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The construction of a low-pressure flash tube and the measurement of some of its properites Robinson, Alexander Maguire 1962

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THE CONSTRUCTION OF A LOW-PRESSURE FLASH TUBE AND THE MEASUREMENT OF SOME OF ITS PROPERTIES by ALEXANDER MAGUIRE ROBINSON B . A . S c , Un ive r s i ty of B r i t i s h Columbia, 1961 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of PHYSICS We accept t h i s thes is as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December, 1962 In presenting this thesis in p a r t i a l fulfilment of the requirements for an advanced degree at the University of Br i t i sh Columbia, I agree that the Library shal l make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for f inancial gain shall not be allowed without my written permission. Department of The University of Br i t i sh Columbia, Vancouver 8, Canada. Date %C. 2.0 /?6Z.  ABSTRACT A low pressure coax ia l f l a sh tube of simple design has been constructed which does not suffer from deposi t ion on the e x i t window. Some of the e l e c t r i c a l and spectro-scopic cha rac t e r i s t i c s of the tube have been measured. A method of measuring the brightness temperature over the v i s i b l e range was used by comparing photoelec-t r i c a l l y the i n t ens i t y of the tube wi th that of a black body. The temperature was found to be lower than expected. ACKNOWLEDGEMENT I would l i k e to thank Dr. R. A. Nodwell for h is guidance and assistance to me i n t h i s work; and thanks also to the other members of the plasma physics group and the members of the physics workshop. I am also indebted to the National Research Counci l of Canada for f i n a n c i a l assistance i n the form of a bursary. TABLE OF CONTENTS Page 1. Introduction 1 2. Theory of Low-Pressure Discharges 6 2 .1 . Introduction 6 2 .2 . P a r t i c l e Theory of Gases 7 2 .2 .1 . D i s t r i b u t i o n Functions 7 2 .2 .2 . C o l l i s i o n s 8 2 .3 . Discharge Mechanics 10 2 .3 .1 . Introduction 10 2 .3 .2 . Primary Ioniza t ion 11 2 .3 .3 . Secondary Ion iza t ion 12 2.4. Radiat ion 15 2 .4 .1 . Radiat ion Theory 15 2 .4 .2 . Recombination 19 2 .4 .3 . Continua 23 3. The Flash Tube 24 3 .1 . The Flash Tube Discharge Model 24 3.2. Desirable Charac te r i s t i c s 27 3.3 . Ea r ly Designs 29 3 .3 .1 . The Elbow Tube 29 3 .3 .2 . Low Inductance Tube 31 3 .3 .3 . Tungsten-electrode Tube 31 3.3.4 Covar-electrode Tube 32 3.4. F i n a l Design 33 3 .4 .1 . Descr ipt ion 33 3 .4 .2 . Operation 36 3 .4 .3 . Experimental 37 3.5. Apparatus 38 3 .5 .1 . Charging Condenser and Charging Unit 38 3 .5 .2 . Trigger Unit 38 3 .5 .3 . Photomult ip l ier Unit 40 4. Brightness Temperature Measurement 42 4 . 1 . Introduction 42 4 . 1 . 1 . Black Bodies 42 4 .1 .2 . Temperature 43 4 .2 . Theory 45 4 .3 . Experimental Procedure 49 4 .4 . Apparatus 52 5. Results 53 5 .1 . F lash Tube Spectrum 53 5.2. Current Waveform 54 5.3. Light In tens i ty 57 5.4. Deionizat ion 59 5.5. Behaviour of In tens i ty wi th Number of Shots 65 5.6. Temperature Measurements 66 5.7. Conclusions 70 Appendix 72 References 74 ILLUSTRATIONS Figure K a ) The Elbow Tube fo l lowing page 29 K b ) Low Inductance Tube fo l lowing page 29 2(a) Tungsten-electrode Tube fo l lowing page 31 2(b) Covar-electrode Tube fo l lowing page 31 2(c) Covar Tube with Dump Chamber fo l lowing page 31 3 F i n a l Design fo l lowing page 33 4 Trigger Unit page 39 5 Photomult ip l ier Unit page 40 6 Temperature-measuring Apparatus fo l lowing page 49 7 Current Waveform page 54 8 Light In tens i ty page 57 9 Light In tens i ty of Elbow Tube page 58 10 Current and In tens i ty of F lash Tube page 58 11 _x j 2 versus Time ?\ fo l lowing page 59 12 Energy Content of Tube page 64 13 In tens i ty Decrease fo l lowing page 65 14 In tens i ty V a r i a t i o n wi th Wavelength fo l lowing page 69 TABLES Table I Brightness Temperature for Var iable Wavelength In te rva l 68 I I Brightness Temperature for Constant Wavelength In te rva l 68 1. Introduction Sources of energy for use by man have always played an important part i n the development of c i v i l i z a t i o n . With each new and improved source of energy that has been evolved, s i g n i f i c a n t advances i n technology have been made. Take, for example, the technological growth which followed the "universa l" use of coa l and o i l as fuels and marked the beginning of the i n d u s t r i a l r evo lu t ion . However, ever increasing energy requirements threaten to deplete the fue l for the wor ld ' s present-day energy sources. Fortunately the development of a new source of energy appears poss ib le , and that i s the process of nuclear fus ion . The fue l required for t h i s process can be extracted from sea water at n e g l i g i b l e cost and affords a v i r t u a l l y unl imi ted supply of f u e l . B i shop 1 , for example, estimates that at the present Q rate of energy consumption (5 x 10 kw) there i s enough sea-water fue l i n the world to l a s t for 2 x 1 0 1 0 years. Control led nuclear fusion i s not without formidable d i f f i c u l t i e s , however. For a p ro f i t ab le reac t ion to take ft place extremely high temperatures (10 K) are needed and hence the fue l i s i n gaseous form and highly ion ized . Such ionized gases are c a l l e d plasmas. - 2 -Because of the problems involved i n containing a gas at such high temperatures, a thorough knowledge of the proper-t i e s of plasmas under many conditions i s expedient. Consequently i n the l a s t decade or so, a great deal of time, e f f o r t and money has been spent i n the diagnosis of plasmas merely to learn more about them, not only with the hope of ultimately achieving controlled fusion, but also to gather useful information i n such related f i e l d s as astrophysics, magnetohydrodynamics, gaseous discharges, and so on. Of the several main diagnostic techniques In popular use today, spectroscopic analysis gives quite precise r e s u l t s and does not suffer from the disadvantage of introducing pertur-bations into the plasmas. Much can be learned from the study of the spectra of plasmas. However i t i s usually necessary i n subsequent analysis to know the r e l a t i v e population densities and the t r a n s i t i o n p r o b a b i l i t i e s between two energy leve l s of the gas molecules. Unfortunately i n many cases these two quantities are not known and so preliminary experimentation must be undertaken to determine them. Ladenburg has pointed out that by measuring the anomalous dispersion and thd absorption spectra of the gas, one may determine the r e l a t i v e population densities and the t r a n s i t i o n p r o b a b i l i t i e s . However, to perform an absorption analysis upon the -3-plasma, a continuum background source i s required whose tem-perature need be greater than that of the plasma which i t s e l f can be as high as 10® °K. Also because one would l i k e to examine the s h o r t - l i v e d plasma reac t ions , such as a shock front or pinch ef fec t , an extremely short-pulsed background l i g h t i s required to get any time-resolved absorption spectra. Both the high temperature and short duration requi re -ments are ap t ly met i n the high-voltage f lash-discharge tube which i s becoming increas ingly popular i n spectroscopic work. These f l a sh tubes are also f inding use i n other f i e l d s such as photography of fast events, and f l a s h photo lys i s . The high i n t ens i t y continuous spectra of the f l a sh tube i s achieved by the impulsive discharge of high energy through a gas at low pressure; the gas i s confined wi th in an i n su l a t i ng tube of small diameter. In ea r ly designs t h i s tube suffered from f a i r l y rapid erosion of w a l l mater ia l because of the high temperatures involved, and subsequent deposi t ion onto the windows present i n the system. Also q u a l i t a t i v e i n t ens i ty work has been impossible because the i n t ens i t y has not been reproducible to a s u f f i c i e n t l y accurate degree. These f lash-discharge sources may be roughly divided in to three main types and although they appear to be quite s i m i l a r i n operat ion, a l l employing the discharge through a gas of c a p a c i t i v e i y stored e l e c t r i c a l energy, there i s a fundamental difference i n the mechanism of emission and the d e t a i l s of operat ion. The f i r s t type of discharge tube i s c a l l e d the Lyman f l a s h tube and has been used extensively i n the production of o the Lyman continuum which extends from about 600 A to the v i s i b l e range on the electromagnetic wavelength sca le . The tube has a narrow bore ( .1 cm) and moderate length ('—' 5 cm This source, however, suffers from the rap id erosion of e l e c t -rode and w a l l mater ia l wi th a consequent reduction of current density . The second type of tube i s a th ick -wa l l ed c a p i l l a r y ( ^ .2 cm diameter by 3 cm length) between heavy electrodes i n se r ies wi th a heavy-current hydrogen thyratron and condensor bank. The ine r t gas i n the tube i s at a r e l a t i v e l y high .:o 4 pressure . The t h i r d general type increases the s i z e of the c a p i l -l a r y tube to about 1 cm and uses r ap id discharge condensors. The c i r c u i t r y i s designed to reduce the inductance as much as possible and hence a c o a x i a l symmetry i s employed. Thus these tubes are c a l l e d coax ia l f l a sh tubes. They show a marked improvement i n e l e c t r i c a l and spectroscopic propert ies over the Lyman f l a sh tube, the main advantage being the i r r e l i a b l e i n t ens i t y r e p r o d u c i b i l i t y which allows them to be used for q u a l i t a t i v e work. Budd 5 describes the construct ion of a c o a x i a l f l a sh tube insp i red by the work of Gar ton 6 and which he used i n some prel iminary experiments i n absorption i n neon gas.-- 5 -D e p o s i t i o n of m a t e r i a l on the e x i t window w i t h consequent decrease of i n t e n s i t y was a great problem and s i n c e the t u b e ' s u se fu lnes s depends on an i n t e n s i t y which does not va ry w i t h the number of f i r i n g s of the tube , the need of a more r e l i a b l y o p e r a t i n g f l a s h tube was apparent . T h i s t h e s i s d e s c r i b e s the c o n s t r u c t i o n of a c o n t a m i n a t i o n -f r e e continuum c o a x i a l f l a s h tube hav ing good i n t e n s i t y r e p r o d u c i b i l i t y . I t s c o n s t r u c t i o n and maintenance i s extremely s imple and inexpens ive and the complete apparatus i s ve ry mobi le which a l l o w s speed and convenience i n i t s use . The b r i g h t n e s s temperature of the f l a s h tube i s measured i n the v i s i b l e wavelength range by comparison w i t h a tungsten f i l a m e n t lamp of known temperature . -6-2. Theory of Low-Pressure Discharges 2.1 Introduction The main object of t h i s experiment has been to design and construct a deposition-free f l a s h tube with f a i t h f u l l y reproducible properties and simple constructional d e t a i l s ; and also to measure i t s temperature. Although some of the early d i f f i c u l t i e s were overcome by a semi-empirical "cut-and-try" method i t i s useful and i n t e r e s t i n g to delve into the physics of a low-pressure gaseous discharge. The r e s u l t s of doing so have explained some of the shortcomings of the f l a s h tube i n i t s present configuration and w i l l doubtless be equally re-warding i n the future. The theory of low-pressure discharge: and a l l i t s ramifications covers an enormous f i e l d and much work has been done both t h e o r e t i c a l l y and experimentally over the l a s t few decades. Much theory i s s t i l l incomplete, however, and consequently interpretation of data i s sometimes somewhat unsatisfactory. It i s obvious that the discussion to follow must be abbreviated perhaps to the point of being incomplete; the main aspects of discharges which are of inte r e s t to t h i s work have been b r i e f l y touched upon and i t i s hoped the above mentioned f a u l t i s not apparent. -7 : 2 . 2 P a r t i c l e Theory of Gases 2 . 2 . 1 D i s t r i b u t i o n Functions To d e s c r i b e e x a c t l y the a c t i o n s of two i n t e r a c t i n g p a r t i c l e s i s u s u a l l y p o s s i b l e but when the number i s three or more the mathematics becomes formidable and a n a l y t i c approxi-mations must be made. In d e a l i n g w i t h plasmas, where the ] 0 —3 2 5 —3 p a r t i c l e d e n s i t y may vary between 1 0 cm t o 1 0 cm , a mathematical d e s c r i p t i o n of the i n d i v i d u a l p a r t i c l e motions i s o b v i o u s l y impossible. Many p r o p e r t i e s of gases and plasmas may be p r e d i c t e d by c o n s i d e r i n g the gas as composed of a l a r g e number of p a r t i c l e s and t r e a t i n g them s t a t i s t i c a l l y . This i s done by the i n t r o d u c t i o n of the d i s t r i b u t i o n f u n c t i o n f which i s d e f i n e d such that f(x,y,z,u,v,w,t) dx dy dz du dv dw represents the average number of p a r t i c l e s between x and x + dx, y and y + dy, z and z + dz w i t h v e l o c i t i e s between u and u + du, v and v + dv, w and w + dw at time t , where x, y and z are the r e c t a n g u l a r c a r t e s i a n coordinate p o s i t i o n s and u, v, and w are the corresponding v e l o c i t i e s . f i s the p a r t i c l e d e n s i t y i n p o s i t i o n - v e l o c i t y 6-space. Many u s e f u l r e l a t i o n s may be deduced from a knowledge of the d i s t r i b u t i o n f u n c t i o n . For example, the p a r t i c l e d e n s i t y In space i s given by n(x,y,z,t) - \\\f(x,y,z,u,v,w,t) du dv dw ~8 and the average v e l o c i t y by where v„„ i s the average v e l o c i t y and dv represents the a v volume du dv dw i n v e l o c i t y space. Many other macroscopic properties of a gas may be calculated from t h i s p o s i t i o n -v e l o c i t y d i s t r i b u t i o n . For precise r e s u l t s i n the k i n e t i c s of plasmas, Boltzmann's equation must be applied. This i s an integro-d i f f e r e n t i a l equation involving f and describes i t s behaviour as a r e s u l t of external forces on the p a r t i c l e s and also encounters among the p a r t i c l e s . It i s derived by considering the conservation of p a r t i c l e s i n a small volume element i n 6-space. In the absence of c o l l i s i o n s , t h i s equation reduces to L i o u v i l l e ' s equation. 2.2.2. C o l l i s i o n s C o l l i s i o n s between p a r t i c l e s i s an event which, at f i r s t sight, seems simple enough, but when a detailed i n v e s t i gation i s made, any apparent s i m p l i c i t y disappears. Even a consistent d e f i n i t i o n of a c o l l i s i o n i s not an easy thing. A dictionary w i l l define i t as an act of h i t t i n g or coming into v i o l e n t contact, which, from an atomic point of view, i s wholly unsatisfactory. For i t i s a well accepted fact t h a t an atom i s not s o l i d and the word " c o n t a c t " has no r e a l meaning on t h i s s c a l e . A c o l l i s i o n c o u l d be d e f i n e d , however, as an event between two or more p a r t i c l e s t h a t approach each other r e l a -t i v e l y c l o s e l y and whose s t a t e s of motion and/or energy are changed s i g n i f i c a n t l y by v i r t u e of t h e i r p r o x i m i t y . C o l l i s i o n s between p a r t i c l e s may be r o u g h l y d i v i d e d i n t o two main c a t e g o r i e s - those i n which the nature of one or more of the c o l l i d i n g p a r t i c l e s i s a l t e r e d , and those i n which the nature of the p a r t i c l e s remain u n a l t e r e d . Those i n the f i r s t - m e n t i o n e d category are c a l l e d i n e l a s t i c c o l l i s i o n s and those i n the second e l a s t i c c o l l i s i o n s . In both e l a s t i c and i n e l a s t i c c o l l i s i o n s , a u s e f u l concept i s the c o l l i s i o n c r o s s - s e c t i o n which i s represented by G~ and d e f i n e d f o r b i n a r y c o l l i s i o n s by the equat ion cr n.nzU. where n^ and ng are the p a r t i c l e d e n s i t i e s of the two c o l l i d i n g s p e c i e s , u i s the average r e l a t i v e v e l o c i t y between the p a r t i c l e s , and i s the r a t e of c o l l i s i o n . A l a r g e va lue of CT i m p l i e s a h i g h p r o b a b i l i t y f o r c o l l i s i o n , and c o n v e r s e l y . The c r o s s - s e c t i o n i s dependent upon the nature of the i n t e r p a r t i c l e f o r c e s and the r e l a t i v e v e l o c i t y of the p a r t i c l e s . d o d t -10-In e l a s t i c c o l l i s i o n s the t o t a l k i n e t i c energy of the p a r t i c l e s i s conserved; t h i s type of c o l l i s i o n i s not of much interest i n the study of the discharge of the gases and w i l l not be further mentioned. On the other hand, i n e l a s t i c c o l l i s i o n s play a cardinal part i n i o n i z a t i o n and ex c i t a t i o n of gases. I n e l a s t i c c o l l i -sion processes may. be subdivided into two classes, which are ca l l e d c o l l i s i o n s of the f i r s t kind and c o l l i s i o n s of the second kind. In the f i r s t , the t o t a l k i n e t i c energy of the c o l l i d i n g system i s reduced by the c o l l i s i o n ; and i n the second, the pot e n t i a l energy of at least one member i s reduced. The product i n both these c o l l i s i o n s i s such things as i o n i z a -t i o n , e x c i t a t i o n , d i s s o c i a t i o n and so fo r t h . Some of the more frequent participants for binary i n e l a s t i c c o l l i s i o n s are electrons and neutral atoms either excited or i n the ground state, electrons and ionized atoms, neutrals and ions, ions and ions. 2.3. Discharge Mechanics 2.3.1. Introduction When a gas i s located i n a region of an e l e c t r i c f i e l d a current w i l l flow i n the d i r e c t i o n of the f i e l d ; however i n small e l e c t r i c f i e l d s gases show l i t t l e conductivity and the current i s of low value. Cosmic rays, ^ - r a d i a t i o n and radio-active traces i n container walls produce t h i s small amount of -11-conduct iv i ty . App l i ca t ion of any agency which causes l i b e r a -t i o n of electrons and ions from surfaces or l i b e r a t i o n of electrons from atoms i n the gas w i l l augment these currents and breakdown of the gas wi th i t s corresponding increase i n conduct iv i ty may occur. 2 .3 .2 . Primary Ion iza t ion ' The processes c o n t r o l l i n g conduction i n the gas may be divided in to two main categories , primary and secondary. In the primary process each e lec t ron l ibera ted creates an avalanche of new electrons and ions by c o l l i s i o n wi th the gas molecules by t ransfer r ing part of the k i n e t i c energy of the impacting e lect ron to the gas molecule which subsequently ion izes . The observed current growth i s given by the r e l a t i o n or more exact ly nX I~Io£xp)ad* ( 1 ) where I Q i s the i n i t i a l current at x = 0 and I i s the avalanche current at x . a i s c a l l e d the f i r s t Townsend coef f i c ien t and represents the number of new ion pa i rs created per un i t distance i n the f i e l d d i r e c t i o n per e lect ron. -12-Th i s can be seen from the fo l lowing considerat ions. Let n Q e lectrons be present at x = 0 ; at the point x the number has been increased to n by i o n i z i n g c o l l i s i o n s . These n electrons i n moving through a lamina of thickness dx i n the d i r e c t i o n x of the e l e c t r i c f i e l d w i l l generate by c o l l i s i o n andx new electrons so that dn = andx. Since I n , equation (1) fo l lows . I t may also be wr i t t en i n the form I = I (H+ I.) where ". xC \ M= exp^Joc dx )-1 o and i s c a l l e d the ampl i f i ca t ion fac to r . 2 .3 .3 . Secondary Ion iza t ion In the process of c rea t ing I Q M avalanche electrons and ions , there may be secondary agencies which can regenera-t i v e l y create yI0M new electrons to s t a r t new avalanches. The current can then be given under many circumstances by T - T ° e * P I*d* ... (2) 7 A der iva t ion of t h i s equation i s given by von Engel . j i s c a l l e d the second Townsend coef f i c i en t and for <yM less - 1 3 -than un i ty , I represents the current of increased magnitude over that caused by the primary I Q ( M + 1 ) process alone. 7 i s i n general r e l a t i v e l y smal l . Some of the possible secondary processes are: 1 ) Secondary emission of electrons due to pos i t i ve ions incident on the cathode, 2 ) Cathode emission of electrons due to incidence of photons from exci ted gas molecules. 3 ) Ion iza t ion by pos i t i ve ions and metastable atoms on impact wi th molecules of the gas. 4) The act ion of photo- ioniza t ion i n the gas. The f i r s t two processes are influenced by the pressure of the gas, for the number of electrons released to a c t i v e l y take part i n the subsequent conduction and i o n i z a t i o n processes i s reduced by back-di f fus ion to the cathode. I t should be pointed out that these mechanisms play a t r u l y secondary role.because they are r e l a t i v e l y small wi th respect to the primary factor M , and the i r most important function i s to sus ta in primary ac t ion . Returning now to equation ( 2 ) , i t i s seen that as long as yM 1 , the current f lowing i n the gas has a de f in i t e value, and i s larger than i t would be i f the primary effect represented by a were ac t ing alone. Ignoring equation ( 2 ) for the moment, note that when 7 M = 1 the condi t ion i s such that for each avalanche of M -14-electrons there i s produced a new elect ron capable of y i e l d i n g a new avalanche. This i s what i s c a l l e d the threshold condi-t i o n of a s e l f - sus t a in ing discharge. An avalanche s tar ted by a s ing le e lect ron becomes sel f -perpetuat ing and the discharge i s capable of maintaining i t s e l f regardless of the value of I 0 . The gain i n e lect ron densi ty r e s u l t i n g from the i o n i z a t i o n of the gas becomes equal to the loss of electrons by d i f fu s ion , recombination or attachment. For <yM > 1 . . . (3) the succession of avalanches creates more current c a r r i e r s than i s necessary for self-maintenance and the current w i l l become excess ively large, the conduct iv i ty nominally going to i n f i n i t y . The gas has undergone an e l e c t r i c a l breakdown to a conducting s ta te . This breakdown condi t ion may be brought about i n severa l ways. One i s to increase the voltage across the electrodes i n the gap. This voltage required to accomplish breakdown i s c a l l e d the breakdown voltage and e f f e c t i v e l y increases the factor M so that condi t ion (3) i s met. A second method i s to use a mechanism which increases the effect of the above-mentioned secondary processes such as an u l t r a v i o l e t l i g h t pulse to increase secondary emission 8 and i o n i z a t i o n or a spark introduced i n the gas across a -15-spark gap (the production of the spark i s accomplished, of course, by the breakdown voltage method just mentioned). Now condi t ion ( 3 ) i s met by an e f fec t ive increase i n y . 2 . 4 . Radiat ion 2.4.1. Radiation Theory Two processes must be considered when r ad i a t i on from gaseous discharges i s discussed; the release of radiant energy from the gas molecules, and the de l ive ry of energy to the gas molecules. In re leas ing radiant energy, the energy s tate of the molecule proceeds from a higher to a lower l e v e l ; the frequency of the released rad ia t ion i s given by the Planck r e l a t i o n where h i s P lanck ' s constant, ynrn the frequency, and E n and Em are the higher and lower states of the molecule. The p r o b a b i l i t y per uni t time that a t r a n s i t i o n from the n t h to the m* n energy s tate w i l l occur i s given by K9. = E where -16-[jJn and ijjm are the wave functions per ta in ing to the energy states n and m , and dV i s an element of volume. I f the states are bound, that i s , negative energies, then the \jj - functions are normalized to un i ty , and i f e i ther s tate i s unbound, that i s , the molecule i s ion ized , then the corresponding wave function has the asymptotic form of a plane-wave. When both states are unbound, c l a s s i c a l l y the free e lec t ron passes close to a nucleus and i s accelerated by the nuclear charge; r ad ia t ion takes place by v i r t ue of the e l ec t ron ' s acce le ra t ion . This process i s c a l l e d bremsstrahlung, I f the f i n a l energy s ta te of the molecule l i e s higher than the i n i t i a l , the reverse process to emission fakes place, absorption. This process i s governed by the p r o b a b i l i t y B m n that absorption w i l l occur per un i t time per un i t density of monochromatic energy i n the region of the absorber, where EL - Af g n stands for the s t a t i s t i c a l weight of s tate n . In addi t ion to spontaneous emission, governed by A n m , there i s the process of induced emission which can occur i n the presence of r ad i a t i on . For t h i s process the coe f f i c i en t Bnm i s the p r o b a b i l i t y for forced emission to occur per un i t -17. time, per un i t density of monochromatic radiant energy i n the v i c i n i t y of the emitter . Theory shows that An energy balance equation can be wr i t t en i f a s tate of thermal equ i l ib r ium ex i s t s between r ad i a t i on and r ad ia to r s , ( / L + B_pX= B_pN m where ^nm) * s t h e m °oochromat ic radiant energy densi ty , and N n and N m are the number of molecules i n s tates n and m respec t ive ly . However i n most p r a c t i c a l instances, the rad ia tors i n a low-pressure gas discharge are not i n a s tate of thermal equ i l ib r ium with the r ad i a t i on . Spontaneous emission grea t ly exceeds absorption, which i n turn occurs much more frequently than forced emission. Before the r ad i a t ive process can occur, the molecule must be i n an elevated energy l e v e l . This brings up the second process that must be considered, the de l ive ry of energy to the gas molecules. This i s achieved by i n e l a s t i c c o l l i s i o n s . The prime source for energy e leva t ion i s e l a t a t ion which i s the name for exc i t a t i on and i o n i z a t i o n by i n e l a s t i c c o l l i s i o n s of the f i r s t k ind . Radiators i n any s tate may -18-absorb the k i n e t i c energy of impinging p a r t i c l e s and transform to a higher energy l e v e l . The condit ions to be f u l f i l l e d for t h i s to happen are that energy and angular momentum must be conserved. The angular momentum requirement p roh ib i t s ce r t a in bound t r a n s i t i o n s . Free electrons are the most e f f i c i e n t impacting p a r t i c l e s because they possess the most favourable mass r a t i o for energy t ransfer . Von Engel shows that the maximum energy, A , that can be t ransferred from the impinging p a r t i c l e to the atom i s given by where m = mass of atom, mj[ = mass of impinging p a r t i c l e , and E Q = i n i t i a l k i n e t i c energy of the impinging p a r t i c l e . For an impinging e lec t ron , m^^^ m and therefore / \ == E Q ; for any heavier p a r t i c l e , A < C E Q • Posi trons are presumably just as e f fec t ive . Another process, mentioned previous ly , which exci tes or ion izes radia tors i s photon absorption. Rigorous se lec t ion ru les govern the exc i t a t i on process and for i o n i z a t i o n there are probably three processes which occur. F i r s t , the d i rec t absorption of photons wi th energy exceeding the i o n i z a t i o n energy and subsequent e jec t ion of an 'i e lec t ron . Second, the absorption of d iscre te l i n e rad ia t ions -19-followed by io n i z a t i o n by c o l l i s i o n with other p a r t i c l e s while the excited state p e r s i s t s . Third, non-monatomlc molecules can be excited to high molecular states and then spontaneously di s s o c i a t e into molecular ions. However, for gases at low pressure absorption of photons does not play as important a part i n e x c i t i n g or i o n i z i n g as do c o l l i s i o n s . 2.4.2. Recombination Once the gas molecules have been ionized and energy i s no longer being injected into the system, the process of de-ionization takes place. The electrons and the ions are recombined and the gas returns to a neutral state. The two types of recombination are volume and surface recombination; volume recombination takes place i n the volume of the gas and surface recombination takes place on the surface of the container walls. occurring i n the volume of the gas. For binary c o l l i s i o n s , the number of recombinations per unit time i s given by where <J~T i s the recombination cross-section, u i s the r e l a t i v e speed, and n, and n_ the density of the Volume recombination depends on random c o l l i s i o n s -20-recombining p a r t i c l e s . The product CTr(X Is averaged. For th ree -pa r t i c l e c o l l i s i o n s , the recombination rate i s given by where i s the e f fec t ive volume of the t h i r d p a r t i c l e and n Q i t s densi ty. In e i ther case these factors are combined in to a s ing le coef f i c ien t a , c a l l e d the recombination c o e f f i c i e n t , so the rate i s expressed as r e l a t i v e speed of the p a r t i c l e s and decreases the faster the p a r t i c l e s move with respect to one another. This i s because the time i n t e r v a l during which they are i n c lose proximity and which i s ava i l ab le for recombination var ies inverse ly with the speed. I t should also vary wi th the e f fec t ive diameter of the ions , being larger for exci ted ions . Volume recombination takes place by f i v e p r i n c i p a l methods. 1) Radiat ive e lect ron recombination. A free e lec-tron combines wi th a pos i t i ve ion in to an exci ted atom and a photon possessing the surplus energy required to s a t i s f y the (4) The p r o b a b i l i t y of recombination depends on the -21 -conservation of energy. The p r o b a b i l i t y for e lec t ron capture in to the lower states i s greater the lower the s ta te . In addi t ion to s a t i s f y i n g conservation of energy, the l ibe ra ted photon must s a t i s f y conservation of angular momentum. 2) Die lec t ron ic recombination. In t h i s instance a free e lect ron combines wi th a pos i t i ve ion and the excess energy of the e lec t ron i s given to a second electron i n the atom so that a doubly exci ted ion i s formed. This s i t u a t i o n i s unstable and may lead to au to- ion iza t ion or be s t a b i l i z e d by c o l l i s s i o n or by r ad i a t i ng . 3) Three-body e lect ron recombination. If a t h i r d p a r t i c l e i s i n the v i c i n i t y of an e lec t ron- ion recombination, the surplus energy from the act i s taken up by the t h i r d body i n the form of k i n e t i c energy. 4) D i s soc ia t ive recombination. When a pos i t i ve molecular ion combines wi th an e lec t ron , the excess energy may be u t i l i z e d i n d i s soc i a t i ng the molecule in to i t s c o n s t i -tuent atoms of which one or a l l may be exc i ted . 5) Mutual neu t r a l i z a t i on . This process i s simply the recombination of a pos i t i ve and a negative ion . Pre l iminary processes must involve the preparation of negative ions which l i m i t s t h i s process to electronegative gases. In a high density mixture of approximately equal con-centrat ions of ions and e lec t rons , the electrons tend to diffuse r a p i d l y away towards regions of lower density such as -22-the wal l s of the containers thus creat ing a pos i t i ve space change. An e l e c t r i c f i e l d i s set up which retards the e l ec t -rons and accelerates the ions so that both diffuse at the same ra te . This process i s known as ambipolar d i f fus ion and i s governed by the ambipolar d i f fus ion constant D a . The equation for p a r t i c l e concentration under ambipolar d i f fus ion effects only i s ^ - 'C^V2n ... (5) dt Under ambipolar d i f f u s i o n , the p a r t i c l e s diffuse u n t i l they s t r i k e the wal l s of the enclosure and surface recombina-t i o n takes place. I t may r e su l t i n luminescence but l i t t l e i s known about t h i s process. Probably most of the surface recombination r e su l t s merely i n heating the surface. Surface recombination i s an extreme case of three-body electron recom-b ina t ion . I f both ambipolar d i f fus ion and volume recombination effects are present, then the equation for e lec t ron concentra-t i o n becomes, from (4) and (5) I t i s assumed that the e l e c t r i c a l discharge maintains a high degree of l o c a l neu t r a l i t y so that n e = n i for s i ng ly -23-ionized gases. E x p l i c i t so lu t ions of t h i s equation are possible but have not been u t i l i z e d . L imi t ing so lu t ions are obtainable, however, both for when recombination i s n e g l i g i b l e , and when d i f fus ion i s n e g l i g i b l e . In the former case, the so lu t ion i s i n the form of an exponential decay, wi th the time constant dependent on the d i f fus ion constant and the geometry of the discharge. When d i f fus ion i s n e g l i g i b l e , the so lu t ion of (6) i s ~ ~ ^ =<*t ... (7) H e where ( n e ) 0 i s t h e e lec t ron density at t = 0 . 2 .4 ,3 . Continua The continuous spectrum observed i n a gas discharge can or ig ina te i n several ways. For the case of e lec t ron- ion recombination, the e lect ron can approach and be caught by the ion , while the energy of recombination may be emitted as a quantum of r ad i a t i on . In general the e lec t ron has a k i n e t i c energy E and so emits r ad ia t ion of frequency = g y + E -24-where V j ^ i s the i o n i z a t i o n po ten t i a l of the ion . I f the electrons have an energy d i s t r i b u t i o n , then the emitted spectrum i s a continuum beginning at the se r ies l i m i t and extending to i n f i n i t y . However, s ince the p r o b a b i l i t y for recombination i s larger for a small r e l a t i v e v e l o c i t y between the e lect ron and the i on , the continuum w i l l be most intense at the ser ies l i m i t and w i l l f a l l r a p i d l y beyong i t . Ce r t a in ly the most important cont r ibut ion to the continuum comes from the so -ca l l ed free-free t r a n s i t i o n of the e lec t ron , or bremsstrahlung. This i s , from a quantum point of view, the displacement of the e lect ron from one free energy l e v e l to another wi th release of energy E of frequency -p- . Thus i n a plasma where electrons move n at random, energy i s radiated continuously over a wide band of frequencies. This r ad ia t ion i s a lso c a l l e d re tarda t ion r a d i a t i o n . Some other types of cbntinua of lesser importance are molecular d i s s o c i a t i o n continua, pressure continua from c o l l i s i o n interference with l i n e r a d i a t i o n , and attachment continua. -24-3. The Flash Tube 3 .1 . The Flash Tube Discharge Model B r i e f l y , the f l a sh tube operates i n the fo l lowing manner. A gas at low pressure i s confined i n an i n su l a t i ng tube between two electrodes. This tube i s placed across the terminals of a low inductance condenser which i s charged to a high voltage. The condenser i s discharged through the gas which emits copious amounts of h igh- in t ens i ty l i g h t . An equivalent c i r c u i t for the f l a sh tube and discharge condenser i s des i rable for ana lys i s . The c i r c u i t i s shown below. where C = capacitance of the discharge condenser, L = con-Rrj. =» f l a sh tube impedance. To make analys is s impler , i t has been assumed that the discharge impedance i s purely r e s i s t i v e . L C denser and tube inductance, R L = tube lead res is tance , and -25-The d i f f e r e n t i a l equation governing t h i s c i r c u i t when the switch i s closed at time t = 0 , corresponding to the f i r i n g of the f l a sh tube, i s [ ^ + Die dt where R = R + R. Three d i f ferent so lu t ions are poss ible . 1) The so lu t ion i s then given by where 7 I2L LC. b = - / L - 7 \/o = i n i t i a l voltage on the condensor. This i s an exponential current form which for 0 ^ t ( ( ~ ~k r i s e s wi th time constant approximately equal to - ^ since -26-]>b , and f o r t ^ 2L — , decays with time constant L C The solution i s L(t) L at where R 2.L This i s a critically-damped wave. 3) (R ) z < i \2.LJ ^ LC This case y i e l d s a solution which i s given by _ R T - V± £ 2 L sinwt c(t) where This i s a damped sine wave. If the logarithmic decrement i s defined by -27 then L and R may be ca lcula ted from L = 2 (8) C 4 V M - * , r where i s the period of o s c i l l a t i o n . 3.2. Desirable Charac te r i s t i c s Before a discussion of the construct ion of the f l a s h tube and measurement of some of i t s propert ies i s g iven, some of the des i rable propert ies of a f l a sh tube w i l l now be mentioned. They are given i n the approximate order of the i r importance. The f i r s t requirement i s that the emitted r ad ia t ion be of a continuous nature. The need for continuum rad ia t ion for absorption spectroscopy i s obvious and any emission or absorption l i n e s introduced by the background source can only r e su l t i n a further complication i n the ana lys i s . A few i so la t ed l i n e s may perhaps be to lera ted provided they dp not l i e c lose to the wavelengths involved i n any experiment, but any effor t to remove them should be encouraged. As was pointed out i n Anerson 's 1 ^ inves t iga t ion of -28-the spectrum of f l a sh tubes, current dens i t ies i n the discharge must be of the order of 20,000 amp/cm2 for the production of a strong continuum. I t can be seen from the equations derived i n the preceding sect ion that high current may be achieved by using a high charging voltage and having a low c i r c u i t inductance. The f i r s t r equ i s i t e i s easy to accomplish. A low c i r c u i t induc-tance demands the use of a low inductance capacitor and a coax i a l design of electrode leads. A low inductance w i l l a lso reduce the discharge time which may or may not be an advantage depending on the desired use of the tube. For absorption to take place i n a gas, the background source must have a greater i n t e n s i t y than the absorber. This requires a high brightness temperature from the f l a sh tube 5 and as pointed out by Budd , both a continuous spectrum and high temperatures are products of the same condi t ion ; both may be achieved wi th high currents . I f the i n t e n s i t y of the tube i s high enough, a s ing le f l a s h through the absorber may be s u f f i c i e n t to get a useful photographic record, otherwise a superposi t ion of more than one f l a sh may be necessary. In any case, the method t h a t , i s hoped to be used for future work i n absorption analys is w i l l require the exposure of at leas t two di f ferent photographic p la tes . A prime necessi ty for the success of t h i s procedure i s that the i n t ens i t y not vary from one shot to the next. i Without t h i s c h a r a c t e r i s t i c , quant i ta t ive analysis i s not -29-poss ib le . I t i s hoped i n the future to use the f l a sh tube for analys is of s h o r t - l i v e d phenomena such as shock fronts and pinched plasmas. This w i l l require fas t id ious t iming i n the t r igge r ing of the f l a sh tube and whether t h i s i s possible depends on the j i t t e r time of the t r igge r ing process. By j i t t e r time i s meant the v a r i a t i o n i n time from the app l i ca t ion of the t r igge r ing mechanism to the i n i t i a t i o n of the discharge through the tube. Since shock fronts move at a speed of the order of 1 cm/u.sec a j i t t e r time of no greater than 1 u.sec i s required for any t ime-resolut ion s tudies . And f i n a l l y there are two mechanical propert ies to be des i red . The f i r s t i s easy alignment wi th other u n i t s , notably the absorber and the spectroscope, and the second i s simple construct ion d e t a i l s for easy replacement or r epa i r s . 3 .3. Ear ly Designs A desc r ip t ion of some of the e a r l i e r f l a sh tube designs w i l l now be given before the f i n a l design i s discussed. 3 .3 .1 . The Elbow Tube In an effor t to e l iminate the deposi t ion of materials on the ex i t windows, i t was decided to t ry to use the scour-ing effect of the discharge current . This could most simply be done by using a r ight-angled tube, as shown schematical ly i n f igure 1(a). The current f lowing around the corner would 1(a) elbow tube scale ; full size Kb) low-inductance tube sca le : half size -30-scour the top sect ion of the tube at the curve and prevent any e b u l l i t i o n from being deposited there. The scouring process worked quite w e l l ; i n i t i a l l y a transparent yellow substance was deposited a l l over the ins ide of the tube, but after the f i r s t 10 shots or so, d id not get appreciably worse. The main drawback was that the spectrum contained too many emission l i n e s over ly ing the continuum; because of the bend, the por t ion of the discharge which was scouring was cooled by the wal l s of the tube and the l i g h t from t h i s cooler gas was entering the spectroscope, as w e l l as the l i g h t from the hot ter , continuum-forming gas i n the center of the tube. A minor mechanical disadvantage was the d i f f i c u l t y encountered i n a l ign ing the tube accurately. The tube was attached to the aluminum electrodes with black wax and the discharge t r iggered by a spark across a pa i r of tungsten wires waxed through a hole i n the grounded electrode. The electrodes were clamped i n copper c o l l a r s by r a d i a l screws which were i n turn attached to the condenser electrodes by copper p la tes . I n i t i a l l y a glass tube was used, but the heat from the discharge crazed the g lass , eventual ly causing i t to break after about 50 shots. With a quartz tube, the craz ing did not occur so the tube d id not break. The waveform of the current was an excel lent reproduc-t i o n of a damped sine wave, case 3) of sec t ion 3 .1 . The 31-resis tance and inductance computed from equations (8) and (9) were .034 ohms and 84.4 mu. henries respec t ive ly . 3 .3 .2 . Low Inductance Tube In an ef for t to achieve a better continuum, while s t i l l employing the scouring ef fec t , a low inductance c i r c u i t was designed, as shown i n f igure 1(b). The low inductance was achieved by use of a more coax ia l c i r c u i t about the f l a sh tube, and by having the connecting leads to the condenser close together. The grounded electrode of the tube was connected to the ground plate by a metal gauze c o l l a r . The discharge was viewed side-on instead of end-on as before, by looking through a hole i n the wire gauze. The spectrum d id not seem to be much improved, i f at a l l . Some of the emission l i ne s were more diffuse but others were sharper than before. Also the i n t e n s i t y was much less so t h i s configurat ion was abandoned. The current was a damped sine wave with R and L found to be . 0 3 6 . \ - & - and 31.3 mp.h . 3 .3 .3 . Tungsten-electrode Tube In an attempt to keep the in t roduct ion of foreign materials in to the discharge to a minimum, a r a d i c a l type of f l a sh tube was t r i e d next. The electrodes at both ends of p u m p t u n g s t e n e l e c t o d e s w i n d o w 2 ( a ) t u n g s t e n - e l e c t r o d e t u b e c o v a r - t o - g l a s s s e a l p u m p c o v a r t r i g g e r p i n - w i n d o w 2 ( b ) c o v a r t u b e z w i n d o w b r a s s d u m p - c h a m b e r 2 ( c ) c o v a r t u b e w i t h d u m p c h a m b e r -32-the tube consisted of 4 r a d i a l tungsten wires set through the glass tube, as shown i n f igure 2(a) . These wires were then joined together ex te rna l ly by a copper s t r i p and thence attached to the condenser. At one end of the tube, beyond the electrodes, was attached the vacuum pump while at the other end, a glass window was cemented on wi th de Kotinsky wax. Tr igger ing was effected by a spark between one of the grounded tungsten electrodes and a f i f t h tungsten wire inserted through the glass close to the grounded electrode. The window stayed clean for the f i r s t ten shots but then a deposi t ion r a p i d l y formed. Also the spectrum, while possessing a good background continuum, had many over ly ing emission l i n e s . For t h i s reason^ and also because of the awkward geometry, work on t h i s tube was ha l ted . 3 .3 .4 . Covar-electrode Tube S t i l l keeping i n mind the necessi ty for e l imina t ion of foreign mater ials from the discharge, the next attempt used covar electrodes wi th a covar- to-glass sea l to the tube. This was to circumvent the use of wax as a sea l which could cause contamination i f any of i t was immersed i n the discharge. The arrangement of the capacitor leads was the same as was used i n the f i n a l design and hence w i l l be described below. The tube was t r iggered by a covar wire sealed through the glass near the grounded electrode and bent back so i t was -33-close to the electrode. I n i t i a l l y the window was Cemented onto the covar (see f igure 2(b)) but t h i s introduced wax in to the discharge so then a brass chamber was soldered onto the covar and the window waxed onto the brass (figure 2 (c ) ) . I t was hoped that l i t t l e of the discharge would reach the wax around the window. Deposit s t i l l formed on the window however, and a lso the covar t r igger p in was affected by the discharge so that a spark between i t and the electrode would not occur after only 5 discharges. F i n a l l y , after c leaning the t r igger p i n , a c i r c u l a r glass baf f le was placed i n the brass chamber close to the covar electrode. The hole i n the center of the ba f f l e was of such a s i z e that the covar electrode could not "see" the window. This led to the f i n a l design of the tube and i s now to be described. 3.4. F i n a l Design 3 .4 .1 . Descr ip t ion The f l a s h tube design f i n a l l y ar r ived and i s shown i n f igure 3. The operation of the tube i s as fo l lows . The aluminum electrode E^ cemented to the quartz discharge tube i s connected to the 4.8 cm long, 2.7 cm inner diameter copper c o l l a r C i by means of 8 r a d i a l screws S . This copper c o l l a r i s connected to the ground terminals of the condenser through the copper lead L 1 . The other aluminum electrode E£ i s attached to the copper c o l l a r C„ by a wire gauze which i s fig. 3 final design scale: full size -34-soldered to the c o l l a r and secured to the electrode by a metal s t rap. C o l l a r C 2 i s connected to the other terminal of the condenser by the copper lead L£ . When the tube i s f i r e d by app l i ca t ion of the t r igger pulse on the t r igger p i n , the current flows from the condenser up through Lg, along C 2 to E 2 by way of the wire gauze, through the ins ide of the quartz tube to and thence to the other condenser terminal v i a S , C]_, and L i . and L 2 are insula ted from each other by a perspex sleeve P g , 7.5 cm long and 2.0 cm inner diameter, set i n a perspex pla te P^, 1.5 mm th i ck . The aluminum electrodes Ej and E 2 are joined to the quartz tube wi th de Kotinsky wax, but because of the snug f i t of the tube in to the inner shoulder of the electrode, the wax remains i n the outer shoulder and i s not immersed i n the discharge i n any way. Aluminum was chosen as electrode mater ia l because of i t s low sput ter ing ra te . The tube i t s e l f was made of quartz 10 cm long and .9 cm inner diameter, 1.2 cm outer diameter. Quartz was chosen for i t s better a b i l i t y to withstand the heat generated by the discharge. Quartz also does not show strong absorption l i n e s caused by absorption i n the vapour scoured from the wal l s of the tube. Glass shows the sodium D l i ne s s t rongly i n absorption. The t r i gge r ing device i s a small covar tube i n glass set in to the electrode Ej and a tungsten wire jplaced far -35-enough through i t so the end of the wire i s c lose to the opposite inner s ide of the electrode. The covar p in i s per-manently sealed to Ej wi th epoxy r e s i n , and the wire with de Kotinsky wax for easy replacement i f necessary. When a high voltage pulse i s applied to the t r igger wi re , a spark jumps from the end of the wire to the electrode and discharge of the condenser begins. A 1/16 inch c i r c u l a r glass baf f le i s set in to the electrode E2 as shown, and stops the discharge debris from reaching the window W2 . The hole i n the baf f le i s small enough so that any p a r t i c l e s t r a v e l l i n g i n a s t ra igh t l i n e from the discharge side of E 2 w i l l h i t the baf f le rather than the window. The baf f le i s held i n place by a th in-wal led aluminum tube which f i t s c l o s e l y in to the chamber of E 2 and i s braced against the window W2 . Both W^  and Wg are glued to t he i r respect ive electrodes with de Kotinsky wax of which a minimum amount i s used to al low as l i t t l e as possible to enter and contaminate the discharge. The coax ia l symmetry of the leads were chosen for the low inductance and also for the low rad ia t ing e f f i c i ency . Because of the high current f lowing i n opposite d i rec t ions i n the copper leads, a repu ls ive force i s set up and the leads tend to be forced apart* The purpose of 'the wire gauze connecting the electrode to the copper c o l l a r i s to absorb t h i s shock. A perspex clamp i s a lso used to help -36-hold the plates together. O r i g i n a l l y both electrodes were clamped by r a d i a l screws, but the wax or even the tube would crack after not too many discharges. 3 .4 .2 . Operation The voltage impressed across the electrodes was from 15 to 20 kV. Below 15 kV the spectrum showed many emission l i ne s over ly ing the background continuum and at 15 kV these l i n e s were few and d i f fuse . An increase i n charging voltage tended to broaden the l i n e s and make the continuum bet ter . Twenty kV was chosen as an upper l i m i t for the charging voltage because t h i s i s close to the maximum voltage rated by the condenser manufacturer and a lso above 20 kV the danger of the tube shat ter ing upon f i r i n g was increased. The pressure i n the tube was about .1 u. or lower. The ac tual value of the pressure was not measured accurately s ince the pressure required was just t h a t which would, "hold" the applied voltage without spontaneous breakdown. This would el iminate the need for any ser ies t r igger spark-gaps which would only complicate the c i r c u i t r y and make a less e f f i c i e n t discharge. I t has been found by other workers i n t h i s f i e l d 1 1 that the i n t e n s i t y of the r ad ia t ion i s indepen-dent of i n i t i a l pressure i n the tube over a wide pressure range. Thus the low pressure was required only because of the high voltage. -37-3 .4.3. Experimental The experimental procedure i n designing the f l a sh tube was f a i r l y s t raightforward. The two important r equ i s i t e s that had to be met were a high i n t ens i t y continuum and a constant peak i n t e n s i t y . The l i g h t output of the d i f ferent tube configurations was examined wi th a Hi lger medium quartz spectroscope and a Hi lger automatic quartz spectroscope to observe the qua l i ty of the continuum. A photomul t ip l ie r -emi t te r - fo l lower u n i t , des-cr ibed below, was used to observe the i n t e n s i t y of the r ad ia t ion from the f l a sh tube. This was done by se t t ing the photomult ip l ier about 10 feet from the tube and observing the i n t ens i t y trace on a Tektronix osc i l loscope type 533. The decrease i n peak inten-s i t y wi th number of shots was recorded with a Polaro id o s c i l l o -scope camera. To observe the discharge current a small pick-up c o i l was placed close to the discharge. The change of magnetic f l ux in ; the c o i l induced an e.m.f. given by d i V = M dt where M i s the mutual inductance between the c o i l and the discharge c i r c u i t and — i s the de r iva t ive of the current . dt •  _ This s igna l was fed through an analog integrator to the o s c i l l o -scope, g iv ing a s i g n a l proportion to the current . -38-3.5. Apparatus 3.5.1. Charging Condenser and Charging Unit As mentioned i n Section 3.2. a low inductance c i r c u i t i s desirable to achieve high current den s i t i e s . For t h i s reason the condenser used was a 1,6 [if low inductance, 25 mu,h, 25 kV condenser manufactured by Cornel1-Dubilier, model NRC 323. The charging unit i s capable of d e l i v e r i n g 27 kV at 50 ma and i s a standard full-wave voltage-doubler c i r c u i t f i l t e r e d by an L-C network. A current-sensitive r e l a y i n s e r i e s with the current meter closes a set of contacts which opens primary power to the high voltage transformer and drops a shorting switch. Thus the voltage may be applied to the charging con-denser up u n t i l the instant of f i r i n g ; when the f l a s h tube i s discharged the charging unit i s prevented from recharging the condenser by the current t r i p and shorting switch. 3.5.2. Trigger Unit The trigger unit was designed after the work of 12 Theophanis and d e l i v e r s a 40 mu.sec, 32 kV pulse to the trigger pin to i n i t i a t e the f l a s h tube discharge. See fig u r e 4. A three-meter long, type RG58u coaxial cable i s charged to 16 kV. The far end of the cable i s terminated with a 500 pf, 20 kV condenser p a r a l l e l e d with a 100 KX1 r e s i s t o r ; t h i s gives e s s e n t i a l l y an i n f i n i t e termination. The sheath of the coaxial cable i s grounded while the inner conductor at 16 kV -39-F i g . 4. T r i g g e r Unit i s connected t o the anode of a 5C22 h y d r o g e n - f i l l e d t h y r a t r o n which i s i n i t s non-conducting s t a t e . When a p o s i t i v e pulse i s a p p l i e d t o the g r i d of the t h y r a t r o n causing i t to conduct h e a v i l y , i t e s s e n t i a l l y s h o r t s the end of the attached c o a x i a l c a b l e , sending a negative 16 kV pulse down the cable. This pulse i s r e f l e c t e d at the f a r end w i t h a r e f l e c t i o n f a c t o r of +1 and i n order that the voltage across the condenser remains " i n s t a n t a n e o u s l y " constant, the f a r s i d e of the condenser must f a l l to minus 32 kV. This pulse i s taken o f f across the r e s i s t o r . 40-The p o s i t i v e pulse required to trigger the thyratron i s provided by a 2D21 tetrode which i s normally i n a state of cut-off u n t i l i t s g r i d i s shorted by a manual micro-switch or by application of a p o s i t i v e pulse. 3.5.3. Photomultiplier Unit The photomultiplier unit was used to determine the va r i a t i o n of the wavelength-integrated l i g h t output of the f l a s h tube with the number of shots. This unit consisted of a 931A photomultiplier and a 2N1177 tr a n s i s t o r i n a common co l l e c t o r or emitter-follower configuration. See figure 5. F i g . 5. Photomultiplier Unit -41-The uni t was completely enclosed wi th i t s power supplies i n a brass box to avoid e l e c t r i c a l pickup from the discharge. Even then i t was found that the uni t had to be placed about 10 feet from the discharge before pickup was n e g l i g i b l e . I t was found that shot noise i n the photomult ipl ier grea t ly masked the output s i gna l at low output voltages; t h i s shot noise or ig ina tes e s s e n t i a l l y i n the cathode-dianode-number-one region and can be reduced by increasing the current between these stages. Non-linear and saturat ion effects were found to occur i n the l a te r stages of the photomult ipl ier when a l l dianodes were connected, however, and so dianode No. 7 was used as the anode, and the anode and dianodes No. 8 and 9 were strapped to dianode No. 6. This almost completely el iminated the noise i n the output voltage range that was encountered. The common c o l l e c t o r t r ans i to r c i r c u i t was used to match the high output impedance of the photomult ipl ier to the 52 ohm cha rac t e r i s t i c impedance of the coax ia l cable connecting the un i t to the osc i l lo scope . With a 52 ohm impedance match at (the 'scope end of the cable , r i ng ing i n the c i r c u i t was e l iminated. The uni t was tested for l i n e a r i t y using a .5 p.sec l i g h t pulse and was found to be l i nea r for an output s igna l up to .4 v o l t s . The r i se - t ime was less than .1 p.sec. -42-4. Brightness Temperature Measurement 4 . 1 . Introduction 4 . 1 . 1 . Black Bodies Light r ad i a t i on i s the transfer of energy t r a v e l l i n g i n the form of electromagnetic waves, and the standard for a l l rad ia tors i s the black body. A black body may be simply defined as a body that absorbs a l l the r ad ia t ion which f a l l s upon i t . I t can be shown theore-t i c a l l y and has been v e r i f i e d experimentally that such a body w i l l radia te energy of an amount which depends only on the temperature of the body. This leads to one of the fundamental laws which determines the manner i n which a black body radiates i t s energy, the ce l e -brated Planck r ad i a t i on law which t e l l s how the radiant energy var ies wi th the wavelength of the r ad i a t i on and wi th the temperature of the r ad ia t ing body. This i s given by at a temperature T i n the wavelength i n t e r v a l (A, \ + dX), (10) where = the spec t ra l radiant i n t ens i t y per uni t wavelength C i and C2 are constants connected to the fundamental constants -43-h, c and k and C2 =• 1.438 cm-deg. P lanck ' s law has two s imp l i fy ing forms for the opposite end of the spectrum. I f AT i s large wi th respect to ' Q2 , then the Rayliegh-Jeans formula i s obtained On the other hand i f AT i s smal l , Wien's formula i s a r r ived at 4 ;1 .2 . Temperature In the measurement of r ad i a t i on from bodies, one usua l ly needs to know, or i s in teres ted i n , i t s temperature. In pyrometry and color imetry the important quant i t ies are brightness temperature and colour temperature. Also of in te res t here i s the e lec t ron temperature. They are defined as fo l lows : 1) Brightness temperature. The brightness temperature of a body i s that temperature of a black body which has the same radiant i n t ens i t y of the surface of the body i n question * at a f i xed wavelength. The r e l a t i o n between brightness -44-temperature . S and true temperature T i s given by Jjs) = r£^,T ) j , ( T ) ( 1 3 ) where (S) represents the radiant i n t ens i t y of a black body wi th a temperature S } J^(T) represents the radiant i n t ens i t y of the body under considerat ion with a temperature T, and £ ( A , T ) i s the emiss iv i ty of the body. i s the t rans-mission factor of any absorbers i n the system between the source and the observer; for example the window of a tungsten filament lamp whose brightness temperature i s to be measured. 2) Colour temperature. The colour temperature of a l i g h t source may be defined as the temperature of a black body which has the same colour . Thus colour temperature has meaning only i n the v i s i b l e range. 3) E lec t ron temperature. I f a c o l l e c t i o n of electrons are i n thermal equi l ib r ium wi th themselves a constant mean energy of the c o l l e c t i o n may be defined. With the equi-p a r t i t i o n theorem for energies i n mind, i t i s poss ible to define the e lec t ron temperature as E =|H = where £ i s the mean energy of the e lec t ron gas, m the e lec t ron mass, k i s Boltzmann's constant, v r the random -45-v e l o c i t y and T e the e lect ron temperature. A l o c a l e lec t ron temperature may be defined i f the electrons are i n l o c a l equ i l ib r ium even though not necessar i ly i n o v e r a l l equi -l i b r i u m . A temperature for other types of p a r t i c l e s can s i m i l a r l y be defined. I f a gas consis ts of two types of p a r t i c l e s , t he i r temperatures need not be the same. 4 .2 . Theory To ca lcu la te the brightness temperature of . the f l a sh tube the radiant i n t ens i t y per uni t wavelength of the tube i s compared to the radiant i n t ens i t y of a tungsten-filament lamp by measuring the i n t e n s i t i e s at various wavelengths wi th a photomul t ip l ie r . I f the i n t ens i t y of the r ad i a t i on emitted by the f l a sh wavelength i n t e r v a l measured and i s a function of wavelength, the i n t e n s i t i e s observed on the osc i l loscope w i l l be deter-mined by function whose value l i e s between 0 and 1, i f 1 i s i t s value at peak s e n s i t i v i t y . 2) Any f i l t e r s which need to be placed i n the path between the lamps and the photomult ip l ier i n order to keep 1) The v a r i a t i o n i n s e n s i t i v i t y of the photomult ip l ier wi th wavelength. sSfhjvtlll be a s ingle-valued - 4 6 -t h e a m p l i t u d e o f t h e i n t e n s i t y b e l o w t h e n o n - l i n e a r l e v e l o f t h e p h o t o m u l t i p l i e r . F o r s i m p l i c i t y , n e u t r a l d e n s i t y f i l t e r s s h o u l d b e u s e d . 3) A n y g e o m e t r i c d i f f e r e n c e s i n t h e e x p e r i m e n t a l s e t u p f o r m e a s u r i n g t h e r a d i a t i o n f r o m t h e f l a s h t u b e a n d t h e t u n g -s t e n l a m p . T h i s w i l l b e s u c h t h i n g s a s t h e s u b t e n d i n g o f d i f f e r e n t s o l i d a n g l e s , d i f f e r e n t s i z e s o u r c e s , a n d s o o n . T h e r e f o r e t h e s i g n a l s s e e n o n t h e ' s c o p e c a n b e w r i t t e n Vtl(A)= K ^ ) ^ G T L y L d A n w h e r e " a m p l i f i c a t i o n f a c t o r o f e m i t t e r - f o l l o w e r a n d ' s c o p e a m p l i f i e r , t3(?\) = p h o t o m u l t i p l i e r s e n s i t i v i t y , VJL , ^ = t r a n s m i s s i o n f a c t o r s o f t h e f i l t e r s f o r t h e t u n g s t e n l a m p a n d t h e f l a s h t u b e r e s p e c t i v e l y ; n o t a f u n c t i o n o f w a v e l e n g t h f o r n e u t r a l d e n s i t y f i l t e r s . G y L ^ ^jrr " g e o m e t r i c f a c t o r s f o r t h e t u n g s t e n l a m p a n d t h e f l a s h t u b e ; a l s o n o t a f u n c t i o n o f w a v e l e n g t h p r o v i d e d s u c h e f f e c t s a s c h r o m a t i c a b e r r a t i o n o f a n y l e n s e s i n t h e s y s t e m m a y b e n e g l e c t e d . - r - T t T F T J . J = s p e c t r a l r a d i a n t i n t e n s i t y p e r u n i t w a v e l e n g t h o f t h e t u n g s t e n l a m p a n d t h e f l a s h t u b e . c\\ A/\ °* t h e w a v e l e n g t h r a n g e o v e r w h i c h t h e T L * U / V T -47-i n t e n s i t y was measured f o r the tungsten lamp and the f l a s h tube. For the tungsten lamp Wien's law can be used i n the v i s i b l e r e g i o n so that whereas f o r the f l a s h tube Planck's law gi v e s so that i f the maximum i n t e n s i t i e s of the lamp and the f l a s h tube are measured at one wavelength and the r a t i o of the i n t e n s i t i e s taken, one gets I f the wavelength i n t e r v a l f o r the two sources are the same then — r - T L R M rn G„ J? Q , I f the geometry i s d i f f e r e n t f o r the two lamps, ^ T L / L 7 F T w i l l be d i f f i c u l t t o c a l c u l a t e ; i f the geometry i s made i d e n t i c a l , then H ( A ' " ^ F T J K r T r F T [ e X P ^ - | ] (14) -48-X ^p1" may be measured on a microphotometer or densitometer, RfX)»^  anC^ S T L a r e * c n G wn, a n d hence S f T m a v ^ e ca lcu la ted from equation (14). 13 This i s the method used by Parkinson and Reeves , i n t he i r experiment of measuring the brightness temperature of. various types of f l a sh tubes. I f , however, the i n t e n s i t i e s are measured at two d i f -ferent wavelengths A and A ' , say, and the r a t i o of the i n t e n s i t y r a t i o s i s taken, then the f i l t e r factors and the geometric factors cancel and where Sp-p a n d 5FT 3 X 6 brightness temperatures at wavelengths A and A ' r e spec t ive ly . Anderson 1 0 found that the r e l a t i v e i n t ens i t y d i s t r i -but ion of the f l a sh tube behaves i n a fashion s i m i l a r to that of a black body and i f t h i s i s the case then one should be able to equate 5p wi th Sp-y- * * n a n y case, looking at the r e su l t s of Parkinson and Reeves1"^, i t can be seen that the temperature there ca lcu la ted i s a s lowly varying function of wavelength so i f the i n t e r v a l J A - A , ! ;J i s not too large, 49-one can put S^ .^ = ^> F T without too much e r ror . Then F T RfX) v L S T L l X A If B = r — B« = - - J A = then (15) This equation can be solved for N by i t e r a t i o n or as i s done here by successive subs t i t u t i on . 4.3. Experimental Procedure A general schematic view of the temperature-measuring apparatus i s shown i n f igure 6. ; Because of the emit ter-fol lower c i r c u i t fo l lowing the m i r r o r s p h o t o m u l t i p l i e r r o t a t i n g m i r r o r c o n s t a n t - d e v i a t i o n s p e c t r o s c o p e f i g . 6 t e m p e r a t u r e - m e a s u r i n g a p p a r a t u s -50 photomult ip l ier uni t a d .c . measurement of the tungsten-filament lamp i n t e n s i t y was not poss ible and so a pulsed tungsten source was necessary. Also to achieve more i d e n t i c a l condit ions wi th respect to t ransients i n the photomul t ip l ie r -erai t ter-follower c i r c u i t s , a tungsten l i g h t pulse of duration of the same order as that of the f l a sh tube was desired. This meant a pulse of the order of 10 p.sec and necessitated the use of a shutter of some so r t . An o p t i c a l shutter using a ro t a t ing mirror seemed idea l for t h i s purpose. Unfortunately, the only appropriate ro t a t ing mirror shutter was being used i n another experiment and hence could not be r e a d i l y removed for use i n t h i s one. See reference 5 wherein i s described prel iminary work i n the study of absorp-t i o n spectra of plasmas, which employs the use of a f l a sh tube. This work i s being continued and the experimental setup i s almost exact ly the same as described except for the subs t i t u t i on of the o p t i c a l shutter for the mechanical one. In order to save the time and expense necessary to b u i l d a s i m i l a r shut ter , i t was decided to mount the f l a sh tube i n place of the one being used i n the above-mentioned experiment and def lect the l i g h t from the tube in to the constant-deviat ion spectroscope being used for i n t e n s i t y measurements. The plasma absorption tube shown i n the diagram i s used i n the other experiment and does not affect the r e su l t s of t h i s one. -51-For measuring the i n t ens i t y of the tungsten lamp, the lamp was placed d i r e c t l y behind the adjustable s l i t and as c lose to i t as possible to ensure maximum i l l u m i n a t i o n . The s l i t was focused by lens A onto the s l i t of the constant devia t ion spectroscope when the ro t a t i ng mirror was l i n e d up. The length of the pulse could be adjusted e i ther by varying the speed of the motor d r i v i n g the mirror or by chang-ing the width of the adjustable s l i t . This second method was employed to procure a pulse of about 10 p.sec durat ion. The i n t e n s i t i e s were measured with the photomult ip l ier and osc i l loscope and 'scope camera. Measurements were made every 100 angstroms on the drum scale of the spectroscope (which was approximately every 120 angstroms upon c a l i b r a t i o n of the drum) from .4440 A to 6555 1. For the f l a sh tube measurements, lens B and C focussed the l i g h t from the discharge onto the adjustable s l i t . The ro t a t ing mirror was stopped and posi t ioned so the s l i t was focused on the spectroscope and s i m i l a r i n t ens i t y measurements were made. I t was found necessary to use a f i l t e r wi th the f l a sh tube and three sheets of mylar were used. The mylar was a good neutra l -densi ty f i l t e r and had a transmission factor of about 45%. -52-4.4 . Apparatus The black body which was used as the standard l i g h t source was a 120 v o l t G.E. projec t ion lamp which was operated on 125 v o l t s d .c . The colour temperature of the lamp was measured with a Hartmann and Braun filament o p t i c a l pyrometer i n the 1500 to 3500°C range. The pyrometer c a l i b r a t i o n was checked using a G.E. T-24, 86-P-50 standard lamp. The brightness temperature of the lamp was then found by using a nomogram ca lcula ted by Rutgers and de Vos 1 ^ which gives the r e l a t i o n between the brightness temperature, true temperature and colour temperature of a tungsten f i lament . The pyrometer was averaged over 10 readings and gave a colour temperature of 2940°K which corresponds to a brightness tem-perature of 2560°/K. The spectroscope used was a Hi lger quartz-prism constant devia t ion spectroscope wi th an adjustable s l i t mounted i n place of the p la te-holder . The photomult ip l ier was placed behind the s l i t and was enclosed i n a brass container attached to the s l i t to reduce pickup. The spectroscope was ca l ib ra t ed using the A 5791, 5770, 5461, and 4358 angstrom l i n e s of mercury and the A 6563 and 4861 l i n e s of hydrogen. The photomult ipl ier c i r c u i t was as was described before except a 900 v o l t supply was used instead of 600 v. This was necessary to achieve s u f f i c i e n t s e n s i t i v i t y when measuring the l i g h t i n t ens i t y of the tungsten lamp and the f l a sh tube at both ends of the v i s i b l e spectrum. -53-5. Results 5 .1 . F lash Tube Spectrum Using the Hi lger medium quartz spectroscope, the spec-o o trum was observed from 6500 A down to about 2300 A . At low condenser voltages (11 kV) quite a few l i ne s and bands were observed on a background continuum throughout the range and as the voltage was increased most of these l i n e s spread out in to the background. Several absorption l i n e s were present o at a l l vol tages; a group of s i x around 2500 A but none i n the v i s i b l e range which i s the region of in te res t for the work the tube i s hoped to be appl ied . Some l i n e s seen i n emission at low voltages were seen i n absorption at higher voltages i nd i ca t i ng a fas ter increase i n temperature i n the centre of the gas than i n the ext remi t ies . An improvement i n the con-tinuum was noted when the capacitance was increased from 1.6 j i f to 3.2 j i f . A t ime-resolut ion of the f l a sh was attempted using the ro t a t i ng mirror shutter and a delay un i t to see at what stage of the discharge the emission l i n e s occurred. Anderson*^ found that the emission l i n e s d id not appear u n t i l the l a te r part of the discharge when the current density was low. This same effect was found here but because the t iming of the -54-shutter was not known very accurate ly , the instant of i n i t i a l occurrence of the emission l i n e s was unknown. In approxi-mately the f i r s t 20 i&sec of the discharge, however, hardly any emission l i n e s were seen. At the present time work i s being done to correct the uncertainty i n t iming of the shut ter . 5.2. Current Waveform The observed current waveshape i s shown i n f igure 7. 1*1111. if \ \, ij F i g . 7. Current Waveform I t i s seen to be a damped sine wave as discussed i n 3 .1 . showing that the model chosen was quite cor rec t , and i s given by -6 . 1 x l 0 5 t 6 i = 81,400 e s i n 3.19x10 t amps Ca lcu la t ion of R and L using (8) and (9) gives R = 0.07X1-L = 58 mu,h. -55-The maximum of the current occurs when tan t = p and gives a value of t = .43 p.sec. The f i r s t zero of d i — was observed at t = .44 fisec which agrees w e l l and gives i m a x ".97,000 amp/cm2 which i s w e l l above the 20,000 amp/cm2 found necessary by Anderson f o r the production of a continuum. To get a simple estimate of the time at which the cur r e n t d e n s i t y ceases to be above the "continuum d e n s i t y " (20,000 amps/cm 2), the s i n u s o i d a l current v a r i a t i o n i s put equal to 1 and one can say 5 t c 81,400 e " 6 * 1 X l ° <^ 20,000 TTYO.45)2 where TT(0'^5)Z i s the c r o s s - s e c t i o n a l area of the tube. Thus t c ^ 2 . 2 p.sec, whereas t c was found t o be greater than about 20 p.sec as mentioned above. Although the i n e q u a l i t y i s c o r r e c t , a p o s s i b l e e x p l a n a t i o n of the order of magnitude d i f f e r e n c e i s that even though the current d e n s i t y f l o w i n g between the e l e c t r o d e s i s zero i n about 3 {isecs, the energy i n the gas i s s t i l l high enough t o ensure that much i o n i z a -t i o n i s present, so th a t the r a d i a t i o n emitted i s of a c o n t i n -uous nature. Of i n t e r e s t i s the time l a g between the a p p l i c a t i o n of the spark pulse and the i n i t i a t i o n of the current discharge. This i s shown i n f i g u r e 7 where the t r i g g e r pulse and subse-quent noise occurs at the beginning of the t r a c e , and the current begins about 1 u.sec l a t e r , at which time i t begins -56-a b r u p t l y . This r a i s e s the question of the mechanism f o r i n i t i a l breakdown of the discharge and the reason f o r the delay. The mean f r e e path between a i r molecules at . 1 p. i s about 10 meters, and i f k i n e t i c gas theory a p p l i e s , the mean f r e e path between an e l e c t r o n and the a i r molecules w i l l be about four times as great. When the t r i g g e r i n g voltage i s a p p l i e d and breakdown occurs between the t r i g g e r p i n and the grounded e l e c t r o d e , the p o s i t i v e ions w i l l be a t t r a c t e d t o -wards t h i s e l e c t r o d e w h i l e the e l e c t r o n s which escape recom-b i n a t i o n w i t h the ions w i l l be a t t r a c t e d and move towards the p o s i t i v e e l e c t r o d e at the f a r end of the tube. Because of the long mean f r e e path, i t i s u n l i k e l y that the e l e c t r o n s w i l l c o l l i d e w i t h any of the a i r molecules and thus most of the e l e c t r o n s w i l l s t r i k e the f a r e l e c t r o d e . Here some s o r t of s u r f a c e process must take place such as the e j e c t i o n of e l e c t r o n s and atoms and p o s i t i v e i o n s . The p o s i t i v e ions w i l l move towards the f a r (grounded) e l e c t r o d e , s t r i k e i t , and a l s o e j e c t e l e c t r o n s and i o n s , so the process i s repeated. Once the p a r t i c l e d e n s i t y i s increased enough by t h i s e l e c -trode s p u t t e r i n g and a l s o s p u t t e r i n g from the quartz tube, i o n i z a t i o n through c o l l i s i o n can take place and a "normal" breakdown can occur. One would expect from t h i s e x p l a n a t i o n , however, that the i n i t i a l c u r r e n t would r i s e g r a d u a l l y and not a b r u p t l y as observed. A reasonable e x p l a n a t i o n i s -57. l a c k i n g and a more thorough i n v e s t i g a t i o n w i l l be necessary. The delay of the i n i t i a t i o n of the current a f t e r the a p p l i c a t i o n of the t r i g g e r pulse was found t o be almost of the same d u r a t i o n i n every case. The j i t t e r - t i m e was about .2 u.sec and allows the tube to be synchronized a c c u r a t e l y w i t h s h o r t - l i v e d events. 5.3.. L i g h t I n t e n s i t y The time v a r i a t i o n of the l i g h t output of the f l a s h tube i s shown i n f i g u r e 8 which g i v e s the i n t e n s i t y emitted I F i g . 8. L i g h t I n t e n s i t y o at a wavelength of 5100 A . The shape of the wave i s very s i m i l a r at other wavelengths. I n i t i a l l y the l i g h t r i s e s r a p i d l y t o a maximum i n about i5 p.sec, then begins to drop o f f . At about 1 u.sec a f t e r the peak, a break i n the r a t e of f a l l sometimes occurs, i n d i c a t i n g the presence of a smaller second peak i n the i n t e n s i t y . In some of the tube c o n f i g u r a -t i o n s , such as the elbow tube, the second peak was very -58-prominent, being almost as large as the f i r s t , as shown i n f igure 9. The degree of prominence of the second peak not A M \ F i g . 9. Light In tensi ty of Elbow Tube only var ied wi th the tube used but also with the wavelength of the r a d i a t i o n , tending to be s l i g h t l y more prominent at higher wavelengths. The current and the i n t ens i t y were examined simultan-eously using a Tektronix type 551 dual beam osc i l lo scope . The trace i s shown i n f igure 10. Notice that the l i g h t 1 A A lyusec \ • \ / • F i g . 10. Current and In tens i ty of F lash Tube -59-i n t e n s i t y does not appear u n t i l about the f i r s t maxima of the current and the peak i n t ens i t y occurs at the f i r s t zero of the current . The second i n t ens i t y peak occurs s l i g h t l y before the second zero of the current . 5.4. Deionizat ion Once the current between the electrodes ceased to f low, the process of de ioniza t ion takes place . I f volume recom-bina t ion i s considered, and the emission of l i g h t i s assumed to be caused by recombination only, then i t seems reasonable that the i n t e n s i t y of l i g h t i n a small wavelength range w i l l be propor t ional to the number of electrons present and thus a lso to the number of ions . I f l o c a l n e u t r a l i t y holds, then n««rV=h and = ^ (16) where j\ i s the constant of p ropo r t i ona l i t y . Thus equation (7) becomes - r - i and a p lo t of J 2versus t should y i e l d a s t ra igh t l i n e of slope • This was done for three d i f ferent wavelengths and i s shown i n f igure 11. Care was taken to ensure the i n t ens i t y was measured after the current had stopped f lowing. -60-To get an estimate of the value of ot , the fo l lowing procedure was used. The r i s e i n pressure i n the f l a sh tube after f i r i n g and after the temperature was back to room tem-perature was about 35 p.. This gives a molecular density of 1.1 x l O 1 ^ c m - 3 using the perfect gas r e l a t i o n If none of the mater ia l sputtered from the electrodes and the quartz tube i s redeposited (highly questionable) and each atom of mater ia l i s s i n g l y ion ized , then an approximation for I C O the e lec t ron density i s 10 cm"" . I f i t i s assumed that t h i s i s the e lec t ron density at peak i n t ens i t y of the f l a s h , a value for r\\ can be ca lcu la ted from (16) and hence can be measured from the slope of the graph. In the three cases shown — 11 °i i n f igure 16 CX was found to be 2 x 10" cm / sec . I t i s d i f f i c u l t to compare t h i s r e su l t wi th others that have been measured because 0( doubtless var ies with the gas, i t s tem-perature, pressure, e tc . Values of CX found under various condit ions given by Loeb 1 ^ show that the value found here could be poss ib le . Massey 1 6 found C< 1 0 ~ 1 3 cm 3/sec for a temperature of 8,000°K i n oxygen. I t should be pointed out that the value for n i s h ighly doubtful for two reasons. One i s the assumption that no sputtered mater ia l i s redeposited after the discharge, and the second i s that t h i s p a r t i c l e density occurs during the discharge and not at a l a te r stage. Some r e su l t s explained below indica te t h i s second assumption may be f a l s e . A lower -61 -value of n would give a higher value of c<\ . The s t r a i g h t - l i n e p lo t of 2 versus time would indica te that the primary process of de ioniza t ion i s volume recombination. However caution should be used because recombination i s a process which i s far from being completely understood and the apparent r e su l t s may be misleading. A look at the di f fus ion-surface recombination process i s necessary. 15 Loeb states that i f the Debye length of the plasma i s much less than the dimensions of the containing vesse l , the d i f fus ion w i l l be ambipolar, while i f the Debye length i s much greater, the electrons w i l l diffuse independently of the ions , and the d i f fus ion w i l l be c a l l e d free. The e lect ron Debye length A D i s given by To get an order of magnitude of AD , assume a value of Te = 10,000°K which i s of the same order as that c a l c u l a -ted by Budd 5 for a s i m i l a r f l a sh tube. He i s as ca lcula ted before I ( | 0 - * f IO16 8 _ 2 ~ , ^ ^ L-^rx- = \0B ro 2 so that ?\t>rsJ 10~^ cm which i s much smaller than the dimensions of the tube, and thus i t appears that ambipolar - 6 2 -d i f f u s i o n w i l l o c c u r r a t h e r t h a n f r e e d i f f u s i o n . F r a n c i s 1 7 s t a t e s t h a t i f f i s t h e mean l i f e t i m e of an e l e c t r o n b e f o r e i t h i t s t h e w a l l then where i s t h e a m b i p o l a r d i f f u s i o n c o n s t a n t and 1— i s a c h a r a c t e r i s t i c l e n g t h o f t h e d i s c h a r g e known as t h e d i f f u s i o n l e n g t h . F o r a c y l i n d e r o f l e n g t h d and r a d i u s r B = (?R?)' which g i v e s L = .18 cm f o r t h e f l a s h tube. Von Engel 1® g i v e s t h e a m b i p o l a r d i f f u s i o n c o n s t a n t by where D and D a r e t h e f r e e d i f f u s i o n c o n s t a n t s f o r t h e p o s i t i v e and n e g a t i v e i o n s , and k + and k~ a r e t h e i r r e s p e c -t i v e m o b i l i t i e s . For the u s u a l case where k~ >^)> k + and Te y y T i , t h e i o n t e m p e r a t u r e , i t can be shown t h a t - 6 3 -I f k + < ^ 10 3 cm 2/volt sec, which should be about the r i g h t order, then and from (18) ? ^ = ^ S e C which i s the c o r r e c t order of magnitude f o r the time of the discharge. Thus from these rough c a l c u l a t i o n s i t seems that t h i s i s a b o r d e r l i n e case - ambipolar d i f f u s i o n may be j u s t p o s s i b l e . According t o Mohler-1-® i f s u r f a c e recombination takes place because of d i f f u s i o n , the curves of J " ^ 4 t w i l l i n general be steeper and concave upwards. This upward c o n c a v i t y i s apparent i n the graphs shown. If the prominant r a d i a t i o n process i s accepted as being a product of volume recombination, then a q u a l i t a t i v e explana-t i o n of the shape of the i n t e n s i t y w i t h time curve can be given. The energy put i n t o the tube during the discharge as a f u n c t i o n of time i s given by E(t)-cVdt = RT$Vdt i f the r e s i s t a n c e of the tube i s assumed constant. 2 2 i , i , and i dt are shown i n f i g u r e 12. I f the energy decay due to r a d i a t i v e recombination i s taken i n t o account -64-F i g . 12. Energy Content the dot ted l i n e shows the energy of the d i s charge as a f u n c t i o n of t i m e . I f the output of i n t e n s i t y i s p r o p o r t i o n a l t o the energy content of the d i s c h a r g e , then the observed output should be s i m i l a r t o t h i s c u r v e . The r e l a t i v e -65-prominence of the second peak would then depend on the value of G(, a high value of 0{ a l lowing a small or no second peak, whi le a small value of 0\ gives a large second peak. C?( decreases wi th increasing temperature, so the hotter the gas, the more prominent the second peak. 5.5. Behaviour of In tens i ty wi th Number of Shots The peak i n t e n s i t y of the f i n a l design of the f l a sh tube was found to decrease by less than about 1% with each shot. The ra te of decrease of i n t e n s i t y tended to vary s l i g h t l y wi th each t r i a l i f some part of the tube had been replaced such as a new window glued on, so the above f igure represents an approximate average. For an experiment r equ i r -ing no decrease i n the peak i n t e n s i t y and not r equ i r ing too many shots, t h i s i s probably a to le rab le decrease. Figure 13 i l l u s t r a t e s t h i s decrease g raph ica l ly for the f i r s t hundred shots . For comparison a curve for a "ba f f l e - l e s s " f l a sh tube i s a lso drawn. For t h i s tube the i n t ens i t y dropped d r a s t i c a l l y i n the f i r s t 10 shots, and then f e l l off more s lowly i n a approxi-mately l inea r manner. To be noted i s the dip and then the s l i g h t r i s e beginning at shot No. 7. This would seem to indica te that i n i t i a l l y mater ia l i s only being deposited on the window so the i n t e n s i t y f a l l s off r a p i d l y . Eventual ly ( in t h i s case, shot No. 7) some of the mater ia l already number of shots fig. 13 intensity decrease -66-deposited i s removed, e i ther by the heat generated by the discharge, or by mechanical impact from other e b u l l i t i o n just produced by the discharge, and the i n t ens i t y r i s e s somewhat. The two opposing processes of deposi t ion and removal then occur concurrently, wi th the deposi t ion process necessar i ly dominating. In some cases the dip occurred at the second shot and the r i s e at the t h i r d . Hence the e b u l l i t i o n i s apparently deposited after the l i g h t has been emitted and thus the ca l cu -l a t i o n above the e lec t ron density during the discharge i s even more precarious. The i n t e n s i t y of the f i n a l design tube, on the other hand, shows none of these cha rac t e r i s t i c s but merely a slow decrease. 5.6. Temperature Measurements The so lu t ion of equation (15) gives the brightness tem-perature of the f l a sh tube; the r e s u l t s were not very s a t i s -factory however. When ( I was small ( = 120 A ) , the ca lcula ted temperatures, as the v i s i b l e range was "scanned", var ied between 1,000 and 60,000°K with no obvious r e g u l a r i t y or pattern with respect to the wavelength. In some instances the equation had no r e a l s o l u t i o n . Some of the possible causes of these unstable r e su l t s were not hard to f i n d . One of these i s an inherent i n s t a b i l i t y i n equation (15). -67-If the de r iva t ive of ( 1 5 ) i s taken B\/B| AdS -exp ( | ) ( f ) f =dA [exp(|)- , ]-ex P( |)( f j s or S B'exp^l 'j-lexp^ now i f | A - A * | i s sma l l , B ' = B and exp ^1 =• exp j | " 5 1 " * A" Since exp ^- cannot equal 1 for f i n i t e S , the percentage change i n S can be large i f A i s close to 1 , which i t w i l l be i f A — > - A ' » A t y p i c a l example can be given. If £>_ 1 and A = .95, then 4^  - 2 0 ^ so any error i n A i s magnified 20 times i n S . Almost a l l error associated with A would come from measuring the i n t e n s i t i e s which has a poss ible error of about 5%. I f | A - A ' | i s made la rger , then A tends to move away from 1 and the so lu t ion may become more s tab le . o This was t r i e d using A =• 4440 A which was the lowest v/avelength i n the range, and A ' ranged from 4700 A o o to 6555 A i n increments of about 250 A . The r e su l t s from one t r i a l are tabulated below. -68-TABLE I Brightness Temperature f o r V a r i a b l e Wavelength I n t e r v a l A;, 4440 A A' 4680 A 3943° K 4923 5666 5177 6891 5448 6268 5720 5624 5997 5850 6276 5277 7555 4490 This method does not allo w a temperature to be asso-c i a t e d w i t h a c e r t a i n wavelength, or s m a l l wavelength range as i t does i f | A - A'| i s s m a l l . S has an average value of 5500°K and a standard d e v i a t i o n of 880°K. I » o == 250 A i s shown below. TABLE I I Brig h t n e s s Temperature f o r Constant Wavelength I n t e r v a l 4440 A 4680 4923 5177 5448 5720 5997 6276 AV 4680 A 4923 5177 5448 5720 5997 6276 6555 3943°K 11549 14669 4826 3787 5850 2994 1848 - 6 9 -The v a r i a t i o n i n the va lues of the temperature was not as great as when j A - "K 'J Tp 120 A. When |x - V | i s not s m a l l , the ques t ion i s r a i s e d as t o how much e r r o r i s i n t r o d u c e d by p u t t i n g S - S' i n eqn (15) . That i s , does the f l a s h tube behave as a b l a c k body? To c a l c u l a t e the r e l a t i v e i n t e n s i t y of the f l a s h tube the T F T ^ JL_ T T L f 1 1 r e l a t i o n & R(K) ^ W a S u s e < * ' w n e r e was c a l c u l a t e d from Wien ' s l aw. T h i s was done u s i n g the va lue s of R(A) observed from the t r i a l of t a b l e s I and I I and the r e s u l t i s shown i n f i g u r e 14. I t appears t h a t the i n t e n s i t y d i s t r i -b u t i o n i s f a r from t h a t of a b l a c k body. C l o s e r spaced p o i n t s and a wider t o t a l wavelength range would t e l l more of the i n t e n s i t y behav iour . Because of the non-b lack body behav iour , i t i s perhaps s u r p r i s i n g the temperatures g i v e n i n Table I are as c l o s e as they a re . I f 5500°K i s a reasonable measure of the b r i g h t n e s s temperature of the f l a s h tube , i t i s obvious t h a t t h i s i s not hot enough f o r a b s o r p t i o n a n a l y s i s of hot plasmas. In f a c t at present work i s be ing done s i m i l a r to tha t done by Budd" u s i n g the f l a s h tube d i s cus sed here , and i t has been found tha t very s l i g h t a b s o r p t i o n takes p l a c e but not enough f o r any accurate c a l c u l a t i o n . Budd was ab le t o achieve b e t t e r absorp-t i o n i n d i c a t i n g h i s f l a s h tube had a h o t t e r temperature . S i g n i f i c a n t l y , the i n t e n s i t y waveform had a prominent second peak. © 444 0 4680 4920 5180 5450 5720 6000 6280 6550 wavelength fig, 14 intensity variation with wavelength -70-5.7. Conclusions A low pressure f l a sh tube of simple design has been constructed which does not suffer from deposi t ion on the e x i t window. The spectrum i n the v i s i b l e range i s a good continuum probably o r i g i n a t i n g from elec t ron re ta rda t ion . A few emission and absorption l i n e s are present but are bel ieved to appear after the f i r s t 20 jisec of the discharge. The de ion iza t ion process i n the discharge appears to be volume e lec t ron- ion recombination and the recombination coe f f i c i en t 0( was estimated to be 2 x 1 0 " 1 1 cm 3 /sec. A method of measuring the brightness temperature of the f l a sh tube over the v i s i b l e range was used by comparing photo-e l e c t r i c a l l y the i n t ens i ty of the tube with that of a black body. The temperatures ca lcu la ted indicate that the in ten-s i t i e s need to be measured extremely accurately and the temperature of the present tube (rsJ 5500°K) i s lower than expected. The r e l a t i v e i n t e n s i t y d i s t r i b u t i o n of the tube shows that i t does not radia te as a black body. I t i s not ce r ta in why the temperature of the f l a sh tube i s so low. The t o t a l energy put in to the tube i s ISO J and greater; other workers have constructed tubes which have achieved much higher temperatures at about the same energy, so other energy-diss ipat ing processes must be looked for to expla in t h i s low temperature. Perhaps d i f fus ion and surface recombination plays a more important r o l e than i t i s thought -71-t o , or the low pressure r e q u i r e s too much energy t o be expended i n s p u t t e r i n g t o achieve breakdown. At any r a t e i t seems t h a t one problem has been s o l v e d at the expense of c r e a t i n g another . The f i n a l des ign of the tube no longer s u f f e r s from d e p o s i t ! on of m a t e r i a l on the e x i t window as i t d i d be fore . But on the other hand, e a r l i e r tube des igns were hot enough f o r use i n c e r t a i n a b s o r p t i o n e x p e r i -ments. What had seemed at f i r s t g lance t o be a r ea sonab ly s imple mechanical problem of p r e v e n t i n g d e p o s i t i o n has turned out to be an extremely complex s i t u a t i o n of which l i t t l e i s known. O b v i o u s l y t o s o l v e t h i s problem, a more thorough i n v e s t i g a t i o n of the mechanisms o c c u r r i n g i n the f l a s h tube w i l l be necessary and w i l l doubt le s s be undertaken i n the near f u t u r e . -72-APPENDIX Computer Program for Solving Temperature Equation Equation (15) was solved on an IBM 1620 computer using Fortran 1A. The method of solut i o n was that of d i r e c t sub-s t i t u t i o n . If equation (15) Is written then the solution i s that value of S for which Eq =» 0 . S was f i r s t put equal to 1000, then increased i n steps of 1000 u n t i l Eq changed sign. S was then increased i n steps of 100 s t a r t i n g at the previous 1000 step. This procedure was repeated down to units. The so l u t i o n was sought only i n the range 1000 — S ^ 101,000. The program i s shown below. DIMENSION WL1(100).WL2(100),VTL(100),VTL2(100),VFT1(100) DIMENSION VFT2(100) 1 FORMAT(6F8.2) 17 FORMAT(13,F8.0) 18 FORMAT(13) READ 18, N DO 19 1=1,N 19 READ 1,WL1(I),WL2(I),VTL1(I),VTL2(I),VFT1(I),VFT2(I) DO 101 I-1,N Bl= (1.438E8/WL1(I)) B2=(1.438E8/WL2(I)) C-EXP ((1.438E8/2560.)*(1./WL1(I)-1./WL2(I))) 73-A- ( (VTL1 (I) *VFT2 (I) )/(VTL2 (I) *VFT1 (I) ) ) *C T-1000. EQ=EXP(B1/T)-(A*EXP(B2/T)+1.-A) IF(EQ)2,3,4 2 T-T+1000. IF(T-1.E5)20,20,3 20 EQ-EXP(B1/T)-(A*EXP(B2/T)+1.-A) IF(EQ)2,3,5 5 T-T-1000. 8 T-T+l00. EQ-EXP(B1/T)-(A *EXP(B2/T)+1.-A) IF(EQ)8,3,6 6 T-T-100. 9 T-T+10. EQ-EXP(B1/T)- (A*EXP(B2/T)+1.-A) IF(EQ)9,3,7 7 T-T-10. 10 T-T+l. EQ-EXP(B1/T)-(A*EXP(B2/T)+1.-A) IF(EQ)1C,3,3 4 T-T+1000. IF(T-1.E5)22,22,3 22 EQ-EXP(B1/T)-(A*EXP(B2/T)+1.-A) IF (EQ) 11,3,4 11 T-T-1000. 12 T-T+100. EQ-EXP (Bl/T)-(A*EXP(B2/T)+1.-A) IF(EQ)13,3,12 13 T-T-100. 14 T-T+10. EQ-EXP(Bl/T)-(A*EXP(B2/T)+1. - A) IF (EQ) 15,3,14 15 T-T-10. 16 T-T+l. EQ-EXP (Bl A ) - (A*EXP(B2/T)+1.-A) IF(EQ)3,3,16 3 PRINT 17,1,T 101 CONTINUE STOP END RELOCATABLE SUBROUTINES CAT •LED EXP OBJECT PROGRAM DATA TABLE 06550 STORAGE POSITIONS. -74-REFERENCES 1. Bishop, A.S., Project Sherwood, New York, Doubleday, 1960, p.6. 2. Ladenburg, R., Rev, Mod. Phys., j5, 234 (1933). 3. Lyman, T., Science, 64, 89 (1926). 4. C h r i s t i e , M.T. and Porter, G., Proc. Roy. Soc. A, 212, 389 (1952). 5. Budd, S.E., M.Sc. Thesis, University of B r i t i s h Columbia, 1961. 6. Garton, W.R.S., J. S c i . Inst., 30, 119 (1953). J. S c i . Inst., 36, 11 (1959). Garton, et a l , Proc. of the Fourth International Conference  on Ionized Phenomena i n Gases, 1961, p.518. 7. Von Engel, A., Ionized Gases, London, 1953, p.152. 8. Curzon, F.L., and Smy, P.R., Rev. S c i . Inst., 32, 756 (1961). 9. Von Engel, A., op.ci t . , p. 49. 10. Anderson, J.A., Astrophy. J., 75, 394 (1932). 11. C h r i s t i e , M.T., and Porter, G., Proc. Roy. Soc. A. 212, 398 (1952). 12. Theophanis, G.A., Rev. S c i . Inst., 31, 4 (1960). 13. Parkinson, W.H., and Reeves, E.M., Proc. Roy. Soc. A, 262, 409 (1961). -75-14. Rutgers, G.A.W., and de Vos, J.C., Physica, 20, 715 (1954). 15. Loeb, L.B., Handbuck der Physik, XXI, p.490. 16. Massey, H.S.W., Adv. i n Phys., 1, 395 (1952). 17. Francis, G., Ionization Phenomena i n Gases, London, 1960, p.112. 18. Von Engel, op. c i t . , p.122. 19. Mohler, F.L., Jour, of Research, Nat. Bur. Stand., 19 447 (1937). 

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