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Measurement of the profile of He I 4471 Å at low electron densities Stevenson, Dale Christian 1973

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'.I MEASUREMENT OF THE PROFILE OF He I 4471 A AT LOW ELECTRON DENSITIES by Dale C. Stevenson B.Sc, University of British Columbia, 1967 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in the Department of PHYSICS We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA March 1973 In presenting t h i s thesis In p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by hi s representatives. It i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of PUMS\C5>  The University of B r i t i s h Columbia Vancouver 8, Canada ABSTRACT The profiles of the He I lines with forbidden components in plasmas with electron densities below 10"^ electrons per cc. are of astro-physical interest. A pulsed-arc plasma device has been constructed and operated at such i n i t i a l conditions that in the afterglow (i.e. up to 200 usee after breakdown), the steadily decreasing electron density passes through the range of interest. The plasma was observed end-on with a monochromator at a wavelength near 4471 angstroms for each discharge, and the intensity recorded as a functions of time. Good shot-to-shot reproducibility of the plasma permitted the line profile to be reconstructed for different times by repeating the measurements at different wavelengths spanning the line . The profile 15 -3 of He I 4471 has been measured for 10 cm and agreement has been found with the results of Burgess and Cairns (1971) and recent calcu-lations of Barnard and Cooper (to be published). i i TABLE OF CONTENTS CHAPTER ONE: What is He 4471 and why does anyone want to measure i t 1.1 Spectral Lines 1.2 The Perfect Plasma 1.3 Allowed Lines and Forbidden Lines 1.4 The Astrophysical Importance of He 4471 1.5 The Trouble with He 4471 at Low Densities 1.6 Layout of the Thesis CHAPTER TWO: The Afterglow of a Wall-Stabilized Discharge 2.1 The Wall-Stabilized Discharge 2.2 Studies of the Afterglow 2.3 The Search for Low Densities 2.4 Foiled by Impurities 2.5 Where to Go CHAPTER THREE: A Pulsed-Arc Low Density Plasma 3.1 Alterations to the Wall-Stabilized Discharge 3.2 Final Experimental Arrangement CHAPTER FOUR: Characteristics of the Low Density Plasma 4.1 Measurement of N by Stark Widths e 4.2 Measurement of N g by Laser Interferometry 4.3 Homogeneity of the Plasma 4.4 Framing Camera adies 4.5 Plasma Reproducibility 4.6 Electron Temperature Measurements 4.7 Ion Temperature Measurements •• CHAPTER FIVE: Measurements of Line Profiles 5.1 Conditions of the Discharge 5.2 Measurement of Line Profiles i i i TABLE OF CONTENTS,, continued Page 5.3 Interpolation of Profiles of He 4471 60 5.4 The Instrument Width 63 5.5 Optical Depth Check 65 CHAPTER SIX: Summary and Conclusions 6.1 Experimental Errors 70 6.2 Final Results 7 3 6.3 The Study of He 4471 as a Weil-Defined National Objective 76 APPENDIX A: Schematic of Operational Amplifier 77 APPENDIX B: Murphy's Law ?8 BIBLIOGRAPHY 79 iv LIST OF ILLUSTRATIONS Figure Page 1 - 1 Energy Level Diagram for Helium 5 1 - 2 BCS Profiles of He 4471 at Low Electron Densities 6 1-3 Spectral Make-up of Stars 7 1- 4 Absorption Profiles of He 4471 from Various Stars 8 2- 1 The Wall-Stabilized Discharge 12 2-2 Typical Characteristics of the WSD lU 2-3 Experimental Arrangement for the WSD 15 2-4 Typical Line Profiles from WSD 17 2- 5 Impurity Lines Near 4471 Angstroms 1 8 3- 1 Characteristics of Low Density Source 2 U 3-2 Electrode Configuration for Pulsed-Arc Device 2 6 3-3 Charging and Discharge Circuit 2 7 3-4 Vacuum Systern 2 8 3-5 Spectral Response of System 32 3-6 Definition of Plasma Volume 3^ 3- 7 Relative Dimensions of Electrode and Plasma Volume ... 4- 1 Variation of He 4471 Half Width with N £ 37 4-2 Half Width of Allowed Component vs. Time 3 8 4-3 Diagram of Interferometer Layout Ul 4-4 Typical Oscillograms of Interference Fringes 4-5 Variation of N £ with F i l l i n g Pressure and Firing Voltage .. U3 4-6 Time Variation of N UU e 4-7 Arrangement for Determination of Radial Variation of N ... U 6 4-8 Radial Variation of N at Various Times U 6 e 4-9 Framing Camera Photos of Plasma hi 4-10 Reproducibility of Plasma U 8 4-11 Ratio of He 4686/He 5876 vs. Time **9 4-12 Boltzmann Plot 5 1 4-13 Ion Temperature vs. Time 5 2 v LIST OF ILLUSTRATIONS, continued Figure Page 5-1 Oscillogram of Photomultiplier Output 56 5-2 Effect of Continuum Choice on Profile 60 5-3 Comparison of Measured and Interpolated Profile 61 5-4 He 4471 Profile for 10 1 5 cm~3 63 5-5 Instrument Function for 20y S l i t s 64 5- 6 Comparison of Profiles for Optical Depth Check 65 6- 1 Accuracy of Measured He 4471 Profiles 73 6-2 Previous Comparison of Theory and Experiment 74 6-3 TEE Profile 74 v i ACKNOWLEDGEMENTS I cannot claim this work to be original. Much of the practical and theoretical knowledge that a graduate student acquires on his way to a degree comes not through books but by way of the technicians and his fellow graduate students. It is only f a i r , therefore, that credit be given where credit is due. I would like to take this opportunity to give a sigh of r e l i e f , and to sincerely thank: Doug Sieberg, without whose help I would never have finished Jack Burnett, for his willing explanations Rob Morris and Hector Baldis, for their technical advice on problems long since forgotten Jon Preston, for unselfishly sharing his knowledge of inter-ferometry, as well as his interferometer and especially Dr. A.J. Barnard, for being my kind of supervisor. I would like to thank Dick Haines for humouring my attempts in the machine shop, and Rose Chabluk for having the patience to type this thesis. I am also indebted to the Canadian Armed Forces for an honorable discharge, without which this work would have been impossible. v i i What is He 4471 and why does anyone want to measure it 1.1 SPECTRAL LINES AND PLASMAS The study of spectral lines involves the study of plasma physics, and studying the detailed shape of various spectral lines allows one to determine many plasma properties. The extent to which theoretical descriptions of the line profiles describe what is actually observed reflects to a certain extent the state-of-the-art in plasma physics. Not surprisingly, some lines receive more interest than others, and a discrepancy of only a few percent between experimental and theoretical profiles has been known to drive some plasma physicists into a frenzy, frighten others, and cause yet scores of others to dedicate a major portion of their lives to i t s ultimate r e c t i f i c a t i o n . And so i t is with He 4471. -2-1.2 THE PERFECT PLASMA In most spectroscopic studies of plasmas, a theoretical model of the spatial variation of the electron density (Ne) and electron temperature (T ) is necessarily assumed in order for any measured line profile to have meaning. Considerable effort is often expended to produce a homo-geneous region of plasma where N £ and T g w i l l have well-defined values, or at least a region where these variables have a convenient symmetry. A further simplification arises i f one can assume (or show) the existence of LTE (Local Thermodynamic Equilibrium); under these conditions, the plasma lends i t s e l f to mathematical description. It may happen that the populations cannot be described by the Boltzmann factor, i.e., the system is not in LTE. It does not follow, however, that the situation i s hopeless. The upper levels of the atoms may s t i l l be adequately populated according to the same rule, but instead of a l l the way down to the ground state, only down to a certain level n. The criterion relating n to the electron density and temperature is given by, for example, Griem (1964): > n i n18 z 7 kT N e ~ 7 x 1 0 e-875, n E a where E^ i s the excitation energy for hydrogen. This is a necessary criterion but i t is not sufficient; i t merely expresses the requirement that before LTE can exist amongst the levels n and above you must f i r s t have enough electrons free to cause excitation and ionization, and that they must simultaneously have energies large enough to interact appre-ciably down to the level n. -3-The point is that in the special case of LTE, there exist theoretical relations which allow the effects of N and T to be separated. The e e mathematics, then, although d i f f i c u l t , i s at least tractable. Under conditions of non-LTE, one must be very careful about any assumptions which are made, since any theoretical treatments of the situation may in fact depend on the existence of LTE. Specifically, the following are consistent with LTE: Q the electron (or any other particle) velocity distribution is Maxwellian Q the population of the states of an atom are characterized by a Boltzmann distribution the intensity of the radiation spectrum i s characterized by a blackbody function for the same temperature 9 a relation exists which links the population of the various ionized species to the electron temperature (the Saha equation). It may not be possible to show that LTE exists, at least not for a l l levels. In many cases, tests which are designed to show consistency with LTE are a l l too often taken to signify existence of LTE, and caution should be exercised when making the assertion. If LTE does not exist for the levels which give rise to the spectral line being studied, then a measurement of the electron temperature by studying the ratios of intensities of lines originating from these levels may yield many d i f f e r -ent estimates of The best that may then be done under the circum-stances i s to use this value of T to specify the excitation temperature. - 4 -1.3 ALLOWED LINES AND FORBIDDEN LINES Cases of special interest arise in spectroscopic studies when a line appears where, according to quantum mechanics, i t should not. He khfl is such a l i n e . 3 3 The transition 4 D - 2 P in helium gives rise to the allowed component of He I 4471 at 4471.48 Angstroms with an oscillator strength of 0.12. 3 3 The transition 4 F - 2 P normally does not occur since i t s probability is zero. Nevertheless, under high electron concentrations, the intense electron microfields cause a breakdown of the parity selection rules which forbid the transition, and the forbidden component appears at 15 3 4469.9 A. The profile of He 4471 at a density of 10 electrons/cm is of interest since i t represents the plasma conditions when the forbidden component is just beginning to emerge. The shape of He 4471 has been measured recently at higher electron den-s i t i e s by Nelson and Barnard (1970) and Jenkins and Burgess (1971), and has received considerable theoretical treatment by Griem (1968), Barnard, Cooper and Shamey (1969) and Burgess (1970). The profile at lower den-si t i e s has been measured only recently by Burgess and Cairns (1971), and illustrates a significant discrepancy in the wavelength region of the forbidden component. The discrepancy is greater for even lower densities. Theoretical profiles computed by Barnard, Cooper and Shamey (1969) (BCS), although not perfect, are sufficiently accurate to allow He 4471 to be used as a diagnostic probe for laboratory plasmas and st e l l a r atmospheres. In fact, He 4471 is one of the more important lines for s t e l l a r abundance studies, being relatively strong and conveniently located in a region of -5-Fig. 1-1, Energy Level Diagram of the T r i p l e t State of Helium, -6-5 B C S PROFILES OF He 4471 Ne (cm"°) (o) IO16 (b) 3 xlO 1 5 (c) IO15 (d) 3 xlO 1 4 Fig. 1-2. P r o f i l e s of He I 4471 for various electron densities (•profiles not normalized to equal area). Shaded area represents the region of concern of t h i s exper-iment. [After Barnard, Cooper and Shamey (1969).] the spectrum where photoelectric and photographic detectors have their greatest sensitivity. Considerable interest has been displayed by various authors [see for example, Leckrone (1971), O'Mara and Simpson (1972)] in comparing observed absorption profiles of 4471 with composite theoretical profiles based on an assumed model for the s t e l l a r atmos-phere. 1.4 ASTROPHYSICAL IMPORTANCE OF He 4471 The chemical composition of stars is an integral part of theories of s t e l l a r evolution, and an analysis of s t e l l a r spectra suggestes that the hotter stars are composed mainly of hydrogen and helium. Fig. 1-3 shows -7-co UJ r-Z LU > f-UJ cr >^ H Y D R O G E N N E U T R A L M E T A L S IONIZED \ / \ M E T A L S X . </ \HeH / ' \ " H e I ^ ^ - ^ ^ O B A F G K M Fig. 1-3, Spectral Makeup of Stars as a Function of Spectral C l a s s i f i c a t i o n . that helium lines are prominent in stars in the 0 and early B categories (corresponding to temperatures of 30,000°K), and consequently have been used for obtaining abundance r a t i o s . The abundance ratio of He to H has been found to vary from 0.08 to 0.20 by considering the widths of neutral helium (absorption) lines. Most stellar models are based on the assumption that the stel l a r interior i s in thermal equilibrium and emits radiation of a continuum nature similar to that of a blackbody at that temperature. However, before escaping, the radiation must pass through the cooler st e l l a r atmosphere and is thus absorbed. The shape of the resulting absorption p r o f i l e is thus indicative of the composition of the s t e l l a r atmosphere. The problem of determining stellar abundance by studies of line shapes is two-fold: -8-• • • • H P i i i I i i i - 2 - 1 0 I 2 W A V E L E N G T H (A) Fig. 1-4. Absorption P r o f i l e s of He 4471 from Stars HR 2154 (BS IV) and HR 1861 CB1V). [After Leokrone (1971).] % to find accurate line profiles and oscillator strengths, and £ to construct a model st e l l a r atmosphere which w i l l interact with the emitted radiation to produce the observed absorption profiles. -9-Stellar atmospheres are usually treated in a "one-dimensional" sense, where scattering i s not considered, and are assumed to consist of a multitude of layers each characterized by i t s own N £ and T . The result is a composite line profile (see Fig. 1-4) which in many cases differs considerably from the measured profiles. At present, however, i t i s not certain how much of the discrepancy can be attributed to the model atmosphere and how much to an inadequate theoretical description of the line shape. 1.5 TEE TROUBLE WITH 4471 AT LOW DENSITIES Most of the studies of He 4471 - and for most other lines as well - have 16 18 —3 been performed at electron densities of the order 10 - 10 cm , and i t should be pointed out here that this i s perhaps the easy region to work i n . Lines are bright, generally wide, and LTE is usually present. For this experiment, such was not the case. Attempting to measure line profiles, and in particular 4471, at low densities involves solving a host of problems not be be encountered in studies at higher electron densities: % a low density source is characterized by low temperatures; consequently, lines are not very bright © since measurements are to be made in the afterglow, the inten-s i t i e s are even smaller £ to reduce the effect of inhomogeneities small portions of the plasma must be analyzed. This further reduces the signal to noise ratio -10-0 wide monochromator s l i t s required to gather an appreciable amount of light degrade the spectral resolution 9 the forbidden component is only a fraction of the intensity of the allowed component; the signal-to-noise ratio i s consider-ably worse $ photon noise in the photomultiplier is a problem due to the low i n t r i n s i c intensity of the source Q measurements of N g are d i f f i c u l t at low densities; Stark widths are narrow, and in some cases less than the instrumental and Doppler widths. Such a low electron density causes only a $ small change in the refractive index of the plasma, and thus interferometric determinations of N are d i f f i c u l t e Q electron and ion temperatures are low (^10,000°K) and d i f f i c u l t to measure accurately Q low density plasmas are l i k e l y to be characterized by inhomo-geneities in N and T & e e % operation of the oscilloscope at high sensitivities causes pickup to be proportionately more significant Q non-reproducibility of the plasma is more, l i k e l y when operating at low f i l l i n g pressures. Most of the above d i f f i c u l t i e s were ultimately solved through the design of a suitable low density plasma source (Chapter 3). Others were only minimized, and contribute to the error bars in the f i n a l profiles. (See Chapter 5.) -11-1. 6 LAYOUT OF THE THESIS Chapter 1 l i s t s briefly some of the fundamental aspects of line profile studies, and in particular indicates the astrophysical importance of He 4471, and the d i f f i c u l t i e s involved in measuring the profile at low-densities in the laboratory. The remaining four chapters are devoted to the experimental pursuit of profiles. The f i r s t approach, taking the path of least resistance, was to take an existing plasma source, a wall-stabilized discharge, and attempt to measure line profiles during the afterglow. After a careful analysis of the afterglow for a wide range of operating conditions, i t became apparent that low densities were never going to be reached during the time when lines were s t i l l v i s i b l e . Chapter 2 summarizes the results of these studies, and indicates what modifications had to be made to achieve these densities. Chapter 3 l i s t s the modifications made to both the discharge tube and discharge c i r c u i t , and details the experimental arrangement which was ultimately used to obtain the He 4471 profile. A detailed analysis of this plasma is carried out in Chapter 4 to establish the homogeneity of the plasma and the su i t a b i l i t y of this source for studying He I line profiles. Chapter 5 illustrates the pro-cedure used to obtain the line profiles, and Chapter 6 presents the 15 -3 measured profile of He 4471 at N = 10 cm The afterglow of a wal l -stabi l ized discharge It was known at the outset but perhaps not f u l l y appreciated that 10"^ - 10"''"' electrons cm ^ is a d i f f i c u l t region in which to perform spec-troscopic studies. A detailed analysis of the late afterglow characteris-tics of a wall-stabilized discharge l e f t over from a previous generation of physicists soon showed that this nonchalant statement was not in fact idle chatter. It was theorized i n i t i a l l y that to measure He 4471 at low electron densities i t I/2& \ \ — D a 80uF Fig. 2-1. The Wall-Stabilized discharge. -13-would merely be necessary to wait u n t i l N £ had dropped to 10"^ electrons/ 3 cm and then follow a similar analysis of the discharge as previously performed by Campbell (1965) and Nelson and Barnard (1970). In fact, i t seemed intuitively obvious that only a change in the i n i t i a l conditions would be required. If this had in fact turned out to be the case, this thesis would have consisted of only three chapters. However, i t was soon realized that the situation was more complicated than a f i r s t glance would indicate, and eventually necessitated the construction of a completely different plasma source. This chapter, although not f r u i t f u l from the point of view of producing a profile of He 4471, is a necessary inclusion i n the quest for He 4471 since i t demonstrates the frustration involved in producing a low density spectroscopic source, and to omit i t would be misleading. 2.1 THE WALL-STABILIZED DISCHARGE The WSD (Wall-Stabilised Discharge) was pulsed with a 12 kAmpere, 100 ysec square current produced by a 16-capacitor lumped parameter delay line. This bank has been described by others and for the details the reader i s referred to Campbell (1965) and Roberts and Barnard (1972). The inductors connecting the capacitors were empirically tuned to give the squarest pulse possible. The decrease in density with time obtained from the measurement of Stark width of He 3889 is shown in Fig. 2-2 for a typical set of operating conditions. -14-(a) CURRENT TIME (jjseconds) Fig. 2-2. Typical Characteristics of the Wall-Stabilized Discharge. (a) Current waveform as measured by Rogowski coil, (b) Peak intensity of He I 3889 (arrow indicates time at which line disappears into continuum). (c) Electron density as measured by Stark width of He 3889. -15-THE DISCHARGE CIRCUIT The capacitor bank is charged to a f i r i n g voltage of 6 - 15 kV using a variable transformer, and is triggered by a spark can which is tickled by a pulse from a thyratron unit. The major part of the energy of the discharge is dissipated in a special 1/2 ohm resistor consisting of two large copper strips embedded in a solution of CuSO^. A Rogowski c o i l placed around the copper lead to the grounded electrode followed by an integrating network with an RC time constant of 2.2 milliseconds, pro-duced a signal proportional to the current through the discharge circuit, Since this signal has a steep leading edge, i t was used in a l l instances to i n i t i a t e the oscilloscope which recorded the photomultiplier output. T H Y R A T R O N T R I G G E R PM L Z J S P E X 1.0 m M0N0CHR0MAT0R B EXT. T R I G . Fig. 2-3. Experimental Arrangement for the WSD. *^ 16^ * The discharge tube was viewed end-on with a single f i e l d lens, and the volume of plasma being "sampled" was determined by an adjustable stop. The system was aligned by shining a laser through the exit s l i t of the monochromator, permitting at the same time an accurate definition of the volume of plasma being studied. The f i e l d lens could have been placed at either of the conjugate f o c i , but the one closest to the plasma was chosen. This produced an enlarged image of the plasma i n the plane of the entrance s l i t and permitted optimum resolution of the plasma. 2.2 STUDIES OF THE AFTERGLOW He 3889 was chosen to estimate the electron density due to the slight 16 dependence of the Stark-broadening parameters on temperature. (N g = 10 -3 cm corresponds to a f u l l half width of 0.25 A. The electron density measurements were corroborated with estimates based on the Stark-broaden-ing of He II 4686 and He I 5876, as well as from He I 4471 i t s e l f . 2.3 THE PURSUIT OF LOW DENSITIES Measurements of the time variation of the electron density were under-taken for f i l l i n g pressures ranging from 20 torr down to 100 microns, and for f i r i n g voltages in the range 6 - 12 kV in the hope of eventually finding a suitable combination of f i r i n g conditions which would result in the production of electron densities in the range of interest. Unfortun-ately, no such set of conditions was encountered, nor was any indication gained of a method of. achieving such a goal. -17-Fig. 2-4. Typical Line P r o f i l e s and Measurements for Various (.Low) Filling Pressures. of Electron Density -18-Th e i n i t i a l plan to reduce the f i l l i n g pressure to 100 microns or so did not result in low values of N g being reached during times when lines were s t i l l v i s i b l e . It i s true that lower peak temperatures were generally achieved, but the lines disappeared into the continuum appre-ciably sooner, thereby nullif y i n g any advantage. Evidently, at lower f i l l i n g pressures, particles migrated more rapidly to the "tube walls, with the result that the temperature dropped more quickly than in the case of higher f i l l i n g pressures. 2.4 FOILED BY IMPURITY LINES Failure to reach low electron densities was not the only problem asso-ciated with attempting to use the WSD to study He 4471 for low densities. An unexpected complication which arose was the masking of the 4471 pro-f i l e by an unknown multiplet. Consultation of Moore's Tables of Astro-physical Interest (1959) yielded a plausible answer as being the 0 II multiplet No. 14. While accurate profiles were obtained for 3889, 5876, 4686, 3203, good profiles could not be obtained of He 4471 at any density due to the presence of this multiplet (see Figure 2-5). 7kV I torr 60 ysec i i i i i i i 4465 4470 A (A) Fig. 2-5. Impurity Lines at 4471 Angstroms. LU 2 -19-The most obvious source for these oxygen impurity lines was of course a leak in the vacuum system, although this appeared unlikely since: (a) the system would evacuate to 5 u as measured with a McLeod gauge, and had a leak rate of only 1 - 2 y/min., and (b) spectrum scans around 3889 A whether taken immediately after a fresh f i l l i n g of gas displayed the same relative intensities of helium and oxygen as those taken after waiting several hours. Other p o s s i b i l i t i e s such as a contaminated He cylinder or leaky f i t t i n g s or contaminated electrodes were investigated and subsequently discounted. Ultimately i t was decided that the lines must be arising from the inter-action of the glass discharge tube and the hot plasma. A plot of the intensities of the 0 II 3882 line as a function of radial position showed a dramatic increase in intensity at the tube walls after approxi-mately 60 usees, corresponding to the time needed for the plasma p a r t i -cles to migrate radially to the walls. Further suggestion that the discharge tube i t s e l f was responsible for the contamination of the helium spectrum by oxygen lines was evidenced by the fact that the ratio of helium line/oxygen line intensities did not increase with f i l l i n g pressure, which would have been the case had the composition of the f i l l i n g gas been at fault. Nelson (private communication) also indicated that impurity lines from the tube walls were evident in his studies of 4471 at higher densities, but that their influence had been minimized by a reduction in the f i r i n g voltage. -20-2.5 WHERE TO GO Two problems were discovered using the WSD as a plasma source: 0 the presence of impurity lines £ a rapid temperature decrease Evidently, nothing less than a hardware change would resolve the d i f f i -culties. Several modifications were made both to the discharge c i r c u i t and the plasma vessel, each time yielding lower densities. The results of these modifications are summarized in Chapter 3. Sufficiently low densities were eventually reached, and Chapter 4 presents a detailed analysis of the low density plasma which was ultimately obtained. I A pulsed-arc low density plasma The search for lower densities was stalemated for a time since the studies of Chapter 2 yielded no indication of the modifications which would have to be made to achieve low densities. It was undesirable for several reasons to convert the discharge tube into a Z-pinch, especially since this apparatus had been recently flogged to death by Burgess and Cairns (1971). A theta-pinch was also ruled out since i t is not as reproducible as would be desired, and has a "hole" along the axis, thereby ruling out end-on observations. In the search for narrow profiles of He 3889, i t was noted one time that the -21--22-temporal variation of the intensity of He 3889 was noticeably different during the f i r s t 5 - 1 0 shots; the intensity did not die away around 120 microseconds as was usually observed but rather lasted out to 180 pseconds and beyond while a slight " t a i l " was observed on the current trace. Profiles of He 3889 obtained during this late afterglow period showed a significant narrowing of the line, and led the way to modifica-tions which eventually produced a low density pulsed discharge. These modifications were mostly a process of try-it-and-see guided by intuition and are summarized in the following section (section 3.1). The configuration which was ultimately acceptable is discussed i n detail in Section 3.2. 3.1 ALTERATIONS TO THE DISCHARGE It was pointed out in the beginning of Chapter 2 that i t had been origin-a l l y thought to operate the discharge tube at as low a f i l l i n g pressure as possible. Unfortunately this had the undesirable effect of emphasiz-ing the importance of impurities and also allowed the plasma to cool faster - the very thing which was not wanted. Consequently the f i r s t modification was to the discharge c i r c u i t , which was converted from the lumped parameter delay line of Section 2.1 to a simple parallel c i r c u i t consisting of 2 of the capacitors. Used in conjunction with the "egg-timer" (WSD), a slight reduction in peak N g was observed, but otherwise no great improvement was achieved. The next step, therefore, was to lower the electron density by expanding the cross-section of the discharge tube, a step also considered undesirable since i t did not necessarily follow that the plasma would remain homogeneous either along the line of -23-sight or for appreciable radial dimensions. A straight 6-calibre Kimax cross-section with a two inch bore (see Fig. 3-2) replaced the egg timer, and at the same time the electrodes were replaced. This produced a pronounced effect on the behaviour of N . The peak N g dropped immediately by a factor of 3, which now brought = 10"'""' within r e a l i s t i c reach. Unfortunately, since the energy was now being dumped into a greater total number of atoms, the temperature of the plasma was reduced to the point where attempts to measure line intensities would have been an exercise in f u t i l i t y . Mere observation of the discharge indicated that high temperatures were not being reached. The problem was, as i t were, to produce a plasma "bright enough to blind a super-visor". Consequently more capacitors were added onto the c i r c u i t and as their numbers were increased, the current pulse decayed with a longer time constant, and the intensities of He I lines were buoyed up for longer periods of time. Extensive investigations were not carried out on a l l phases of the modifications to the discharge, since experience with the WSD of Chapter 2 showed that the behaviour of the plasma would depend primarily on the shape of the discharge tube and the current pulse, and only to a lesser extent on the f i r i n g voltage and f i l l i n g pressure. Also, modifications were being made to the apparatus at the rate of two per week in a desperate attempt to find a suitable combination of capacitors, electrodes and glass discharge tubes. By sampling only a few points on the profile of He 3889, i t was possible to t e l l by inspection whether or not a particular experimental arrangement was worthy of extended inves-tigation. -2k-in O. E o ro O 'e o m 0) 10 0 INTENSITY OF He 3889 ELECTRON DENSITY _L _L 0 20 40 60 80 100 120 TIME (^seconds) 140 (b) (c) 160 180 Fig 3-1. Characteristics of the plasma source, (a) Current waveform (b) Intensity of He 3889 (c) Electron density as determined by interferometer -25-REPLACEMENT OF ELECTRODES The brass electrodes used with the WSD were guilty of excessive sputter-ing, and the quartz windows of the inserts [see Figs. 2-1 and 3-2(a)] rapidly acquired a metallic deposit which required that the tube and quartz inserts be cleaned frequently. Cleaning of the quartz inserts involved treatment by hydrofluoric acid which degraded their optical quality to the point where they had to be replaced. In addition, since i t seemed to take the apparatus a long time to "settle down" after a cleaning, one hesitated to disturb the arrangement once i t was functioning correctly. To overcome both this and the problem of sputtering, new electrodes were fashioned from aluminum following the design of those inherited with the WSD, but which were more flexible in the arrangement of the inserts (i.e. the quartz extending into the plasma). The vacuum seal was improved by the use of two O-rings to seal the insert instead of one as in the f i r s t model and the procedure for adjusting i t s position was streamlined to a simple threaded sleeve as shown in Fig. 3-2. It was duly noted that the expansion of the plasma vessel to a larger cross-section resulted in a lower peak electron density; i t was also noted that a "hole" now had developed along the axis of the plasma, and this was most undesirable. The quartz inserts were then replaced by aluminum inserts, so that the portion of the aluminum cylinder protrud-ing into the plasma acted as a hollow electrode (see Fig. 3-2). The "hole" pa r t i a l l y disappeared, and yet other aluminum inserts with an even smaller inner bore were fashioned and ultimately found acceptable. The result was a considerable increase in light intensity, and an acceptably f l a t N profile across the observable portion of plasma. -26-VACUUM CONNECTION Fig. 3-2. Electrodes for the Pulsed^Arc Source. Electrodes on either end are i d e n t i c a l except for vacuum connection. -27-3.2 FINAL EXPERIMENTAL ARRANGEMENT The modifications to the basic apparatus of Chapter 2 consisted of changing the tuned capacitor bank to a simple network of 6 capacitors in parallel, and replacing the discharge tube. The charging T H Y R A T R O N T R I G G E R - C H > ONE-SHOT P B T H E O P H A N I S VOLTA G E DOUBLER Hi P U L S E D I S C H A R G E XFORMER T U B E ROGOWSKI COIL SIX 5 u F CAPACI BUILDING G R O U N D Fig. 3-3. Charging, Discharge and Triggering Circuits. c i r c u i t , triggering, vacuum system and recording electronics remained unchanged. The f i n a l result was an overdamped current pulse produced by the dumping of six 5-yF capacitors charged to 10 kV through a dis-charge tube consisting of a straight length of 2" I.D. Kimax tubing 1 foot long, using hollow electrodes. Fig. 3-3 shows the charging, dis-charging, and triggering c i r c u i t s . -28-THE VACUUM SYSTEM Fig. 3-4 below shows the vacuum system which was constructed of copper tubing, aluminum Speedivalves with 0-ring joints, and which was evacuated by a single mechanical forepump down to 5 u as measured by a McLeod gauge. DISCHARGE TUBE Fig. 3-4. The Vacuum System. (To prevent contamination of the system by mercury, the gauge was isolated by a valve when not being used, and when in use was isolated by a nitrogen cold trap.) An NRC 804 thermocouple gauge and readout unit (as well as the Speedivac 0 - 2 0 torr mechanical gauge) was calibrated from the McLeod gauge and was sufficiently responsive to permit r e f i l l i n g the system each -29-time to an accuracy of ± 5 microns at lower pressures, and ± 100 microns at pressures of 1 torr. The operation of the discharge was similar to that of the WSD described in Section 2.2, and need not be restated here. The optics x^ere also identical to that of Section 2.3, and the alignment was carried out in an analogous fashion. OPERATIONAL AMPLIFIER The results of Chapter 2 had been obtained by taking the signal right off the anode resistor of an IP28 photomultiplier by means of a compensated probe, and as the system seemed relatively insensitive to pickup from the discharge, proved to be satisfactory. However, the new current wave-form caused considerably more pickup, and the compensated probe was replaced by an emitter follower terminated in 50 ohms. This arrangement, as i t turned out, had the serious drawback of a d-c output level which shifted downwards as the signal increased. This varying dc level was eventually eliminated by replacing the emitter follower with an operational amplifier (see Appendix A for details). The linearity of this c i r c u i t was checked before installation by feeding in a pulse of a similar magnitude and duration from a pulse generator. No distortion was discernible from zero m i l l i v o l t s output up to 80 m i l l i v o l t s , where the amplifier saturated. (A judicious combination of s l i t widths, photomultiplier supply voltage, etc., ensured that under real operating conditions this saturation level was never reached.) -30-The operational amplifier was shielded completely by the brass housing of the photomultiplier, but had the disadvantage of necessitating two external power supplies. Discharging the thyratron and capacitor bank caused a discouraging amount of high frequency noise to appear during the f i r s t 5 or so microseconds of the oscilloscope trace along with the PM signal. Wrapping the cables from the power supply to the operational amplifier around f e r r i t e cores significantly reduced but did not com-pletely eliminate the noise. However, since no measurements were going to be made in the f i r s t 5 microseconds of the oscilloscope trace, no laborious efforts were undertaken to completely eliminate the pickup. Blocking the light path into the monochromator while discharging the bank showed that there was no measurable distortion of the signal after the f i r s t 5 - 1 0 microseconds. CALIBRATION OF THE PHOTOMULTIPLIER AND SYSTEM RESPONSE An IP28 photomultiplier had been used in conjunction with the WSD of Chapter 2 since i t had the required spectral response (i.e. maximum o sensitivity around 4000 - 4500 A), and had the further advantage of being conveniently at hand. However, the above modifications to the discharge resulted in a considerable reduction in light intensity and to improve the signal to noise ratio (SNR) the RCA IP28 was replaced by an EMI 9558B photomultiplier. The 9558B has a similar (S - 20) spectral response, but has almost twice the quantum efficiency at the wavelengths of interest. (Note that i t was not amplifier noise but rather photon noise which had to be reduced. Simply increasing the gain of the photomultiplier by increasing the supply voltage would not improve the SNR; only increasing -31-the number of photons arriving per second or stepping up the quantum efficiency of the PM would improve the SNR. The former was undesirable since either spectral resolution or spatial resolution would be down-graded. ) The line a r i t y of the photomultiplier was tested in standard fashion by measuring the intensity of several spectral lines from a helium geisler tube as various calibrated neutral density f i l t e r s were placed in front of the entrance s l i t . Linearity to ± 2% was observed over most of the signal range, with ± 5% at low signal levels (around 5 m i l l i v o l t s or less). The limitation of 80 mv imposed by the operational amplifier ensured adequate linearity over the range of interest. SPECTRAL RESPONSE . In order to estimate the plasma temperature by the comparison of inten-s i t i e s of spectral lines (see Section 4.7), the transmission of the system as a function of wavelength f i r s t had to be established. A tungsten ribbon lamp was shone through the apparatus, and with the s l i t s open to 500 y the output of the photomultiplier was obtained as a function of wavelength using the automatic wavelength scan. The signal was recorded on an X-Y plotter. The temperature of the lamp was measured with a pyrometer and found to be 2300 °K + 15°K, and during the time of one calibration run (lasting 2 - 3 minutes) changed by less than 0.3% or 5°K •— less than the calibra-tion error. The measured system response was combined with the De Vos (1954) data following the procedure of Jones (1970), according to -32-r CA) = eCA,T)I CX,T )T(X) m o 1 c where I is the measured system response, T G O the transmission of the system (the quantity desired), and e(A , T ^ )I q(A,T ) i s the spectral power output of the tungsten ribbon lamp for the colour-corrected temperature (e i s the emissivity and I is the Planck function). The temperature was interpolated by a linear routine from the data given in Jones (1970). The results of the measurements and calculations are shown in Fig. 3-5. 3500 4500 5500 6500 3 5 0 0 4500 5500 6500 WAVELENGTH (&) WAVELENGTH (A) Fig. 3-5. Ca) Spectral response of photomultiplier and grating according to manufacturers data. Cb) Measured and computed response curves. THE MONOCHROMATOR Observations were made using a Spex 1.0 metre monochramator fi t t e d with o a 1200 line/mm grating blazed at 5000 A ( f i r s t order). Both the entrance and exit s l i t s were adjustable from 2 microns up to several millimeters, and for most line measurements were both set at either 10 or 20 microns. (The transmission function for the 20 micron setting i s given in Fig. 5-4). -33-In order to f a c i l i t a t e accurate scanning of narrow line profiles, i t was necessary to improve the accuracy to which the wavelength could be set. This was accomplished by mechanically amplifying the motion of the wavelength control knob with a 10-inch arm fastened to i t . A 10-inch arc was fastened out of lucite and mounted on the side of the mono-chromator concentric with the wavelength control knob, along which ran the 10 inch arm driven by a rubber drive wheel. The motion along the arc was further sensitized by gearing down the rubber drive wheel by another factor of three. This allowed one revolution of the geared control knob to correspond to 0.3 A, with the result that wavelength adjustments of 0.03 A or less were feasible. The mechanism which was fastened to the wavelength con-t r o l knob by a f r i c t i o n clutch which permitted manual scanning either in the normal way or by using the fine setting control above, but which s t i l l did not interfere with the normal functioning of the automatic wavelength drive. . ALIGNMENT OF OPTICS AND DEFINITION OF PLASMA VOLUME The optics were identical to those of Section 2.3, as was the alignment procedure. Fig. 3-6 below shows the "cone" of plasma defined by the monochromator and entrance optics, with the widest diameter of the ad-justable aperture stop closely approximating the maximum solid angle of the monochromator optics. The entire grating of the monochromator was illuminated by a laser beam diverged by a short focal length lens and refocussed on the exit s l i t . -34-ADJUSTABLE STOP CENTRE OF DISCHARGE TUBE ENTRANCE SLIT LUCITE BLOCK s s s s s <• s * < ' f f ' • s ' ' ' s f ' f J r y 12.5 cm-22.8 cm Fig. 3-6. D e f i n i t i o n of Plasma Volume. (Dimensions not to scale.) WALL OF DISCHARGE TUBE HOLLOW ELECTRODE AREA OF PLAMA CONE AT SECT AA (FIG. 3-6) Fig. 3-7. Relative Dimensions of the Electrodes and Plasma Volume. -35-The brightness of the laser light then allowed direct observation of the path which a l l light rays would take through the system, and in particular allowed a correlation of the diameter of the aperture stop with the area of the plasma cone Csee Fig. 3-6) which would be "sampled" by the f i e l d lens. (The diameter of the cone was measured at the plane of the quartz f l a t as a function of the diameter of the adjustable aperture, and by simple proportion was deduced for the volume of plasma contained between the ends of the hollow electrodes.) The volume of plasma thus sampled was for the chosen setting of the adjustable aper-ture - 4% of the total volume of the cylinder of plasma defined by the inner diameter of the hollow electrode, the same area over which electron density measurements showed the plasma to be homogeneous. Characteristics of the plasma The physical arrangement of the plasma source on which the studies of He 4471 were made was detailed in Chapter 3. This chapter summarizes the procedure and results of investigations into the s u i t a b i l i t y of this apparatus as a low density spectroscopic source. In particular, studies were made of the spatial homogeneity of electron density, and the time variation of both N g and T . For reproducibility and compar-ison of results taken on different f i l l i n g s , i t was necessary to establish how the characteristics of plasma afterglow changed with f i l l i n g pressure and f i r i n g voltage. Section 4-2 details the procedure 15 -3 used to establish the time at which N = 10 cm is reached. e -36--37-4.1 ELECTRON DENSITY BY MEASUREMENT OF STARK WIDTHS In Chapter 2, the Stark width of He 3889 had been used as a monitor of the electron density, a suitable choice for high electron densities. However, for this plasma i t was no longer as useful. Although 3889 had an appreciable width during the period of peak 30 usee) at the times of interest 120 ysec) the line width is comparable to the instrument width. In fact, one of the only lines having an appreciable 4.0 0.2 I I I I I I I I I I | I I I 1 I I I I 0.1 0.2 0.4 0.7 1.0 2.0 4.0 6.0 10.0 E L E C T R O N D E N S I T Y ( x I0 1 5 cm" 3 ) Fig. 4-1. Variation of He 4471 half width with N . (Based on p r o f i l e s of Barnard et al (1969)). e -38-15 -3 width at an electron density of 10 cm or less i s He 4471 i t s e l f . Fortunately, since the forbidden and allowed components are well sep-arated at these densities, the width of the allowed component, by comparison with theoretical profiles, can be used as an indicator of the electron density. 80 120 TIME (psec). Fig. 4-2. Half width of Allowed Component vs. Time 200 -39-Th e theoretical profiles of BCS were used to obtain the graph of Fig. 4-1, and measurements of the electron density based on a compar-ison of experimental and theoretical half widths cannot be expected to yield an accuracy better than the accuracy to which the theoretical o profiles themselves have been specified. (An uncertainty of ^ 0.04 A in the measurement of the half width would therefore result in an un-certainty of 20% in N .) The time at which N = 10^ was reached was e e indicated by the data of Fig. 4-1 to be 120 - 130 microseconds, and was later specified more accurately as 127 microseconds by comparison with a more recent and more accurate profile at the same density computed by Mssrs. Barnard and Cooper (see Fig. 6-3). This time was also corrob-orated by interferometer measurements. 4. 2 ELECTRON DENSITY MEASUREMENTS BY LASER INTERFEROMETRY An extended effort was made to apply the sophisticated laser interfer-ometric techniques of Funk (1972) and more recently Preston of this laboratory to measure the electron density. In this system, the length of an FP cavity is increased with time essentially by reflecting the beam back into the laser via a retro-reflector mounted on a rotating turntable, thereby setting up interference fringes which are of v i r -tually constant frequency over the times of interest. A change in electron density in the plasma causes an additional change in the opti-cal path length of the resonator and shows up as a frequency modulation of the fringes. The fringes are then fed into an FM detector, and the output signal is proportional to the electron density. -40-This interferometer has been used successfully by Funk and Curzon (1972) and Preston and Curzon (1972) for studies of higher density plasmas, but in this experiment was not found to be useful at low den-s i t i e s . The output of the FM detector is an amplitude -modulation of a baseline, the slope of the baseline depending on the frequency of the fringes. Ideally, i t should be absolutely horizontal for every revolu-tion of the turntable, but in practice i t is not so. The slight change in frequency of the fringes due to variation in the rotation speed of the turntable causes the baseline to vary with time, and since the scope necessarily had to be set at high sensitivity to detect the small signal expected, the baseline was rarely v i s i b l e on the screen. Had more time been available for pursuit of such a method of measuring low electron densities, the instrumentation undoubtedly could have been improved. Interferometric measurements of the electron density were ultimately carried out using a form of Fabry-Perot interferometer. The cavity i s formed by the addition of a third mirror, and the intensity of the laser beam is monitored by sending the rear beam of the laser into a photo-multiplier (see Fig. 4-3). In this particular experiment i t was found that both the laser and external mirror had to be mounted on specially constructed weighted tables (see Fig. 4-3) in order to reduce the frequency of the background fringes to an acceptable value (approximately 5 msec/ fringe). Otherwise, a distinct curvature of the oscilloscope trace was discernible over the time of interest (200 ysec). Fig. 4-4 shows sample oscillograms of: (a) typical background fringes; (b) and (c), two typical traces at the same pressure and f i r i n g voltage seen on different time bases, and (d) i s a repeat of (c) to show the reproducibility of the fringes. -41-MIRROR LASER FRAME OF APPARATUS Fig. 4-3. The Interferometer. The shaded areas represent weighted tables to dampen the o s c i l l a t i o n s caused by v i b r a t i o n s of the apparatus. 5 msec/cm 50 usee/cm Fig. 4-4. 20 usee/cms; 20 usec/cm Tracings of Oscillograms of Fringes. (Vertical sensitivity for a l l traces = 5 mv/cm.) (a) Background fringes at 5 msec/ cm. (b) Plasma fringes at 50 ]xsec/cm. (c) Same fringes seen at 20 \isec/cm. (d) Repeat of (c). -42-FRINGES DUE TO THE PLASMA A significant electron density causes a change in refractive index from the value produced by the neutral gas alone, and is given by the well known relation 2 .2 N e X i e n = 1 j 2tr m c e 2 where A indicates the wavelength dependence. A laser beam passing through a region of length L with a refractive index n(x) along the line of sight experiences a total phase change of 6 = 0 (n(x) - 1) dx. If one can assume, or more preferably establish, that (and hence n) is constant along the line of sight, then the integration i s t r i v i a l , and a change in path length A/2 corresponds to a change in electron density of 2 13 7rmc 1.1 x 10 -3 N = —=— = — cm e 2T, A L e L A where L and A are both measured in centimetres. For this case L = 25 cm and an He-N laser ( A = 6328 A = 6.328 x 10~5 cm). This becomes e AN = 6 x 10 1 5 cm"3, e The results of the analysis of fringes similar to those in Fig. 4-4 for -43-a range of f i l l i n g pressures and f i r i n g voltages are shown below in Fig. 4-5. The points shown represent measurements taken at A/2, A, 3A/2 etc. E £ ° O 60 80 TIME (/JSOC) 60 SO TIME (/isec) Fig. 4-5. Variation in N with (a) F i l l i n g Pressure and (b) Firing voltage. The most obvious result of the interferometric determination of N is e that the decrease in N £ can be described over the major portion by an exponential decay, N (t) oc N 10~ a t e eo where a depends on the f i r i n g conditions. -44-Casual inspection of the curves in Fig. 4-5 shows that the last data point corresponds to ^  3 x IO 1 5 cm 3 , and that N = 1 x lO 1^ can only e be inferred by extrapolation. Nevertheless, the exponential f i t i s 15 good, and the time of occurence of N g = 10 is placed at 125 usee, ± 3 - 4 usee, consistent with measurements based on the half width. 60 80 100 120 140 TIME (yxsec) Fig. 4-6. Electron Density vs. Time for P = 1.2 t o r r t f i r i n g voltage = 10 kV. -45-AMBIGUITY OF THE LAST FRINGE The ambiguity of 1/2 fringe which usually accompanies interfermoetric determinations of N was resolved essentially by taking enough photo-e graphs. The background fringes were of such a low frequency that no appreciable phase change occurred over the time of interest, thereby eliminating the need for fractional fringe estimation. True, the interferogram s t i l l had an undefined phase, but this could be resolved with a l i t t l e patience. Since the electron density goes to zero, the oscilloscope trace returns to a position corresponding to the phase established by the relative positions of the laser and the exter-nal mirror. If the front mirror of the laser and the external mirror were separated by an integral number of wavelengths, then the intensity would then be at a maximum. Provided that the fringes are of constant amplitude (see for example the fringes i n Fig. 4-4), these photographs are easily identified out of any collection of li k e photos. For the case of 180° phase, the beam w i l l return to the position of minimum signal. In either case the phase is known and the positions of phase = ir/2, ir, 3TT/2, 2TT etc. can be readily established. The results of the measure-ments of two such photographs are shown in Fig. 4-6. 4. 3 HOMOGENEITY OF THE ELECTRON DENSITY An analysis of the radial variation of the electron density was neces-sary to confirm that contributions to the intensity were not being received from regions of differing N^. That would spell disaster for the He 4471. - 4 6 -Th e laser interferometer of Section 4.2 was modified as shown in Fig. 4-7 to allow density measurements at arbitrary radial positions. The maximum radius possible was limited by the inner diameter of the hollow electrodes. M I R R O R D-r, L U C I T E B L O C K - £ L A S E R D I S C H A R G E T U B E L U C I T E B L O C K Fig. 4-7. Arrangement for determining Radial Variation of N . The radial position of the laser beam (about 2 mm diameter) was measured with a conveniently placed scale to an accuracy of ± 0.5 mm or less. A second lucite block then returned the beam to i t s original path, and was also used to "tune" the background fringes to maximum amplitude. 2x 10 16 N , Ix 10 16 — o . -o~ 7.0 5.0 6 0 jUsec 110 ~t>. RADIAL POSITION (mm) Fig. 4-8. Radial Variation of the Electron Density. -47-Previous checks of the spatial homogeneity by comparing profiles of He 4471 at various radial positions were borne out by measurements by the laser interferometer. At times of interest 120 useconds), the density varied only slightly across the v i s i b l e region of plasma. The electron density i s evidently homogeneous over an area considerably larger than the area sampled for line profiles. 4.4 FRAMING CAMERA STUDIES As a further (more qualitative) check on the homogeneity of the plasma, time resolved photographs of the discharge were taken using an image converter framing camera which was capable of taking five sequential photos of 50 - 500 nanosecond : . . j ' " y% ' • IOO ^ 60 20 0 u in a. UJ c 3 1 I / / / Fig. 4-9. HI— 500 usee Photos of the plasma, for initial conditions of 1.2 torr, 10 kv. duration at intervals v a r i -able from 1 usee to 20 usee, the camera was stopped down to f/10 to improve resolution, and adequate time resolution was achieved even using maxi-mum exposure time. For f i l l i n g pressures below 300 microns, considerable tur-bulence of the plasma was ob-served, confirming the undesir-a b i l i t y of working in this pressure region. Photographs for pressures above ^0.5 torr showed no plasma inhomogeneities, nor any kinking of the plasma column. -48-4.5 PLASM REPRODUCIBILITY The d i f f i c u l t i e s in obtaining an accurate profile of He 4471 at low electron densities have been tabulated in Section 1.5, not the least of which is the reproducibility of the plasma. It was important to establish that the plasma was not only homogeneous, but also that neither the temperature nor electron density fluctuated drastically from shot to shot. Interferometric studies showed that the N vs. e time curve for successive shots were identical (within the error bars of the measurement), and that after 10 or so "warm-up" shots, fluctua-tions i n the light intensity at a particular wavelength showed a mean deviation of ^  6%. Fortunately, charging up the capacitor bank pre-ionizes the plasma, greatly improving the shot-to-shot reproducibility. U J 0 5 10 15 20 25 30 35 NUMBER OF SHOTS Fig. 4-10. R e p r o d u c i b i l i t y of the Pulsed Arc Plasma at a Wavelength of 4471.5 for t = 80 usees. -49-4.6 ELECTRON TEMPERATURE MEASUREMENTS Previous calculations of He 4471 profiles revealed that the line shape is only weakly dependent on electron temperature. Nonetheless, to enable a meaningful comparison to be made with existing published pro-f i l e s i t was considered desirable to obtain an estimate of T . e At low densities the electron temperature is not simple to measure accurately, since techniques commonly used i n studies at higher densi-ties are not applicable here. The simplest technique, that of measur-ing the ratio of the total intensities of He II 4686 to He I 5876 is less accurate at low electron temperatures due to the low intensity of He 4686, and the lack of tabulated information concerning the corres-ponding temperature. Nevertheless, the procedure was f a i t h f u l l y carried out. Tp.(eV) 80 120 TIME (usee) 200 Fig. 4-11. Temperature Estimate Based on the Ratio of the Total I n t e n s i t i e s of Ee 4686 to Ee 5876. -50-Th e total intensities were obtained directly using a sufficiently wide exit s l i t . (Comparison of the area under the He 5876 profile with the measured total intensity showed accuracy to within 2%.) A correction was applied to account for the transmission of the system, and the temperature estimate was obtained by simple extrapolation of Fig.13.1 in Griem (1964). A check on both the existence of LTE and the value of T was also e attempted by measuring the total intensities of a number of He I lines and constructing a Boltzmann plot. Neutral density f i l t e r s were used where required to maintain the range of measured intensities within the linear range of the photomultiplier. The procedure for construct-ing a Boltzmann plot is b r i e f l y summarized below. For an LTE plasma, the population of the energy states is governed by the Boltzmann factor, and the relative intensity of two lines may be expressed by I T A 3 g f E — E L L u u _ u L T ,3 . e kT I X g T f T u u L L In general, therefore, we can write, 3 i F e | f = c o n s t a n t or in logarithm form, E = kT in ^ -r + constant. IX -51-It follows that the slope of the line on a semi-log plot (provided LTE exists) should yield the electron temperature. The result of such ca l -culations for this plasma at 120 microseconds are shown below in Fig. 4-10. Unfortunately, i t can also be seen that not much useful information i s gained. From this plot, an electron temperature of vevy approximately 0.6 ev is obtained. Combined with an estimate of 1.5 ev from Fig. 4-11, T = 1 ev is an acceptable compromise. At any rate, T is observed to be positive, a fact which i f not helpful is at least encouraging. Reference to the theoretical profiles of Barnard, Cooper and Shamey (1969) and more recent calculations of Barnard and Cooper (unpublished results) indicate that the variation in intensity due to a change in electron temperature i s of the order of magnitude of the error bars of the measured data of this and l i k e experiments. Consequently i t was not f e l t that an extended program of investigation of the electron temperature would be j u s t i f i e d since the results would not be discern-ible in a comparison of the measured and theoretical profiles. 5 > •Z. o> !ZLU o z X LU UJ L O G +• CONSTANT I X ? Fig. 4-12. Boltzmann Plot of Total Line Intensities at t = 120 ^seconds. -52-4.7 ION TEMPERATURE Since considerable interest has been expressed recently in the contri-butions of ion dynamics to the He 4471 profile, i t was f e l t that in order to be contemporary the ion temperature should be estimated. For this purpose, He 4713 was chosen since i t is negligibly stark broadened. (Any broadening is due to the thermal motion of the emitter plus instrument broadening. However, He 4713 is very narrow for these temper-atures, and the value of T. extracted is only ah estimate.) Fig. 4-13. The half width of Re I 4713 at various times during the afterglow. The instrument width is .08 A. -53-The s l i t s were closed to 4 microns which was considered the minimum setting feasible under the circumstances. The i r i s defining the observed plasma volume was f u l l y opened permitting the maximum amount of light to enter, with a corresponding loss in spatial resolution. Profiles of He 4713 were thus reconstructed for various times in the afterglow (see Fig. 4-13). The half width of a Doppler broadened profile i s related to the temper-ature by [Huddlestone and Leonard (1965)] 7 AX = 7.16 x 10 X / r p -D • / M. V x which for the case of He 4713 becomes T = 3.51 x 10 5 A X p where A X ^ is in Angstroms and T^ in degrees Kelvin. Unfortunately, a significant portion of the measured line width is due to instrument broadening. It was therefore necessary to extract the true Doppler half width from the measured profile. A program was written to produce the profile of a Gaussian line shape folded with a triangular instrument profile of .08 A half width, following the ( corrected) results of Dalton (1965). For a measured half width of .26 A, the true Doppler half width was estimated to be .23 A, corresponding to an ion temperature of 18,000 °K. -54-However, due to the low intensity of the source and the narrow s l i t s , the accuracy of the profiles of He 4713 is not great, and an uncertain-ty of .03 A in the halfwidth corresponds to an uncertainty in the ion temperature of 4,000 °K. The ion temprature corresponding to N £ = 10^ cm"^  is therefore estimated to be T ± = 18,000 °K ± 4,000 °K. Measurements of line profiles Chapter 4 analyzed in some detail the s u i t a b i l i t y of this plasma as a reproducible region of homogeneous electron density and provided measurements of the electron density and temperature. Chapter 5 now details the procedure involved in obtaining line profiles, and the various uncertainties and errors involved. 5.1 CONDITIONS OF DISCHARGE It was observed by studying temporal profiles of He 3889 and He 4471 that densities of l O ^ were not being reached for neither low f i l l i n g pressures 100 y) nor high f i l l i n g pressures (>10 torr). However, was observed that for f i l l i n g pressures around 1 torr, lower densities were in fact being reached. Fig. 4-5 showed that the electron density - 5 5 -- 5 6 -in this region has less dependence on f i l l i n g pressure, so that P =1.2 o torr was chosen as the operating pressure. A f i r i n g voltage of 10 kV was chosen primarily due to limitations imposed by the discharge c i r c u i t . 5.2 MEASUREMENT OF LINE PROFILES The light from the discharge was focussed onto the exit s l i t of the monochromator in a similar manner to that shown in Fig. 2-3. Since measurements were to be made in the afterglow where intensities were small, the output of the photomultiplier (operational amplifier) was fed into a, Tektronic 555 dual beam scope, with the second beam starting late in the afterglow and displayed at a greater sensitivity. (See Fig. 5-1 below.) (B) TIME (usee) 220 80 120 160 200 @ TIME (usee) Fig. 5-1. Typical oscillogram of photomultiplier output showing rela-tionship between time bases. Lower beam is displayed at 10 mv/cm3 upper at 2 mv/cm. -57-In Fig. 5-3 the forbidden component is shown on a scale expanded by a factor of 10 to i l l u s t r a t e more clearly the detailed shape of the for-bidden component. The error bars are, therefore, also 10 times as large. Improved accuracy cannot be achieved due to two reasons: Q the signal is becoming comparable to the magnitude of fluctuations caused by photon noise Q the continuum is a significant fraction of the intensity of the forbidden component. Furthermore, the signal to noise ratio i s related to the i n t r i n s i c bright-ness of the source, which had already been optimized. On a sensitivity scale suitable for measurements of the allowed component, the continuum intensity is l i t t l e more than the thickness of the scope trace and contributes less than 0.5% to the intensity of the allowed component. However, when displayed at a greater sensitivity, the measure-ments do indicate the presence of a continuum, and i t then becomes a sig-nificant problem to determine exactly what this continuum intensity i s . It must be borne in mind that any misjudgment of the continuum level based on a f i t of the allowed component w i l l be magnified by a factor of 10 for the forbidden component, and what at f i r s t inspection may appear to be a good f i t w i l l be seen not to be so when the continuum is subtract-ed. In view of this, therefore, i t was necessary to arrive at a value of the continuum consistent both with the uncertainties in the measuring process and with the desired aim of obtaining a good f i t to both the allowed and forbidden components. The following procedure was followed: -58-(1) an interpolated profile was produced for t = 127 usee, the time at which N = 10^ was deemed to occur. (See e following section.) (2) an approximate value of the continuum was selected based on the measurements of the intensities in the line wings (3) the continuum was subtracted, and the profile normalized to unit area (4) the best over-all f i t was obtained by emphasizing the f i t in the line wings (5) any remaining discrepancy remaining in the continuum was measured, and using this new continuum value, steps (3) to (5) were repeated. This procedure was f e l t j u s t i f i e d for the ends for which i t was intended since the continuum was so small and therefore d i f f i c u l t to establish. It has three redeeming features: (1) the line wings are described better theoretically than is the rest of the profile, (2) the f i t of the allowed component is very good, and (3) very l i t t l e change in the shape of the line profile was observed by making different estimations of the value of the continuum. (Renormalization of the profile tends to scale the inten-s i t i e s by a factor comparable to the factor by which they were reduced by the subtraction of a l i t t l e more continuum. The greatest, influence occurs near the peak of the allowed component, and hence the error bars are largest there. Even this, however, was slight.) -59-Th e signal strength of 4471 was only 40 T I I V at best, with entrance and exit s l i t s at 20 u. It was considered undesirable to open the s l i t s wider, since any improvement in the signal-to-noise ratio would be defeated by an increase in the instrument width. At low densities He 4471 is narrow and by necessity the instrument width needs to be kept as narrow as possible. The triggering process occasionally involved a few microseconds of j i t t e r in the breakdown of the discharge, with the result that a hori-zontal displacement of the trace would occur. Before measuring the intensities at given times, the j i t t e r was subtracted. The start of the trace could easily be identified to within 1 or 2 microseconds and thus the j i t t e r did not contribute significantly to the scatter of points in the line profile. The signal was considered to be the weighted average of the noise f l u c -tuations, and the position of the mean of the trace could generally be established to within 0.05 cm. The plasma reproducibility contributed another 0.05 - .15 cm and i t s effect was reduced to a minimum by taking 2 or more shots. In most cases, the measurements were identical to within the reading error on both photographs. The instrument width was accept-able, and the spatial homogeneity was adequate to permit sampling of a a f a i r l y large volume. However, a smaller volume (.35 cm diamter - see Fig. 3-6) was chosen to' avoid accusations of contributions from regions of differing Ng. The contributions to the accuracy (or inaccuracy) by the various factors are discussed again in Chapter 6. -60-t 0.8 Ul 0.4 0.0 o CONTINUUM I t. CONTINUUM 2 * 2 o A A A A -3 AX (A) Fig. 5-2. Effect of different continuum choices on He 4471 profile. Continuum (1) is 85% of continuum (2). 5.3 INTERPOLATION OF He 4471 PROFILES It had previously been discovered that N £(t) was clearly exponential over a major portion of the afterglow. This is consistent with the findings of Gerber et a l (1966) who studied the recombination processes in decaying helium plasmas and observed similar results. The rate equations describing the equilibrium process He + + 2He -> He* + He considered by Gerber et al to be the dominant process are 3 N 1 2 -r-T = D 1V N - v N - a.N.N 9t a l 1 conv 1 l i e 8 N2 2 -r-=: = D V N. - V N„ - a N N 3t a2 2 conv 2 2 2 e + + where N. and N. are the densities of He and He„, D , „ are the ambipolar 1 2 I al,z - 6 1 -diffusion constants, and a „ are the recombination coefficients. 1, z v i s the conversion frequency of He"** into He"!", conv 2 During the late afterglow both v and a are small, and to a f i r s t approx-imation the time dependence w i l l be exponential, i.e., N x(t) = N^fDe T etc., Also, as found by Villarejo et a l (1966), the decay constant depended only on the f i l l i n g pressure - as observed in Fig. 4-5. Exponential time dependence of the light intensity depends greatly on the existence of the exponential dependence of N^(t) and N g(t). Speci-f i c a l l y , the light intensity due to the recombination process He + + e He** He + hv Fig. 5-3. Comparison of Measured and Interpolated P r o f i l e for t = 128 microseconds. - 6 2 -is proportional to a^N^(t)N £(t). Experimentally i t was found that the intensity of light emission was exponential with a well-defined time constant over a 20 - 40 microsecond time span around the time of N g = 10^. Later in the afterglow, the decay was also exponential but with a different time constant, indicating that a different recombina-tion process was perhaps responsible for the light emission in the dying stages of the plasma. Plotting the intensity vs. time on semilog paper showed an excellent straight line f i t at a l l wavelengths. Consequently, a computer program Bt was written to perform a least squares f i t to the function I(t)=Ae of measurements at 120, 128, 130, 124 and 140 microseconds. Interpolated profiles could then be generated for other times in this period of the afterglow. The result of following this procedure i s an averaging of the measurement uncertainties caused by photon noise and plasma repro-ducib i l i t y , and a considerable reduction in the scatter of the points, (see Fig. 5-3). The interpolated profile i s considered to be the more accurate. The error bars of ± .05 cm as measured from the oscillographs are thus reduced to more like .03 cm or less for the interpolated values (as estimated from the rms deviation in the least squares f i t parameters). 15 -3 The time at which N g = 10 cm was reached was determined (Fig. 4-6) to be 127 ± 5 usee, and consequently an interpolated profile was generated for the corresponding time. With the continuum subtracted as indicated above and the intensities normalized to unit area, the profile for 1 5 - 3 10 cm is shown below in Fig. 5-3. -63-1.2 >-(/) U J 0 . 8 I -2 0 . 4 0 . 0 E F F E C T OF N e = I O % ON P R O F I L E i : i ! l-O-H KM 0 i - i I I 1 I ° o 0 0 1 0 A X (A) Fig-. 5-4. He 4471 P r o f i l e for N = 10153 T _ 1 ev. Error bars indicate uncertainty aue to uncertainty in N' . 5.4 THE INSTRUMENT WIDTH Up u n t i l now l i t t l e reference has been made to the influence of the instrument function on the observed profiles, other than to point out that i t was minimized. Clearly for these and narrower profiles, instru-ment broadening is important and contributes significantly to the half width of measured profiles, causing amongst other things, an over-estimate of stark-based N g measurements. Fig. 5-4 shows the approximately t r i -angular instrument function obtained by scanning the spectrum of a helium Geisler with exit s l i t = entrance s l i t = 20 u, ( s l i t height = 0.2 cm). It can be interpreted either as a rounded triangle or as a rounded trapez-oid. (For the purposes of folding with the calculated profile of Barnard -6k-and Cooper, a trapezoidal shape was chosen, with dimensions as shown.) No attempt was made to de-convolve the experimental profiles, as such a procedure is numerically complicated and beyond the scope of this pro-ject. Rather, the recent results of Barnard and Cooper were folded by Barnard with the measured instrument function, and the results compared with experiment. The effects of the f i n i t e resolving power of the mono-chromator were thus v i r t u a l l y eliminated. (The fact that such a theor-eti c a l profile was available for comparison was of no small help in elucidating the shape of 4471 at this particular density.) -0.3 -0.2 -0.1! 0 0. A \ ( A ) Fig. 5- 5. The Instrument Fuation for 20\i Slits. unpublished - 6 5 -5.5 OPTICAL DEPTH CHECK It was without question necessary to confirm that at 4471 Angstroms the plasma was optically thin. The presence or absence of self-absorption was f i r s t tested experimentally by mounting a 2 metre focal length front-surfaced concave mirror on the optical axis (on the side of the discharge tube away from the monochromator) to redirect the light leaving the dis-charge tube back through the plasma and into the monochromator. The © S I N G L E P A S S X(A) Fig. 5-6. Comparison of P r o f i l e s of Light Making Single and Double Pass through the Plasma. (Double pass means light is r e f l e c t e d back through plasma.) -66-mirror was carefully aligned with the aid of a laser shone into the exit s l i t of the monochromator; the returning beam emerged from the exit s l i t and illuminated the front of the laser and f a c i l i t a t e d accurate align-ment . Under these conditions, the intensity of light at any wavelength should now be doubled. In practice, however, losses occur, and the intensity can be expected to be less than double. Just exactly what the ratio i s can be determined by measuring a region of the continuum both using and not using the mirror. If I^(A) represents the intensity normally measured (with no concave mirror), and represents the intensity measured when the mirror i s used . The intensity of the radiation which has passed back through the plasma is I^M = - I^(A). For a comparison of profiles (as shown in Fig. 5-5)1^ (A) and 12(A) are normalized to the same total intensity. Inasmuch as the results of this optical depth check were favourable, due to the d i f f i c u l t i e s involved and the large error bars associated with this method i t was f e l t that an additional check was desired. Consequently the optical depth was calculated for a 25 cm plasma of homogeneous electron 15 -3 density N g = 10 cm and temperature 1 ev. The expression for the opti-cal depth of an LTE plasma of the above conditions is [from Griem (1964)] hw T(U) = 2ir r cf N_[l - e"kT] L(u>)i o o 2 The symbols in the above expression have their usual significance, with - 6 7 -N 2 - density of upper state 3 (2 p state) kT - 1 ev (nominal value) I = length of plasma L(u>) = line shape, normalized to unit area is calculated by assuming (a) the system i s in LTE and (b) almost a l l of the atoms are in the ground state, so that g2 -hw N = N e W2 LN1 § 1 6 kT The constants in the above expression can be found in most physics texts, and the factor (1 - e -j^ -) evaluates to 0.603 for this wavelength and temperature. The value of T, the optical depth at the allowed peak thus is calculated to be T, . = .004 The plasma is confirmed to be optically thin at this wavelength. At this low temperature, i t was assumed that the majority of atoms were in the ground state. This perhaps requires j u s t i f i c a t i o n . In a recom-bining plasma, transitions by c o l l i s i o n a l and (to a lesser extent) radiative de-excitation causes the atoms to decay to states close to the ground state, but not necessarily the ground state i t s e l f . It is necessary to worry whether under such conditions sufficient interaction occurs between the singlet and t r i p l e t states to ju s t i f y the taking of the l^s state as the ground state. (It may be, for example, that atoms 3 are "piling up" in the 2 s metastable state for a significant time to significantly alter the velocity distribution of the electrons.) To confirm that sufficient interaction of the metastable state to the ground state was occurring, the cross-section for the c o l l i s i o n a l de-3 1 excitation 2 S higher s t a t e s — * - l S was calculated. Using the experimentally obtained values for this cross-section weighted by the t a i l of the Maxwellian distribution for T = 1 ev, the average time between collisions was evaluated to be T _ 1 = <va„o 1 Q > N = w ( v ) N I. o — J . O o o which gives T 2? 30 nsec, N q being the density of helium atoms. (This result indicates that the metastable and ground states do interact rather quickly, since the average time between collisions leading to excitation of the resonance line i s of the order of 90 nanoseconds, using the treatment from Griem (1964): E z - l , a 7 3 g Z - l , a _2 = 1-1 x 10 Z 21 kT kT , T f o i N 2T7 2* 6 21 e z E z E rt rl once again assuming that most atoms are in the ground state. (E = ionization potential of hydrogen, E^ = excitation energy of upper states of resonance line . The remaining symbols have their usual connotations.) -69-These considerations of the timescales involved for the interaction of different species in the plasma indicate that for a l l intents and pur-poses, the relative populations of the metastable and ground states are consistent with the use of the Boltzmann factor, and furthermore, that the calculation of the optical depth is sensible. Summary and conclusions Section 6.1 outlines the accuracy of the profiles- due to experimental uncertainties. Experimental profiles of He 4471 are presented in Section 6.2. 6.1 EXPERIMENTAL ERRORS In Section 6.2 a comparison is made with the recent theoretical profile of Barnard and Cooper. In this section the various experimental factors are taken into account and the general accuracy of the profile is discussed. The factors contributing to the error bars are: -TO-- 7 1 -® plasma reproducibility © photon noise on oscilloscope trace (signal to noise ratio) Q plasma inhomogeneities Q measuring errors A determination of N and T e e £ self-absorption © establishing continuum Each has been discussed in detail at another point in the text, and the results are only summarized here. Briefly, self-absorption was shown to be negligible for this line, and is borne out by the compari-son with Burgess' experimental results, and hence w i l l not be discussed further. Similarly, an analysis of the plasma shows that only a very small variation in N was observed across the observable diameter of e plasma, an amount not expected to contribute significantly to a change in shape of the profile. Besides, any contribution from regions of differing electron density would result in a reduction of the relative heights of the two peaks, not the reverse. No such reduction was observed. Plasma reproducibility, as previously discussed, contributes an error bar of % 5%, and averaging 2 or 3 shots per wavelength setting minimized the effects of plasma variation. No substantial gain in accuracy was -72-achieved by attempting to average more shots, since the target error occurred in the establishing of the electron density. As pointed out in Section 5.2, no experimental parameters could be varied to increase the signal to noise ratio without simultaneously destroying spatial or spectral resolution. Simply increasing the supply voltage to the photomultiplier or increasing the gain on the scope accomplishes nothing since the photon fluctuations scale propor-tionately. (Only increasing the quantum efficiency w i l l help; for this purpose, the IP28 photomultiplier was replaced by an EMI 9558B as discussed in Section 3.2.) Unfortunately, the noise becomes progress-ively more important at lower signal levels, with the result that pro-f i l e s at lower densities have larger error bars, and the forbidden component has the largest error bars of a l l . However, the effect of photon noise was considerably reduced by f i t t i n g the intensities at each wavelength to an exponential, with the result that the photon fluctuations were effectively averaged out (see Section 5.3 for details). This was a marked improvement over the accuracy which could be obtained by using measurements based at only one time. The combined contribution of the errors from plasma fluctuations and photon noise are shown as error bars in Fig. 6-1. Two remaining uncertainties are (a) the determination of N g and (b) the establishing of the continuum level. These are discussed in detail in Section 5.3, and their contributions to the profile are shown below in Fig. 6-1. -73--3 Fig. 6 A A ( A) c -1. Uncertainty in Ee 4471 p r o f i l e at Ne = 10A cm . Error bar represents photon noise, plasma repro-d u c i b i l i t y . Dotted lines indicate limits of accuracy based on ability to determine Ne. >-H CO Ld h-UJ > < _ J LU CC 4471 A - B C S I - — GRIEM • BURGESS a CA IRNS -4 AX ( A ) Fig. 6-2. Previous Comparison of Theory and Experiment. [After BCS (1969) and Burgess and Cairns (1971).] 6.2 FINAL RESULTS The principal achievement of this experiment is shown in Figure 6-3, and the associated errors resulting from the reproducibility of the plasma, photon noise on oscilloscope traces, determination of and T^ and inhomogeneities in the plasma have just been presented i n Fig. 6-1. Good agreement has been obtained with the recent measure-ments of Burgess and Cairns, and the calculations of Barnard and Cooper. Fig. 6-3. Comparison of most recent t h e o r e t i c a l c a l c u l a t i o n (Barnard and Cooper) and most recent measured pro-f i l e (this experiment). -75-Th e solid line is the recent theoretical profile of Barnard and Cooper convolved with the instrument profile shown in Fig. 5-5. (All profiles have been normalized to unit area.) It can be seen that the general agreement is good, the f i t of the allowed profile being o excellent. The instrument profile contributes ^ 1A or 16% of the half width. The peak intensity of the forbidden component is shown to be sli g h t l y lower than that suggested by the calculated profile. The agreement of both the red and blue wings is shown to be good, and the discrepancy at the allowed peak has been vi r t u a l l y eliminated, at least within experimental accuracy. However, the region between the two peaks (i.e. the "valley") s t i l l shows a slight disagreement, although considerably less than that indicated previously (see Fig. 6-2). The over a l l agreement of the present state-of-the-art He 4471 calculations with the most recent experimental profiles i s more apparent when one remembers that the profile as shown in Fig. 6-3 has i t s forbidden component plotted at 10 times i t s actual intensity. With this in mind, i t can be seen that the quibbling over discrepancies which culminated in this project is to a great part resolved, and any remaining discrepancy can be almost eliminated by making larger data points and drawing thicker lines. - 7 6 -6.3 WHAT YOU CAN DO WITH He 4471 The close comparison of the theoretical profiles of Lee (1971) and Barnard and Cooper (unpublished), with the measured profile of Burgess and Cairns (1970) and that of this work suggests that the discrepancy 14 for most purposes has been resolved. At lower densities (^Ne=4xl0 ) a difference s t i l l exists, and future calculations w i l l undoubtedly show improved agreement. It would appear that He 4471 can be specified sufficiently accurately for the range of electron densities of astro-15 -3 physical interest (less than 10 cm ), and that the gross discrepancies observed for theoretical profiles computed using model stellar atmos-pheres can either be resolved or at least attributed to faults in the theories pertaining to st e l l a r evolution and model atmospheres. The procedure used to evaluate the profile of He 4471 w i l l l i k e l y be extended to other lines with forbidden components (e.g. He 4922, 4058) with equal success to be anticipated. He 4471 is dead. Long l i v e He 4471! -77-APPENDIX A: OPERATIONAL AMPLIFIER -78-APPENDIX B: MURPHY'S LAW (1) In any f i e l d of s c i e n t i f i c endeavor, anything that can go wrong w i l l go wrong. (2) Left to themselves, things w i l l always go from bad to worse. (3) If there i s a possibility of several things going wrong, the one which w i l l go wrong is the one that w i l l do the most damage. (4) Nature always sides with the hidden flaw. (5) Mother Nature is a bitch. (6) If everything seems to be going well, you have obviously over-looked something. -79-LIST OF REFERENCES Barnard, A.J., Cooper, J. and Shamey, L.J. (1969), "The broadening of O He I 4471 A and i t s forbidden Components", Astvon. and Astrophysics 1: 28-36. Barnard, A.J. and Cooper, J. (To be published). Burgess, D.D. and Cairns, C.J. (1971), "Experimental studies of helium line broadening in a plasma: II. Low electron densities (lines with forbidden components)". J. Phys. B: Atom. Molec. Phys. 4_: 1364-76. Campbell, H.D. (1965), Measurement of Some Relative Transition p r o b a b i l i t i e s in Singly Ionized Argon, Ph.D. Thesis, University of British Columbia. Curzon, F.L. and Funk. L.W. (1972), "An improved optical resonator for measuring time-dependent electron densities", Can. J. Phys. 48: 915-18. Curzon, F.L. and Preston, J. (To be published). Dalton, M.L., Jr. (1965), "Determination of line widths by slit-width alterations", Appl. Opt. 4_: 603-6. De Voss, J.C. (1954), "A new determination of the emissivity of tungsten ribbon", Physica 10} 690-714. Funk, L.W. (1971), A High Performance Laser-excited Interferometer for Measuring Electron Densities, Ph.D. Thesis, University of British Columbia. Gerber, R.A. et a l , (1966), "Studies of decaying helium plasmas", Physica 32: 2173-91. Griem, H.R. (1964), Plasma Spectroscopy, McGraw-Hill. -80-Griem, H.R. (1968), "Calculated electron and ion Stark broadening of the 3 3 3 3 allowed and forhidden 2 P - 4 P, D, F transitions in neutral helium", Astrophys. J. 154: 1111-22. Huddlestone, R.H. and Leonard, S.L. (1965), Plasma Diagnostic Techniques, Academic Press. Jenkins, J.E. and Burgess, D.D. (1971), "Experimental studies of helium line broadening in a plasma: I. High electron densities", J. Phys. B: Atom. Molec. Phys. _4: 1353-63. Jones, O.C. (1970), "Standard spectral power distributions", J. Phys. D. 3: 1967-76. Leckrone, D.S. (1971), "The He I line profiles in normal B-type spectra", Astvon. and Astrophys. 11: 387-406. Moore, C.E. (1959), A M u l t i p l e t Table of Astrophysical Interest, NBS (U.S.) Tech. Note 36. Nelson, R.H. and Barnard, A.J. (1971), "Profiles of He I 4471 and 4922 angstroms in a pulsed arc", J. Quant. Spectrosc. and Radiat. Transfer (GB), 11, No. 3: 161-7. O'Mara, B.J. and Simpson, R.W. (1972), "The helium abundance in thirty-three main sequence B stars", Astron. and Astrophys. 19_: 167-180. Roberts, D.E. (1972) and Barnard, A.J. (1972), "Check of quantum mechanical + + electron broadening calculations for Mg and Ca resonance lines", J. Quant. Spectrosc. and Radiat. Transfer (GB), 12, No. 8: 1205-16. -81-Villarejo, D., et a l , "Spectroscopic study of the early afterglow in helium: Visible bands and Hopfield continuum", J. Opt. Soc. Am. 56; No. 11: 1574-84. 

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