in order. Unlike magnetic or mechanical hysteresis, the above phenomenon is believed to be due to slight changes in the apparently constant experimental conditions between rise ara~ fall rather than to an influence of history under constant environmental conditions.

Li/ear 1-0 Region I I- Dark z Current Hystersis W I RgIIRegionon i a r 0 N z 0 PRESSURE - (LOG P) Fig. 1.4. Actual i-P characteristic showing the hysteresis and dark current regions.

1.4. OBJECTIVES The purpose of the work reported here was to study systematically the general properties of radioactive ionization gauges. Such a study is necessary to achieve a better understanding of the potentialities as well as of the limitations of this device for measuring pressure. It may then be possible to improve the general performance of the gauge and in particular to: (1) Extend the linearity of the current-pressure relationship to both higher and lower pressures. (2) Reduce or eliminate the causes of the undesirable hysteresis effect experienced at high pressures. 1.5. PROCEDURE (1) In Chapter II, the general properties and behavior of the different charge carriers are reviewed, especially those properties pertaining to pressure, temperature, and nature of gas. The production of ions, their mobilities, and their loss by recombination are also discussed. (2) In Chapter III, two relations between the current and pressure are analytically derived, assuming, first, complete electron attachment, and then variable attachment. Gas temperature, gauge configuration, and collector voltage appear as parameters in both relationso (3) Finally, in Chapter IV, the theoretical results of Chapters II and III are compared with experimental results. The most probable causes of the hysteresis phenomenon are also discussed.

CHAPTER II SURVEY OF IONIC PROCESSES ENCOUNTERED IN A RADIOACTIVE IONIZATION GAUGE 2.1. INTRODUCTION A gas becomes a conductor of electricity if free charges such as ions, electrons, or heavy charged particles are present. Positive ions are atoms, molecules, or groups of molecules which have lost one or more electrons and thus carry single or multiple charges. Negative ions are atoms, molecules, or groups of molecules to which electrons, usually only one, have become attached. A negative ion which arrives at a positive electrode will deliver the electron which has been attached to it, and in general the resulting neutral molecule returns to the gas. On the other hand, if a positive ion arrives at the negative electrode, it picks up an electron from the metal and then returns, as a neutral molecule, to the gas. It follows that the contribution of a newly formed ion to the current in the outside circuit will depend on the time during which the ion stays in the gas as a free entity. Therefore, before deriving an expression for the output current as a function of pressure for a radioactive gauge, it is in order to give a brief account of the most important properties and characteristics of the basic processes which take place inside the gauge with special attention to the effect of pressure, temperature, and electric field upon them. The main processes

10 encountered are: (a) production of ions, (b) motion of ions and electrons, (c) recombination of oppositely charged carriers, and (d) electron attachment and formation of negative ionso 2.2. PRODUCTION OF IONS 2.21.1. General Considerations.-Ionization in gases can be produced by irradiating with X-rays, by bombarding with alpha or beta particles, and in several other wayso In a radioactive pressure gauge, the ionizing agent may be alpha, beta, or gamma rays emitted from a radioactive material usually deposited on a plate and mounted inside the gauge chamber. The number of ion pairs produced by the passage of any of these rays through a gas varies greatly between the three cases, being roughly in the ratio 10,000: 100: 1, respectively. Since the contribution of gamma rays to ionization is so minute compared to the other rays, most of the sources used in such gauges are either alpha- or beta-particle emitters. In either case the average number of ion pairs produced per unit path length (called the specific ionization) depends on the gas density, the nature of the gas, and the velocity or residual range of the particle. 2.2.2. Ionization by Alpha Particles. —A typical long-life alphaparticle emitter employs a gold-radium alloy containing approximately 0.2 to 0.5 mg of radium. The amount depends on the volume of gas to be ionized, 5 the desired pressure range, and the lowest desired output current. To: make the active area a highly efficient alpha-particle emitter and yet with a relatively low emanating power, the radium alloy is electroplated

11 with a very thin film of metal such as nickel. The nickel film acts as a seal which retains radon gas (the first decay product of radium) and its subsequent decay products, which yield three additional alphas for every alpha particle originally emitted from the radium. This film should be very thin so that the particles lose only a small fraction of the total energy in penetrating into the gas in the chamber. The degree of constancy of source activity can be determined by the use of Bateman's equations for radioactive decay and the well-known values of the half-lives for the daughter products of the radioactive series. The buildup in the activity of radium source as an alpha emitter is analytically developed in the Appendix (case I). In Fig. 2.1 the ratio of total alpha-particle activity to the initial value (i.e., of radium only), is plotted as a function of time. It can be seen that after one month the source activity remains almost constant; the slow increase is caused by the buildup of polonium, with its consequent activity. Alpha particles are positively charged particles initially projected from the radioactive substance with high velocity, which varies for different substances between 1.4 x 107 and 2.2 x 107 meters per second. Normally the alpha particles at the moment of expulsion carry two positive charges and are to be identified with the nuclei of helium atoms. They are distinguishable from other radiations by their absorbability; they are completely stopped by less than 10 cm of air under standard temperature and pressure or by 1/10 mm of aluminum. An alpha particle possesses an appreciable kinetic energy, 7.7 Mev in the case of those emitted from

>-5n0.J4n0 - _ x 3no - a.. Li. 0 0 2n nn H 0 I0 - -- 0.01 0.1 1.0 10 100 TIME IN YEARS Fig. 2.1. A plot of the calculated alpha-particle activity for a source that is initially radium alone (emitting n, particles/see) and retains all of its decay products.

13 radium C'. Because of their great energy, they pass freely through the electronic structure of the atoms in their path, and it is only rarely that they pass close enough to the nucleus to experience a sensible deflection. In consequence of its charge, when an alpha particle passes close to an atom or penetrates it, it must disturb the motions of the electrons in the atom, resulting in excitation and/or ionization of the atom. The primary ionization due to the incident particle is a consequence of the liberation of an electron from the atom or molecule. Depending on the closeness of collision, these electrons or delta rays, as they are often called, may have velocities between 0 and 2u, where u is the velocity of the incident particle. If the speed of the ejected electron is sufficiently high, it may in turn produce a number of ions in the gas before it comes to rest. This is known as secondary ionization. As a result of detailed calcula7 tion, Fowler found that about three-quarters of the energy of a swift delta particle can be used in producing ions. The longest delta-particle tracks were found to be about.5 mm in air at standard conditions. The primary ionization constitutes about one-third of the total ionization, whereas the major part thereof is due to the absorption of the energies of the secondary delta rays. The average energy absorbed as observed experimentally in the formation of an ion pair by an alpha particle varies somewhat from one gas to another; it is between 20 and 40 electron volts for gases commonly encountered in gauges of the type under discussion. This energy is invari

ably higher than the ionization potential of the gas involved for two reasons: (a) the incident particle may excite some atoms without ionizing them, and this requires energy; (b) the electrons freed from those atoms which are ionized are given some kinetic energy, and this, as well as the ionization energy, must be furnished by the alpha particle. The number of ion pairs produced per unit length along the track of the particle depends on its velocity and increases rapidly as the velocity diminishes. Although the charged particle exerts the same force of interaction on a given planetary electron regardless of the particle's velocity, the length of time during which this force is exerted is also important in determining whether or not the electron is to be freed from the atom. As a first approximation, the probability of freeing an electron would be proportional to the product of the force and time of interaction.9 This is a very interesting point of view, which is used later in explaining the variation of specific ionization of a gas with temperature even for constant densities. 2.2.3o -Ionization by Beta Particles. -Ionization of gas inside a gauge can also be achieved by bombardment with beta particles (electrons) as emitted from radium or other radioactive substances. They are ejected from different radioactive materials with a wide range of velocities, the greatest approaching within about 2% of: the velocity; of light.. Beta particles are distinguishable from alpha particles by their greater penetrating power for the same amount of energy~ With beta particles, too, ionization takes place along and around the

15 trajectory of the particle as a result of primary and secondary collisions. The number of ion pairs produced per unit length by a beta particle is considerably smaller than the corresponding number produced by an alpha particle. This is partly due to the higher velocity with which the beta particle travels through gas particles, thus decreasing the duration of interaction, and partly due to the smaller collision cross section compared to that of an alpha particle. 2.2.4. Columnar Ionization. —The ionization produced by either alpha or beta particles is characterized by a high concentration of ions very close to the particle track, thus forming what is known as columnar ion10,11 ization. This occurs at pressures near atmospheric and above. However, as the pressure drops below atmospheric, the size of the column increases as a result of the broadening in the range of secondary ionization around the main path, being about 3 mm at a pressure of 100 millibars (mb). Because 3 mm is much greater than the typical spacing between tracks, it seems justified to assume that the ionization is macroscopically uniform at and below this range of pressure. Taking into account recombination within the column, the net rate of volume ionization for an entire region is given by10 g N (2.1) 1 + P N f(x) where go = the average initial ionization, ion pairs per unit volume per second, throughout the region,

16 p = coefficient of volume recombination, No = number of ion pairs initially produced per unit length, D = coefficient of diffusion, f(x) = (ix) (ix) (1) ( is the Hankel function and x is 2 a dimensionless parameter depending on the mobility of the ion, the field, and its direction as described in section (2o5.2). 2o 3. IONIC MOBILITY 2.3.L.-1Definitions. -If ions of a certain type form a swarm so that the velocities of individual particles are equally distributed in all directions about an average velocity, the applied electric field acting on the swarm will move it as a group. The average speed with which the center of the swarm moves in the direction of the applied field is called the drift velocity. The ionic mobility, i,' is thus defined as the ratio of the drift velocity, vi, to the field E causing it, Vi = 41 E (2.2) where ti is expressed in meter/second per volt/meter. A similar equation relating to electron motions is obtained by using the subscript "e" instead of "i." At the gas densities and field strengths here considered, the mobility pi can be assumed a constant for the gas in question~ Also, Ki has been found to be inversely proportional to the gas density, 6; in other words, the mobility is inversely proportional to the pressure, P, at constant temperature, T. Thus

17 = G ~ = -G 3\ (2.3) where bo is the density of the gas used at a pressure of 760 mm Hg, and at a temperature of 273~K (called normal temperature and pressure), and G is the reduced mobility or mobility constant, which is a slowly varying function of temperature at normal conditions. 2.3.2. Langevin's Theory of Ionic Mobility. — The ionic mobility has been analyzed according to several theories which range from one based on the simple mechanistic approach using average free paths, average velocities, and assuming elastic collisions between ions and gas particles, to the more correct and generalized theoretical approach based on the Maxwell and Boltzmann procedures, using force fields instead of the simple mean free path concept. Langevinl2 made a thorough and complete theoretical study of ionic mobilities, in which he assumed solid elastic impacts of ions with molecules, and considered the fundamental role played by the dipole character of gas molecules. According to the theories preceding Langevin's work, a negative ion, for example, would travel in the forcefield direction colliding only with molecules in its path. But in Langevin's theory an ion approaching a distant molecule displaces its electrons with respect to the positive nucleus, inducing an electric dipole in the molecule. Hence the ion is attracted by the positive end of the dipole and deflected toward this molecule, as illustrated in Fig. 2.2. So without colliding in the classical sense, an exchange of momentum between the negative ion and the neutral molecule takes place.

18 0 -— O 0 + 0 DIRECTiON OF ELECTRIC FIELO Fig. 2.2. Path of a negative ion under the influence of an induced electric dipole.

19 An ion of charge qe has an electric field of strength qe E = 2 volts per meter, (2.4) 4t e r at a distance r. This field is of the order of 108 volt/meter at intermolecular distances under atmospheric pressures. In fields of this magnitude, all molecules experience a displacement of their electron clouds relative to the nuclei, so as to produce an electrical dipole of moment, Pi. Certain molecules such as H20, NH3, etc., possess an additional permanent electrical dipole moment, pp. Thus an effective average moment, p = yE, is induced on the molecules by the ionic force field at a distance r, with y as the total polarizability of the molecule. Now this dipole with its axis aligned by the field E of the ion will experience an attractive force 2p qe F = 4[ c r3 (2.5) Since the dipole moment 7 _qe p = E -4n o r2 (2.6) substitution in (2o5) gives the force between the molecule and ion: F = 27 A ) 1 (2-7) This law is correct while r is sufficiently great, so that the field E is sensibly uniform within the space occupied by a gas molecule. The total molecular polarizability is determined from the ClaususMossotti relation:

20 __.NA M N, (2.8) er+2 6 3Eo where Mo = molecular weight, 6 = gas density in kg/m3, Er = relative permittivity of gas,,o = permittivity of a vacuum, value 10 8/366 farad/meter, NA = Avogadro's number, value 6.025 x 1026, and y = the total polarizability per molecule. Since the relative permittivity of the gas, Er' has a value very close to unity, cr + 2 3 and the above relation becomes Mo N NA (or-1) M NA or Co(Er-1) Mo = -o(rl) N0 (2.9) NA 6 From (2.9) one can also write (Er-l) =(Er) _ 6, (2.10) (Er-l)o 6o where (rl-1)o and 65 are the dielectric constant and gas density, respectively, at normal temperature and pressure. Langevin assumed, according to the relation (2o7), that the attractive force between an ion and a gas molecule obeys the fifth-power law, and thus his complete treatment led to the following form for the ionic mobility:

21 / y 33 3.16 x 10o-31 + (mg/mi) Hi rn) m/sec per volt/mn (j)I5.16 (Er-) (2.11) where mg and mi are the mass of molecule and ion, respectively, and (3/16Y) is a function of a variable ~ containing the effects of the integration over all classes of orbits involved in solid elastic impacts. 13'1,14 The relation between (3/16Y) and i, as computed by Hasse, is shown in Fig. 2.3. Here, 5 is given by 2 = ( kinetic energy of molecule kpotential energy of polarized molecule at ionic molecular impact 32 Eo Og2 P (Er-l)q2 where _g = solid elastic collision cross section, P = gas pressure, and q = ionic charge. At low temperatures, and with small ions and molecules, the value of (3/16Y) approaches a limiting value of 0.51. On the other hand, as the temperature, and the radii of the molecules and ions, increase, the value of (3/16Y) increases, reaches a maximum, and then decays to about 0.1. In the derivation of Langevin's relation (2.11), it was assumed that the ionic drift velocity was small compared to the random velocities, and that the ions remain in thermal equilibrium with the gas molecule, i.e., - mi ci _ 1 mg = kT (2.12) -rn* 2 g g 212) 2 1c1 = -rn c =

22 0.6 0.5 0.4 3/16 V 0.3 0.2 0.I 0 I 2 3 4 Fig. 2.3. Plot of Langevin's quantity (3/16Y) as a function of the parameter 32 =co a2 P (E r-)q2

235 where ci, cg are the mean-square values of random velocities of ions and molecules, respectively, and k is Boltzmann's constant. The numerical agreement between Hasse's theoretical values and experiment has proven to be reasonably good. Loeb put the mobility equation (2.11) in the more convenient forml5'16 _5 4.62 x 10-3 1 + ( mg/mi) m/sec per volt/m. (2.13) 16Y (6/6,) o The ionic mobility behavior will now be summarized; for low values of E/P it is given adequately by Eq. (2.13). (1) The ionic mobility is independent of the electric field strength, E, except at high values of E/P where the energy of the ion caused by the field begins to exceed thermal energies by a considerable amount, causing a reduction in the attractive-force action. Figure 2.4 shows the limiting value of E/P at which the mobility of N2 ion in N2 ceases to be independent of E/P. (2) The mobility is inversely proportional to the gas mass density. This is illustrated by Fig. 2.5 in which the mobilities of different ions are plotted against their masses. (3) At constant density, the mobility is a slowly rising function of temperature, usually changing insignificantly within the range of temperatures experienced in the laboratory. Figure 2.6 shows the effect of temperature on the mobility of N2 ions in N2 for constant pressure and for constant density; this is accounted for in the 3/16Y factor.

3.2 > 2 o 2.8 2.4 2.0 0 10 20 30 40 E/P VOLT) Fig. 2.4. Limiting values of E/P at which mobility of N2 ions in N2 gas ceases to be independent of E/P.

4.8 e 4.4 4.0. 3.6 3,2 NH3 2.8 0 2.4 Xe Hg 2.0 0 20 40 60 80 100 120 140 160 180 200 220 MASS OF ION Fig. 2.5. Mass-dispersion curve of Langevin's theory and experimental values for various ions in N2 gas.

26 7.0 6.0 //(Pressure constant at 760 mm Hg) 5.0 w E j 0 4.0: 3.0 0 O~ ~ ~ ~ ~ ~ ~~~~, (Density corresponding to n. t.p.) 2.0 1.0 -' -N2 0 100 200 300 400 500 600 TEMPERATURE IN OK Fig. 2.6. Effect of temperature on mobility of N2 in N2 gas.

27 (4) The mobility depends on 1 + (mg/mi) (er-l)o MO which is a property of the gas; this prediction from the theory has been in good accord with observations. 2.4. ELECTRON MOBILITY The electron mass is so small compared to molecules of the gases in which they find themselves that in elastic collision with the heavier molecules they rebound and retain a large fraction of their momentum. Thus even where low fields are present, the electrons retain energy gained from the field and thus possess energies different from those of the surrounding molecules. In this respect one expects them to behave differently from the more massive ions. A simple expression for the electronic mobility, as derived by Langevin from the kinetic theory is12 5 -e qee = m -- (2.14) 4 me ce where ce is the electron average random velocity, determined from electron temperature, and Re is the electron mean free path. The latter is given by =e Oe P Tg (2.15) where eR is the Ramsauer electron mean free path in meters at 273~K and a pressure of 1 mb, a value which varies in a most complicated fashion

17-19 with electron energies. Compton's equation for electron mobility will be used here as adapted by Bradbury and Nielsen,21-23 and arranged in terms of standard-of-comparison mean free paths, Be, the electric field strength, E, the gas pressure, P, and the gas temperature, T. This equation reads: 1.825 x 106 e0 (l/P) (T/273)1/2 m2 kte 2 2 1/2 1/2 volt-sec ~e [1 + (1 + 9.82 x 105 Mo 4eo (E/P) volt-sec (2.16) where Mo is the molecular weight of the gas, and the pressure, P, is expressed in millibars. 2.5. RECOMBINATION OF IONS 2.5.1. Definitions.-Since the ions are in general oppositely charged particles, they attract each other according to the ordinary laws of electrostatics. When they collide, their charges may neutralize each other, and the ions again become neutral particles. The chance of a given positively charged ion, for example, meeting a negative ion in a given time is proportional to the number, nn, of the negative ions present per unit volume, while the number of positive ions finding partners in a given time is proportional to the number np, of positive ions actually present per unit volume of the gas. The rate at which recombination goes on is thus proportional to nn np. This rate is usually written as p nn np, where p is constant under given conditions and is known as the coefficient of recombination. There are various types of recombination, such as preferential,

29 initial, columnar and volume recombination. In the radioactive gauges of the type considered here only two of these are of significance, viz., columnar and volume recombination. 2.5.2. Columnar Ion-Ion Recombination. — Ionization by high-energy particles is by no means isotropic, especially not at the high range of pressure. However, such anisotropy is removed (by diffusion) when pressure is lowered, as a result of the secondary ionization around each track. In columnar ionization the ions have their highest concentration along the particle's track, or column; hence columnar recombination is liable to take place there. The effect of such recombination is only on the value of saturation currents, i.e., on the net rate of ion production, g. This value is found to be dependent on the angle a column makes with the electric field. Maximum saturation currents are achieved when the field is perpendicular to the path of the ionizing particle and minimum when parallel. Moulin25 studied this phenomena and then Jaffe10 developed his now well-known theory of columnar ionization and recombination. Jaffe assumed that electrons, just released in ionization process, diffuse outward; and -3 at the end of 10 or more of a second, most of them will have attached to give negative molecular ions. Oxygen is a typical example of such electronegative molecules which can readily attach electrons to form negative molecular ions, as explained in Section 2.6. Jaffe also assumed that the negative and positive ions are symmetrically distributed radially about the track axis, with density declining radially outward, following a

30 Gaussian error curve, the form of which will not change by subsequent recombination. Under these conditions one finds that the number of ions, N., escaping recombination is given by N 1 (2.17) NO 1 + PN~ f(x) 8&D where No = number of ion-pairs initially produced per unit length, p = coefficient of volume recombination, D = coefficient of diffusion, (x) ex i H( (ix), 2 0 HI (ix) is Hankel's function (for definition and tables see Watson, Bessel Functions, Cambridge, 1952), and x is a dimensionless parameter defined by 2 = 2( 0o sn)(2.18) where [ is the ionic mobility, ro, the average displacement of the Gaussian curve from the columnar axis, a function of pressure,l0 and G the angle between the particle track and the direction of the electric- field E. The agreement of this theory with experiment is good, particularly at pressures above 1 atmosphere (Fig. 2.7). In fact, the net saturation current is a result of ions escaping this type of recombination. Thus the net rate of ion production per unit volume is given by

1.0 I/ Atm. go 0.5 0 200 400 600 POTENTIAL IN VOLTS Fig. 2.7. Calculated theoretical saturation currents compared to experimental points.

32 g go (2.19) 1 + pNo f(x) $TD where go is the average rate of initial production, assuming no recombination of any type, called the true saturation value. 2.5.3. Volume Ion-Ion Recombination — Due to the diffusion of ions the ionization columns expand radially so that they touch and merge. The ions then are likely to be evenly distributed and the recombination from then on follows the relations for general volume recombination. Thus, 26 following Thomson's calculations, the coefficient of volume ion-ion recombination is given by p = A d2 w o + c2, (2.20) where cp = the average velocity of positive ions, Cn = the average velocity of negative ions, do = the radius of sphere of active attraction, defined by do 6t Eo kT w = the chance of recombination, given by w = wp + n -wpwn and w 1- 14Fi - 2do/i (do + 1)] with Hi as the mean free path of the ith type of ions. Assuming the ions and gas particles are in thermal equilibrium, we then have

33 2n = 2p = ~ Also cp = n, = c and consequently Wp = n =Wo Thus the recombination coefficient becomes p = Ed c \2 w(z), (2.21) where w(z) = 2Wo -, wa = 1 - 2 [1 - e-Z (z-l)] and 2do The distance of active interaction, do, depends solely on the thermal agitation, and therefore on the gas temperature, do = 4.075 x 108 273 meters The ionic mean free path, 2, is affected by several complicating factors such as the attractive forces between the ions and neutral gas molecules, and the energy gained by ions in the presence of a strong electric field. However, most of the investigations here are made under such conditions that thermal equilibrium of molecular ions with gas molecules is usually assured; it is therefore permissible to assume 2 = 2g, where 2g is the mean free path of gas molecules. 2g is a function of temperature and pressure, and is given by27

34 1 T g go p 273 where P is the pressure in mb and go is the Maxwell's mean free path in meters at 273~K and a pressure of 1 mb and is given by 213 x 10 (2.23) go b2 (1 + TT/T) with bo as the effective radius of collision at T = co, T' the temperature constant of gas; both constants have been determined for a large number df gases. Air, for example, has boo = 1.57 x 101~ meter and T' = 111.3~K Therefore, for air z = 9.47 P + 111) ( 10 The average random velocity, c, is given by o3kT c = 0.922 X. (2.24) mg Thus the final form of the coefficient of volume recombination is given by 3/2 p = 2.47 x 10o-1 i ( )73 w(z) (2.25) where M is the molecular weight of the ions relative to hydrogen, chosen as 1o The above formula for the recombination coefficient, as a function of pressure and temperature, is in good agreement with actual values as

illustrated in Figs. 2.8 and 2.9 for pressure and temperature, respectively. 2.5)4. Electron-Ion Recombination. —So far we have considered only ion-ion recombination which is predominant under the prevailing conditions. Recombination of electrons and positive ions is a highly improbable proc29 ess, and consequently is neglected in the present investigation. 2.6. ELECTRON-ATTACHMENT AND FORMATION OF NEGATIVE IONS 2.6.1. General Considerations. — Negative ions appear in gases under different circumstances 3 1. They may be created in the gas largely through the attachment of free electrons to neutral atoms or molecules. 2. They may be introduced into the gas by interaction of fast particles of atomic mass with surfaces or by liberation of adsorbed and absorbed gas molecules from hot metallic surfaces such as filaments or oxide-coated cathodes. The first type, however, is a predominant source of negative ions under the conditions usually encountered in the study of radioactive ionization gauges. In general there are three widely varying types of behavior in regard to the formation of negative ions in different gases. The first of these may be characterized by the fact that no electron attachment is observed, for electrons having any value of kinetic energy, and can be explained as due to the absence of an electron affinity. Such cases are found in the rare gases, and in nitrogen and hydrogen. In the second type,

36 2.5 2.0 wO E/z 0. 1.5 0 A/r 1.0 0.5 0., 0 I I I 0 400 800 1200 1600 2000 PRESSURE IN MILLIBARS 51 Fig. 2.8. Sayer'. data of Pi in air as a function of pressure. The full curve represents Thornson's theory for Pi in thlis range.

37 5.0 4.0 - 3 0~ \02 Ez 0 Z3.0 0 0 2.0 1.0 O 0.0 100 200 300 400 500 TEMPERATURE IN OK Fig. 2.9. Gardner"'a data of Pi in 02 as a function of temperature at constant density, compared with calculations froml Tllosmson's theory.52

38 negative ions are formed only by sufficiently high-energy electrons so that dissociation of gas molecules can occur. Examples of this are found in N20, NH3, and HC1. The reaction of this type is XY + e - X + Y Finally, there are gases in which electrons of very low kinetic energy can be captured, and in fact show a decrease of cross section with increasing energy of the electron. Oxygen and water vapor are good examples of gases possessing an electron affinity. This can be represented as X2 + e + X2 The electron affinity of an atom or molecule is defined physically as the difference in energy between the ground state of atom or molecule with a free electron at rest at infinity and the ground state of the corresponding negative ion.31 For atoms, this is simply the binding energy of the extra electron on the negative ion, whereas in the case of molecules, the change in nuclear motion too must be taken into account. An example of molecular ion potential energy curves for oxygen is shown in Fig. 2.10. The electron affinity of 02, by definition, corresponds to the difference in energy between the lowest vibrational and rotational levels of the 02 (3Zg) state (point A) and the 02 (2TTg) state (point B). However, the minimum energy required to detach an electron from an unexcited 02 molecule corresponds to the transition BC, for no change in the nuclear separationo This transition is known as vertical detachment, which is distinguished from the affinity BAo32

0 0*0 *100 L I.2.25 o e -$ z -/ " -4 /(H)'17 z C =5 ~ f-/ Vertical de tachment NUAI I I 2.5 NUCLEAR SEPARATION (c ) Fig. 2.10. A possible potential energy curve for 02, compared with the known ground state of 02 (dashed curve).

4o On the other hand, a negative electron affinity implies an extremely small or zero probability of formation of a negative ion. This is illustrated in Fig. 2o11 which shows the theoretical calculations of the potential energy curves for a hydrogen molecule (H2) and its corresponding negative molecular ion (H2).33 From this figure one finds +0O9 ev for the vertical detachment energy, and -3.58 ev for hydrogen electron affinity. Negative molecular hydrogen ions have never been observed experimentally. There is no experimental evidence of the existence of double-charged negative ions in the gas phase. If such ions exist, they are probably very unstable,31 because small values of the electron affinities for attachment of single electrons make it improbable that a second electron could also be attached with a decrease of energy. In either direct or dissociative attachments, the excess energy of the attacking electron is removed either by (a) radiation, (b) subsequent collision with a third body, or (c) by resonance with an excited electronic, or vibrational or rotational state of the ion with subsequent loss of energy by radiation or collision. 2.6.2. Basic Theory of Attachment. —Following J. J. Thomson, it is assumed that electrons do not readily attach to molecules to form negative ions, i.e., there is a certain small probability be that, in a collision between an electron and a molecule, the electron will attach to the molecule, thus forming a negative ion. If the average random velocity of an electron is ce and its mean free path is Le, then the collision frequency is ce/~e. The drift velocity ve of an electron in the direction of a field of strength Ex is ve = Pe Ex, [e being the electron mobility.

-41 Vertical 9v) H6+H 0Q)~~~~~~~ ~detachment z z2 The c)O~~~ / ~~~~negative 0nE e/elctron (-3.58ev) affinity 0 3 0 a 2 3 4 5 NUCLEAR SEPARATION IN A Fig. 2.11. Theoretical potential energy curve for H-, compared with ground state of H2

42 Thus, in advancing a unit length in the field direction along the x-axis, the electron travels a time t = l/ve; it then makes ce/(Ieve) collisions per meter. If the attachment process is a pure chance event, of probability be that attachment will occur at any given collision, then out of n electrons starting from a point x at a time t = 0, the number of attachments dn occurring in a distance dx will be bece dn = n dx. (2.26) ~eve Integrating and setting n = no at x = 0, the number of electrons n, out of the initial no, that do not experience attachment within a distance x is given by beCe n = n e eve (2.27) This shows that the number of electrons surviving attachment after traversing a distance x in the field direction is a negative exponential function of distance. The average distance x for attachment under the present conditions is thus given by - e Ie Ex x =. (2.28) 6e Ce This gives the average free path in the field direction before attachment. The electron drift velocity ve, is, according to Compton or Langevin related to ~e and ce by the fundamental relation qe Ex ~e ve = 0.815 e (229) me Ce where the energy distribution is assumed to be Maxwellian. For other

43 types of energy distribution, only the numerical fraction in Eq. (2.29) is to be slightly modified, with values being, however, near unity. qe and me are charge and mass of an electron, respectively. From (2.29) we have _ — =, (2.30) Ce 0.815 qe Ex so that the survival equation becomes 0.815 be qex me ~ea Ex n n me e E (2.31) The attachment process can also be described in terms of collision cross section for capture. An electron moving with average random velocity ce among the relatively fixed gas molecules describes a random path of total length ce meters in one second. All molecules, the centers of which lie within a distance rm, collide with the electron, causing appreciable deflection in the otherwise straight trajectory. Thus a volume 2it rm ce = am Ce is swept out in one second. Here am is the collision cross section of one atom or molecule, for electron deflection, and is known as the collision cross section for electrons in a gas. Since there are Nq molecules per m3 of a gas at temperature of 273~K and pressure of 1 mb, then the Nq am ce molecules lying within this broken cylinder will have collided with the electron in a second. But the total distance traveled in one second is e'. Therefore the average distance between collisions or the mean free path is e = e = 1. (2.532) Nq am Ce Nq am

44 This is not a precise relation because of the Ramsauer effect; electron free paths are a rather complex function of energy and differ for each type of gaso If P is the pressure in millibars and T the gas temperature in degrees Kelvin, then the survival equation for the n electrons, out of no, that have traversed a random distance, s, in the gas without a deflecting collision with molecules is -s/~e -NqamP (273/ T)s n = no no = no e1qm(2.33) The probability of attachment, 6e, as defined by Thomson may now be stated more precisely in terms of collision cross sectionso Thus a be = a (2 54) m or Ca = be gm o (2.35) This enables 0a, the attachment cross section, to be calculated if am and be are known from measurement. Since the collision cross section is inversely proportional to the mean free path, Eqo (2-34) could be written as 6 e = ye/We (2~36) actually represents the mean time elapsed between two successive ~e/Ee actually represents the mean time elapsed between two successive collisions, whereas Bea /e is the mean lifetime of a free electron before experiencing any attachment~ Accordingly the coefficient of attachment, be, could be redefined as

b - mean time between collision (2.37) e mean lifetime of a free electron Using Eqs. (2.35) and (2.36), it is then possible to express the survival equation for attachment in random motion in a gas as n = no e /e = no e qPa( (2.38) with 1 Re ea 2 - 39) ea =NqPa (273/T) e(239) the average random free path for attachment. It should be noted here that Eqs. (2.27) and (2.31), which deal with the distances, x, for attachment involving motion in the field direction, are not to be confused with Eqs. (2.33) and (2.38) dealing with distances, s, of random motions involved in attachment. A similar distinction applies to x of (2.28) and lea of (2.39). The average random free path for attachement, le, can be determined directly from microwave techniques.35 Since the random path s is given by s = Wet, then substituting in the survival equations (2.38) renders n = n0 e (<e/Aea)t = n Nqua(273/T)Cet = n e~ t/Ta (2.40) and nw -t/Ta dn = — e dt (2.41) Ta a

46 2.6.3. Attachment in a Mixture of Gases o-It was stated in the previous section that the number of collisions in dt second is (ce/~e)dt, with ce the random velocity of electrons and Le the corresponding mean free path. In a mixture of gases, the calculation of the collision frequency is not so simple, for one must compute the relative:rumber of impacts with each type of molecules, which will in turn. be a function of the mean free path and the molar fraction of the respective gases. The attachment in air, for example (which consists of oxygen and nitrogen, and only the former with attaching molecules), is36 eair: - (2.42) + e2 where fl and elm are the molar fraction and the deflecting mean free path of nitrogen, and f2 and ~e2 the corresponding values of oxygen. Since the molar fraction is proportional to the partial pressure of the gas, Eq. (2 42) could be written as 6e02 (2 43) eair 1 + P1 e2( P2 ~e, where P1 and P2 are the partial pressures of nitrogen and oxygen, respectively In general, for mixtures containing more than two gases, the effective attachment probability is given by k ek (244) k ~ek

47 where 6ek, Pk. and Iek refer to the kth gas in the mixture. 2.6.4. Attachment Properties of Oxygen and Water Vapor. —Examples of electron-attaching gases most likely to be found in air are molecular oxygen (02) and water vapor (H20). The attaching properties of both gases are summarized in the following. It has been observed that in oxygen the attachment probability, 6e' is not pressure-dependent above about 4 mb. 3 For oxygen it appears likely that the energy of attachment is taken up into the vibrational system for some period. If an impact does not remove this energy during the lifetime of the vibrational negative ion state, the electron will separate again. In this case the formation of a negative ion depends on two successive collisions so that the newly formed ion must collide with a neutral molecule before spontaneous separation of the electron takes place. In such a process the higher the energy of the electron, the less likely the initial attachment will be, and consequently be quickly goes down as the energy of the attacking electron increases. Thus, a characteristic of this process is a rapid decline of 6e with increase in E/P. This is illustrated by Bradbury's data3 (Fig. 2.12). At low electron energies the attachment process in molecular oxygen is direct and can be represented by the reaction 02 + 02 + e + 02 + 02, in which excess energy goes into vibrational state until it is lost in impact later. Another feature of the above data is the subsequent rise of the value of 6e as the energy increases. This is believed to be due

-4 31C ~~~~~~~~~~~~~~Oxygen 02 * 24.7 mb A 20mb. o /9. 4 9,33 0 6.4 4.67 00 1 2 3 4 5 6 7 8 9 0 1 1 12 53 14 4 5 m X I"'2(VO LT/m mb.) Fig. 2.12. Probability of electron attachment in oxygen as a function of E/P. The points indicate data taken at different pressures.

49 to an added different type of attachment, known as dissociative attachment, which may set in at higher electron energies. Under these circumstances the energy of the attacking electron is so great that the electron is captured and molecular dissociation occurs giving rise to neutral atomic oxygen and atomic negative ion. This type of attachment may be represented by the reaction 02 + e - O + O Bloch and Bradbury developed quantum-mechanically a theory which accounted for the mechanism of capture of an electron by 02, S02, or NO at low-energy values in which a dissociation process does not occur. They assumed that the capture of the electron is a uni-molecular process involving the excitation of molecular vibrational levels and subsequent loss of energy by collision or radiation. Their theoretical curve is compared with experimental data in Fig. 2.13. The theoretical curve has a peak at some lower energies. There has been no experimental evidence in the available literature to support this theoretical peak. Yet some of the experimental results obtained in the present work may be adequately explained if such a peak in the attachment probability is present. Figure 2.14 is Bradbury's experimental curve for air.36 In the case of water vapor, at appropriate pressures of H20, the H20 polymerizes to (H20)2 and the equilibrium concentration of (H20)2 is a function of pressure and gas temperature. Thus negative ions in H20 are likely to be formed by an electron attachment to the (H20)2 complexes with

5o 8 O xygen 6~~~~~~~~~~~~~ ~~0 0 0 0 0.2 0.4 0.6 0.8. 10 1. 1. I8 2.0 2. 4 E. xl 0- (VOLT/m mb. ) Fig. 2.13. Plot of 5e as a function of E/P as given by Bloch and Bradburyns theory. The theory is fitted at one pointl Note the peak and decline of theory at lower E/P.

40 36 0 32 Air,28 z E 24 La. 0 L20z~ I 16 12 8 4 0 0 I 2 3 4 5 6 7 8 9 10 1 E -2 x 10 (VOLT/m mb) Fig. 2.14. Bradbury's values for be as a function of E/P in air.

dissociation to give an H20 ion and an H20 molecule. At low values of E/P, the attachment probability, be, is pressure-dependent (Fig. 2.15). In fact, at a fixed E/P, the value of be increases approximately in a linear relation with pressure. The reaction in this type of attachment is (2H20) + e + (H20)- + H20 Above an E/P of about 103 volt/meter per mb, a pressure-independent dis-4 sociative attachment occurs with a probability of the order 4 x 10

4 H. _ 20 o 1-3.33 mb. + -6.66 mb. 3A = 0 mb. 4. = 0 0-(V Fig. x10. Bradbury's values fr (VOT/mPmb.) Fig. 2.15. Bradbury's values for be in H20 as a function of E/P.

CHAPTER III THEORY OF RADIOACTIVE IONIZATION GAUGE 3.1. INTRODUCTION In this chapter the current-pressure relation in a radioactive ionization gauge will be derived from the basic equations of current conduction and of electric field in weakly ionized gases. Two cases will be considered. (1) the case in which complete electron attachment is assumed and thus the conduction current is entirely due to ionic currents alone, and (2) the case in which the electron attachment is variable, and hence the electronic current in addition to the ionic is of importance in determining the conduction characteristics of the gauge. Two methods are adopted in the derivation of the current-pressure relationship; first an approximate method in which the electric field is assumed constant, and then a general method in which the electric field is modified due to the presence of a thin layer of space charge in the vicinity of the electrodes 3.2. APPROXIMATE METHOD As mentioned in Chapter I, a simple form of a radioactive ionization gauge can consist of two parallel plates, between which there is an appropriate gas sample. One plate can be the ionizing source and if between this and the other plate an appropriate voltage is applied, the collected

ion-current can be taken as a measure of the gas pressure. A first approximation of the problem can be achieved by assuming (1) a constant field throughout the gap between the two planes; (2) that the gas is weakly ionized so that there will be no space-charge effects; and (3) that the electric field is strong enough to effect collection of ions, yet too weak to accelerate the electrons to velocities sufficient to produce ionization by collision. Let the gas be uniformly ionized and let g be the number of ion-pairs produced per unit volume in one second. As the space-charge field is negligible compared to the applied field, Eo = V/so, where V and so are the voltage and distance between the plates, respectively (Fig. 3.1), the ions of the same kind will have as a group a constant drift velocity, pEo, where i is the ion mobility. In the ideal case, where there is no loss of ions by recombination, nor any additional ionization by collision, all the ions produced by irradiation are collected, giving a maximum value of current known as the saturation current. On the other hand, if some of the ions recombine during their drift towards the respective electrodes, the net current flow will be less than the saturation value and the collection efficiency, f, is thus defined by f - measured current (3.1) saturation current If there is no recombination loss, i.e., f = 1, the total number of positive ions crossing a unit area at a distance x from the positive plate is

56 / V f q 2 E:~o unv n / + P x S-x dx Fig. 3.1. Ionic density distribution between the two parallel plates -simple theory.

gx ions per second. Thus the positive ion density, np, at any point in the field is given by np gx (3o2) pEo Therefore, the positive-ion density varies linearly from 0, at the positive plate, to (gso)/(pEo0) at the negative plate. Similarly, the negative ion density, nn, at a point x, is g(sO-X). (3.) Eo The saturation current, Jm, in this case will be Jm = %e gso (3o4) where qe is the unit ionic charge~ If the collection efficiency, f, is less than unity due to loss of ions by recombination, the current density,J, reaching each plate becomes J = f qe gSo = f (35) To determine the effect of recombination on the distribution of ions between the plates, one may proceed as follows. Since the positive and negative ions are assumed to have the same value of mobility, the distribution of one type of ions will be the image of the other. This can be expressed by nn(x) N(x) (3>6) and rp(x) = N(so-x), (5~7)

where N(x) or N(so-x) is a general function, the form of which will be determined for the particular conditions imposed by this problem As a result of the continuity of flow, the current density should be the same throughout the gap. Therefore, the collected current at any time is J = qe E0o [N(x) + N(so-x)] (3.8) which could be written as - N(x) + N(s -x) (3~9) qeEo According to Eq. (3o9), the sum of the negative and positive ion densities is always constant at any point. This condition, together with the requirement that both densities be zero at one or the other electrode, is satisfied if and only if the function N(x) is linearly proportional to x, i.e., nn = N(x) = Kx (3 10) and np = (so-x) = K(so-x), (3.11) where K is the constant of proportionality, which from (3.2) and (3.3) has the value g/pEo. Therefore, one can assume triangular distribution of ion density, varying linearly from 0 to (fgso)/pEo, for the approximate case now being considered. This can be confirmed by a mechanistic analysis using an integration of the introduction and loss terms. The number of ions lost by recombination in a unit volume per second is

f2g2X(so-x) p nn np = p 22 fg (s-x)x Therefore, the total number lost throughout the space per unit area is R = fSop nn np dx (3.12) 0 =, -fg52) ion-pairs per second. The total number of ion-pairs produced per second in the same space above is gso. Therefore, the collection efficiency is given by f = 1 (3 13) gso Substituting for R and reducing, we get f = 1 _f2, (3.14) where 9 \ Solving for f, we thus get = - 1 J (_/) +/2i Only the + sign is true, since f must be a positive real quantity. The 40 above solution could be written as j 2 _ - 1 + + 4 (3515) This equation defines a generalized saturation curve, as illustrated in

60 Fig. 3 o2, for plane-parallel geometry. The dimensionless quantity,, consists of two parameters: (pg/l2) is a characteristic of the gas at given temperature and pressure, whereas (S4/6V2) is dependent on the external conditions such as the geometry of the chamber and the voltage applied to the electrodes. The latter parameter naturally varies for different geometries. For cylindrical chambers, for example, 5 becomes41 = P (rr2)4 F rl+r2 l in r (16) Ct I// 6V2 L_2 (rl-r2) r2j where rl and r2 are the radii of the cylinder whose outer electrode is at a potential +V with respect to the inner one. The output current as calculated on the basis of (3.15) for the planar geometry is shown in Fig. 3.3, for different plate voltages. An approximate picture of the general behavior of the gauge could be determined by computing the proper values of ~ in each case. Such detailed study, however, will be postponed to the next section when a more exact treatment is considered. In the forthcoming solution, the modification of the electric field intensity near the electrodes, as a result of the nonlinear distribution of ion densities, will be taken into account. 3.3. GENERAL METHOD The basic relations which are required to study the conduction of electricity through gases under the most general conditions are the equation of continuity and the field equation. The field equation, known as Poisson's equation, may be written in the following form

0.9 0.8 0.7 0.6 0.5 l\o 0.4 0.3 0.2 0.. 0.0.. 0.01 0. I 1.0 10 100 Fig. 3.2. Generalized saturation curve-simple theory.

62 10-8 Planar configurationS= $-cm. Temp. = 300K (Air) V=50v. w Cr 2v>~~~~~~~~~-0 2v W Z a- z z w 0A_?... cr~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~..... O~~~~~~~~~~~~~~~~~~~~~o w -J 4-) _j~~~ 0'0 lo-IO 10 I 0-10 2 10 J. _.._ PRESSURE IN MILLIBARS Fig. 3.3. The effect of plate voltage on the i-P characteristicsimple theory.

63+ div = - (np n - ne)' (3.17) 0 where E - the electric field intensity at any point, volt per meter, a vector quantity, np = number density of positive ions per m3, nn = number density of negative ions per m, ne = number density of electrons per m3, qe = the electronic charge, value 1.6 x 10-19 coulomb, and co = permittivity of vacuum, value 10-9/36r farad per meter. On the other hand, the equation of continuity is, in fact, a mathematical statement of the principle of conservation of charge. The derivation of this equation for the positive ions in a radioactive ionization gauge is as follows. Consider a small region in space, dx dy dz, centered at x, y, z. The rate of change of positive ions is dx dy dz. (3.18) at These ions arise from the excess of production over recombination in the volume and from a net flow across the surfaces. The former contribution is represented by (g - ri - re) dx dy dz, (3.19) where g is the average rate of production of positive ions per unit volume per second, ri, the rate of decay by recombination with negative ions,

64 and re, the rate of decay by recombination with electrons. The second process contributing to the rate of change in ion density is the net flow of the respective ions across the boundaries of volume under consideration. Let Jpx(x,y,z) be the current density due to the flow of positive ions in the x-direction at the center of elemental volume dx dy dzo Then the corresponding current density in the x-direction at the midpoint of the dy dz face located at [x - (dx/2)] is dx Jpx(Xyz) - Jpx(xyz) 2 This midpoint value will be the average value for the face so that the positive-ion flow across the face into dx dy dz will be ~1 lJpx d dy dz Similarly, the flow out of dx dy dz across the face at [x + (dx/2)] is lF p 6x dxz e + - a 2 dy dz 0 1 px dx dy dz qe ax Proceeding in a similar manner for the faces dx dy and dx dz leads to a total net flow into dx dy dz of 1 4. - div Jp dx dy dz (3.20) qe Equating the net rate of change inside dx dy dz to the sum of expressions (3.19) and (3.20), one gets

65 6np1 - dx dy dz = (g-ri-re) dx dy dz - div Jp dx dy dz Dividing through by dx dy dz gives -np = (g-ri-re) 1 div Jp, (3.21) 6t ce which is the continuity equation for the positive ions. The corresponding equations for electrons and negative ions differ only in the first term of the right-hand side of the equation. Thus for electrons it become s _ne = (g-a-re) + 1 div Je (3.22) ~at qe where a is the rate of decay of electrons as a result of attachment to neutral atoms or molecules forming negative ions. Also, for negative ions, the continuity equation is 6nn + ant = (a-ri) + - div Jn (3.23) We can suppose that the motion of each charge carrier is governed, independently of all others, by the random diffusive action provoked by thermal agitation as well as the systematic drift produced by the electric field. We shall also suppose that the electric field is small enough so that it does not appreciably disturb the equilibrium distribution of velocities of carriers and thus their drift velocity is directly proportional 24 to the electric field. Under these conditions it is justifiable to consider the current of different carriers as the resultant of densities.of. a conduction and.a diffusion current. The latter is directly proportional

66 to the gradient of carrier concentration, grad n. Thus we can write for the different current densities Jp = qe p np E - q e Dp grad np (3.24) Je = qe ~e ne E + qe De grad ne, (3.25) Jn = e ~In nn E + qe Dn grad nn, (3~26) where 4 is the mobility of the respective carrier, and D the corresponding diffusion coefficient. The diffusion coefficient D is related to the 27 mobility k by Einstein's relation D = 1VT. (3.27) where VT is the voltage equivalent of the temperature T, also called the kinetic temperature. It is defined by the relation VT = kT/qe, where k is Boltzmann's constant, value 1.38 x 10-23 joules per degree Kelvin, and qe the electronic charge, 1.6 x 10O19 coulombs. The total current density, J, is the sum of all ionic and electronic current densities. Thus + -+ + 4 J = Jp in + Jn (3(28) The rate of electron-ion recombination, re, as used in Eqso (3.21) and (3.22), is proportional to the probability of encounters with oppositely charged carriers, as mentioned in Chapter IIo Therefore, the rate at which electrons disappear by recombination is re = Pe ne np (3.29) where pe is the coefficient of electron-ion recombination Similarly, the rate of recombination of negative and positive ions is given by

67 ri = Pi nn np, (330) where Pi is the coefficient of volume ion-ion recombination. Substituting the above expressions in Eqs. (3.21), (3.22), and (3.23), one can summarize the relations governing electrical conduction in gases as follows: div E e (np - nn n Field GO Equation_ tnn = (g Pinpn - Penpne) F div J = (a - pinnnp) + div Jn LEquations 6t qe 6ne 1 + at (g - a - Penenp) + Ci div JJ J = Jp + Jn + Je Jp = qe e (np E - VT grad n.) + F Flow Jn = qe kn (nn E + VT grad nn) Equations Je = qe Ie (ne E + VT grad ne) Inspection of the above relations readily shows that they form a system of simultaneous nonlinear partial differential equations. The mathematical problem in finding a general solution is rather involved. However, the problem becomes easy to handle in the case of certain simple geometries or when the density of ionization is sufficiently small so that it will not appreciably affect the field strength and therefore the drift velocities.

3.4. THEORY OF PLANAR GAUGE —COMPLETE ATTACHMENT 3.4.1. Statement of Assumptions and Basic Equations. —In this section, the relationship between the collected ion current and the pressure of the irradiated gas is developed for a cylindrical volume of unit cross section between two infinite plates. It is assumed that the electric field intensity is not strong enough to cause any ionization by collision; the field is, however, sufficient to render any contribution due to diffusion current negligible. It is also assumed that all electrons are attached to neutral gas molecules, forming negative ions and leaving them as the sole carriers of negative charges. Let the gas in the active volume between two parallel plates be uniformly irradiated by a source of ionization of constant intensity, and let g be the number of ion-pairs produced per second in a unit volume. Let us also assume that the collecting electrode is surrounded by an appropriate guard electrode so that the electric field is practically uniform up to the boundary of the sensitive volume. Take as a frame of reference a Cartesian coordinate system with its origin on the positive electrode and its x-axis in the direction of the electric field (Fig. 3.4). Under equilibrium conditions the number densities of the ions, np and nn, are independent of time at any given distance, and therefore a function of position, x, only. As mentioned earlier, unless the electric field is very weak the motion of ions by diffusion is insignificant compared to that under the influence of the electric field. This can be easily illustrated by the fol

69 VI Vo~~~~~~~ V2 O VO 0X 1 O \ 2 So Fig. 3.4. The potential distribution in planar configuration.

70 lowing example. Consider the positive ions in a planar configuration in which the total current density is given by Jp qe p i p Ex - VT'(331) where Ex is the electric field component in the x direction, which equals (- dV/dx). As a first approximation one can put Ex = - Vo/so and dnp/dx as (np)o/so, where so and Vo are the distance and potential difference between the plates, respectively, and (np)o the maximum number density of positive ions near the negative plate. Substituting this in the above formula gives Vo -VT Jp = ce Pp (np)o 0(3S32) so The kinetic temperature, VT, at normal temperatures is of the order of 10-2 volt, whereas the potential difference, Vo, in typical gauges is usually higher than 30 volts. Therefore it is clear that the diffusive contribution can be omitted with no appreciable error in the current which becomes almost completely due to conduction contribution. Since complete attachment is assumed, all electrons cling to neutral molecules immediately after their generation and thus the rate of attachment will be equal to that of ion production, i.e., a = g. Hence, under equilibrium conditions, the gaseous conduction in a planar gauge is governed by the following basic equations: dx =

71 dnpEx = g - Pinpnn, (334) dx -n ndx = g - Pinnnp, (335) J = qe Ex (ipnp + innn), (3-36) where the ionic mobilities, ~p and Aknn are considered constant at all points of the field. 3.4.2. Derivation of Current-Pressure Relation. —In the derivation of the current-pressure characteristic for a planar radioactive ionization gauge, one needs first to determine the electric field distribution in the ionized gas between the two parallel electrodeso Subsequently, an expression for the current will be developed from the equation of the total voltage resulting from the integration of electric field across the distance between the plates. Thus to determine the distribution of electric field inside the gap one proceeds as follows. From Eqs. (3.33) and (3.36), one gets qn 1 V + dEx-i [ p+ n jiEx o n dJx and qe nn -= [+k LE ~P xj ( J 8) cie -tp+-E-Ex ktP dox (3~38) Multiplying Eq. (3>33) by Ex and substituting in the sum of Eqs. (3.34) and (3.35), the following differential equation is obtained, governing the process: dx2e [g _ Pinpnn] -p + (59) dx2 P 0 n

72 From this equation, (d2E2 )/dx2 always has the same sign as (g - pinpnn), since the mobilities are always positive quantities. Inserting into Eq. (3.39) the values of np and nn given by (3~37) and (3~38) yields42'43 d2E 2'' \ i a+x 2"x \a dx2 Go >'p 1pn< q (~p+n) E+ \E 2 2 dx (3.40) As yet no general solution of this differential equation has been obtained except when g is constant and kip = pn. Particular solutions, however, have been worked out under special conditions44'4 such as in the study of currents near saturation assuming equal mobilities, ~p = itn = k, and under particular values of pressure, chosen to make (PiEo)/qe~' have special valueso For constant values of g and equal ionic mobilities, Pkp = n = k Eq. (3.40) has a general solution which can be found by changing variables. Putting Ex = y and dy/dx = W. in Eq. (3.40), one gets - -d.. g _- Pi _ (3.41) dy CoP- 4qe P- y 4 i Integrating this gives P Co e~2 cqo Cie P-2o -J = 2qe g o 2qeP where C is a constant of integration. From this relation one can determine the ratio of the electric field intensity midway between the plates, Eo, to the field intensity near the plates, E.o Since Up = ~n, the field is symmetrical and midway between the

73 plates dE/dx = W = 0 (Fig~ 3 5). If the net charge between the electrodes is zero in the center, d2E/dx2 will vanish there too. Hence from (3.41) and (3.42), 2 p J2 0 4qf g [12 and Peo 2 4qe g kt PGO 9 l -E g 1 C - (3 44) At the positive plate, np = 0O as ions are repelled from it and none is created beyond its boundary to replace those that move away. For similar reasons nn = 0 at the negative plate. Hence at either plate npnn= 0O and recombination does not occur. But, in general, the solution gives np n 4q E j2 4 (3 45 hence if El is the field strength at either plate, we have Peo -El (2q, g k o () \ El (3>46) Hence from Eqs. (3.44) and (3>46) and after rearranging, Do 21 o -o 1 (3 47) where Po = (2qe[)/(Pso), a dimensionless parameter. One notices from this equation that Eo is never greater than El, for 0o ~/( o~) diminishes from unity to zero as Po increases from zero to infinity. Again, since Bo depends on [1/p and is independent of either g or J, the ratio of the electric intensities does not depend on either the intensity of ionization or the current between the electrodes. At low pressures

74 El_ - El..... 1EO o X, XB So Fig. 3.5. Variation of the electric field E across the gap as modified by space-charge effects near the plates.

Po becomes large and under such conditions El/Eo =N o, approximately~ Experiments on the distribution of electric field between the electrodes showed that, when the current is small, the regions where E1 differs appreciably from Eo are confined to two layers near the plates of thicknesses X1 and k20 Variation of the field E between the electrodes is illustrated in Fig. 3.5, where the negative and positive ions have the same mobility~ The values of X can be roughly evaluated in the following manner. At the coundary of the layer next to the electrode there are as many positive as negative ions per unit volume, and since the velocities of the ions are the same, half the current must be carried by the positive and half by the negative ions. Thus if J is the total current density and qe the charge on an ion, J/(2qe) positive ions must cross the area of a plane through the boundary point in unit time, and these can only come from the quantity g created in the volume of unit area and X meters long. This makes g% = J/(2qe), so that X = J. (3548) 2qeg Since at the electrodes, npnn = 0, the volume ion-ion recombination is negligible, and the field E1 is therefore produced by the space charge of positive ions at the cathode and of negative ions at the anode. The corresponding potential distribution is shown in Figo 35s4, where V1 and V2 are the potential drops near the anode and cathode, respectively, Vo, the uniform potential drop in the central portion of the gap, and V is the anode potential above the cathode at groundo In the middle region,

76 between X1 and A2, where the field is uniform, Eo, npnn has a significant value, and recombination is occurring, presumably at a rate just to compensate for g, so that the density remains constant and np equals nn. Thus in the central portion of the gap np = nn = n = (5.49) and Eo = Ci'7g (3-50) Let us now determine the total current density between the electrodes. First consider the state of things near the positive electrode between x 0 and x = X, where X = J/(2qeg). Since there is no recombination in this region, Eqs. (3533), (3.34), and (35.535) become dEx = qe (np-nn), (351) 0 dx (npEx) =g (3.52) - Tx (nnEx) = g (3553) If g is uniform and assuming no positive ions near the anode, i.e., np= 0 when x = O., then integration gives np Ex = gx, (3.54) and [ nn Egx= - x. (355) Substituting these values for np, nn in Poisson's equation, Xd,]o~e

77 or x= gx2 -+ C (+. 6) where C1 is a constant to be determined from the condition that when x = X = J/(2qeg), Ex = Eo, where 2 j( Eo = - (3o7) Substitution in Eq. (35.56) C1 = Eo (1 + ) where o 2-qe P Co as before. The fall of potential across the layer next to the positive electrode is Vp = x Edx. (3.58) 0 Substituting the value of Ex given by Eq. (3.56) and integrating, VP = k { N3 + in (N/ + NFi )}. (3.59) Also, the potential rise next to the negative electrode is V = 2 1 n (4+ o Y * } (3.60) The potential drop due to the uniform field in the space between the layers is Vo = E0 (so-2X),(3.61)

78 where so is distance between the two electrodes. The total voltage drop, V, between the electrodes is made up of the sum of the three already determined expressions (3-59-3561). Adding all three expressions yields V = Eoo + 1 ln ( N/ +I T+o)I + Eo(so-22) (3.62) Substituting for Eo and X their values, and rearranging, V = AJ2 + BJ (3 63) where A = p47/g 4q1gt T 5s B = p7 g —1 \+/ = + -i In ( + N/3 ) -2 The solution of Eq. (3.63) is given by + /B ) V] / (3.64) On substituting the values of B/2A and V/A in Eq. (3.64), one finds b Jm J = m, (3.65) where Jm = saturation current density = qegso, and 4 kv So apg As seen from Eq. (3.65) above, the expression for the current density in the ionized gas between the two electrodes involves a host of different parameters. Some of these are characteristic of the gas involved, such

79 as the rate of ion production, g, the coefficient of recombination, p, or the mobility A. Others are function of the geometry, and external agents such as the applied voltage. 3.5. COMPUTATION OF CURRENT-PRESSURE CHARACTERISTICS For the sake of comparison of the theoretical results with the corresponding experimental results later, it is necessary to evaluate the collected ion current, J, as given by Eq. (3.65). One has first to determine the numerical expressions for the saturation current, Jim and the dimensionless parameters b and Po. The saturation current, Jm,, is directly proportional to the gas density and the effective ionized volume of the gauge; in the case of the planar gauge, Jm = qegSo. The number of ion pairs produced in a unit volume per second, g, was obtained by measuring the saturation current experimentally and use of the above expression. This gave g = 1016 P ion pairs per m3 per sec, (3.66) T where P is the pressure in millibars and T, the temperature in degrees Kelvin. Consequently the saturation current density is determined by Ps Jm = qegso = 1.6 x 10-3 - amp/m, (3.67) where so is the distance between the electrodes in meters. The ionic mobility in air, according to Langevin (see Chapter II), can be put in the form = 9-35 x 10-4 T (meters)2 (3.68) P volt-second

80 Also, the recombination coefficient of ions in air in the pressure range of interest can be expressed as p = 4.6 x 10-12(27) w(z) (3.69) where 2 w(z) = 2wo - wo wo = 1 - [1 - e-z (z+l)] z and 2do ~g 9.47 x 10-4 1 +.)P Hence the dimensionless, parameters O and b can be determined by substituting the above values of [ and/or p in the following expressions: ao = 3.618 x 10-8 -P and b 3= 374 x 10-"1 (T)3/ Knowing the values of Do and b, one can readily compute any i-P curves for different temperatures, plate voltages, or spacings as illustrated below. 3.5.1. Variation of Output Current with Plate Voltage. —Figure 3.6 shows a set of calculated curves relating the output currents to pressure in a planar gauge, at room temperature, taken as 300'K, with g given the value 1016 P/T. These curves were calculated for different plate voltages; meanwhile the distance between the plates was held at so = 1 cm. By inspec

IO 10 ~ ~ ~ ~8-8L Pl/nar gauge s -/cm- et Temp, = 3000K ____!_X_(Air) V 50v.'I) W rr o a20 v. w.O v. cr D — 9 _ I0 v. w _J / 10-10 10 10I02 PRESSURE IN MILLIBARS Fig. 3.6. Calculated current-pressure characteristics for different plate voltages-modified theory.

82 tion, one can generally divide each output characteristic into two distinct portions; a linear part in which almost all ionization products are collected, known as the saturation region, and a nonlinear portion where some of the ions are neutralized by recombination, resulting in a decrease of the net output current. The output increases and approaches the saturation value as the voltage is raised. From Figs. 3.6 and 307 one observes the similarity in shape of the calculated i-P curves and the experimentally observed curves; in both cases the linear part of the characteristic is readily extended to higher-pressure regions at higher plate voltages. As the applied voltage is increased, the sweeping of ions becomes more effective, thus lowering the chance of recombination between them., and hence producing more output currente 3.5.2. Effect of Temperature on the Gauge Output. —Figure 3.8 shows the output-pressure characteristic as computed for several temperatures, with the voltage and spacing between the plates kept unchanged. It is clear from the curves that in the linear region the output current is inversely proportional to temperature. This follows from the fact that the saturation current is directly proportional to the rate of ionization, g, which was given as g = constant (P/T) o(370) Experimental verifications indicated a slight deviation from the above relation which was based on the assumption that the ionization density is a function of the gas density alone~ However, a better approximation for the rate of ionization may be given by g = constant (P/Tn), where n is slightly higher than 1.

83 10-7 ( A 1r) Planar con figuration - 1 I 10 0102 1~~~~~~~~~~~30V. 0 0Q ~~~/0 w 10-9.I10 PRESSURE IN MILLIBARS Fig. 5.7. Variation of i-P characteristics with plate voltage for an experimental planar gauge.

84 I08 - _..... —...-.. P/lonar con fi/guration S$pacing = c/m. - Plalte vol/age 10v, -- (Air) (4 w w _ _ _ _ _ _ _ _ _ _ a! I z T 3 50~ K r -69 D 21~~~'0010" 31011K- 91~" 2 2___73_ __OK__ 0 w Iw -J 0 -I0~~~~~~~~~~~~~~~~~~0 I0~~~~311 Q~~~ 950 I0 102 03 PRESSURE IN MILLIBARS Fig. 3.8. Calculated i-P characteristics for different gas temperatures —modified theory.

On the other hand, the output current in the nonlinear zone increases with temperature for the same pressure. Such an increase results from the collection of more ions escaping recombination. The ions attain higher mobilities at higher temperatures, thus reducing the probability of recombination, and more ions are collected and therefore more output current is obtained. 3.5.3. The Effective Volume and Output Current. —The current output -12 -9 in a device of the kind here considered usually varies between 10 - 10 amp for a pressure range of from 10-1 to 100 mb. Because of the relative difficulty of handling such small currents, it is highly desirable to find some means by which one can achieve greater currents. One way to do so is to ionize larger volumes of gas. However, this method does not always increase the current output. This is illustrated by the computed examples shown in Fig. 3.9. In this case the ionized volume is changed by varying the distance, so, between the parallel plates. The proportionality of output current relative to volume is valid only when saturation currents are collected, that is, where the current-pressure characteristic is linear. The degree of proportionality diminishes, however, as the characteristic falls in the nonlinear portion, and it may even be reversed at the higher end of the pressure range. These analytical results are fairly analogous to the experimental observations, as seen in Fig. 3.10. 3.5.4. Correlation of Theoretical and Some of the Experimental Resuits. —In Fig. 3.11, the experimental results are compared to the corresponding computed curve for a particular case where the distance between

86 10-s P/laner con figurat/oni ~ P/ate voltage =Ov -. remp. = 300 /(f (Air) C,1' w~ w ____ __ _ a f w 00. I-: W 10 Ca w 0 6 cm$, O~~~~~~~~~~~~~J w iCJ ~........ _ _........ I0 102 -03 PRESSURE IN MILLIBARS Fig. 3.9. Calculated i-P characteristics for different ionization volumes —modified theory.

87 -8 10 Planar Gauge Plate voltage=50 v Room temp. -2983K tIl//. z + 0 0 -10 10 I0 102 10 PRESSURE IN MILLIBARS Fig. 3.10. Experimental i-P characteristics of a planar gauge using different plate spacings.

88 iO-e X I 0- 1B T Planar gauge V= 50 v. 2o7 cms., Temp,.= 3000K (Ai) - -' 03 C,. J a. - z I-.c w w -J tion-saturation current. I0 102 103 PRESSURE IN MILLIBARS Fig. 5.11. Correlation between experimental and theoretical i-P curves. The experimental curve is adjusted to yield agreement in the linear portion-saturation current.

89 the plates was 3 cm, and a potential difference of 50 volts. The broken line represents the experimental curve adjusted for purposes of comparison to the theoretical curve such that both the experimental and calculated lines coincide in the linear region, where saturation prevails and presumably all ionization products are collected. In the nonlinear portion, we notice that, as the pressure goes up, the experimental characteristic departs from the theoretical, reaches a maximum, and then gradually drops until they meet at the higher end of pressure range. This departure may be explained in the following manner: the theoretical calculations were based on the assumption that both types of charge carriers were ions, i.e., complete attachment throughout the pressure range. This is not always true, since the negative charge carriers are, in fact, a mixture of free and attached electrons. The proportion of the attached electrons usually diminishes as the pressure decreases. But the major loss of charge is caused by ion-ion recombination; thus one expects a reduction in this loss when the pressure is decreased. As a consequence of this reduction in recombination, more charges will reach the electrodes and this is indicated by the increase in the output current. A modified solution considering the effect of electron attachment on the conduction current will be considered in the following section. 3.6. PLANAR-GAUGE TKEORY-VARIABLE ATTACHMENT 3.6.1. Assumptions. —It was stated in Section 2.6 that certain molecules and atoms have the property of forming stable negative ions by the

90 capture of an additional electron. Thus it is highly improbable that a purely electronic current will pass through a gas composed of such molecules and atoms, and the entirely different properties of negative ions and electrons as current carriers make the attachment process of great importance in determining the conduction characteristics of the gas. Therefore, in determining a current-pressure curve, one can assume that: (1) the mobilities of both negative and positive ions have the same value, (2) the negative charge carriers are both electrons and molecular or atomic ions; their proportion is a function of pressure, electric field and type of gas, (3) the electric field is sufficiently large for the diffusion currents to be negligible, (4) at either plate carriers with similar charges are repelled, and thus in the vicinity of either plate there is no recombination, and (5) electron-ion recombination is negligible. Here again, following the same line adopted in the case of complete attachment, only the planar configuration will be considered. 3.6.2. Derivation of i-P Relation. -Proceeding in a manner similar to that of Section 3.4 in finding an i-P relation, the general equations governing the conduction in a planar ionization gauge are: d dx (ppEX) = g p n np. (3.71) dx dx - (np 7nn ne) dE~~ = -2"(n~~.n..n) (~(377) d x

91 with a = the net rate of negative-ion formation and ne = the electronic density averaged throughout the volume. Subtracting Eq. (3.72) from (3.71) and then integrating the result gives the total current density, J, due to flow of both ions and electrons: J = Je + qePEx (np+nn), (3.74) where Je is the average electron-borne current density, qe(g-a)so, with so denoting the distance between the two plates. Thus the current due to the flow of ions alone is J' = Je = qepEx (np+nn) (3.75) The field is minimum, E, at some point between the plates where (nrp) = (nn)o + (ne)o (3.76) Due to the comparatively very high mobility of electrons, their concentration (ne)o will be considerably smaller than that of negative ions, (nn)o. Thus one can again assume that at the minimum field point (np) (nn) = no ~ (3.77) O 0 Also at that point ( di) (dInn) 1 (3.78) Substituting these values in the continuity equations, one can get from the positive ion equation iEx dx p x

92 which becomes ~ = g - P no (3 79) Similarly for the negative ions, /'dnn 2 -tp4 ) a-t) p n2 (3.80) Adding Eqs. (3.79) and (3.8o0), and by the aid of Eq. (3.78), one gets 0 = (g+a) - 2 p no or g' = g (_+9) = p no, (3.81) where g' is the average rate of negative-ion production and rl = a/g, the negative-ion-formation factor. The net ion-current density, JP, is thus given by J = 2cqe x Ex o 2 (3.82) from which the minimum field is E' J' (3.83) XO 2qne (no With Eq. (3.81), this could be written as o 2 /qe (3.84) The above equation has the same form as the corresponding one, (3.57), with J' and g' replacing J and g, respectively. As in Section 3.4, it is assumed that there is no recombination in a layer of thickness X1 from the positive plate and one of 2 from the

93 negative plate (Fig. 3.12). Then the number of positive ions leaving the layer X1 per unit area per second is J'/2qe. But the region furnishes a maximum number of positive ions gkl per unit area in one second; thus J' 1= __ *(3.85) 2qeg In this region Eqs. (3.71), (3.72), and (3.73) become =x e (np - nn - ne) (3.86) dx eo dx x ( pnpEx) = g (3.87) - x (d nEx) = a (3.88) Since g and a are constant under steady-state conditions, integration of Eq. (3.87) with np= 0 and x = O, gives PJPE = gx. (3.89) Similarly, for negative ions, nnEx = J - ax. (3.90) qe From Eqs. (3.86), (3.87), and (3.88), one gets: 2 dEx 2e [2g'x (91) dx eco Ce [ Integration gives 2 2q r 2 = e'xa_ J'x 0+ C2, (3.92) wEr C iacContto tge v where C2 is aq constant of integration hose value is determined by the

94 *P ns Fig 3.12. D istrib>ition of net ion density in a planar gauge.

boundary conditions when x = = J'/(2qeg'), the field Ex = E'. Thus C2 E12 (1+1), 0X where:a. = -~o (l+n) (5-n) with ao = bei CoP as before. Let us now consider the situation at the negative plate, i.e., between x = so-X2 and x = so, with X2 = J'/2qa. Here again recombination is negligible; therefore Eqs. (3.86), (3.87), and (3.88) are valid in this region. Since the negative ion density vanishes due to repulsion at the negative plate, nn = 0 at x = so. Thus integration of Eq. (3.88) gives, for negative ions, knnEx = - a(x-so) ~ (3~93) Similarly, for positive ions PfnpEx = g(x-so) + JL (3.94) qe Substituting in (3.86), and integrating, Ex (x-s) + (x-so) + C3, (3.95) where C3 is to be determined from the condition that Ex = Elo at x = So-A2. Thus C3 = E'2 (1+ 2)

96 where The voltage drop across the layer next to the positive electrode is V1 -f Ex dx (3 96) 0 Substituting the value of Ex given by (3.95), V1 = f alx2 + bx + c dx, (3.97) 0 whe re Ci a, = (l+n) Eokt 2J' bl = _ and cz = E'2 (1+x) 46 Using Dwight's Tables of Integrals, one can write the value of the voltage drop in this layer as 4al x - Et' V1 xo 2qeg ed 2 2Y ~j

97 E'p XO qekt 2g(1+r) E = E 1+ and from (3.91) __2\ 2J' X0= _ \dXx=o Ck and dEx - Substitution of these values in the above expression for V1 and then reducing gives Eot~ (,_2 11 -- (l-~)2 - (1- in - 2 (L1-1 + 2n (3.99) It may be interesting to note that.when;B- =l, 51 becomes Po, and thus Eq. (3.99) reduces'to, Eq. (:359), the corresponding one forthe case where complete' attachment was assumed, viz., r = 1. Similarly, the voltage drop in the layer next to the negative plate could be written in the form ___ __- 1-71- 1 1 V2 - 2 [ + 1 2n 1 + o1 2 P-,o (3.100) This again reduces to (3.60) when q = 1. The potential drop in the middle region is determined by

98 Vo f _ 0/2 Ex dx which gives V0 = Eo (So-X1-x2) ~ (3101) The total voltage drop between the two plates is simply the sum of all three expressions above. Therefore, adding them up and simplifying, one gets V = A'J'2 + B'J' (3.102) where Al ='_ Bt 2qevM g(!l+) J = qgso e saturation current density, and 1(orl) 1 = 2 /yv+ +/- -3 1 0 (1 _l)2 1PO(a-t + In 2 1 (1 ( ) Solving Eqo (3.102) for the ionic current density, J', gives 2A' A'

99 But B' Jm(l+l) 2A' 2*(Po,rl) v _ bJ2 (l+B) C2(l+ ) Al 4 (O and b = 4v so pI g Substituting in (3.103) for B'/2A' and V/A' gives.: = Jm(l+ol) P1 +2bj(..,.) 22(-n,L 42(l+r) J This could also be written bJm 4 (1/2) (1+r) J' =: -- _ *. (3.o4) 1 + A/i + bI(:0n) 2/(l+rj) But J' = J - Je J - Jm(:l") Hence the total output current will be: J = JmL + i ~ \22/(ltf) + (l-r-)J ~ (3.105) + 1+ b+ (or)4a/(~+') Inspection of the above equation reveals its similarity to the corresponding one, Eq. (3.65), Section 3.4.2, for complete attachment, although the former is modified by the presence of the negative -ion-formation factor, rl. Assuming different values of rl will naturally produce different char

100 acteristics; this is shown in Fig~ 3.139 where the characteristic curve is calculated for air assuming complete attachment (the solid line), and partial attachment (the broken line) (see next section); the corresponding experimental curve is also shown. 3.6.3~ Determination of the Negative-Ion-Formation Factor.-It is necessary to find a means to evaluate r As stated in Section 3.3, the electron density, ne, is governed by the continuity equation (3.22), viz., 6ne 1 at =- (g-a-re) + - div Je Under the same conditions assumed there, the above equation for a planar configuration becomes dne e Eo d + (g-a) = 0 (3 106) where Eo is the average electric field intensity, value V/so, with so and V as the distance and voltage applied between the two plates, respectively. The rate of electron attachment, a, depends on the collision frequency between electrons and neutral gas molecules, Ze, the electron number density, ne, and the probability of attachment, be. Thus the negative ions are formed at the rate of a = be n (3107) e e e (5o107) where Ce 3qe e le 4me le On substituting in Eq. (3.106), one can determine the distribution of electron density by solving the following equation

101 10 Planer Guage V- 50 volts S= 2 cms. T = 00~ K (A ir) ~~3a.K - z z w -9 r10 z cO o z 0 W os w o -_ _ _ _ _ /___ 0 0 /-O- -0 — Experimental curve Theoretical (complete attachment) -.... — Theoretical (variable attachment) -I0 10 - 10 10 2 103 PRESSURE IN MILLIBARS Fig. 3.13. Correlation between experimental and modified theoretical curves, assuming variable electron attachment.

102 dne gso dx + = 0 (3 0io8) dx v where s z 0 e e 1eV' If: g is uniform and assimi-g no leCtO:ns near the cathode, i' = O= when x = so the. itegration o0 Eq. (' 108) gives n.e =! e o o (3.109) The average electron -n. ens-ity,,'ne is Ssitne - + K A~- V (i ( teai o) ShlbsLtituting in Eq (35107) gives tihe average rate of negative ion formation a.g (l e 0j(3.111) Therefore, the attachmenr.t factor, = a/g, will'be given by 1= % ( e e),3 (3J.12) where 4w~e V Fo -reasons that willb be d.iscussed in Section 4o5.6 of the next chapter, Bloch and Brad.bury s theoretical values of be were utilized in evaluating y above. The ellectrlon mobility, ee was computed from the approximate relat~ion,' Eio (2~16), based on Compton's derivation~ 3 e6 oAi Interp'retation of Somei Nume3r ical Exampleso -! n calculating

103 the i-P curves, as determined by Eq. (3.105), a method parallel to that adopted in Section 3.5 will be followed. Some of the parameters can be used here with the same values as employed there; then the earlier values are re-usable in Eq. (3.105). On the other hand, the negative-ionformation factor, ~, is a dimensionless parameter depending on two new quantities: the probability of attachment, be, and the electronic mobility, e'e Both be and te are functions of the ratio of the field strength and pressure, E/P. Neither are the rate of ionization, g, and consequently the saturation current, Jm = qegso, the same as before, because in a mixture of gases the effective rate of ionization is the sum of the partial ionizations of the component gases, i.e., N gmix= Zgkfk, (3.114) k where gk and fk are, respectively, the rate of ionization and molar fraction of the kth gas present in a mixture of N gases. Let us first consider a mixture of nitrogen and oxygen. The average probability of attachment becomes e= (X ee02 )~ (35115) where (f/~e)0 is the molar fraction of oxygen divided by the corresponding electron mean free path and (f/e)Ni is the same quantity for nitrogen. But (f)02 + (f)N2 = 1; hence the above attachment probability can be expressed by

104 I "- (f m -e (b~e)0 N ( (3e)116 The experimental values for Sie)o are given in Bradbury's36 data for oxygen as a function. of f/P (Fig. 2.12). The molar fraction, (f)Na, is considered constant for a given rmisxtu-e th.roughout the pressure range. Simila~rly, the effective rate of ionization is given by -ixs (g- (gf)N + (gf) 02 which can be Written 4mlx -g) [ (g)Ne | (3-117) The above relation is empirically modified by Bortner and Hurst 7 in terms of the energy required to produce an ion pair, Wi, in the ith component gas o It can be written for a gas mixture as: I02.. 2 W i~x =A 1 F]\T (2( W )0 (3018) where A is a constant whose value depends on the temperature and density of the gas used as well as on the'ype and the average energy of the ionizing particles W02 and W1Ta are the erlergies required to produce an ion pair in pure oxygen and nitrogen. respectively P1'z is the effective molar fraction of nitrogen, with PN12 and Po2 as the partial pressures of nitrogen and oxygen, whereas a is a constant related to

105 the stopping powers of the gases present; it has been determined experi47 mentally for different gas mixtures. It has the value 1.06 for N2 - 02 mixtures. Using the above relations in conjunction with Eq. (3.105), it was possible to determine the i-P curves for any mixture of oxygen and nitrogen. Some calculated examples are shown in Fig. 3.14. Striking new results appearing in this theoretical prediction are that: (a) only one part in a hundred of oxygen is sufficient to upset the linearity of the i-P relation at high pressures; (b) as the oxygen content is increased in proportion, the nonlinear portion sinks rapidly until it reaches a minimum value at which the trend is reversed and a gradual increase in output sets in with higher oxygen proportions; and (c) in the linear portion where saturation prevails, the current always increases with increasing proportions of oxygen.

o106 10-8 Planar gouge V= 50v. SO= 3 cm S. T = 300 OK f(Air) /%0_-99%N U) /oo~ o,_ ~~ r I I I i I i i i i ~-i ~~~5% 02 -95% NE w w,oo~.~~~~~~ o~ -~ /. ~,z II0 I00 i00 o /002-0%N02 ___ PRESSURE1 II MILLIBAR Fig, 3.14. Theoretical i-P curves for several mixtures of nitrogen and oxygen —variable attachment. 50% 02 -50%5 02 NN 0~~~~~~~~~~~%0 w -j -J _ 0 -20 % 02 -80 % N2e - T10 __ _ _ _ _ _ __ _ _ PRESSURE IN MILLIBARS Fig. j5.14. Theoretical i-P curves for several mtixtures of nitrogen and oxygen-variable attaclmient.

CHAPTER IV EXPERIIMENTAL CONSIDERATIONS 4.1. INTRODUCTION The scope of experimental work which might be carried out on radioactive ionization gauges is almost unlimited. Examples of the many areas in which laboratory investigations could be made are: 1. The effect of the different configurations on the gauge characteristics. 2. The size of and the material used in the chamber's environmental envelope and electrodes. 3. The strength and type of the ionizing source. 4. Limitations imposed on the value of collecting voltages. 5. The effect of temperature on the rates of ionization, recombination, or electron attachment. 6. The hysteresis phenomenon, that is, failing of the risingdensity curve to follow the immediately preceding fallingdensity curve. 7. Dark current. In this work, however, we shall restrict ourselves to the study of only a few of the aspects which appear more important as needed, under the circumstances encountered in the technique of performing pressure measurements at high altitudes. 107

108 The construction and characteristics of a commercially known radioactive ionization gauge is briefly described, followed by a short discussion of the dark-current phenomenon. The major part of this chapter is devoted to investigating and comparing with theoretical prediction some of the probable causes of the hysteresis phenomenon. A number of other aspects are also discussed; a specially made planar radioactive ionization gauge was used in this work. Finally, as a result of the experience gained and better understanding of the different ionic processes in radioactive ionization gauges, two different types of gauge designs are described. In one of them, with radium as the ionizing source, the hysteresis is largely eliminated, whereas in the second, with a tritium source, the sensitivty of the gauge at low pressures is considerably increased while the early tendency toward a constant dark current is successfully pushed to a lower density. 4.2. CHARACTERISTICS OF NRC RADIOACTIVE IONIZATION GAUGE The early work of this investigation was carried out using a NRC type 510 gauge.5 This radioactive gauge has been known commercially as the "Alphatron,T?* since the particles used there for ionization are alphas emitted from a radioactive material. The construction of the chamber of this particular model is schematically shown in Fig. 4.1,** It consists of a radioactive source (B), an ion collector (C), and an ion*Copyright, National Research Corporationo **Courtesy of National Research Corpoation.

109 A/u (A) electrode, (B) radium source, (C) collector electrode, (D) feedthrough insulator.

110 ization chamber (A) which acts as positive electrode in the polarizing field. Ti-he radioactive source consists of a small plate 1 cm2, one side of which is the active area made of a gold-radium alloy containing approximately 0.2 mg of radium. The plate is electroplated with a thin film of nickel which acts as a seal and thus enables retention of the first by-product, radon gas, and its subsequent decay products. The ion collector electrode (C) is supported by the high-leakage-resistance feed-through insulator (D) and is connected to the electrometer tube of a d-c amplifier outside the vacuum chamber. A four-wire construction is used to shorten the ion collection distances and so to prevent excessive ion recombinations and consequent loss of output and linearity at high pressures. The ionization chamber (A) is a cylinder closed at both ends having holes at each end for gas passage and for introduction of the collector electrode (C). Electrical connection and mechanical support are provided by three metal-to-glass seals soft-soldered to the vacuum-chamber bulkhead. The chamber is maintained at a positive potential to provide an electric field driving positive ions in the direction of electrode (C). A 45-volt battery is used between the electrode (A) and ground to create the necessary electric field for ion collection. A Kiethley* electrometer was used to measure the output (ionization) current, and a typical i-P characteristic is shown in Fig. 4.2. The re*Kiethley electrometer model 200, Kiethley Instruments, Cleveland, Ohio.

1CF7 NRC 5/0 gauge Temp. =2990K (Air) C) w aCr w 0Z IZ a: 0 z 0 N 0 la-1 0 w i-j1 1010': 10-2 lo-, 100 lo, 102 103 ~~~~~~~~~~i03 PRESSURE IN MILLIBARS Fig. 4.2. Typical i-P characteristic of NRC No. 510 radioactive ionization gauge-room temperature 270C.

112 sults are discussed in the following sections. The significant items are the departure from linearity at low as well as at high densities, and the slow variations, referred to as hysteresis, at high densities. As shown in Fig. 4.2, the linear range lies between 10 2 and about 30 msL. The departure from linearity at the upper end of the pressure range is mainly due to recombination of ions an the fashion explained in Chapters II and III. -2 The nonlinearity at the low portion of pressures, below 10- mb, is attributable to secondary electron emission from the collector occurring as a result of the impacts of the high-energy alpha particles and X -ray radiation emitted from the gauge walls, and results in what is called dark current. 4.3. DARK CURRENT As mentioned above, the current-pressure characteristic of a radioactive ionization gauge levels off at very low pressures, approaching a particular low value known as the dark current. This was illustrated earlier in Fig. 1.4 and is shown in Fig. 4.2. As the density decreases, the ionization current correspondingly decreases until the dark current becomes a larger and larger fraction of the total current and finally masks the ionization current. This unwanted -effect, appearing as a constant current in the gauge output at low pressures, is believed to be due too (a) X-rays emitted by the electrodes and the chamber walls as

113 a result of the impact of alpha or beta particles upon them, and (b) the considerable number of secondary electrons emitted as a result of bombardment by the source particles of the collecting electrode. When an alpha or beta particle hits a metal surface, part of its energy is expended in ejecting a few secondary electrons, mostly from the outer regions of the atoms. The balance is absorbed in exciting the electrons of the inner shells, with the subsequent production of X-rays. It has been found experimentally that the magnitude of the dark current depends upon the intensity of the impinging corpuscular and electromagnetic radiations which undergo no appreciable change under pres-2 sures lower than aboutlO' mb. In general, the greater the number of particles reaching the positive-ion collector, the greater the magnitude of the dark current. It was thus possible to lower the value of the dark current and consequently to extend the linear portion of the i-P characteristic to lower densities by, in effect, reducing the number of direct impacts of the ionizing particles on the collector. This is illustrated in Fig. 4.3, which shows the i-P characteristics of three gauges, identical in every respect except for the shape of the positiveion collector, which is a plane disc in one case and a thin wire in the other two. It is interesting to note that the secondary emission exists throughout the pressure range, but is of significance only at low pressures, since at high pressures its value is very small compared to the corre

C0l 9 z 0 Disc 10ol0ec0or0 10 2- wFi.45rChneefd rccrrn vle ih oleto hae

1L5 sponding ionization current. 4.4. THE HYSTERESIS PHENOMENON At high density, in addition to departure from linearity, the NRC as well as other radioactive ionization gauges exhibit an undesirable phenomenon: If one observes the current as the pressure is permitted to decrease from relatively high density to some arbitrary value and then permitted to increase to the original pressure, the two currentpressure curves observed may not coincide. This deviation occurs mainly in the nonlinear portion at the high-density end, as illustrated in Fig. 4.2 for the NRC gauge. 4.4.1. Possible Causes of Hysteresis. —The following were considered as the possible major causes of hysteresis: 1. Time variation in source activity. 2. The effect of field configuration. 3. Change in temperature, with resulting variations in the coefficients of the ionization, attachment and recombination processes. 4. Slow change in concentration of one or more of the minor constituents of the gas, having attachment properties different from those of the major constituent. These factors were investigated, either separately or along with other experiments, through the course of the experimental part of -this

116 research, Various aspects of the results will be discussed in turn. 44,~2. Verification of the Constancy of Source Activity. -To examine the constancy of the source activity, the pressure inside the gauge was maintained at about 10-4 mb for about 72 hours and then abruptly increased to about 1000 nrb; concurrently, the collected current was observed until it attained a steady value. This procedure was repeated for different final pressures, all lower than atmospheric. Typical results of this experirrent are shown in Fig. 4.~4 From these curves one notices that the current first decreases until it reaches a minimum after about an hour, and then slowly increases to reach a final value only slightly higher than the minimum. It should be noted that the greatest dip in current happened at a pressure roughly equivalent to the pressure at which the peak of the i-P characteristic occurs. It was then speculated that the variation of current under the above conditions could be attributed to some kind of instability of the source activity, For example, the radium source might not remain in a state of equilibrium with the other decay products as a result of escape of radon gas, and hence the subsequent radioactive daughter-products. A mathematical analysis of the source strength as an alpha emitter was then developed, taking into account the various levels of- alpha particle energy involved and assuming an exponential leak (see Appendix). Although the general shape of the calculated curves bears some similarity to the experimental ones (Fig, A.2),9 the relative dip in the calculated ones is comparatively much smaller and sometimes negligible, indicating

117 Temp. 298 OK 5 Final pressure = 500 mb 213mb Cr z 980 mb Id Cr 2 2 x H I~~~~~~~~ I " I I I50 mb 0 Co 1 2 3 4 5 6 TIME IN HOURS Fig. 4.4. Variation of output current with time at given constant pressure and temperature. Before zero time, the pressure was 10-4 mb; after zero time, the final pressure was as indicated.

118 fair constancy of the source activityo Another indication of constancy of source activity was obtained by means of a specially built scintillation apparatus. The source and main components of the device are shown in Fig. 4.o5 The radium source was mounted on a monel frame inside a glass tube facing a tmica window (about 2.0 mg/cm2), which served as a vacuiu!m-tig-t seal, wh:`le being sufficiently transparent for most alpha particles to pass. The external sid.e of the mica seal faced the window of a DuMont 6467 photomultiplier tube. An appropriate layer of ZnS~Ag phosphor (about 8 mg/cm2) was deposited on the outer surface of the photocathode according to the following procedure. The activated zinc sulphide powder was dispersed in distilled water and poured into a settling chamber made from a piece of glass tubing fitted over the face of the photomultiplier with a rubber gasket to prevent leakage. Suitable amounts of: arium acetate and potassium silicate were also added to give an evenly dispersed and highly adherent film. The phosphor was allowed to settle, then most of the water and unused potassium silicate solution were slowly removed with a pipette, and the remainer was permitted to evaporate into the atmosphere. The minimum practical distance between the source and the phosphor film was determined (a) to protect the phosphor film from destruction by the high-energy-particle bombardment, and (b) to minimize dispersion of the alpha particles. The glass tube and the photomultiplier were enclosed in a light-tight magnetic shield. The required voltages at the phototube dynodes were so

TO POWER SUPPLY a INDICATING METER | \ | T l Wa s GG TO VACUUM SYSTEM S - RADIOACTIVE SOURCE G - GLASS TUBING M - MICA WINDOW (2.0mg/cm2) R - BLACK FOAM RUBBER F - PHOSPHOR FILM (8.0mg/cm2) 0 - OPAQUE COATING T - PHOTOMULTIPLIER (DU MONT 6467) Fig. 4.5. Scintillation apparatus.

120 adjusted that the average anode output current was limited to about 60 iamp, a value which is far below the maximum rating of the phototube (5 ma). This low value is advisable to assure adequate stability conditions in the performance of the phototube as far as multiplication factor is concerned. The dynode voltages were supplied by a convenient power supply, illustrated in Fig. 416, from which voltages up to 2400 volts were available. Owing to the fluorescent property ofZnSoAg material, some of the energy absorbed from the incident particles, alphas in this case, is reemitted as faint bluish light (scintillations) quantitatively proportional to the energy lost by the incident radiation, ioe., proportional to the number of incident particles, The section containing the radium source was connected to the vacuum system to determine any variation with pressure of the activity of the source as an alpha emitter. The system was pumped out to about 10-3 rob, then maintained at this pressure for about 72 hours during which the activity, as indicated by the scintillation apparatus, was checked and recorded. Air was then admitted into the system, increasing the pressure abruptly to about 400 mb, or atmospheric pressure (1013 mb), where it was held constant for about eight hours. The source activity was again recorded every fifteen monuteso This procedure was repeated several times while keeping the source for longer and longer periods under vacuum. A summary of the results obtained is shown in Fig. 4.7~ It is

121 1400 V. + O- 1.0 40 ma An ee 40~~mo + k D-0 I R 10 D-9 R9 D-8 R8 D-7 R7 D-6 R 6 D-5 R5 D-4 R4 D- 3 R3 D-2 R2 CONSTANT HIGH D-l I 15 V. VOLTAGE VOLTAGE 60~HR 60 TRANSFORMER SUPPLY I PHOTOCATHODE RI - 6000 ohms, 20 watts R2 -R II- 3000 ohms, 10 watts Fig. 4.6. Photomultiplier circuit diagram.

0.8 Under t ih' vacuum - 6 0.7, I0-3mb I E I H I 0.6 o c~ 0.5 _ 0.4 CL -JF~~~~~~~~~~~0 0 0 Final press. 4 00 mbs. > ~~~~~~0. ~~~30 1/ A A Final press. /0/3 mbs:20.3 0 H — 0 r-. a. 0.2 cIO.2 0.1 tI i I Ii 0 1 2 3 4 5 6 7 8 9 72 hours or more. ~-I~~ I ~~TIME IN HOURS Fig. 4-7. Observed scintillation data for radium source activity.

123 clear from these data that there was no appreciable change in the source activity with pressure as indicated by the constancy of the anode current of the photomultiplier tube. Thus it was concluded that the hysteresis in the i-P curves at high densities was not due to a change in the source intensity. 4.4~,3. Effect of Electric Field on Hysteresis.-Interesting conclusions were drawn from consideration of the distribution of the electric field inside the NRC model 510 radioactive ionization gauge. The field between the positive-ion collector and the wall is quite nonuniform (see Fig. 4.8*)a The effective collection of positive ions is confined largely to the small volumes around the four collectors, outside the dashed circle where the field intensity is appreciable. On the:. other hand, the bulk of the ionization chamber lies in a region of considerably lower intensity (Fig. 4.9*')o Thus it is very hard to attain saturation current collection under the normal operating conditions where the potential differences between the positive-ion collectors and the chamber wall is around 40 volts. Electron attachment due to the presence of electronegative impurities and hence ion-ion recombinations are responsible for the deviation from the saturated values of collected currents. On applying a much higher voltage, about 500 volts for example, the effective collection volume is considerably increased. Though the field *The writer washes to thank Professor Ao De Moore of the Department of Electrical Engineering of The University of Michigan for his assistance in mapping the above fielda

124 Fig. 4.8. Electric field map of NRC 510 gauge.

125 POSITIVE ION COLLECTOR WEAK FIELD i''REGION ~o~~~~~~~~~ I ~~`30 POTENTIAL ALONG PATH BETWEEN WIRES n/A,iiI I'/I I U, H~~~~~~~~~~~~~~!111~~~~~~~~~~~~~~~~~~~~d 0 20 >~~~~~~~~~~~~ z POTENTIAL ALONG cr PATH THROUGH W -i -~A \' I / I WIRES z~~~~~~~~~~~~ I I I 0 1, a. Fig. 4.9. Potential distribution in an INRC 510 gauge.

126 is still nonuniform, it was possible in this manner to extend the linearity of the i-P characteristic of the NRC gauge up to about 400 mb, i-e., ten times its normal range of pressure measurement. It was also noticed that the new curve became linear and reproducible in a region where nonlinearity and hysteresis once prevailed under lower electrode voltages (see Fig. 4.10). This result leads to the belief that the lack of reproducibility in the upper nonlinear region is due to a variation in the rate of electron attachment. The other possible causes of the hysteresis in radioactive ionization gauges were studied using a laboratory-built planar gauge and will be explained in the next section. 4.5. EXPERIMENTAL RADIOACTIVE IONIZATION GAUGE 4i.5.1. Constructional Detailso -The constructional details of the experimental gauge were chosen primarily to permit comparison of its performance with expectations on the basis of the theory presented above. However, some details of the design were chosen partly with a view to other considerations, among them ease of transferring what was learned to an instrument for use in rockets. The design chosen employed two parallel stainless-steel plates arranged so that the separation between them could be adjusted to any value between 5 and 40 mm in 5-rm steps (see Fig. 4,11). The guard rings were used to obtain an essentially uniform electric field intensity in the central zone which contained the sensitive volume of the gauge. The

127 10-6 - 10 -7! CO LECTO R VOLTAGE =5 401 Cn Lb~~~~~~~~~~~~~~~~1 Iii 0 0' Z~ sClo-II 4;;; g A;.1 _ _ --'I,<'111'1 1 1 11 1 031 I0- I 10 -.. )"~ ~ ~ ~ ~~~~~~~~~~~~~. O 1 0 -9R fe H 10 10 ff 10 1 1111 PRESSURE IN M COLLEBAR o F 4I0 I of Fi ls and h1strs 1 v Fio g. EE10E Re1=tio frtobntion 101s 1n hyseeis usin~~~~~~~~~~~~- LTAGEr:50et vo..... = = = r 4 I I ==~~~~~~~~I I I Idw,II1.-I, -.-. _~ ~ ~ ~ ~~~l =/.=____ lii 5ilt us ingnge olco r ll/e

1.28 I I AMPLIFIER o Scale 1.0 t M) I P I X INLET INCH TO MAI N VACUUM SYSTEM Fig. 4.11. Experimental radioactive ionization pressure gauge. (1) brass bell jar, (2) glass spacers, (3) metal support, (4) high potential electrode, (5) grounded guard electrode, (6) radium source, (7) collecting electrode, (8) supporting rod, (9) and (10) glass-tube insulators, (11) bottom plate, (12) and (18) bellows sealed vacuum valves, (13) Giannini pressure transducer, (14) kovar glass seal, (15) leads to thermistor, (16) lead to high potential electrode, (17) O-ring seal.

129 gas between the plates was ionized by alpha particles emitted from a radium source of about 166 microgram alpha-equivalent emission (166 microcurie). This source acted as a part of the high potential electrode to collect the electrons or negative ions that reached that plate. This assembly was housed under a brass bell jar fastened to the base plate and kept vacuum tight by an O-ring gasket. The inlet and outlet parts, in the base plate, were controlled by two sealed-bellow valves. The pressure inside the jar was determined by a calibrated aneroid pressure transducer with a range of from 0-1300 mb. The temperature of the gas between the plates was indicated by a glass-coated-bead thermistor having a relatively short thermal time constant (about two seconds). Two more thermistors, one at the inlet and the other at the outlet, were used to determine the temperatures of the admitted and pumped-out gas, respectively. All the electrical connections tothe elements inside the bell jar were made by means of a special commerically available hermetic metal-to-glass multiheader seal. 4K5~ 2. Effect of Plate Voltages on Output Current~ —Figure 4K12 is a chart of a typical set of data taken with the experimental device. The output current in general increases under higher voltages. The rate of increases however, is seen to vary for the different ranges of pressure. For the discussion of the results represented in Fig. 4013, one must consider three different distinct regions on the i-P characteristic These will be designated by high-, medium-, and low-pressure ranges~ The downward (to the right) bend in the high-pressure region of the

130 lo- U,, 300 mb. 82 mb. 10-8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0r7) C-) E1i0-",'-I~ -'-'- -:' -- _:., w 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~II w~~~ a 1610 t~~~~~~~~~~~~~bd ~ ~ ~ ~ ~ ~ ~ ~ ~ mm P~ ~ ~ ~ ~~ E-'. —-: — I- "'''''"'''''']''IStt~it-ii-lb 4-~1 i 1I-Uk~l iL0.00 Mb. 0-1 10 -~~~~~~~~~~~~~~~~~~~1. b 0 10 20 30 40 50 60 70 80 90 100 110 PLATE VOLTAGE Fig. 4.12. Observed collected currents as function of plate voltage for different constant pressures at room temiperature (270C) -planar gauge.

131 ow- pressure Medium-pressure High-pressure Fo-. region region regon to-t ~ ~ ~ ~ ~ ~ ~~~=0 — i _ I~~~~~~~~ V.=20V 10-9lf /0% ~~n' I I I I I I I i I I ~~~~~I I I b' I=~ I. C,) w w r - - _ I __300V.w' 0. V=200 v z (10 z w Z C - __/ 0 v.0 V=50 v - _ -___ - V~~~~~~~~=20v V,~~~~~~~~~~~~XO Planar gouge Spocing = 0.5 cm Temp. = 298 OK 621 1251 a 2 5 2 S 1 a a 2 a62 5 K 10-3 10-2 Io-' 100 101 102 103 PRESSURE IN mb. Fig. )-h15. Variation of collected ion current with pressure at room temperature (2500) for different electrode voltages in a planar radioactive ionization gauge.

132 i-P characteristic is mainly due to the loss of oppositely charged ions by recombination~ The increase in the intensity of the electric field at constant density accelerates the sweeping action of the ions to the electrodes, thus reducing the average transit time of ions between the electrodes, This in turn decreases the duration of encounters between the positive and negative ions while moving in opposite directions, thus reducing the chance of recombination and hence more ion collection as anticipated in Chapter III (Figo 3.6). Therefore the 300-volt curve remains almost linear in this region, whereas recombination causes the 20-volt curve to bend. In the medium range the i-P relation is usually linear. In this range the ion density is relatively small, so that recombination effects become unimportant and thus all the ion products are collected~ As the pressure goes down, the probability of electron attachment decreases, leaving some of the electras free, subject to the electric field acceleration, When the kinetic energy gained by such electrons from the field becomes high enough to ionize the gas molecules as a result of inelastic collisions, a considerable increase in'the ionization occurs in addition to that due to irradiation by alpha particles. This phenomenon, known as gas amplification, is undesirable for the intended use, and normally is prevented from occurring by maintaining a sufficiently low field strength. This particular type of ionization is observed to increase until it reaches a maximum at a certain lower value of pressure, and then declines as the pressure continues to drop.

133 It is interesting to note that the i-P characteristic exhibits some hysteresis (in the sense referred to in Section 1.3) under these conditions even after hysteresis is no longer apparent in the linear part of this medium region. This hysteresis is also believed to be a result of the variation in the environmental conditions which results in the attachment of some of the electronic to gas molecules, thus terminating the life of a free electron and consequently its ability to act as an ionizing agent. This change might take the form of the appearance of a small quantity of a kind of gas favorable to electron attachment. In this gas amplification region, the ratio of the resulting current, i, to the saturation value, io, similar to Geballe's equation,4850 will be given as (-) (L 0 o>-s 1 ] (41) Here aO is the first Townsend coefficient which gives the number of new electrons created by a single electron per unit distance of advance in the field direction; no0 the rate at which an electron may attach to make a negative ion per unit length advance in the field direction; and So, the separation between the parallel plateso The saturation current, io0 is measurable by use of a low-voltage i-P curve. Here aO and %o are functions of the field-to-pressure ratio, E/P, for the kinds of gases involved~ The observations at the lower part of the medium-pressure range

134 give additional evidence in support of the theory presented in Chapter III, which states that the hysteresis phenomenon in radioactive ionization gages may be attributed to the change in the rate of electron attachment, as a result of alteration of environment. This change may be in the gas composition, as, for example, in forming ozone, a highly electronegative gas, between times of taking the two curves. If the voltage is continually increased, the number of electrons released by collisions increases as well as their energies until electron avalanches may occur, resulting in a break-down discharge between the plates. This was occasionally observed in the experimentation. Finally, at the low-pressure range, better known as the dark-current region, the output current levels off and stays constant regardless of any further decrease in pressure. This residual current is found to be a function of the area of the collector and is due to some action taking place at its surface, leading to the emission of electrons from it, The residual current starts off, due to the unbalance in the surface emission, with a negative value and then rises as the field is increased between 0 and 2.5 volts per cm above which the current tends toward a maximum (see Fig. 4.14). One may thus conclude that a substantial part of the dark current is caused by electrons detached from the electrodes or the insulation wall by impact thereon of alpha particles of X-rays in the manner discussed in Section 4.3. 4.5.3. Determination of a_/P vs. EP Curves. —The marked rise of the curves above the saturation value of Fig. 4o13 renders a useful

135 IO Z W r 6 v,P/nar gouge 0 y 4 rSpacing/ cm. Cr sPressure =1/04mb. 2o~~~~~ Lfi Source (Ro)- /66fgm E.aE. 2 -I -2 0 1 2 3 4 5 6 7 8 9 10 PLAT E VOLTAGE Fig. 4.14. Variation of dark current with plate voltage.

136 basis for determining one of the most important relations in ionization by collision, viz,) the ionization coefficient, a/P, as a function of E/P. Figure 4.15 shows a plot of a typical ionization curve U/P versus E/P, as calculated by means of (4.1) from the experimental results charted in Fig. 4.13, assuming ~o to be negligible. It should be noted here that the above c/P vs. E/P curve satisfies all the points in the ionization-by-collision region regardless of their position with respect to the peak of of the voltage used. The loss of some of the electrons in attachment process, however, results in a reduction on the measured values of the ionization coefficient, O, which assumes a new value' = a -o,, with oas the attachment coefficient; this is represented by the broken line in Fig. 4.150 4o5e4. Effect of Temperature on Gauge Output o-The review in Chapter II covered the main processes that would take place in a radioactive ionization gauge. Among the many important properties discussed there was the temperature dependence of the different processes. Thus one would naturally expect the ion collection currents to vary as a result of temperature variation. In a vacuum system a momentary rise of drop in the gas temperature occurs adiabatically due to a pressure change. Differences in the gas temperature up to + 40~C were observed in many instances when the pressure was suddenly changed. The magnitude of these differences depended on the gauge volume, the initial pressure, and of course on the rate at which the pressure was varied.

137 0 10 - - (Air) 08 - Erroneous data due to excessive o7 // 0 steepness of i-P 7 /0 E 6/ E o 5 =5 Townsend' s first coeff (m'/) P Pressure (mb) 0iP 4 Iz / E Field intensity (v/m) 0 0 200 400 600 800 1000 E x102 VOLT/m'mb. Fig. 4.15. Ionization coefficient (a/P) as a function of the electric field (E/P) in air as derived from Fig. 4.13.

138 In dynamic tests where the current measurements were made as the pressure was continually changing, the output current was found to respond to the manner in which the pressure was changed in the system~ For example, the recombination hump of the i-P characteristic was observed to be high during pump-out period (adiabatic drop in temperature), and vice versa. It was possible then to reduce or even sometimes to eliminate the difference between the two current peaks by reducing the pumping speed and consequently the adiabatic changes in temperature~ This is illustrated in Fig~ 4.16, where the output current and the corresponding gas temperature were recorded for three different pumping speeds. It can be noticed from these results that the large difference occurred when the temperature change was greatest, and diminished for small temperature variations The theoreticalstuiy of the expected effect of temperature on the electron attachment and ion recombination would, however, lead to results quite contrary to those experimentally observedo Thus for lower temperatures, one expects more electron attachment, and thus more recombination of ions, ioeo. less collected ion current. Therefore, the observed change could be exlamned by assuming that the primary ionization of a particular gas is not only a function of the density but also of the temperature. The temperature in this test, however, did not stay constant during each cycle of the tests So to examine this unexpected phenomenon, two more experiments were carried out~ In the first test sequence, the temperature was held constant while changing the density, whereas in the

139 PRESS. DECREASING /'N- PRESS. INCREASING - - __ ___ _- ___ _ -+ _t_ — l Case (a). Full Pumping Speed 0 20 - 40 0- 60 80 100 120 TME- SEC Rm Temr - -- - _ C — - -PA,C =I000mb + 1 - TIME - — t - EC Rm Temp Fig. 4.16. Change of output current and gas temperature with time for various pumping speeds.1000 mb PI I mb -t-o —t —2po2~-420 ~- 40 80.o 120 1240SEC Rm Temp..... PAX = I000 mb PJ r I mb

40o second the density was kept constant while varying the temperature. The results of the first experiment are shown in Fig. 4.17 for two temperatures, 22~C and 52~C, by three pairs of i-P curves for three different plate voltages, Although the curve in the upper nonlinear end tends to straighten upward for higher temperatures in accordance with the theoretical predictions, as shown in Fig. 358, yet the i-P curve as a whole shifts downward as the gas temperature is increased. In the linear portion, the output current expectedly falls with increasing temperatureso This drop, however, is found to be more than would account for the corresponding change in gas density at a constant pressure. The additional decrease in the collected Saturation ion. current is attributed to a variation with temperature of the total ionization. This was shown in an experiment to be described next. 4o5.5o Variation of Primary Ionization with Temperature — In this experiment the density of the gas was maintained constant by confining the planar gauge in a bell jar whose inside temperature was regulated by heating or cooling the outside walls. The measurements were made at certain points on the linear portion of the i-P curve, where saturation of the collected ion current prevailed. Such a choice insured no detrimental contribution from recombination effects, thus leaving the rate of ion production as the predominant factor in the output. A typical curve, summarizing the experimental results, is shown in Figo 4o18. It is clear from this curve that the rate of ionization, as determined from the collected saturation ion cu rents, increases slowly with decreasing temper

lclv 10'7 Planar gauge V35 Spacing =/cm. (Air) V= 86 v. LLI) Uj w a. Cr Lii c0 z:: II1I t~ V= 2Ov. z w a: 10-8 ~_ -0,-"O 0 00 z~~~ 0~~~~~~~~~~~~~~~~~-0, 0 A —,-.0 o — o —- Temp.- 220 C + + = 520C I0-9 9_ 0 IO0 ro toe ~~~~~~~~~~~~~~~~~~~~~~~~~103 PRESSURE IN MILLIBARS Fig. 4.17. Effect of gas temperature on i-P characteristics under different plate voltages.

2. 1 Planar gauge u~ ~~~~~~~~~~~~ ~Spacing = 1cm. w |Voltage = 180 v. w 2.0 (Dry Air) o 0 z 1.8 21.6 L |!| o~~~~~~~~~~T M EAUR ERE EL/ l o density. Theoretical, forced H agreement aret 29~K 0 w _J -J 0' 1.7 1.6 I I! I I 2500 260 270 280 290 300 310 320 330 ~K TEMPERATURE IN DEGREES KELVIN Fig. 4.18. Variation of ionization with temperature under constant density. Theoretical curve (dotted) is fitted with experimental at 29~0K.

143 atures. This is in accord with'the observed rise in the peak value of the collected ion current during pump-out period of the previous dynamic test. In effect, the change of the primary ionization with temperature can be attributed to the influence of thermal agitation on the time of interaction between the ionizing particles and the gas molecules just before producing an ion pair. At constant density, the time of interaction, t, is approximately proportional to 1/cg and hence to 1/Nf, where cg is the thermal velocity of gas molecules and T, the corresponding temperature. Therefore, the relative change of ionization with temperature is given by Ag _ 1 AT (4.2) g 2 T provided the density of gas is maintained constant. The above relation (shown by a broken. line) was found in general agreement with the experimental results (Fig~ 4o18). The slight deviation (about in the ratio of 2 to 3) between -the slopes of the two lines, however, may be attributed to a probable variation in gas density due to outgassing or adsorption, which may take place) respectively, at high or low temperatures. The important thing is that the experimental curve has the same general shape. 5o1 -6 The i-P Characteristic in Mixture of GaseS o-It is of interest to compare the theoretical predictions of Section 3.6A4 with some of the experimental results concerning the electric conduction in mixtures of ionized gases. Here, too, only mixtures of nitrogen and oxygen were considered; nitrogen gas was obtained from liquid nitrogen, and tank oxygen was used for the other constituent. This series of experiments was

144 performed on the previously described planar gauge (Section 4o501)o The results obtained by using different proportions of the above two gases are represented in Fig. 419o Generally speaking, the experimental curves fall according to the respective gas proportions in the same order as their theoretical counterparts, appearing in Fig~ 3.14. However, the all-nitrogen curve shows a major dip in the collected ion current at pressures ranging from about 100 mb to 300 mb at the given electric field intensity. The other curves exhibit the same type of deviation, only to a lesser degree. A study of the E/P values in this range as represented in Fig. 4o19, or Fig. 4220 for different plate voltages, revealed some rather striking conclusions. The dip in the collected ion current falls in a range where the field-to-pressure ratios, E/P, have values such that the electron attachment passes through a maximum according to Bloch and Bradbury's theory (see Fig. 2.14)o The increase of the attachment rate combined with the low mobility of the resulting ions produce higher negative ion densities. Recombining with the positive ions, which are already there, the negative ions terminate their role as negative charge carriers and thus reduce the collected ion current. In Fig. 4o21 the corresponding i-P curves were recalculated by using Bradbury's experimental values of be, as given by Fig. 2.12, wherein at low E/P (low electron energies), the extrapolated values of be were used~ The new i-P curves fail to show the type of dip being discussed. Thus these results not only explain the observed dip in the i-P curves,

Planar gauge V=86 v. so; 2 cms. Temp. =299 ~K C,) w w a. z z if I. 10 19' 10 2 and oxygen at room temperature-planar aue. w __ w'< 0,/00 % 0% -,,r-a 50 50 + + /0 90 Q-o 0 ~1/00 10I02 I PRESSURE IN MILLIBARS Fig. 4.19. Experimental i-P curves for different mixtures of nitrogen and oxygen at room temperature-planar gauge.

146 10-7 Planar gauge 50 $350 v~ Spacing =Icm. Temp. =298BK (Air) 50v. v, ~~~~~~~~~~~~~~~~~~~~~20 &c w r -8 w~~~~~~~~~~~~~~~~~~~~~~~~~~~~~'IO —, w oa-_ o I z -— i All,4 o _ _ _ _ _ o I 1 t 1// I 1 ~ w ir I"0 w lo 0 io-IO 10' I0 10 10 PRESSURE IN MILLIBARS Fig. 4.20. Variation of recornbinatio l dip witli plate voltage.

I47 10-7 Planar gauge V=50 v. S5.6 3 Cms. /00% N ~ SooS cm.. Temp. =3000K 2_ o./% 0o2 5% O2 /00%(20 w w a0% 02 Z-5 % 02 z,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~01 z w C -8_ O I 0 z I00_ _ 0 o~~~~~~~~~~~~~N o 0, __________ __ _0 80 w 10-9 /00 0 At 0 I01 10213 PRESSURE IN MILLIBARS Fig. 4.21. Theoretical i-P curves for several mixtures of nitrogen and oxygen using Bradbury's experimental values of 6e'

148 but could also be taken as evidence in favor of Bloch and Bradbury1s theory of electron attachment in diatomic molecules.39 They confirm the steep rise of the attachment coefficient, 6e. at low energies and point to the existence of a peak value as predicted by the theory, and illustrated in Fig. 2.13, The general agreement between the theoretical results of Fig. 3.14 and the experimental of Fig. 4.19 also supports the validity of the approximate analysis presented in Chapter III. 4.6. DESCRIPTION OF TWO PROTOTYPE RADIOACTIVE IONIZATION GAUGES In an effort to realize a radioactive ionization pressure gauge suitable for rocket measurements, two different gauges were designed in the light of knowledge and experience gained in the studies reported above. In designing such a device, one must consider the operating limitations imposed by the rigors of a rocket flight. Consequently, these gauges should meet the following requirements: 1. Adequate output current for measurement by ordinary d-c electrometer 2. Linear response at least within the required range of measurements. 3. Short response time for transporting gas out of or into the gauge; the chamber volume should consequently be kept to a minimum. 4. Large area-to-volume ratio to facilitate adequate accommodation coefficient.

149 Consideration of the above requirements led to the design of two successfully used gauges. In one, alpha particles from radium alloy were the ionizing agents; in the other, beta particles from a tritium source were used. Each gauge is'briefly described below. 4o6.1o Radium Prototype Gauge — The first gauge, which was designed for the use of radium as the ionization source, had a basically planar configuration in which the source formed one of the plates (the positive electrode), and the ion collector, the other electrode. The main constructional details of this gauge are shown in Fig. 4.22o It was possible, with this arrangement, to achieve an almost linear response between 300 and 1 x 10 mb, pressures attained typically in the rocket experiment at altitudes of approximately 15 and 80 km. It is clear from Fig. 4.23 that the gauge is still useful at lower altitudes (higher densities), but with some sacrifice in the linearity and consequently a reduction of the output current due to the loss of some ions by recombination. The linearity of the resulting i-P characteristic could have been extended up to atmospheric pressure (- 1000 mb) by applying a higher voltage. This practice was not adopted on account of the gas amplification by electron collision which would occur at low pressures in the presence of high accelerating fields. The voltage between the plates, however, could have been varied so as to maintain a linear response throughout the range of interest~ However, the data below 10 km were not sufficiently importarnt to the experimental program to justify the

150 Scale 0 0.5 Inch GLASS- METAL SEALS BRASS CA RRa SOURCE PUMPING-OUT ION CHAMBER ~~ HOLE COLLECTING ELECTRODE HIGH POTENTIAL SOFT SOLDER LEAD Fig. 4.22. Radiau prototype gauge.

10-7 G o-8 1 1 1 1 1 110-91 Ioo 0 0 Io 10- 10 0 102 03 0 ior3 i Ci Io0I 100 10 102 1 3 PRESSURE IN MILLIBARS Fig. 4.23. Typical i-P curves for radium prototype gauge.

152 complexity that such voltage adjustment would require in the associated circuits. Of course, the gauge sensitivity might have been increased by the use of sources of higher intensity, but possible improvement would be limited chiefly to the high-pressure range, since an increase in radiation often offsets the lowest measurable pressure as a result of the relatively high dark current produced. Another drawback in using a stronger radium source would be the gamma radiation from this source, which would constitute a health hazard. This is completely eliminated in the gauge next described, in which the tritium source, (H3), emits beta particles only. 4~6~2. Tritium Prototype Gaugeo -As stated above, the radium gauge was useful only for altitudes up to about 80 km. The carrying rockets, however, were capable of attaining altitudes of about 150 or 200 km, the lower altitude for the Nike-Cajun type, and the higher for the Aerobeee It was naturally desirable to extend the useful range of the radioactive prototype gauge to higher altitudes. This required an increase in the current sensitivity at higher altitudes (lower pressures) with less dark current effect~ These requirements, as well as those discussed in the previous section for the planar radium gauge, were realized to a substantial degree in the new design illustrated in Fig. 4o24, which shows a completed chamber with an attached low-leakage ceramic wafer and associated high-megohm resistorso Here tritiumn was adopted as a source material~ Tritium is a high

153 0 H wft4~'-1:......:?.................................r~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~........... a::~~~~ (ba 0 rd.....:.......... 0 61) 0 "3 bD -pd::::::iii!...:....:::::::-:-:::-::::: -:i:::::i:-i:~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~iiiiii::?.i:::.:/:!::f/::::::.... ~ "3,- o 0........~~~~a~t::::::::::::::: ifiiiiiil:::..... iiiit.......iiiiiiiiiii-............::~:''iii:i:'':i C)I NcD ~~~~~~~~~~~~~~~~~~~~~~;~::"::....... ~1U:~~~~}:ii!.... ~~~~~~~~~~~~~~~00)J on/ ~ ~ ~ ~ ~ ~~~~~~~::):::::l I-~~~~~~~~~~~~~~~~~~~~~c aa: bO~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i~~~~I::: — z~~~~~~~~~~~~~~~~~~~~~_ *H- c'3 i-: ~-:ii i~ -i 0~~~~iiie Co~ ~~~~~~~~~~~ii- ii_ 4:2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ iiii ii: ~-::iii:-iii — H~~~~~~~~~~~~~~ ft~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;iii~i~~i~l~-_:::_:ii_-~~i:-ii:iiH ~ ~~~~~~~~~~~~~~~~~~~~~~~Xiii:i~iiii:iiiiiii

154 activity beta source, emitting 18-kev electrons and no gamma radiation. It has a half-life of twelve years, which is long enough so that calibration is adequately constant. This is very desirable for the present applicationo Under normal conditions tritium exists as a gas, which readily combines with titanium to become solid titanium tritideo Figure 4.25 shows the titanium-tritide-stainless-steel foil source secured to an ionization-chamber end plate. It was estimated from chamber measurements that an effective activity of approximately 1 curie per square inch (1 curie = 3.7 x 1010 disintegrations per second) was attained. The physical aspects of the ionization chamber are shown in Figs. 4.24 - 4.29. The chamber consists of an outer stainless-steel cylinder closed at the bottom by a disc carrying several glass-to-metal seals to provide for external electrical connections and element assembly mounting. The top is closed by the source-bearing end plate, fastened by four screws. Internally the gauge consists of a cylindrical polarizing electrode (Fig. 4.27) and a collector assembly (Fig. 4.28) which supports two collectors, one for the high-pressure end of the range, the other for the low-pressure end. The source faces the open end of the polarizing cylinder, directly adjacent to the high-pressure collector, which is the circularly formed wire shown in Fig. 4.29. This collector is supported on two glass-to-metal seals, which in turn are supported by a bridge which spans the open end of the polarizing electrode. The low-pressure collector is supported by another glass-to-metal seal in the center of

155?~iiiiiii,~~~~~~~~~~~~~~~~............ Fig. 4.25. End plate of ionization chamber showing titanirum tritide source.

156........... x................ A................................................:Lux............. -:X: v:::::::............................................................... x:....................................................;x:::: :;::::::::::::::::::::::::::::::: - -:: -: -,.- - %.....,..-..,-....l-................................... xj:::::: x:::::::::::::.::............................................................................ X.......................................... X.........:p X -......................................................'imperialistically 1.............. F............................................................................. X..................................................... X....................................................................................................... X............... X IX X X X :::,:V::................................................... \110............................................................................................................................................ w:.............

157 THERMISTOR Fig. 4.27. Ionization-chamber polarizing electrode.

158 i;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~* oif.0;D n Fig. 4. 2 8. Ioni zat ion-s chamber colle c t or ass embly. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.-Z I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Z:::';~iiii!~~~~~~~~~~~~~~~~~iigi F:g. 4o25. -i Zon~7,i ati o n -hambe coil:~iiil e c t o r a s s e m b' ly.

159 4chamber element assembly.

160 the bridge, and is shielded from direct source radiation by the bridge itself. The area of this collector is also minimized to reduce electron emission. that occurs due to X-ray radiation from the surface of the polarizing cylinder under the influence of the impinging beta particles as discussed above. These precautions substantially reduced the dark current, thus extending the gauge applicability to lower pressures. The relatively low energy of the ionizing particles means that their path length in air decreases sharply as the density increases. Thus at higher densities, little ionization is produced in the vicinity of the low-pressure collector, so that an alternative collector near the source must be employed. Thus the chamber is provided with both a low- and highpressure collector. They are proportioned so that in their linear region, near 1 mb, the currents are roughly equivalent, eliminating a step when changing from one to the other. Typical i-P characteristics of each are shown in Fig. 4.30, and a compositive curve, in Fig. 4.31. The chamber elements are fashioned from stainless steel; spot welding is employed in the assembly of the structure. Two thermistors are usually employed during flight measurements, one in air, visible in Fig. 4.27, the other held in a small depression in the outside of the polarizing electrode end plate; the depression is visible in Fig. 4.27. These thermistors permit the gas temperature in the chamber to be estimated. The above gauge proved to be adequate for pressure measurements up to altitudes of about 100 km, beyond which the mean free path of the gas particles becomes long with respect to the gauge dimensions. This would

/ Current loss due;o / /recombination -rret8 loss due to High-pressure Current loss due to ~ collector loss of source particle energy characteristic a. -9 z Low-pressure W H a collector characteristic O -I0 o - II -4 -3 -2 -I 0 1 2 3 LOGo PRESSURE, MB Fig. 4.30. i-P curve of typical ionization chamber showing low-pressure and high-pressure characteristics.

Liof I I I I iii~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i I Ot8 jo 2 2 CL LL bli ~7_ V~~~~~~~~~~~~~~ < I011 I0~~~~~~~~~~0 10-12 LE I 10 10-4 io-3 10-2 lo-, 100 lo, 102iiil 1 i 1 i PRESSURE IN MILLIBARS Fig. 4.51. Typical composite i-P curve for ionization chamber showing corresponding load resistances.

163 require a quite different method of interpreting measurements from the one employed in the instrumentation dealt with here. 4.6~3. The Amplifier — MA detailed description of the amplifier, switching circuit, and power supply can be found in Refo 2. A schematic diagram of the amplifier section is shown in Fig. 4~32. The amplifier consists of three direct-coupled stages with an electrometer input and -12 a cathode follower output. The ionization current (ranging from 10 to 108 amp) passes through the appropriate high-megohm resistor, causing a voltage drop which appears as a portion of the voltage in the feedback loop of the amplifier for which the feedback factor is unityo Thus a voltage change effected at the output of the amplifier is nearly equivalent in magnitude to the voltage change across the high-megohm resistor but opposite in sense. The amplifier, therefore, acts as an impedance matching device. The complete schematic and assembly are shown in Figs. 4-33 and 4.34, respectively. 4~7. THE VACUUM SYSTEM Figures 4~35 and 4~36 show the vacuum system used to determine the previous experimental data and to calibrate the prototype radioactive ionization pressure gaugeso The system was capable of producing and en-6 abling the measurement of a wide range of pressures from about 10 mb to atmospheric (1013 mb). The vacuum system consisted of mechanical pumps, an oil diffusion

+45 v IONIZATION GAGE _ _ _ _ _ _ _ RI 6.8 M R2 R3 R4 " "" 82 K ~~~~~~~~~~15 K 1I% PRECISTOR 82 K 270'K 390 K CI.0033 39 6112 vl DI'SK R~~~~~~~~~~~12, v DISK V2A V4A R I0 V3 820K V2B R15 B 680 K'" 2 CERAMIC A R 14 CERA~~VI'I@ ~390 K lOOK L I1 4P.00 K 5886~ Rh-II TRIM POT. S-IA 6112F 4I 510K,. R40 R 16 L'~~~~~~': 5390 K R 13 620K +.~'" — 620 K RM 400R 560 Hg Z ~~~~~~~~~~~~~~BA I CELLS A BA 2 ".6 R 25 R.6 R5 I 330C ~ RELAY 27K CONTACT SG 22 470 K.8 M R26 4.7 K II R8 0 7 Irv ~~~ 33OQZ~ RY-1I _ 3 Cr 5 MFD9 REF. 6 OUTPUT -45 RELAY Fig. 4.32. Amplifier schematic diagram.

IONIZATION GAGE RI 6.8 M R2 R3 R4 K: K.!~'1% PRECISTOR 82 K" 27n 390 V5 11 l 11 ~~~~~~~~~~~~~~~~~~~~~~~~~8 I 6111 — ICI ~~~7 2.0033 8 R I2 11 VI DISK V2A V4A I RI1O V3 82O K 8K V213 R15 vI ~ ~ ~~~ ~ ~ ~ ~~~~~~~~~~~ V4AI, V21 ~~CERAM ~IC 1~390 K 470K =8 V485 4 2 ~ ~ 2 R4 7 17 D R6 /Iy___ _ 390K K=620 KK C8 4 5 40 KX* 2 Hg 0R -= LI ~200 L2 3 RI-5 _7R C 7 mf CELLS R 29 R 23 100 f.~='~'I}~~~~~~~~~~~~ 29R ~ R7 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~150 v R 7iii I * 47K 1.0 MEG 330K 330K R20 7.5 K'R-25 1.2m R.6 R.30 27a 2.7 K Tu 30 V O REL~Y 6U 390 4LR36 T HER ISO COTACT Rj ~i 7R35 IE SG 22 470 K R.M 26 1 K R22 NE-2 RM_ 4_4.7 K 31____. _____,__ 1.0 MEG SILVE CELLS90K R34as R27" R 7 R4 R8 39K:.180 K'.5 R 21 RY- I ~ ~ ~ ~ ~ ~ ~ ~ 82'KT R32 20( v I.5 MEG'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 3LI~ O o, ~ ~ ~ ~ ~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~12 K T G4 v L2IT* Id AL VAUE ADJUSEI I E + II- I +II- I I~~~~~~~~~~~~~~ ~ ~ ~~K COLLECT BAT I 117 150 v CIO0 150 v R3 K 2S OUTPUT 4705~Lf 5~f 2.2 K i Z R51'g';';, ~HI I I I I I ] 5[75643 "N C8 150 v 11 150 vO R 5Ccf SC~f R 32 0 01 1 0 I I + 1_150 VOLTS 2.2I f _ Di IC9 150 v C I0 150 v OFF IN 39 5pf IN 91 F1 ** 5% TOLERANCE -ALLEOTHERSL0% IN 39 S- IN 91 2FSF-I SF- 455 S-2 A 2: (D C GROUND!~ ~~~~~~e 2.2K, +t[~ a-RN ON C80a 150 vk II 0 I 2 f 5F0f R:3I 0 450 VOLTS IN K:' ~ 1 V 2.2 IK0- It It to lB %-0 THERMISTOF ~~~~~~~~~~~~~R3D IK C 9 1 5 0 v D5!][~~x 50 IN~~~~~~~2 3 9 725C\S5 S-1c S~~~~~~~lB K ~~~~5.8 VOLTS D.C 4-HR-1 SILVER CELLS ~cALL VALUES ADJUSTED IN EACH UNIT 5%JC 5W TOLERANCE -ALL OTHERS 10% Fig. 43 System schematic diagram.

JON CHA BER~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~iiiliii Hiiiiiii ONiiiiii O! Fig. 4*15L1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~* Complete system out of enclosing~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~??ii~

ANEROID GAUGE ALPERT GIANNIN I ION PRESSURE GAUGE PRAN TRANSDUCER GAUGN INLET i I BELLJAR MAIN LINE VAL vE VALVE VALVE CALIBRATION INLET VA LVE -Fig.~ 4.5.VauuMc LEOD DIFFSION GAUGE EXPERI-MENTAL ROUGHING V PU GAUGE /d i i -VALVE COLD TRAP LIQUID NITROGEN TRAP MECHANI PUMP Fig. 4.35. Vacuum system layout.

168 Haiti! Establiilshim:eirniit:ia6r:::::: I CH 4-) I):iii iiiii mle~~~~~~~~e............ ~ ~ ~ ~ ~ ~ ma.. 6- ~ ~ ~ ~ ~ ~ ~

169 pump, and a number of different types of pressure-measuring devices. It was also equipped with typical accessories for rough pressure indication, protection in the event of glass breakage, air dryer inlets, and cold traps. For pressures lower than 103 mb, an Alpert ion gage was employed, whereas a three-range McLeod gauge served for pressures between 10-3 mb and 5 mb. Two Wallace and Tiernen aneroid gauges were used to cover pressures greater than 1 mbo

CHAPTER V CONCLUSIONS An analytical as well as an experimental study of a radioactive ionization pressure gauge has been made in an effort to acquire a better understanding of the properties of such a device in measuring pressure. Some of the conclusions drawn have a direct bearing on the particular gauge under investigation; other conclusions, although closely related to the gauge, are also of general interest. These conclusions are summarized below. 1. An approximate relationship between the ionization current and the gas pressure, developed analyticallyl for a planar radioactive ionization gauge, and taking into consideration the variation of electron attachment as. a function of fieldto-pressure ratio, was found to be in general agreement with experiment, thus verifying the validity of the assumptions made there. 2. There is a strong indication that the hysteresis phenomenon may be caused by one or both of the following factors: a, The temperature dependence of the main electronic processes inside the gauge. b. A variation in the environmental conditions which may result in a change in the composion of the 170

171 present electronegative gases. The primary ionization in a gauge varies with the temperature of a gas under constant density. The variation is such that more ionization current is collected with decreasing'temperature. The planar gauge used would be a useful tool in the study of ionization by electron collisions in gases. Some of' the experimental results obtai-.:led confirm the existence of a peak value for electron attachment at low energies, as predicted theoretically L y Bloch and Bradbury for diatomic molecules.

APPE1NDIX ANALYTICAL INVESTIGATION OF SOURCE STABILITY The disintegration of radium and its decay products results in the emission of alpha, beta, and gamma rays which, in their passage through gases, produce ionization. The specific ionization varies greatly for the three products, roughly in the ratio 10,000: 100: 1, respectively. We need, therefore, concern ourselves with the alpha particles only. The successive transformations of radium and its decay products are illustrated in Fig. A.1 which shows the type and range, in standard air, of particles emitted, as well as the half-life time of the successive elements. All the decay products of radium (Ra) are solid substances except radon (Rn) which is gaseous under normal conditions. CASE I Since the half-life time of disintegration of radium is considerably long (1620 years), it is perfectly justifiable to assume that, for an interval of a few days, the disintegration of radium (Ra) takes place at a constant rate, no particles per second. This also means that radon gas is emanating from radium at the same rate, no particles per second. It is known that the rate of disintegration of any radioactive material depends on the amount as well as the kind of material. This could be expressed as 172

ELEMENTS Ra -~ Rn -R aA ~ — RaB — RaC >RaC' RaD -RaE HALF L LFE I 1620wy |3.825d 3.05min 26.8 min |19.7min iIOsec 22y TIME sec PARTICLE a a a a- - a,8- a - MEAN RANGE (cms) 3.389 4.1 4.7 - - 6.97 OF a-PARTICLES IN AIR AT 150C Fig. A.1. Radioactive transformation of radium and its decay products.

174 dN - dt where N is the number of particles at any instant, t, and X is the decay constant, a characteristic of each element and independent of all physical and chemical conditions. The net change of radon (dp) in an interval dt is then given by dp = (no - kip) dt or dpp + P = no dt where p is the amount of radon present at any instant and X1 is the characteristic constant for the same material. Assuming radon was initially absent, then p is given by p = - (1 - e-it) Similarly for Ra A dq -= p - %2q, dt where q is the amount of Ra A at any instant and k2 is the characteristic constant of Ra A. Substituting for p and transposing, we get dq + 2q = no (1 - e-Hit) dt Considering Ra A initially absent, then the solution for q is no no lt - no -Xt n = -- e - e

175 In the same way the values of Ra B and Ra C are, respectively, no no X2 -klt no el -k2t no kl A2 -e3t r - e - -- e.... A3 (%2-%l)(k3-A) (l-%2) (s3-k2)' 3 (X% -%3) (2-X3) and no no k2 k3 e-%t no %k k3 -%2t S = - e )-e -4 (X2-X1)(X3-X2)(X4-\1) (\- X2)(X3-X2)(%4-%2) no l,2e -A3t nO X1 X2_ 3 e X4t - (x1-x3 3)(x2-3)(X.4- 3) e - X4(Xl-4 ) (2-4) (.3-4) e Since the half-life time of Ra C is very small, 10-6 seconds, no further calculations are needed beyond Ra C to account for the fourth alpha particle. Therefore, the build-up of the alpha activity N(t) of the sealed source becomes N(t) = no + XP + X2q +,4s alpha/sec or N(t) no [ 4- aie z - a2e - a3e t-3t a4e -4t where a. = 1 2 + k2 + h2 s3 X, n a1 = + 1 X3 a2 _ k2, a3....,= and (x%-%3 )(%x2-%3 )( 4~-3) a4 = 3 At the steady state, no= k = -2Qo = 30o = 4o

176 where P, Qo, Ro,, and So are, respectively,the contents of radon, Ra A, Ra B, and Ra C, when they all attain the same rate of disintegration as that of radium, no. A radium source, as such, is often said to be in equilibrium with its daughter products. CASE II In this case it is considered that the source is not perfectly sealed under vacuum; consequently the alpha activity will be partially affected as a result of the continuous loss in the active radon. The source, how-. ever, is assumed to be well sealed under atmospheric pressure. Because of the loss in radon through the seal, the rate of supply of radon is taken as noe, where a is a constant, for mathematical simplicity, and c < K. The source activity, in this case, undergoes two different changes: (a) during the pumping out period the activity is continuously affected by loss of part of the radon generated, and (b) under atmospheric pressure no further losses are assumed and the source starts to build up its activity. To summarize the procedure carried out in Case II: (i) one starts with a source under equilibrium, i.e., with no o o no no P =- Qo - Ro = and So = X1 X2 X3 X4 as the initial contents of Rn, Ra A, Ra B, and Ra C, respectively; (ii) the source is then kept under vacuum for an interval of time T, at the end of which the radioactive contents, as a result of radon loss, will

177 have the values PT, QT, RT, and ST, respectively; (iii) radon loss is then assumed to stop after exposing and keeping the source under atmospheric pressure for a long period during which it builds up its activity with PT, QT, RT, and ST as the new initial contents. To find p, q, r, and s under vacuum, one follows the same procedure used in Case I with Po, Qo, Ro, So, the equilibrium contents, as initial values for radon, Ra A, Ra B, and Ra C, respectively, and noe t instead of no as the rate of production of radon. Then the instantaneous values of radon, Ra A, Ra B, Ra C, respectively, are: p(t) - eCte + N no e- C( t +IN e-kt _2t q(t) K= e +le-a(k-a e + A2 er(t) 1 2 _eX1 % 2 N Xlt X2A e-X2t +B e-Ast 1( -a) (2 0)( 3-a)-%2 and no sk k2 k3 -Olt = k2 k3 N e-lt 1 (X-aC) (%2 -a) (%3 ) (%4-C) (%2- % ) F%3 ) (% -1'+ 3 A -e2t + B_ e3t + C e4t (%3-x2)(%4-x2) (x4-%3) where no n0 N = - - 3 A nO _no kl T 2 Q 2T, n (Taac) (hays) o B2A 23 no PTB QT~ RT, and ST could then be calculated by substituting T for t.

178 Now, on raising the pressure to atmospheric and assuming no further loss of radon under these conditions, the activity of the source as an alpha emitter could be evaluated by following exactly the same lines as before. In this case the total activity is given by the sum of the activity in Case I and that of radon, Ra A, Ra B,and Ra C with PT, QT, RT, and ST as initial amounts, respectively. Then the activity of the source becomes: n0%2 A3 4 an' e - N(t) = 4 no - al(no- )- — Qt e 1\O "T ( X3-\2) (%4-X2) n- na s - R] e-X3t _[noa4 - X4S7] e -4t where al, a2, a3, a4 are the same as in Case I, Q = QT — P T t R = RT - 2 QV _ T,and T 3B 3-2 (X3 2 ) (X2-X1 ) A3 Rv 2 k3 q' k/ 2 X3 PT ST - X4-X3 -(X3-X2)(%4'-X2) (- 4-XL)(k3-kl)(k2-l) The result of some numerical examples is shown in Fig. A.2, where three cases are considered: (A) T = 72 hours, C = 0.2 kl, (B) T = 72 hours, Oc = 0.6 k1, (C) T = 240 hours, oa = o.6 i,. The values of \l, X2, \3, and ~4 are the conventional values for radon, Ra A, Ra B, and Ra C, respectively.

4n. ~~~~~~~~~~~~~~~~~~a0.2 Xi T=72 HR a=O.6 XI T 72 HR 0 0 t 3 n. T=240 HR aQ=O.6X 0. 0 1.0 2.0 3.0 4.0 TIME IN HOURS Fig. A.2. Calculated alpha activity of a poorly sealed source

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