University of Southern California Dissertations and Theses

Vacuum-Ultraviolet Plasma Spectroscopy On A Double-Arc With Measurements On Line-Strengths And Lineshapes; And On The Lowering Of Ionization Potentials

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Vacuum-Ultraviolet Plasma Spectroscopy On A Double-Arc With Measurements On Line-Strengths And Lineshapes; And On The Lowering Of Ionization Potentials

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Content VACUUM UV PLASMA SPECTROSCOPY ON A DOUBLE ARC WITH MEASUREMENTS ON LINE STRENGTHS AND SHAPES, AND ON THE LOWERING OF IONIZATION POTENTIALS by Santosh Kumar Srlvastava A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Physics) August 1973 INFORMATION TO USERS This material was producad from a microfilm copy of tha original document. While the most advanced technological means to photopaph and reproduce this document have been used, the quality is heavily dependant upon the quality of the original submitted. The following explanation of techniques is provided to help you understand markings or patterns which may appear on this reproduction. 1. The sign or "target" for pages apparently lacking from the document photographed is "Missing Page(s)". If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting thru an image and duplicating adjacent pages to insure you complete continuity. 2. When an image on the film is obliterated with a large round Mack mark, it is an indication that the photographer suspected that the copy may have moved during exposure and thus causa a blurred image. You will find a good image of the pegs in the adjacent frame. 3. When a map, drawing or chart, etc., was part of the material being photographed the photographer followed a definite method in "sectioning" the material. It is customary to begin photoing at the upper left hand corner of a large sheet and to continue photoing from left to right in equal sections with a small overlap. If necessary, sectioning is continued again — beginning below the first row and continuing on until complete. 4. The majority of users indicate that the textual content is of greatest value, however, a somewhat higher quality reproduction could be made from "photographs" if essential to tha understanding of the dissertation. Silver prints of "photographs" may be ordered at additional charge by writing the Order Department, giving the catalog number, title, author and specific pagas you wish reproduced. 6. PLEASE NOTE: Some pages may have indistinct print. Filmed as received. Xerox University Microfilms 300 North ZMb Road Ann Arbor, Michigan 43100 73-30,041 SR1VASTAVA, Sastosh Kumar, 1941- VACUVM Wf PLASMA SPECTROSCOPY ON A DOUBLE ARC WITH HSASOHMVTS ON LINE STRENGTHS AND SHAPES, AND OR I B LOWERING OF IONIZATION POTENTIALS, University sf Southern California, Ph.D., 1973 Phyaica, spsctroaeopy University Microfilms, A XEROX Company, Ann Arbor, Michigan THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED. UNIVERSITY O F SOUTHERN CALIFORNIA THE GRADUATE SCH OOL UNIVERSITY PARK LOE ANOELEE. C A LIFO R N IA S 0 0 0 7 This dissertation, written by SANTOSH KUMAR SRIVASTAVA under the direction of h.X$... Dissertation Com mittee, and approved by all its members, has been presented to and accepted by The Graduate School, in partial fulfillment of requirements of the degree of D O C T O R O F P H I L O S O P H Y Deem Date DISSERTATION ^COMMITTEE TABLE OF CONTENTS Page LIST OF FIGURES....................................... Ill LIST OF TABLES..................................... v ABSTRACT........................................... vi Chapter I. INTRODUCTION............................... 1 II. A WALL STABILIZED DOUBLE ARC AS A STANDARD INTENSITY SOURCE IN THE VUV............... 12 III. /-VALUES OF NINE Aril LINES IN THE VUV FOR THE TRANSITIONS 3p5 - 4s AND 3P5 - 3 d ......... 37 IV. STARK BROADENING OF LYMAN-a, -8, -Y LINE WINGS OBSERVED IN AN ARC................... 46 V. LOWERING OF THE IONIZATION POTENTIAL AND THE ADVANCE OF THE SERIES LIMIT OF AN ATOM IN A HIGH TEMPERATURE AND HIGH DENSITY PLASMA..................................... 70 REFERENCES......................................... 87 ii 19 20 2k 26 28 33 39 56 59 60 61 6k LIST OF FIGURES The wall stabilized double arc ............. The spectroscopic vuv and visible arrangement........................... . . . A recorder trace showing the optically thick hydrogen Lyman lines, NI lines, and Arl lines............................... A recorder trace showing the optically thick Lyman lines and the carbon and hydrogen continua in the 900A-1216A region. . . A typical spectrum of Aril lines and Arl continuum between 650X and 932A emitted along the axis of a He-Ar arc............... Variation of R - 1919/^750 w*th temperature T in degrees Kelvin........................... A spectrum of Aril lines superimposed over Arl continuum............................... A recorder trace of Lyman continuum.......... c/2 Experimental and S(a) ■ C/aJ/ best fit profiles for Ly-a........................... Experimental and S(a) * C/a**^ best fit profiles for Ly-B......................... . Experimental and S(a) ■ C/a*^2 best fit profiles for Ly-y........................... Comparison of the measured ratio C/Cjj, where Cu Is the Holtsmark constant, with two theories and a previous arc experiment for the profile of Ly-a......................... ill Figure Page 13. VUV spectrum of hydrogen near its series limit for different electron densities, . , 7** ' e 14. VUV spectrum of atomic carbon near its series limit ............................... 75 15. A plot of the ratio Imin^max wlth respect to wavelength for three lines of hydrogen near its series limit....................... 77 iv LIST OF TABLES Table 1. 2 . 3. 4. 5. 6 . Page Temperatures of the He-Ar Plasma Obtained from Visible and VUV Diagnostics........... 35 Absorption /-values, Emission Transition Probabilities, and Life Times for Some 3p5 - 4s and 3p^ - 3d Transitions of Aril. ... 44 Ratio of Flow Rates of Hydrogen and Argon. . . 52 Parameters C for Ly-a, -6, and -y Lines. ... 62 Comparison of the Observed Values of AE , the Advance of the Series Limit for Hydrogen and Carbon Atoms with the Results of Different Theories....................... 79 Comparison of the Observed Values of AE , the Advance of the Series Limit, with the Results of Several Theories for the Lowering of the Ionization Potential, AE.. . . 83 v ABSTRACT Vacuum ultraviolet spectroscopy of hot plasmas Is a relatively new field for the measurement of line strengths, line broadening, and photoionization cross sections of those atoms and Ions which are chemically unstable at room tem perature and are found in large concentrations only in stellar and in laboratory plasmas of Bpecial types. Of the latter ones, we are interested particularly in the plasma produced in a wall stabilized arc by passing a high current of 100A or more through a gas at atmospheric pressure. The radiation emitted by the atoms in this plasma is analyzed in order to obtain various atomic parameters. For this pur pose, it is important to know whether the emitted radiation is optically thick, i.e., the radiation whose intensity corresponds to that emitted by a black body at the tempera ture of the plasma, or optically thin, i.e., the radiation which escapes the plasma without any significant absorption. ThlB work concerns itself with the development of a modified arc source, a wall stabilized double arc, which consists of two wall stabilized arcs in tandem. With this arrangement, it is possible to differentiate between optically thick and optically thin radiation, and it can be used to measure the absorption coefficients of the plasma generated in one of the two arcs. These properties have been utilized in (1) vi the calibration of a grazing Incidence vacuum uv spectrom eter, (2) the measurements of oscillator strengths of nine Aril lines in the vuv, and (3) the comparison of Stark broadened profiles of the Ly-a, -B, and -y lines of hydrogen with theory. In addition, a single wall stabilized arc has been employed to obtain experimental values of the lowering of the ionization potential of an atom immersed in a high temperature and high density plasma. vii CHAPTER I INTRODUCTION Vacuum ultraviolet measurements of oscillator strengths, photolonlzation cross sections, line broadening, and line profiles of atoms and their ions are not only few in number but in most cases represent preliminary data in terms of accuracy. This is particularly true for those atoms which are usually in molecular states at room tempera ture. A knowledge of the above mentioned parameters for such atoms is important to the understanding of various processes that take place in photon-particle interactions In the upper atmosphere of the earth and other planets, and also of many other types of plasmas either of astrophysical or man-made nature. In general, there are three main problems associated with the quantitative spectroscopy of these atoms. They are (1) the production of these atoms in sufficiently high concentrations, (2) the measurement of their densities, and (3) the determination of the absolute intensity (scaled to that of a black body) of radiation emitted by them in the vacuum uv. In any electrical discharge (e.g., Phillips, electrodeless, microwave, glow, spark, etc.), sufficient numbers of atoms can be produced from their molecular species, but the remaining problems (2) and (3) do not 1 permit an accurate determination of their atomic parameters1 from the emitted radiation. However, there are two labora tory sources, namely (1) the shock tube, and (11) the wall stabilized arc, In which not only the atomic species can be produced in large concentrations, but where their number densities can also be determined. In the case of both the shock and arc plasmas, experience has shown that a single parameter, the temperature In conjunction with the Maxwell- Boltzmann equation, will describe the distribution of the energies of all particles In such a plasma. The approach taken here is to raise the temperature of the molecular gas to say 12,000 K when it becomes nearly completely disso ciated into atoms and their lone. It Is found, that at this temperature the resulting gas plasma can then be described as being in a state of local thermal equilibrium. This local thermal equilibrium is a special case of a more general problem related to the concept of complete thermodynamic equilibrium. In a plasma which 1b not in a complete thermodynamic equilibrium, the temperature of each component of the plasma is different. For example, in such a plasma the electron energy distribution can be described by a temperature T , ions by T., neutral atoms by T , and 0 X cl the temperature which governs the ionization equilibrium can be given by T (s after Saha). For a plasma in complete thermodynamic equilibrium ■ T^. Under this 3 condition, a knowledge of the temperature of the plasma is enough to specify all of its properties, and the following well known relations can be utilized for the calculation of densities of its constituent particles. (a) The Maxwell-Boltzmann relation: This can be used to obtain the densities of atoms (ions) In an excited level n relative to their total number densities: Nn * N* (*n/U)* exp <-En/kT) * (1) where Nn is the number density of atoms (ions) in an excited level n, N their total density, gn and En the sta tistical weight and energy of the level n, U the partition function of the atom (ion), k the Boltzmann constant, and T the temperature of the plasma. (b) The Saha-Eggert equation: With the help of this equation the ratio of the densities N between all r-fold and (r + l)-fold ionized atoms (ions) can be obtained and is usually written in the following form: (Nr+i‘Nt/Nr) - ( 2U_., /U.) • ( 2 irak)3/2 -h-3 • T3/>2 • exp t - (E - AE_ ) AT] , r+± r r r (2) where Nr is the number density of all r-fold ionized atoms, Nr+1 the number density of all (r + l)-fold ionized atoms, Ne the number density of electrons, Ur the partition func- i t tlon of the r-fold Ionized atoms, ur+i the partition func tion of the (r + l)-fold Ionized atoms, m the electron rest mass, h the Planck constant, k the Boltzmann constant, Ep the Ionization energy for ionization process r • + • (r + 1), T the absolute temperature of the plasma, and AEr is the lowering of ionization energy due to neighboring charges. Cc) Dalton's law of partial pressures: In a plasma the sum of the partial pressures of all the constituents equals the total pressure P. If the plasma consists of species A, B, C, . . . etc., then the following expression gives the relation between their densities: NA + NB + NC + NA + NB + NC + * ‘ * + Ne “ P/kT * (3 * where the property of the quasi-neutrality of the plasma, i.e. , NA + NB + NC + • • • • Nt > (i,) can be employed and NA, Ng, Nc, . . ., N^, Ng, nJ, . . . are the densities of atoms and their ions in the plasma, N the electron density, and P the pressure of the plasma. £ All other symbols have been defined before. In addition to above relations, Planck's Law gives the value of emitted radiation, namely, B(X,T)dX - (2he2/X5)-[exp(hc/kXT)-l]*dX , (5) 5 where B(A,T)dA 1b the energy emitted per unit time, per unit surface area, and per unit solid angle in the wave length interval between A and A + dA.c is the velocity of light and all other symbols have been previously defined. In general, the radiation emitted by a plasma is not Plancklan over all wavelengths, but can be made to corre spond to that of a black body over a limited region of spectrum. Therefore, the concept of local thermal equilib rium is introduced, which is less restrictive than the assumption of complete thermal equilibrium. Local thermal equilibrium is based on the assumption that collision Induced transitions and reactions dominate the radiative ones and that there exists a micro-reversibility between the collision processes. Then, the steady state solution of the rate equations yields the same populations, which are represented by a system in complete thermodynamic equilibrium at a radiation temperature equal to the kinetic temperature of the reacting particles. With this assumption, one can obtain the intensity of radiation emitted by a plasma in local thermal equilibrium: Ix - BX(T) [l-exp<-Tx.JO] , (6) where Ix Is the intensity of radiation at a wavelength A, BX(T) the Planck function given by Eq. (5)> tx the absorp- 6 N tlon coefficient of the plasma, and t is its length. If xx is very large, then Ix ■ an(* t* ie ra<^^a^^on *s known as optically thick. On the other hand, if xx << 1, then Ix " BxTX®’ and the Plasma radiation is called optically thin. Equation (6) can he understood in the following way. Each element of the plasma simultaneously emits and absorbs radiation. If x is the length of the plasma in the direc tion of observation, then the change in the intensity Ix of radiation as it travels a length dx is given by the differ ential equation: (dl^/dx) - £x “ TXIX * ^ « where ex is the emission coefficient of plasma and xx, which includes the effect of induced emission, has been defined before. Using Kirchoff's law, ex ■ B^x^, one obtains: (dlx/dx) - xx[Bx(T)-Ix] . (8) Integration of Eq. (8) for the length t of the plasma yields Eq. (6). A few years ago, this laboratory at U.S.C. undertook the study of absorption by such a plasma using vacuum uv 2 radiation as a probe. Blackwell, et al. employed a shock a Word used by many authors of books on Plasma Spectroscopy. 7 tube and studied the absorption cross sections of singly Ionized xenon. In this case a shock was produced by a high voltage condensor discharge which travelled with a velocity of about 10^ cm/sec through the gas and thus produced a shock heated plasma, which was transient in nature and therefore permitted measurements only during short Inter vals of time. Therefore, the only other known method for producing a time-independent plasma, namely the high current, high pressure, wall stabilized dc arc was selected as more prom ising for the study of the above mentioned atomic para meters. Such an arc was first developed in Germany by Lochte-Holtgreven and extensively studied by Maecker^ and i i Pinkelnburg. In its most often used arrangement, the arc consists of a number of about ten hollow, water cooled copper discs, which are pressed together and electrically isolated from each other by a thin Insulating material such as Neoprene or Teflon. Each disc has a central hole of about 0.5 cm. In diameter, and at each end the arc is fitted with a tungsten electrode. A high current discharge of the order of 100 A dc is passed through the gas under Investi gation, providing a high temperature plasma In LTE. In our case the discharge proceeds through argon as the main carrier gas, and the central portion of the approximately 10 cm long argon plasma is seeded with the molecular gas, whose atomic constituents are to be studied. 8 s In this laboratory S. Ogawa has studied the thermal properties of such an argon plasma at various pressures of the gas. It was found that It could be described as being In LTE above 300 Torr. Hofmann and Weissler^ determined the absolute values of the photolonlzatlon cross sections of atomic carbon in the vuv by flowing carbon dioxide into the central portion of the argon plasma and by measuring the absolute value of the Intensity of radiation emitted by the carbon atoms. In other laboratories, similar measurements (primarily in the visible region) have been made on the atomic transition probabilities of several different atoms, for example by Richter,^ Mastrup,® Hey,^ Gericke,'L0 Boldt^* etc., to name a few. In spite of the fact that with a wall stabilized arc photolonlzatlon cross sections, oscillator strengths, line profiles, etc., could be measured in the uv, two factors limited the accuracy of the results, namely (1) the uncer tainty In the measurement of absolute value of intensity of the emitted radiation and (2) the plasma corrections needed for the accurate calculation of particle densities. The use of branching ratio techniques and application of detectors of known spectral response for the measurement of absolute intensity in the vuv have several unavoidable disadvantages. The branching ratio technique is limited to a few selected wavelengths, because a pair of lines have to originate from 9 the same upper excited level of the transition. One of the lines of this pair has to be In the visible region of spec trum where the absolute value of Intensity can be measured accurately and the other has to be in the vuv. In addition, the ratios of transition probabilities necessary for the calculation of absolute intensity are not known with suffi cient accuracy for all excitable line pairB, particularly in the vacuum uv. 12 The late 0. Boldt has suggested the use of the wall stabilized arc itself as a standard intensity source. In his method, the thermal properties of the arc are employed, and by appropriate flow of certain gases into argon plasma the intensity of some of the spectral lines can be made to correspond to that of black body radiation at the tempera ture of the arc. The absolute value of intensity of such spectral lines can thus be calculated from a knowledge of the temperature of the plasma alone. However, the method employed by Boldt and others in ascertaining that the intensity of a spectral line is equal to that of a Black body radiation has been Improved upon with the arrangement of a double arc, which will be considered In detail later In Chapter II of this report. The other source of major uncertainty in the quanti tative spectroscopy of an arc plasma is the error in the calculated values of the densities of the constituent par- 10 tides due to the uncertainty in the value of the lowering of the ionization potential of an atom. This particular quantity is used in the Saha equation. Generally, It is defined as the difference in ionization energies of an atom when it is immersed in a plasma and when it is Isolated. It will be considered in detail in Chapter V of this report. It seems worth while to point out that the arc operated in argon has a wavelength limit beyond which the emitted radiation is completely absorbed. This limit is set o by the ionization energy of argon, namely at about 800 A. Thus, an argon plasma provides a window for vacuum uv radia- o tion from about 800 A to larger wavelengths except for itB o o two resonance lines at lOM A and 1066 A. In order to extend this limit, one can operate the arc in helium whose o ionization continuum begins at about 510 A. However, it has 13 been shown that such a He-plasma does not attain local thermal equilibrium which is required for the measurement of various atomic parameters. The present work concerns itself with the development of a new standard source which can be used for the accurate measurements of the intensity of radiation emitted in the o o region between 600 A and 1216 A of spectrum. It consists of two wall stabilized arcs in tandem, a double arc. Vlth this arrangement, one can differentiate between optically thick and optically thin radiation emitted by one of the arcs, and it can be used to measure the absorption coefficient of the 11 plasma generated In one of the arcs. These properties have been utilized In the calibration of a grazing incidence vacuum uv spectrometer, in the measurement of oscillator strengths of nine Ar XI lines in the vuv, and In the com parisons of the Stark broadened profiles of the Ly-a,-B, and -y lines of hydrogen with theory. In addition to this, a single wall stabilized arc has been employed to estimate the lowering of the ionization potential of an atom immersed in a high temperature and a high density plasma. Organization of This Work In Chapter II, a description of the double arc and its application as a standard intensity source is presented. In the following chapters, i.e., Ill, IV, and V, details are given on the measurements of oscillator strengths of nine Ar II lines in the vacuum uv, on the comparison of the measured line shapes in the wings of the Ly-a,-0, and -y lines of hydrogen with theory, and on the determination of the lower ing of the ionization potential of an atom from its advance of the series limit. Since all these measurements involve different experi mental procedures, it was decided that it would be best to give them here in the form of separate, self-contained chap ters. This permits a very clear description of each of the problems, their respective Importance, the methods of their measurements, and the conclusions to be drawn. CHAPTER II THE WALL STABILIZED DOUBLE ARC AS A STANDARD INTENSITY SOURCE IN THE VUV The measurement of absolute Intensity In the vacuum uv (vuv) region of spectrum Is of Importance to astro physics, among other areas, In order to provide more Insight In our understanding of hot and cool plasmas, Including planetary atmospheres. Specially, such absolute Intensity measurements can be used to produce secondary standards or to calibrate the response of vuv spectrometers. To the lii several methods which have been employed for this purpose, there must be added the use of a wall stabilized arc which gives values of absolute intensities with a high degree of accuracy. This arc, when operated in argon, hydrogen, nitrogen, krypton, etc., may emit optically thick spectral lines which reach a saturation value, and their peak intensity is given by the Planck function. This property has been used by 12 the late Dr. 0. Boldt to develop a radiation standard in o o the 1100A-3100A region. In this arc, high temperatures of about 10,000 °K can be produced by flowing high currents of more than 100A through different gases at approximately atmospheric pressure. Under these conditions, a state of local thermodynamic equilibrium (LTE) can be shown to exist 12 13 in the hot plasma of many gases, and the emitted Intensity, Ix, Is given by the modification of Kirchoff's law of emis- sivlty being proportional to absorptivity, namely - t . . Jl Ix - BX(TK1 - e ) , (1) and BX(T) - ((2hc2)/X5)(exp(hc/kTX) - l) , (2) where BX(T) Is the Planck function of the source, tx the absorption coefficient of the plasma at wavelength X, and h, c, k represent the well known constants. If t x is large, then Ix ■ the radlatl°n * becomes optically thick. The intensity of an optically thick spectral line can thus be accurately calculated, If the temperature of the source Is known. In the visible and near ultraviolet region of spec trum, there are two methods to determine if the center of a 15 spectral line is optically thick or not. In the first, the profile of a line is scanned end-on as well as side-on. The length of the emitting plasma is quite different for these two observations. If at a certain distance from the line center the ratio of Intensities obtained in this fashion is very much less than the geometrical ratio, i(en<l-on)/1(»lde-on)* then the lntenalty at the center of the line is optically thick. In the second method, a mirror I l l Is placed behind the plasma. If the intensity at the center of a line does not change, then the line is optically thick. The above methods can not be used in the vuv region of spectrum because of the following reasons. First, most of the lines in the vuv are resonance lines and side-on and end-on observations may give a false value of their intensities because of absorption due to colder regions of the arc. Secondly, reflectivities of mirrors may be too small in the vuv. In the vuv there have been two approaches to evaluate optically thick conditions of spectral lines. First, one may plot the intensity of a spectral line with respect to the flow rate of a gas in the plasma. That rate at which the Intensity at the center of a line reaches a saturation value gives the optically thick condition. Second, one can use the LTE properties of the plasma and calculate the number density of atoms emitting a particular line. Then, the optically thick condition can be estimated. In the present work we describe a third approach, which not only permits the accurate evaluation of the optically thick condition of emission lines, but which also utilizes emission or resonance contlnua (free-bound transi tions) to obtain B^(T), the black body radiation limit. 15 Analysis and Method of Measurements For this purpose, a double arc has been constructed which consists of two arcs In tandem. Its use can be explained In the following way. The intensity output 1^ of the first arc (closest to the spectrometer) is given by Eq. (1). If behind this arc No. 1 a second arc No. 2 emits i „ radiation Ix which is incident on arc No. 1, then the resulting output intensity Ij^ from both arcs Is given by H ■ h * *'V t • <3> and eliminating tx from (1) and (3)» we obtain BX(T) - (Ix ljn)/(ljn + Ix - Ip. (K) If radiation Ix from the arc No. 1 Is optically I — thick, then the Introduction of radiation Ix into this arc will not change its value and Ix will be equal to I£. On the other hand, when radiation Ix Is not optically thick, i passage of radiation Ix through the arc will change its value to I£. The measurement of these three quantities then permits the calculation of BX(T) from Eq. (4). In the double arc, the first one serves as a source j n of Ix and the second provides Ix . In both arcs identical spectra are produced and the spectrum of one is superimposed over that of the other. Thus we find that such an 16 arrangement Is not only useful in the vuv for checking optically thick conditions, but it can also be used in the visible and near uv regions. In actual practice, for these measurements the Intensity of a line or a continuum is measured in terms of Its height, recorded photoelectrically by a paper recorder, which can be related to the actual intensity at the source by the following relation ** - K x hx » (5) where Is an instrumentation constant which depends on the geometry of the apparatus and the response of the opti cal recording system. Substitution of Eq, (5) into Eq. (4) gives VT ) ■k* K hi n> /< hin+h* - hP) ■ ka hx • < 6 ) and hj « (hx hjn)/(h*n + hx - hp , (7) where h^ is the height of the recorded spectrum at wave length X for an optically thick radiation. If Kx, the instrumentation constant, is known then the absolute value of intensity Ix of a source, recorded as hx, can be calcu lated from Eq. (5). The instrumentation constant, Kx, is obtained from Eq. (6) by measuring the height, hjj, of the optically thick spectral lines and calculating &X(T) from 17 Eq. (2). The optically thick height, h J, can also be calcu- 1 n lated from Eq. (7) If the heights , h^ and hj are known. We have made use of the double arc to obtain the o o spectral response In the 600A to 1216A region of a two meter grazing Incidence spectrometer. Optically thick hydrogen lines, Ly-a, Ly-B, Ly-y and Ly-6, nitrogen NI lines at 1200A, 113^A, and 1100A, and a Cl line at ll^A were used o o between 9**5A and 1216A. In addition, the carbon emission o continuum, which begins at about 1100A and the hydrogen ° t * continuum at 900A were used to calculate h^ from Eq. (7) in those regions where optically thick lines were absent. o o In the 600A to 800A region the argon resonance con tinuum was obtained In emission by operating the arc in a He-Ar mixture, and It was employed to obtain relative Intensities, which were then converted to absolute values t ° by extrapolating via Eq. (2) the h^ value at 950A to shorter wavelengths. For the absolute value of B^(T), an accurate knowledge of the plasma temperature is required. This was determined in all cases reported here from the line lnten- o o sity ratio of Arl 4300A to Aril 4806A, measured in the visi ble region. The temperature, so obtained, was accurate to within ±2%, giving rise to an error of about 20% in B^(T). 18 The Double Arc Figure 1 shows a double arc consisting of nineteen copper plates with a central bore of 4.8 mm. Each of them has one inlet for gases, and one inlet and one outlet for cooling water (not shown). Plates number 1 and 19 serve as anodes, with two tungsten Inserts and a central hole 1.65mm in diameter. The plates themselves are 7-65 mm thick and 91 mm in diameter. Plates number 9 and 11, the cathodes, are also fitted with tungsten inserts with 2.4 mm diameter holes. Plate number 10 is 12.7 mm thick and has a rod as a light shutter which can be moved in or out of the light path. All plates are electrically Insulated by teflon sheet spacers and are pressed together by four stainless steel screws (not shown). One end of the two arcs is optically coupled to a vacuum spectrograph and the other end via a window of glass to a monochromator operating in the visible region. The Experimental Arrangement Electrical connections are shown in Fig. 2. Power to the two arcs is supplied by two separate and electri cally Independent welding power supplies, which can deliver each a current of 325 A at 320 volts D.C. Inductances and 1*2 are the windings of two electromagnets which are a s * Tungsten He He Ar Exit C02,H2,N2 a r CO2.H2 .N2 Exit j j 1 Arc No.2 i * 1 Arc No.11 I i 7 a 7 a I W A ' A ' A f , To V O C . U V Spect. /S/7/Z7Z V/ . H /II 1 2 13 14 15 1 6 17 1 8 O v _ Li aht Shutter 19 2 3 4 5 6 7 8 Cathode £3 To Seya-Namioka Spect. Anod Figure 1 The wall stabilized double arc Anode Seyo- Namioko Spectr. ¥ Ory Ice and Methyl Alcohol [Liquid Nitrogen He N 2t Lea, Ar VUV Spectrograph & L R 2J L E Figure 2 The spectroscopic vuv and visible arrangement. The primary slits, gratings, exit slits and photomultiplier detectors are marked by S, G, E and M, respectively. Pumps are indicated by P. 21 cooled by water , and resistances and are water cooled stainless steel tubes of about 0.9 ohm each. These two arcs are thus electrically Isolated and any change In the current of one does not affect the other. Each arc is started by a high voltage condenser discharge of about 3KV between anode and cathode at a pressure of 5 torr in argon. Our spectroscopic arrangement, also Bhown in Fig. 2, is the same as reported earlier in detail by Hofmann and Weissler.^ o o Calibration Between 900A and 1216A The double arc was operated at a current of 100 A, and argon was flown into it at the rate of 40 cmJ/sec at plate number 10 and at 20 cm^/sec at plates number 1 and 18. After passing through the arc channel, the gases were allowed to exit into the surrounding atmosphere via a 50 cms long plastic tube to prevent back diffusion. These exit ports were located at plates number 3 and 17 of arc No. 2 and arc No. 1, respectively. Helium was flown into the arc at plate number 19 at the rate of 11 cm /sec and into plate number 20 in such amounts that the pressure in the fine hole Joining the arc with the differential pumping system was measureably greater than one atmosphere. Commercial grades of argon and helium were used. When these unpurifled gases were flown into the arc, 22 impurity lines of hydrogen, carbon and oxygen appeared in the vuv spectra. Therefore, argon was passed through a cold trap containing zeolite, cooled by a dry ice and methyl alcohol mixture and helium was passed through a liquid nitrogen cooled trap. Under theBe conditions, impurity lines of oxygen and carbon disappeared, but hydrogen llneB were still present, though at much lower intensity. The following procedure was adopted for recording optically thick lines. In arc No. 2, hydrogen and nitrogen were flown in at plate number 7 at the rates of 1.5 cm /sec and 2 cm^/sec, respectively. Then the intensities of hydrogen lines, Ly-a, Ly-B, Ly-y and Ly-6, and nitrogen o o o lines at 1200A, 113*tA and 1100A were recorded. This pro- 1 n vided the value of h^ Eq. (7), for these lines. The mix ture of these gases was then also flown into arc No. 1 through plate number 13, and the output radiation provided the value of h£. Following this, the light shutter at plate number 10 was closed, so that light from arc No. 2 could not pass through arc No. 1, and the spectrum was again recorded and provided the value of h^. The flow rate of hydrogen and nitrogen was then Increased in arc No. 1 to such a value that closing or opening the light shutter did not make any difference in the value of h^, i.e., h^»h£. When this condition was fulfilled, then the intensity at the maximum of the line was optically thick and its height was 23 given by hj. A typical recorder trace of the optically thick hydrogen and nitrogen lines is shown in Pig. 3. The peak intensities of these lines are joined by a jolld line, which gives the measured value of hjj in this region. It is seen that while hydrogen lines are self reversed in the center, nitrogen lines are not. This is due to the fact that argon and helium both contained hydrogen as an impurity which could not be removed by the cold traps and thus was present in the colder region between the arc and the vuv spectrometer. In order to check that this self reversal did not give a false saturation level, the height of the optically o thick nitrogen line at 1200A was extrapolated to Ly-o at o 1216A by using Planck's function with the temperature obtained from visible diagnostics. This extrapolated value agreed very closely, within ± IK, with the height of the observed Lyman line. One more test was applied to check that the satu rated level given by the Lyman lines was true. For this purpose, they were recorded for two plasmas at two differ ent temperatures, and T^. Using one set of data at a temperature T^, the instrumentation constant, given by o o Eq. (6), was determined between 950A and 1216A. Since does not depend on temperature, its value should remain the same when determined from the optically thick line heights c c > 1048 1066 1100 1134 1170 1200 1216 A c o It H H Ar Ar H N 94 9 972 1025 1048 1066 1100 A Figure 3 A recorder trace showing the optically thick hydrogen Lyman lines, NI lines and Arl lines. Solid curve gives the value of h\ a B^(T) obtained by joining the peak intensities of these optically thick lines. 25 at a new temperature T2. It was found that the values obtained from these two temperatures were in close agree ment. Thus, we have further support that the self reversal of the Lyman lines did not falsify our results of h^. In order to evaluate hjj between lines and beyond Ly-6 towards shorter wavelengths, we used the Cl resonance con- o o o tinuum (1120A to 98OA) and the hydrogen continuum at 910A, which were NOT optically thick. The double arc was operated in argon, and carbon dioxide and hydrogen were flown in at A n plates number 13 and 7. Thus, values of h^ , h^ and h£ for these contlnua were obtained as described above and Eq. (7) was then used to calculate h^. Figure H shows a typical recorder trace of these contlnua together with optically thick Lyman lines. (As is seen there, the vuv radiation Is completely absorbed by the two resonance lines of Arl at o o lO^loA and 1066A due to the presence of cold argon in the light path.) The points with error bars are the values of hjj obtained from the underlying carbon and hydrogen con- f tinua and the solid curve showB the values of hj^ for this region, obtained by Joining the optically thick Lyman lines, the optically thick Cl line at 119**A, and the above men tioned points for the contlnua. This method can lead to large errors in the calcu lated values of hjj, if the absorption coefficient for the carbon atoms in the arc No. 1 is not large. We found that < 0 X < 0 . i 1 -1 -1 -J * 1 1 I • < E 3 • < Oi 0 i >\ « c 0 ♦- c > o 0 a: i 0 Level 9 0 0 1000 1100 1200 Figure 4 A recorder trace showing the0optically thick Lyman lines and the carbon and hydrogen contlnua in the 900A-1216A region. Solid line gives the experi mentally obtained value of h^ a B^(T). r o o\ 27 the best results were obtained when the absorptivity, ■ l-exp(-T^), was between 0.3 and 0.4. In our measure- t ° ments, errors in the h^ values varied from ± 5% in the 1100A o region to ± 16% in the 900A region. o o Calibration Between 600A and 600A A pure argon arc has a short wavelength transmission limit at its Ionization potential corresponding to about o 800A. Therefore, the arc was operated in helium as a o carrier gas, which transmits down to 510A, and small amounts of argon were flown into it. In actual operation, the arc was first started in argon which was slowly replaced by helium, since a pure helium arc was found to be electrically unstable. A small admixture of argon in helium, when flown in from the cathode end, completely removed thiB instability. Therefore, a gas flow scheme was chosen in which a mixture of argon and helium entered into the arc at plate number 10 and pure helium was flown through plates number 19 and 20. These gases were then allowed to exit at plate number 17* Only arc No. 1 was used and all the inlets of arc No. 2 were closed. A typical recorder trace of the argon resonance con- o o tlnuum and some Aril lines between 650A and 950A is shown in Fig. 5. Since it is known that LTE does not exist in a > • < £ 5 •< CM ro 0> 800 8 5 0 9 0 0 A Aril Lines Aril Lines JU A j l ] J U _ A - w W 650 700 750 8 0 0 Figure 5 A typical spectrum of Aril lines and the Arl continuum between o o 650A and 932A emitted along the axis of a He-Ar arc. 29 IQ helium arc, J the question arises as to whether or not this Ar- continuum can be assumed to be in LTE and can be described by Kirchoff's law given by Eq, (1), It seems that in a mixed plasma of this nature argon atoms can be in LTE, if the electron density and temperature are each above a certain minimum value. Therefore, both electron density and temperature, which would describe argon in LTE in a helium plasma, were determined experimentally. For this purpose, the temperature of plasma was obtained by two methods: A. Spectroscopic Temperature Determination in the Visible Region. Here, the temperature was obtained, as before, from o o the line intensity ratio of Arl 4300A to Aril M806A, while the corresponding electron density was calculated from the Stark - broadened H-0 line. The details are given by Stuck and Wende,^ who show that temperatures thus determined are accurate to ± 2%, B. Temperature Determination from VUV Measurements. In this case, it Is assumed that the Arl and Aril atoms are in LTE, and that the radiation emitted by them in the vuv is optically thin. Under such conditions, the inten sity, 1^, of the argon recombination continuum is given by 30 B ^ T T - Ng ’ C8) where is the number density of neutral argon atoms in the ground state, the photoionization cross section at wave length X and I the length of emitting plasma. Similarly, the intensity of a resonance line of an argon ion is given by I+ 2 X ne^ , 2 > „+ ? K 'mn V • »X MeC + mn 6 where l£, X+ and are the intensity, wavelength and the oscillator strength, respectively, of the Aril line. N+ is 6 the ground state density of the argon ions and £ is again the length of the emitting plasma. The ratio of Eqs. (9)/C8) is IX BX _ ne2 ,2 'mn Ng (10a) i f * « { • In addition, we have from the Saha equation N* p g* (E - AE ) (2IIm k)3/2 ,/2 < ■ ^ - - T T - = - • ^ r ~ • tV2 <10b) where Ne Is the electron density, gQ and g* are the statis tical weights of the ground states of the Arl and Aril atoms, respectively. Ew is the ionization energy of an isolated neutral argon atom, AE the lowering of the lonlza* 31 tlon energy due to neighboring charges, and T the tempera ture of the plasma. Quantities with a + sign correspond to argon Ions, and all other symbols represent customary quan tities . In the present experiment, the Intensity of the Aril o line at 919A was compared with the intensity of the Arl ° *+ continuum at 750A. The oscillator strength, of this 17 line is given by Wiese ' which is obtained from the life 18 time measurements of Lawrence, and the photoionization cross sections, , for the argon continuum are given by 10 0 Samson. * The intensity of 919A Aril line was measured from the area enclosed by the line and the Intensity of continuum o at 750A was given by its height. The temperature of the plasma was thus measured using Eqs. (10a and 10b). It is important to point out that in the derivation o of Eqs. (10a and 10b) it is assumed that the 919A Aril line o and the argon continuum at 750A are both optically thin and that the response function , Eq. (5), of the vuv record ing system is constant in this region. This response depends upon the quantum efficiency of the sodium salicy late radiation converter placed in front of the photomulti plier and shown by Samson20 to be substantially constant. In addition, the response depends upon the reflectivity of the grating. Since our grating was a Slegbahn type, lightly ruled on glass, and was used to grazing incidence 32 of about 80°, its reflectivity and therefore its response o o in this arrangement did not change much from 950A to 750A. o In order to check whether the Aril line at 919A was o indeed thin, it was compared to another Aril line at 932A, 17 the oscillator strength of which is also accurately known. If the argon atoms were in LTE and these lines were opti cally thin, then the ratio of their intensities should be given by the ratio of their oscillator strengths, multi plied by the ratio of their statistical weights. This was found to be true within ± 10J C . The following criterion was used to prove that the Intensity of the Arl continuum was optically thin. Near o 750A (Pig. 5) the spectrum consisted of an Aril line at o 723A on the shorter wavelength side and an Aril line at o 919A on the longer wavelength side. If their peaks were o Joined by a straight line, then we obtained at 750A the minimum possible height for optically thick radiation. A o comparison of the height of the Arl continuum at 750A with this extrapolated optically thick height showed unambigu ously that it was optically thin. Thus, the ratio *919^*750 could be used in Eq. (10a) for the determination of the temperature of the plasma. This ratio is sensitive to small changes in temperature, and therefore T should be accurate to ± 2%, Figure 6 shows this ratio for two elec tron densities of the plasma. 8 0 - 7C“ 6 C- 50 2C- f3 It 12 14 3 Temp. X 10 K » Figure 6 Varltlon of F t - wlth temperature T in degrees Kelvin 34 Temperatures obtained from the above two methods, A. In the visible and B, in the vuv region, for various electron densities and flow rates of argon in helium are presented in Table 1. It can be seen there that for elec- 16 tron densities of about 5.0 * 10 cm and temperatures of about 13,600 °K the two temperatures agree. Since the method for obtaining the temperature from visible diagnos tics assumes excited state densities in LTE and the method for the vuv region assumes ground state densities in LTE, this agreement of the two temperatures confirms that neutral and singly ionized argon in helium can be described as being in LTE. This optically thin Ar continuum was then used to calibrate the relative response of the optical recording o o system between 600A and 800A. This was done by measuring the heights, h^, of the recorded continuum at different wavelengths and obtaining the relative values of the instru mentation constant , given by Eq. (5), from V T> • K x • n 4 rr • E A which is derived from Eq. (8) and Eq. (5); Its various symbols have been defined previously and the values of the IQ photoionization cross sections obtained by Samson 7 were used. For the determination of the absolute intensity of a source we need absolute values of K^. Therefore, these TABLE 1 TEMPERATURES OF THE HE-AR PLASMA OBTAINED FROM VISIBLE AND VUV DIAGNOSTICS FOR DIFFERENT ELECTRON DENSITIES, Ne, AND THE RATIO OF ARGON AND HELIUM FLOW RATES Ar Flow Rate Ne“ (xlO16) ± 2% -3 cm J Temp. from visible spectra °K Temp. from vuv spectra °K AT/T (f error) He Flow Rate 0.15 1.97 13,400 ± 100 11,600 ± 100 - 14J 0.33 3.0 13,200 ± 100 11,800 ± 100 = 11% 0.36 3.35 13,300 ± 100 12,000 ± 100 = 10< 0.54 4.22 13,100 ± 100 11,900 ± 100 C T n 1 1 0.67 4.56 13,100 ± 100 13,100 + 100 — 0.78 5.0 13,500 ± 100 13,600 ± 100 — 0.86 5.56 13,200 ± 100 13,400 ± 100 36 relative values of were normalized to absolute ones by extrapolating, via Eq. (2), the optically thick height hjj o of the radiation at 900A (obtained from the double arc) o o down to 750A. The absolute value of at 750A was then calculated from Eq. (6) in which B^(T) was obtained from Eq. (2). Conclusion Thus, this standard Intensity source provides a con- o o tinuous value of from 600A to 1216a, which makes it pos sible to calibrate the response of an optical recording system and to obtain the absolute values of intensities of spectral lines and resonance contlnua required for the determination of oscillator strengths and photoionization cross sections In this region. We are hereby gratefully acknowledging many valuable discussions with Professors S. and M. Ogawa. CHAPTER III /-VALUES OF NINE Ar II LINES IN THE VUV FOR THE TRANSITIONS 3p5 - **s AND 3p5 - 3d Aril lines in the vacuum ultraviolet (vuv) region U * i * 5 arising from the states of 3p **s and 3p 3d to those of 3p configuration are used as wavelength standards and were recommended by the commission 1*1 of the International Astro nomical Union In 196 2. A determination of their transition probabilities or oscillator strengths not only extends their application to the field of quantitative spectroscopy, but also provides a check for the theoretical models used for calculating them. The experimental /-values of these lines are not known. Analysis and Method The wall stabilized double arc was operated in helium and argon mixture. These gases were flown into the arc in Buch a way that helium provided a window up to about o 510 A where its ionization began and the radiation emitted by the argon atoms entered unabsorbed into a two meter grazing incidence spectrometer via a differential pumping system required for the vuv spectroscopy. The details of 37 38 the wall stabilized double arc and the experimental arrange ment have been given In Chapter II. o o Between 800A and 510A the emitted radiation con sisted of Aril multlplets which were superimposed over argon resonance continuum. A typical spectrum, recorded photo- electrically, Is shown In Pig. 7* Only nine Aril lines (7^0A, 730A, 725A, 723A, 679A, 666A, 66UA, and 661A) could be fully resolved. The method of measuring the oscillator strengths of the above lines employed a comparison of intensity of an Aril line with the Intensity of the underlying neutral argon resonance continuum. It has been shown In Chapter II that In a mixture of argon and helium plasma argon atoms can be described In LTE (Local Thermal Equilibrium) and the intensity, Ix, of radiation emitted by the argon atoms Is given by a modification of KIrchoff's law of emissivity being proportional to absorptivity, namely, Ix - BX(T) [1-e Tx’£] , (1) where is the Planck function and tx Is the absorption coefficient of the plasma at the wavelength X. If tx « 1 the above relation reduces to V Bx - Tx-** <2> 39 Y " ' u + > o 0> p* no and the radiation at the wavelength X Is called optically thin. The intensity, 1^, of an optically thin resonance continuum is obtained from Eq. (2) V B* ■ N g °x * ■ (3> where Ng is the number density of neutral argon atoms in the ground state, a^ the photoionization cross section at the wavelength X, and A is the length of the emitting plasma. For an optically thin spectral line the intensity is given by its profile and from Eq. (2) it is written as [ J IxdX/Bx]+ - (»e2/meC2)(X+)2 t*n , (H) where [ J I^dX/B^]+ is the total intensity emitted by the spectral line at the wavelength X*, its absorption oscillator strength for a transition from a lower energy level m to the upper level n, N* the density of atoms in the energy level m, and A is again the length of the eraitt ing plasma. The + sign indicates a spectral line from the singly ionized atom. For an Aril line at the wavelength X* which is superimposed over argon resonance continuum at the same wavelength, both being emitted from a plasma of length A, division of Eq. (4) by Eq. (3) gives 41 [(IXd* )+/IA ] ‘ ("e2/mec2 )(Xo )2( (5) Equation (5) was used In calculating the oscillator- strengths, Aril lines. The Intensity, (Jl^dX)+, of the lines was measured in terms of the areas enclosed by them by the usual methods of planimetry and the intensity of the argon resonance continuum was obtained from Its height. It was assumed that the intensity, 1^, of the con tinuum remained the same over the entire width of an Aril line. Under these conditions the ratio [(I^dX)+/I^] gave the equivalent width of the line which was converted into wavelength units and substituted in Eq. (5). Temperature of the plasma was measured by the ratio of the Arl line at 4 300A to the Aril line at 4806a in the visible. The elec tron density of the plasma was determined from the half width of the Stark broadened H-(J line. These lines were recorded by a Seya-Namioka spectrometer and the radiation emitted by the plasma along its axis was focused onto its entrance slit. The theoretical details of this measurement are given by Stuck and Wende.1^ The photolonlzatlon cross sections of argon resonance continuum have been measured previously by Samson1^ and were used in Eq. (5)* In Eq. (5) the ratio, of the population densities of Aril atoms in the energy level m and of neutral argon atoms in the ground state is needed. This can be M2 obtained by the U8e of Saha equation. But due to an error of about ± 2% In the measurement of the temperature of the plasma, the error In the calculated ratio (N^/Ng) becomes high. Therefore, this quantity was obtained from the o measured ratio of the intensities of the Aril line at M806A o and the Arl line at M3OOA. These intensities are directly proportional to the population densities in the upper levels of transitions which can be used to find the ratio (N^j/Ng) by applying the Boltzmann relation. As will be dis cussed later, this method gives a better accuracy for the ratio (N*/N ). This ratio is given by m g (nV n ) - m g U +/lKA/A+)(A+A)(ge/g+)(gJ/8g) exp[(E*-Ee)/kT] , (6) where I , A , A , g„, and E* are the Intensity, transition V “ probability, wavelength, statistical weight, and the energy of the upper level of transition, respectively, for the o Aril line at M806A and I, A, X, ge and are the corre sponding quantities, respectively, for the Arl line at O X U30OA, g^ and gg are the statistical weights of the level m of the Aril atom and ground state of the Arl atom, respectively. 43 Results and Error Analysis The absorption oscillator strengths, transition probabilities and the life times for these lines are pre sented in Table 2. Along with our experimental values we have presented the theoretical life time data based on the 21 intermediate-coupling calculations of Statz, et al. While J i , 2 ° writing this paper life time for 3p 4s P (725A) was 22 reported by Livingston, et al* It has also been included in Table 2. From Eq. (5) it is seen that the errors In the measured values of /+ are contributed by the uncertainties mn + IQ In the determination of the ratio (N /N„) and the reported ? m g values of o.. The ratio (N+/N ) depends on the accuracy of a m g the measured temperature T and the ratio (A/A+) of the transition probabilities. Our temperature measurements are accurate only to within t 2$, contributing an error of about ± 12% to the ratio This explains the experi mental spread of ± 10$ In our results. The values of the individual transition probabilities A and A+ have been 17 determined by several authors. It is found 1 that these values differ by about i 30$. However, there is a close agreement of the ratio (A/A+) between many authors. This agreement is within ± 5$. Thus, the error in the measured value of the ratio (N*/N ) is within ± 15$. m g TABLE 2 ABSORPTION -VALUES, EMISSION TRANSITION PROBABILITIES AND LIFE TIME FOR SOME 3p5 - 4s AND 3p5 - 3d TRANSITIONS OF Aril IN THE VUV Transitions (i - k) X O (A) This Experiment Tk Theoretical4 CIO"9 sec) Tk Lifetime1 3 Measurements (10~9 sec) ik±20S Alk±20% (108 sec"1) Tk CIO"9 sec) 3d6 V -WT » PV2 1 , 8 3/2 723 0.024 3.06 1.95 ±0.78 0.3623 — *,5 2 $ ^ 2p * 1/2 ,s 3/2 730 0.033 2.06 3P5 718 0.028 7.20 0.69 ±0.28 0.3564 0.909 ±0.059 3p5 725 0.059 7.40 661 0.044 4.48 2.23 ±0.45 — — 3p5 666 0.016 1.604 6.23 ±1.25 — — 740 0.013 1.583 — — — * ZpL*', *Z l C2 679 0.047 3.399 — — — *>5Z^ * » Zd3/2 664 0.024 3.63 — — — ^Reference 21. The values of the photoionization cross sections ig are known ^ with an accuracy of ± 5%. The total error in the values of reported here is thus ± 20%. Prom Table 2 we find that there is a large differ ence between our life time values and the theoretical 21 values of Statz, et al. The life time values of this experiment have been calculated from the transition proba bilities and are thus accurate to within ± M0%. Within this limit of accuracy our results agree with the life time ii. 2 22 value for 3p P, reported by Livingston, et al. CHAPTER XV STARK BROADENING OF Ly-a, -3, AND -y LINE WINGS OBSERVED IN AN ARC The Stark broadened profiles of spectral lines emitted from a plasma are often used for the determination of its electron density. They are calculated by consider ing the interaction of free electrons and ions with the optical electrons of the emitting atoms. However, in these calculations a number of assumptions are made, which should be supported by experimental measurements of these profiles. For this purpose spectral lines of atomic hydrogen are ideal since unperturbed wavefunctions are known exactly, thus eliminating one source of uncertainty. Several experimental measurements on the profiles of Balmer lines of hydrogen have been reported previously. Among them two recent ones are by Wiese, et al. J and 24 Hill, et al. In general there is a satisfactory agree- pc ment between the experimental and theoretical profiles. This is particularly true for the H-3 line, which is there fore extensively used for the electron density determina tions of hot plasmas. The situation is not so convincing in the case of the Ly-a and Ly-B lines of hydrogen, whose Stark profiles 46 47 27-29 have been measured in the past. ' ? They were produced in two different types of light sources: One was a wall stabilized arc, similar to the experiment reported here, and the other was a T-type shock tube. The line profile of 27 Ly-a obtained from the arc work of Boldt and Cooper ' deviated considerably from the theoretical asymptotic wing profile calculated by Grienr and no arc measurements have been reported on Ly-B and -y. On the other hand, the shock p Q p Q tube experiments * y provided the satisfactory agreement with a theory for both Ly-a and Ly-B. However, a recent 31 theoretical calculation by Vidal, Cooper, and SmithJ 27 shows that the arc measurements of Boldt and Cooper 1 are in good agreement with their theory. In the arc experiment of Boldt and Cooper the experi mental arrangement was such that the measurements could be made only during a short interval of time (~ 10 sec.) and thus the observations on the line profile were recorded by repeating the experiment several times. Such a procedure can introduce some errors in the measurements. Our experi mental set up permits a very stable operation for several hours and thus allows us to record all the observations under one condition. This prompted us to undertake the study of Stark broadened profile of Ly-a and to extend the arc measurements to Ly-B and Ly-y lines of hydrogen. In addition, further data on asymptotic wing profiles would be 148 of significance In astrophysics, since lines emitted from stellar plasmas have cores which are highly self-absorbed and thus accurate measurements can be made only In the wings. Experimental Arrangement The apparatus used for this purpose consisted of a wall stabilized double arc, a grazing Incidence vacuum uv spectrometer utilizing a two meter grating lightly ruled on glass with 691 grooves/mm, and a one meter Seya-Naraioka monochromator with a 1200 lines/mm grating for measuring the visible Bpectrum, together with photoelectric recording systems. Constructional details of the double arc have been given in Chapter II and will only be summarized here. Figure 1 shows a schematic diagram of this arc, together with the flow system of gases used here. It was operated by passing a high current discharge of about 100 A dc through argon at atmospheric pressure. This produced a plasma of about 12,500 K and an electron density of about 17 —^ He ■ 10 1 cm , which was confined in a narrow central arc channel of 0.5 cm in diameter. Into the central portion of this plasma, hydrogen gas was flown as shown in Fig. 1. Due to the high temperature, molecular hydrogen was 49 completely dissociated Into neutral and ionized atoms, and any neutral hydrogen atoms were thus immersed in an environ ment of high density electrons, argon and hydrogen ions and neutral argon atoms. The double arc was mounted on the optical axis of the vacuum uv spectrometer, as shown in Pig. 2, and the radiation emitted along its axis entered the spectrometer through a differential pumping system, which consisted of two chambers as shown in Fig. 2. The first chamber, directly behind the arc, operated at a pressure of —2 —2 4 x 10 Torr and the second one at 1 * 10 Torr. In this manner, the pressure was reduced from one atmosphere at the —• 5 arc to 10 Torr in the vuv spectrometer. This spectrometer was equipped with entrance and exit slits 70 and 40 microns wide, respectively. The exit slit was mounted on a carriage, containing a photomultiplier with a sodium salicylate radiation converter, which could be moved along the Rowland circle by an external multiple speed synchronous motor. The reciprocal linear dispersion of o o this grating was about 3 A/mm at 1000 A, and the apertures In the optical system were arranged in such a way that the radiation entering the spectrometer originated essentially from a narrow region of about 1 mm diameter along the axis of the double arc. 50 The visible radiation emitted along the same axis was recorded by the Seya-Namioka monochromator, shown in Fig* 2, and its exit and entrance slits were fixed at a width of 40 microns. The electron density of the plasma was obtained from measurements of the full half width of the H-6 line with an accuracy of ± 10%, and the temperature was obtained from the ratio of Intensities of the Aril line at 4806A to the Arl line at 4300A, Details of this method have been given by Stuck and Wende.^ Method of Measurement Our main Interest was in the measurement of the variation of the wing intensity of Ly-a, -6, and -y with respect to distance from the line center. In order to obtain a sufficiently high intensity in the wings, an amount of hydrogen was flown into the arc, such that the center of the line saturated, and its height corresponded to the black body radiation limit at the temperature of the arc. This peak intensity of an optically thick line is given by the Planck's function BX(T) - (2C1/X5)texp(C2/XT)-l]“1 , (1) 2 — 6 2 —1 —1 where ■ he ■ 5.951 * 10” erg. cm .s” ,sr , C2 * (hc/k) - 1.4386 cm.deg., T the temperature of the arc, X 51 the wavelength of radiation in units of cm, h and k the Planck’s and the Boltzmann constant, respectively, and c is the velocity of light. There were two advantages in using optically thick Ly-a, Ly-B and Ly-y lines. First, the maximum possible intensity was obtained In the line wings, and second, with the help of Eq. (1) the absolute intensity could be calcu lated which in turn permitted the evaluation of absolute values of the absorption coefficients in the line wings. Since it was crucial to know that the peak intensi ties of these lines corresponded to their black body limit, arc No. 2 of the double arc in Fig. 1 was used. Its radia tion passed through arc No. 1 before entering the vuv spectrometer. For optically thick lines emitted by arc No. 1, this additional radiation should not cause any change in the observed peak intensities, a very sensitive check for the optical thickness of the Lyman lines. With the help of this arrangement, we could find the precise rate of flow of hydrogen into arc No. 1, for which the peak intensities of these lines reached the black body limit. Ratio of the argon and hydrogen flow rates employed here are presented in Table 3. The intensity 1^ of radiation at wavelength X emitted from a source in LTE (Local Thermal Equilibrium) is given by Ix - BX(T) Cl-exp (-Tv t)] , (2) TABLE 3 RATIO OP FLOW RATES OF HYDROGEN AND ARGON. Ne IS THE ELECTRON DENSITY OF THE PLASMA, Te ITS TEMPERATURE, AND Ng THE NUMBER DENSITY OF THE HYDROGEN ATOMS IN THE GROUND STATE IN THE ARC OPERATING AT ATMOSPHERIC PRESSURE. THE LENGTH OF THE PLASMA WHICH CONTAINS HYDROGEN ATOMS IS 2.92 CMS. Hg Flow Rate Arc Current (Anp.d.c.) Ne x1016 (cm"3) ± 10% Te x io4 (K) ± 2% Ng (cm"3) ± 5% Measured Intensity of the Line Peak Intensity Corresponding to the Optically Thick Condition Ar Flow Rate Ly-a Ly-B Ly-y Lyman Con tinuum, at 905A 0.15 85 5.25 1.18 1.56xl017 1.00 1.00 1.00 1.00 0.05 120 7*67 1.26 2.8lxio16 1.00 0.92 0.92 0.40 u i w 53 and tx.A - (7re2/mc2) Ng* f k Xq2S(AX) , (3) where B^(T) is the Planck function, the absorption coef ficient of the plasma at wavelength X, N the number density O of atoms in a state g, t the length of the emitting plasma, fgk the absorption oscillator strength for a transition from a level g to a level k, and S(AX) the normalized line shape with AX - where XQ is the central wavelength. If >> 1, the optically thick case, then 1^ ■ B^(T). In this work, the peak intensities of Ly-a, -B» and -y corre sponded to this condition. For the calculation of the intensity 1^ at any point on the line wing, the value of S(AX) at that point is needed. There are two theories which give this function. 26 One of them has been described by Smith, Cooper, and Vidal in a series of papers and is known as the unified theory based on classical path methods. The other has been riQ ^2 developed by GriemJ and more recently extended by Xepple and Griem, which utilizes a generalized Impact theory. According to Kepple and Grlem, S(AX) - F0“1S(a) -F0"1.(CH/a5/2)[b(a) +d(amax/a)3/2] , (*> 54 where CH is the usual Holtsmark constant,33 a - (AA/F0), and F„ * 2.61 e N 2 / ^3. is the electron density and b(a) o e e is a slowly varying function of a and accounts for the con tribution of electron impacts to the line broadening together with quasistatic effects (arrangement of fixed charges in the neighborhood of an H-atom). The factor d(a_0„/a)3^2 represents the higher order terms in the quasi- IU&X Btatic broadening, where «max gives the inner limit, closest to A0, and the asymptotic wing formula, Eq. (4), should be used from this value on outward, away from XQ. It was found in this work, that the profiles of Ly-a, -6, and -y were described by the 5/2-power law of a in Eq. (4) and that the quantity CH [b(a) + d(araax/a)^2] was a constant for one value of Ne and one T. Therefore, rewriting Eq. (4), yields S(dX) - (Fo3/2/AX5/2) C , (5) where C - CH Cb(a) + d<amax/«>3/23 » (5a) Substitution of Eq. (5) into Eq. (3) and then into Eq. (2) gives an expression for the variation of the wing inten sity with respect to its distance from the line center, namely Ix« BX(T) [1-exp <-P/AA5/2)] , (6) and 55 P - (7re2/mc2) NgA fgk *02.P03/2.C , (6a) where all quantities have been defined previously. In order to draw a theoretical profile following Eq. (6) we need the value of P. ThiB was obtained by mea suring the one-half value of the full width at half of maximum intensity of the line i.e., 1/2 FWHM « a*i/2’ Equation (6) can then be written in the following form. -P - (AX1/2)5/2.Jtn (1/2) or (7) P * (AX1/2)5/2. 0.693 By combining Eq. (6a) and Eq. (7) the experimental value of the constant C waB found. However, for this determination the total number of hydrogen atoms in the ground state (i.e., Ng£) was required, which could perhaps be obtained by utilizing the thermal properties of the arc plasma and the Saha equation. But this procedure introduces a large error in the calculated quantity Ng.i. Therefore, we used the well known absorption cross section of the Lyman con tinuum for this purpose instead. A typical spectrum of this continuum is shown in Fig. 8, and the intensity IQ^ at a wavelength X of this continuum is given by IcX “ V T> Cl-exp (-Nglox)] , Relative Intensity Lyman Continuum n 01 rOI Ly-y pLy-8 Ar||(932.o5Jl) r A r 11(919.78 A) 9 0 0 1000 Figure 8 o A recorder trace of Lyman continuum which begins at about 930A for the present plasma 57 or Ng. & - - (l/0xHn [1 - (IcX/Bx(T))] , (8) where ax is the known photoionization cross section at the wavelength X. In order to calculate the value of Ng.A, from Eq. (8), the value of BX(T), the intensity corresponding to the black body level, is needed. For this purpose, the hydrogen flow rate into the arc was gradually increased until the Lyman continuum also became optically thick, together with the Lyman lines. Flow rates for this condi tion are given in the first horizontal row in Table 3* The spectrum was then recorded. Then the flow rate of hydrogen was reduced to such a value (second horizontal row of Table 3), that the intensity of the Lyman continuum became much less in comparison with its saturated value, while the Intensity of Ly-a was still saturated, i.e., It corre sponded to the black body level BX(T). The H-8 line in the visible was simultaneously recorded for these two flow rates, for which the temperatures of the arc plasma also changed. Suppose T1 was the temperature for the optically thick Lyman continuum and T2 the one for the reduced hydro gen flow rate. Then using Eq. (1), BX(T2) can be obtained from W - Bj^) exp {C2/X [l/T^-l/Tg]) , (9) 58 where all quantities have been defined previously. In the above expression, the quantity within the square brackets (1/T difference) was obtained from the known values of B^(T^) and B^(T2) of the optically thick heights of Ly-a at these two temperatures. The ratio of the intensities of H-3 for the same two temperatures gave the ratio of the densities of hydrogen atoms in the ground state, i.e., Ng(T^)/Ng(T2). Thus, from a knowledge of Ng.A for the plasma at T2 emitting the opti cally thin Lyman continuum, the value of this quantity for the plasma at temperature T2 was obtained. In this way we obtained within ± 5% the value of Ng£ required for Eq. (6), describing the variation of the wing intensity. The con stant C depends both on Ng and the electron density N , which was known to within ± 10J{, and the experimental value of C was obtained to within ± 15%- Results and Discussion In Figs. 9 through 11, experimental line profiles, together with the theoretical best fit following the 5/2- power law for Ly-a, Ly-B, and Ly-y are shown. These pro files were drawn with respect to the undisplaced position of the lines determined from their self reversed peaks. Table 4 gives the experimental values of the constant C, Relative Intensity EXPERIMENTAL LINE SHAPE 59 •SCo)* C{a)-5/2 © INSTRUMENT PROFILE “ Saturation Level L y-a Red Wing Blue Wing r l 2 O 0 * 7 N I 1200.2 NI rll99.5NI A\(A) Figure 9 c/2 Experimental and S(a) * C/a^ best fit profiles for Ly-a. a is the reduced wavelength given by a ■ AX/Fq, where Fq ■ 2.61 e . « and 0 represent convolution and zero level of intensity, respectively. Relative Intensity 60 EXPERIMENTAL LINE SHAPE S<a)«C(a)-5/2 © INSTRUMENT PROFILE — Saturation Level Ly-/3 Blue Wing 5 ^ . 5 AX(A) Figure 10 c/p Experimental and S(d) - C/a best fit profiles for Ly-B. a is the reduced wavelength given by a - AX/F , where F - 2.61 e N?/3. o o e The red wing of this line is distorted due to the o presence of an Arl resonance line at 10^8A. • and 0 represent convolution and zero level of Intensity, respectively. Relative Intensity 61 EXPERIMENTAL LINE SHAPE S(a)> C (a)*5/2 « INSTRUMENT PROFILE L y -y Saturation Level RedWing 10 5 0 5 10 AXCA) Figure 11 S/2 Experimental and S(o) ■ C/a best fit profiles for Ly-y. a Is the reduced wavelength given by a ■ AX/Fq, where Fq ■ 2.61 e The blue wing of this line is distorted due to the line merging at the series limit, e and 0 represent convolution and zero level of intensity, respectively. TABLE 4 PARAMETERS C FOR Ly-a, -8, AND -y LINES. Cg IS THE CONSTANT CHARACTERIZING THE ASYMPTOTIC HOLTSMARK PROFILES (3.3593 * 10 , 1.7888 x 10~5, AND 3.9706 x io“5 FOR Ly-a, -6, AND -y LINES, RESPECTIVELY. THE UNITS OF C AND CH ARE (A/CGS FIELD STRENGTH UNITS)3/2) Ne x V 6 (cm*3) ± 10$ Te x 10H (K) ± 2% Biis Experiment Theory8 Ly-a Ly-B Iy-Y Ly-a I t f - 8 C -6 xlO ± 5% C/CH ± 5% ^ _5 xlO 5 ± 5% c/cH ± 5% ^ ~5 xlO ± 5? o/cH ± 5% C -6 xlO C/CH C -5 xlO p c/cH 5.25 1.18 5.27 1.57 2.89 1.62 7.68 1.93 6.3 1.87 3-75 2.09 7.67 1.26 5.28 1.57 2.76 1.55 8.32 2.09 6.0 1.78 3.65 2.04 “Ref. 31. o\ ro 63 together with its theoretical values obtained from Vidal, 31 Cooper, and Smith's paper. The results of the present measurements show that the value of C for the region of the o o line profile lying between 2A and 15A away from its center is a constant. In other words, C does not depend on AX for this region of line profile. In Pig. 12 the variation of measured ratio C/CH, where CH is the Holtsmark constant, with respect to the wavelength distance from the center of the line is presented for the Ly-a and is compared with the results of Vidal, et al.^ and also with the results of 30 Grlem. In the same figure we have also Included the 27 experimental results of Boldt and Cooper. It is seen that the measurements of Boldt and Cooper (curve C) run exactly parallel to the theoretical results of Vidal, et al. (curve B) but the measured values are about 20% lower than the theory. On the other hand, Griem's^® results (curve A) do not agree at all with the values of Boldt and Cooper, The results of the present experiment (curve D) show that this ratio C/Cjj is a constant over the entire wavelength region measured here and the numerical valueB are closer to the ones obtained by Boldt and Cooper. Details of the sources of errors in our measurements will be presented later in this paper. We find that our results have a systematic error of ± 15% and a statistical error of ± 5$. If we assume that this systemic error is negative then our 64 2.5 o N. 0 1 2.0 1.5 1 . 0 ±5% / 1 .0 5.0 AX (A) Figure 12 10.0 15.0 Comparison of the measured ratio C/C^, Where Is the Holtsmark constant, with two theories and a previous arc experiment for the profile of Iy-a. Curve A for Ne « 8.0 *101° cmr3 by Qriem, curve B far Ne ■ 7.67 x lO1^ cm“3 by Vidal, et al.. curve C far Mb ■ 8.0 x lO1^ crrr3 by Boldt and Cooper, and Curve D far ML * 7.67 * 10*° cnr*3 gives the results of the present experiment, froicen lines (— ) around curve A give the error limit shown by Qriem and around curve C repre sent the spread in the experimental data of Boldt and Cooper. 65 results will be in near agreement with the theoretical results of Vidal, et al. However, the shape of the two curves (curves B and D) will still be very different. In this respect our measurements have a better agreement with the results of Oriem (curve A). In the following we Bhall discuss the individual line shapes. (a) Lyman-a: It is seen from Fig. 9 that there is good agreement between the 5/2 power law of a and experiment for the blue wing of this line. However, the red wing does not follow this profile. It is asymmetrical and has been discussed by Qriem. The Increase in the red component over the blue one is caused by quadrupole interactions, slowly varying functions of the frequency which are ignored In the definition of theoretical line shape, and the near trivial transformation of frequency Into wavelength units. 30 Grienr gives an expression from which a quantitative value of this asymmetry can be evaluated to within ± 10%. Since the asymmetry observed in this work is well within this limit, we did not try to correct it. (b) Lyman-6: Figure 10 again shows the experimental profile and the profile following 5/2 power law of a for this line. Due to the presence of the Arl resonance line o at 1048a, the red wing of Ly-0 could not be utilized for this comparison. However, for the blue wing the agreement was good. 66 (c) Lyman-v: This line ia close to the series limit where other lines begin to merge into each other. For the electron density used here, Ly-6 became quite broad and its blue wing overlapped Ly-y. However, the red wing was not affected, and its profile agreed very well with the 5/2 power law of a; contrary to our expectations: the red wing should also deviate from this profile, as in the case of Ly-a and for the same reasons of asymmetry. Sources of Error The values of C for Ly-ct, -6, and -y were calculated from Eqs. (6a) and (7)» and the quantities which can con tribute to the total error are: (i) Ng£, the total number of neutral hydrogen atoms in the ground state; (ii) Ne, the electron density; and (iii) the (1/2) FWHM-(half) half width of the line. It has been shown previously that (1) and (ii) introduce a possible systematic error of ± 15% in the calculated value of C. This systematic error arises due to ± 10% uncertainty in the theoretical value of a con stant which is used in the calculation of N and ± 5% error © in the experimental value of o^, the photoionization cross section of atomic hydrogen, which is employed in the deter mination of Ng£. Apart from this systematic error there is about ± 5% statistical error which comes from the 67 uncertainty In the measurements of the half widths of the lines and temperature of the plasma. In the measurement of AXjy2 we assumed that the line profile was entirely due to Stark broadening and neglected other broadening mechanisms, such as (a) resonance broaden ing, (b) Van der Waals broadening, (c) Doppler broadening, and (d) broadening due to apparatus profile. It can be BhownJ that broadening due to (a) and (b) are about two orders of magnitude less than the Stark broadening in the present case and, therefore, can be neglected. The AX^y2 of the Ly-a due to (c) for a temperature of about 12,500 K o is approximately equal to 0.05 A. This is also about two orders of magnitude less than the AX^y2 value of Ly-a obtained here and can again be neglected. The apparatus profile could be the main source of error in AXjy2. Mack, et al..^ have derived expressions for the resolving power and line width of a spectrometer equipped with a concave reflection grating, while Namioka^ has calculated these quantities from the point of view of geometrical optics alone. Both give essentially the same results. According to Mack, et al..^ the width of a line and the resolving power are given by V - Apparatus line width ■ 1.1 (sc/pm) (10) and R ■ Resolving power * 0.91 (pXm/so) , (11) 68 where s is the entrance slit width, a the grating constant, p the radius of curvature of the grating, and m the order of diffraction. For our 2-meter grazing incidence spectrom eter with a grating of 591 grooves/mm and with a 70 microns wide entrance slit, W ■ 0.65A and R * 1.52 x 10^. With this resolution one should be able to resolve a line pair sepa- . o rated by 0.65A. In Fig. 9 we find an NI triplet on the blue wing of Ly-a line, which is Just resolved and has a separa- o tion of 0.7A. These experimental and theoretical values agree very well. Similar criteria for checking the experi ment against theory were employed by Mack and associates. The theoretical value of the Instrumental width Is also supported by the observed half width of the self reversed profiles of Ly-a and Ly-B shown In FIgB. 9 and 10. This self reversal is caused by hydrogen atoms in cold regions lying in the path of the vuv radiation. The widthB of these self reversed profiles should be entirely due to Instrumen- o tal broadening and were found to be equal to 0.7A. Thus, the measured half widths of the Lyman lines should be - O corrected by this Instrumental width of 0.65A, and the corrected results are presented in Table * 4 . 69 Conclusion We thus conclude that the Stark broadened profiles of Ly-a, -B, and -y lines of hydrogen follow the 5/2 power law of a from at least two angstroms away from the line o center and up to about 15A and the ratio C/CH, where CH Is the Holtsmark constant, remains constant for this region of the line profile. CHAPTER V LOWERING OP THE IONIZATION POTENTIAL AND THE ADVANCE OF THE SERIES LIMIT OP AN ATOM IN A HIGH TEMPERATURE AND HIGH DENSITY PLASMA In order to produce an electron and an Ion at rest from a neutral atom Immersed in a high temperature and high electron density plasma, the energy required is less than the energy needed for the same process when a neutral atom is Isolated. This reduction in the Ionization energy is Interpreted as a "lowering of the ionization potential'1 for an atom in a plasma. In the past, there have been several attempts to calculate theoretically the magnitude of this, based on either quantum mechanical or thermodynamical con siderations. Both approaches lead to the conclusion that the lowering of ionization depends on two factors: One given by the polarization energy of the plasma, and the other by the microfield effects of neighboring charges on 37 the bound electrons. However, it has been pointed out- " that there is a certain critical electron density, Nc, of the plasma below which only the polarization term is effec tive, while above this value the term due to mlcroflelds becomes significant. 70 71 ■ a g 01senJ has determined the lowering of the Ionization potential of argon from the advanceJ7 of its series limit (i.e., a certain shift to the red in the absorption edge of a Rydberg series) in the visible region of the spectrum and also by measuring the emission coefficients of both neutral 4 n and ion lines of argon in conjunction with the Saha equa tion. His data agree with the theoretical results of 41 - 3 f t Brunner, though it is the opinion of Olsen, as well as 4 p of Ecker and Kroll, that Brunner's results are in error on the grounds that he counts his lattice (or microfield) term twice. The present work describes the measurement of lower ing of the ionization potentials of hydrogen and carbon atoms in terms of the advance of their series limits in the vacuum ultraviolet (vuv) region of the spectrum for various electron densities and temperatures of a plasma generated in a wall stabilized high current arc operated in a mixture of argon and helium. The spectrum of hydrogen or carbon is obtained by flowing hydrogen or carbon dioxide gases into the central portion of this arc. The results are compared with the theoretical predictions for the advance of a series limitas well as for the lowering of the ionization 41 46—50 potential. * J Ve shall also discuss the question of the validity of our assumption that the value of the lower ing of the ionization potential given by the advance of 72 a series limit Is the same as that used In the Saha equation. Experimental Arrangement and Method A wall stabilized arc was operated in argon and helium in such a way that helium provided a window up to o about 510A where its continuum absorption due to ionization begins. The radiation emitted by the arc was observed end on along its axis, and a differential pumping system reduced pressures required for vuv spectroscopy. A 2-meter -5 grazing incidence spectrometer evacuated to 10 ^ Torr was used for recording the spectrum photoelectrically in the o o 600A-1200A region with a reciprocal linear dispersion of o ~ 3A/mm. For obtaining the electron density, and tempera ture of the plasma, visible radiation emitted by the arc along its axis was focused on the entrance slit of a Seya- Namloka spectrometer and its spectrum was recorded photo electrically. Details of the experimental arrangement have been given in Chapter II. The spectra of atomic hydrogen and carbon were recorded near their series limits in the vuv by flowing hydrogen and carbon dioxide gases into the central portion of the arc. Electron densities and temperatures of the plasma were varied by changing the ratio of the flow rates 73 of argon and helium into the arc and by varying the arc current. The electron density was calculated from the half width of the Stark broadened H-6 line of hydrogen, and the temperature was obtained by the ratio of the intensities of o neutral argon line at U30OA to that of the singly ionized o line at 4806A. Details of this method are given by Stuck and Wende.^ Results and Discussion The spectrum near the Lyman series limit of hydrogen was recorded for five electron densities between 1.45xlO1^ cm~^ and 9.82x lO1^ cm”^ of the plasmaB. Three such records for the electron densities of 1.45x 10^ cm"^, 5.0 x lO1^ ■ a i —>' a cm ” , and 9.82 x 10 cm are presented in Pig. 13 where it is seen that as the electron density of the plasma increases the lines gradually become broader and the approximate position where the lines merge into continuum shifts towards longer wavelengths. A similar vacuum uv spectrum near the series limit of carbon was recorded and is given in Pig. 14. However, such a spectrum was obtained only for l6 one electron density of 7.76 x 10 cm” . The aim of record ing the spectra of carbon was to verify whether various theories for the shift or advance of a series limit of hydrogen are applicable to a heavier atom or not. 74 0 < to i f ) o t o - S to I____ CD in (A iDJ||qJD) A j t s u a j u l Figure 13 VUV spectnon of hydrogen near Its series limit far different electron densities, N . The letter n represents the principal quantum rubber of the upper level of transition. The presence of Aril lines (932 a and 9 1 9 a ) In the above spectra has been Ignored. The shaded portion gives the observed series limit. Relative Intensity 75 1194,4 1194.6 N-« 8.79X10 cm 4 Te* 1.29 X 10 K Ionization Limit r 0f an Isolated Atom Cl 1158.9 1100 1150 1200 ► X( A) Figure VUV spectrum of atomic carbon near Its series limit. The shaded portion gives the observed limit. 76 It is evident from Pigs. 13 and 1*1 that the position of the beginning of the continuum is not very well defined. Therefore, this position was estimated by employing a SI i method similar to one used by Mohler. In Pigs. 13 and 14 we find that as the continuum is approached, the peak intensities of the spectral lines go on decreasing con tinuously. At the same time, the Intensity underlying the lines increases. Thus, we can draw two envelopes: One corresponding to the maximum intensity and the other for the minimum Intensity. The position where they meet each other can be defined as the beginning of the continuum. We determined the ratio between the maximum intensity and mini mum intensity for a few lines near the series limit. This ratio was then plotted against wavelength. This plot is a continuous curve and is shown in Fig. 15 for the spectrum emitted from the plasma of 9*82 * 10 cm”3 electron density. For other electron densities these curves are similar in shape and are very close to each other. There fore, we do not present them here. At the position of the beginning of the continuum this ratio between the maximum and minimum intensity of a line should be equal to 1.0. The curve shown in Fig. 15 was extrapolated to this value and the corresponding wavelength was obtained. In this way the position of the beginning of the continuum was estl- o mated with an accuracy of ± 2A. If the hydrogen and carbon 77 1 . 0 * -3 934 A 9 0 0 9 5 0 Figure 15 A plot of the ratio Invtp/Imav with respect to wavelength for three lines of hydrogen near Its series limit. Imln the background Intensity present below the line and Imax 18 Its peak Intensity. This plot, given for the plasma of 9.82 * lQl® cmr’ electron density, 1b representative of similar plots at other electron densities fran which the position of the beginning of the cant Inman has been obtained. 78 atoms were Isolated from the plasma then this position would o o be at about 911A and 1101A, respectively. The difference between the two positions is defined as the shift or advance of a series limit. The experimental values of this shift or advance for different plasmas as obtained here are pre sented in column three of Table 5- In the literature there are three J different theoretical expressions which give the value of the shift or the advance of the series limit. Earliest among them is due to Inglis and Teller. J According to them, the energy levels of an atom immersed in a plasma become broad due to the linear Stark effect caused by the electric fields of electrons and ions. Since excited levels near the series limit of an atom are very closely spaced, they begin to overlap and thus some of the energy levels merge into each other. This merging occurs at such an energy level whose Stark broadened width is equal to the energy difference between the two neighboring terms. The following expres sion derived by Inglis and Teller, gives the principal quantum number n of the last term observed in the series: N.n15/2 - 0.027 a”3 , (1) where N is equal to the sum of ion and electron densities —8 and aQ ■ 0.53 * 10 cm, the Bohr radius. If suppose EQ is the energy of the last discrete level of an Isolated atom 79 TABLE 5 COMPARISON OF THE OBSERVED VALUES OF AE , THE r ADVANCE OF THE SERIES LIMIT, FOR HYDROGEN AND CARBON ATOMS WITH THE RESULTS OF DIFFERENT THEORIES HYDROGEN N x io16 C^f3) ± 10* i i T x 10 e CK) ± 2% Shift or advance of a series limit AEp Tills Experiment (eV) ± 0.028 Inglis and Teller1 (eV) 2 Armstrong (eV) Ecker apd Kroll-3 (eV) 9.82 1.31 0.322 0.348 0.331 0.107 6.84 1.23 0.301 0.316 0.301 0.095 5.0 1.22 0.270 0.291 0.276 0.085 3.09 1.20 0.222 0.255 0.241 0.073 1.45 1.20 0.164 0.209 0.194 0.057 CARBON 8.79 1.29 0.300 0.339 0.330 0.103 "Stef. 43 ^Ref. 44 \ef. 45 80 and En is the one corresponding to the energy level where merging takes place when an atom is Immersed in a plasma then the advance of a series limit AE„ can be obtained from the following relation: AEr - Eq -En - (13.605/n2) (eV) , (2) where n is given by Eq. (1). The values of AEr calculated from Eq. (2) are presented in the fourth column of Table 5. The agreement with the experimental values obtained here is quite good. i i i Inglis and Teller J actually use half the width between the outermost Stark components of an energy level and equate it to the half the distance between the two neighboring terms. These outermost components lie in the wings of a spectral line. Thus, if one uses the Inglis and Teller criterion then merging might be predicted at the line whose line core is still identifiable. For example, in Fig. 13, according to Inglis and Teller, the line with n - 4 16 — o for the plasma of 9.82><10 cnT^ electron density and with n-5 for the plasmas of 5.0 x 10^^ cm’^ and 1.^5 * 10^ cm”^ electron densities will be Interpreted as the last discern ible line, while the position where the series seems to be terminating is at a shorter wavelength. This situation is iili improved by Armstrong. Instead of using the quasi-static approach for electron broadening of the spectral lines 81 utilized by Inglis and Teller, he considers the impact broadening due to electrons which dominates the line core. According to him, a spectral line will be completely indistinguishable from the next neighboring line If the full width at half maximum (FWHM) of this line equals the dis tance from the next neighboring line. He arrives at the following expression for the advance of a series limit: AEr - 4.707 * 10"6. N^/7/(kT)1/7 (eV) , (3) where N is the electron density of the plasma, T its tern- perature, and k the Boltzmann constant. Values of AEr cal culated for various plasmas investigated here are presented in column 5 of Table 5- Within the precision of our measure ments, both the Inglis and Teller, and Armstrong results agree very well with this experiment. Ecker and Kroll^^ derive an expression for the shift or advance of a series limit from an entirely different approach. They consider a plasma consisting of only elec trons and protons. In such a plasma they define three dif ferent kinds of particles. In the first group are those particles which are completely free, In the second group are bound particles (neutral hydrogen atoms), and the third group consists of quasl-free particles. With this model they find, by quantum mechanical treatment, an energy level diagram for the plasma. This energy level diagram gives a 82 boundary which separates free particle states from the bound ones. The exact position of this boundary is rather uncertain. Due to this uncertainty they give the following approximate relation for the shift or the advance of a series limit: A E r - n - ( e 2/ r 0 ) , C 1* ) where n is an uncertain factor, e the electronic charge and J l c r0 the average interionic distance. Ecker and Kroll J put n ■ 1. The calculated values of AEp from Eq. (4) are given in Table 5. We find that these values do not agree with this experiment. The close agreement between the results iiq till of this work and with the two theories described pre viously indicates that probably n is not equal to 1.0. Therefore, we substituted our experimental values of AEr in Eq. (4) and calculated n- The least squares fit value of / l c this factor is 3.06 ±0.18. Thus, Ecker and Kroll1s 3 theoretical expression for the advance of a series limit will agree with this experiment only when the above value of n is employed in Eq. (4). Now, the question arises how the advance of the series limit, AEr, of an atom is related with its lowering of ionization potential, AE_, as used in the Saha equation. Some authors^®***1*52-54 identify these two quantities with 42 46 each other while others * do not. In Table 6 the values TffltE 6 ctmuaaot cp am cgsrveu values cf 4^,, tie acvance cp tee sties loot, vnn he resotas op SBVEWL VBCHBS PCB VK lOCHOU CP THE XCMTWUCK KJTEHTIAL 4Eg. 4^ B THE TOW COB TO THE KCHC7IKU8 AND 6F THAT POE TO FCOHITATICU CP IHS PUSH P HmnjEH ^xlO1 * i 10f T « 10* e (» t a 4 E , . ( « V ) _TM» t 0.028 S» of tt*5ld ml Debw AE/eV) Ecker nd (Uni AEgleTJ Btimar fekr ml M U U»9U C stops md also Orlm “ p «4 9.82 1.31 0.322 0.321 o . o e o 0.401 0.31 2 0 . 0 6 1 0.380 0.558 0.068 0.626 0.03 2 0.080 0. 112 6 . 8 4 1.23 0.30 1 0.28? 0.069 0.354 0.27 6 0 . 0 5 9 0.335 0.494 0.05 9 0.5 53 0.02 7 0.06 9 0.096 5 . 0 1.22 0.2 70 0.255 0.059 0. 3 14 0.249 0 . 0 5 1 0.3 00 0.444 0.051 0.495 0.02 3 0.059 0.082 3.0 9 1.20 0.2 22 0.219 0.047 0.266 0.21 2 0 . 0 4 C 0.25 2 0.379 0.040 0.419 O.OlB 0.047 0.065 1.4 5 1.20 0.1 68 0.171 0.032 0.203 0.16 5 0 . 0 2 7 0.192 0.296 0. 027 0.323 0.012 0.03 2 0.044 CAJBCM 8.7 9 1.29 0.30 0 0.309 0.07 7 0.386 0.300 0.06 5 0.365 0.536 0.065 0.601 0.030 0.07 7 0.1 07 00 L O 84 of the lowering of the Ionization potential, AE_, calculated 4l 46-50 from some well known theoretical predictions * are presented. The lowering due to microfields (i.e., due to free-bound interactions) is indicated by AEm and that due to polarization effects (i.e., due to free-free Coulomb interactions) by AEp. As has been stated before, there should be a certain critical electron density of the plasma below which only the value of AEp should be used in the Saha equation, while above it the value of AEm should be employed. This critical electron density, according to Duclos and Cambel,3^ is given by the following relation: N + I - (81TD3)*1 , (5) z,a where N is the critical electron density, is the density v « of ions of specieB a, z is the ionic charge, and D is the Debye radius. For an atmospheric plasma at 10,000 K the critical electron density is usually given to be of the IQ order of 10 J cm . From Table 6 it is found that the values of AE . the r advance of the series limit, closely agree with the theoret ical values only when AE^ and AEp are added together, while the electron densities of the plasmas investigated here are 16 _ " 3 of the order of 10 cm . If we assume that the advance of the series limit, AEr, is equal to the lowering of the 85 ionization potential, AE * as used In the Saha equation, then this seemingly good agreement between the experiment and theory leads us to the conclusion that the validity of the criterion of a critical electron density, N , is ques- tlonable, at least as used at present. Olsen^® measured the advance of the series limit of argon from the spectrum in the visible region emitted by a pure argon plasma generated in a 5 mm, 400 A dc thermal arc. 41 His result was in agreement with Brunner’s theoretical value, when microfield and polarization terms were added 40 together. In a second experiment he measured indirectly the value of the lowering of the ionization potential (one which is required for the Saha equation) from the ratio of the emission coefficients of a neutral argon line and a singly ionized line. He again concluded that the lowering was best given by the sum of the polarization and the micro field term of Brunner. Although our results do not agree with the theoretical values of Brunner, Olsen’s work supports our interpretation that the advance of a series limit is equal to the lowering of the ionization potential required for the Saha equation. Conclusion Thus, we conclude that: (a) the shift or advance of a series limit is adequately explained by either the Inglis 86 and Teller's relation or Armstrong's theory, (b) in Ecker and Kroll's expression for the advance of a series limit the uncertain factor n should be equal to 3.01±0.18 instead of 1, and (c) if the criterion of a critical electron density is ignored then the advance of a series limit is equal to the lowering of the ionization potential as used in the Saha equation. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. A. W. Ehler and G. L. Welssler, J. Opt. Soc. Am. 45, 1035 (1955). H. E. Blackwell, G. S. Bajwa, G. S. Shipp, and G. L. Weissler, J. Quant. Spectry. Radiative Transfer 4, 249 (1964). H. Maecker, Z. Naturforsch. 11a. 457 (1956). W. Finkelnburg and H. Maecker, "Handbuch der Fhysik," Berlin: Springer-Verlag, 1956; XXII Gasentladungen. S. Ogawa, U.S.C. Internal Technical Report No.: USC- Vac-UV-122, dated 15 April 1970. W. Hofmann and G. L. Weissler, J. Opt. Soc. Am. 61, 223 (1971). J. Richter, Z. ABtrophys. £1., 177 (1961). F. Mastrup and W. Wiese, Z. Astrophys. 4J^, 259 (1958). P. Hey, Z. Physik 151. 79 (1959). W. E. Gericke, Z. Astrophys. 53. 68 (1961). G. Boldt, Z. Naturforsch. 18a, 1107 (1963). G. Boldt, Space Sci. Rev. 11. 728 (1970). J, UhlenbuBCh, Report HMP 125, Fhyslkalisches Institut Der Technischen Hochschule Aaachen (1969). E. Ya. Schreider, Sov. Phys-Tech. PhyB, 1609 (1965). G. Jurgens, Z. Physik 134. 21 (1952). D. Stuck and B. Wende, J. Opt. Soc. Am. 62, 96 (1972). W. L. Wiese, M. W. Smith, and B. M. Miles, "Atomic Transition Probabilities," Vol. II, Natl. Bur. Std. (U.S.) NSRDS-NBS 22 (U.S. Government Printing Office, Washington, D.C.), (1969). G. M. Lawrence, Bull. Am. Phys. Soc. 13. 206 (1968), (F-l). 87 88 19. J. A. R. Samson, J. Opt, Soc. Am, 54. 420 (1964). 20. J. A. R. Samson, "Techniques of Vacuum Ultraviolet Spectroscopy," (John Wiley & Sons, Inc., 1967), p. 214. 21. H. Statz, F. A. Horrlgan, S. H. Koozekanani, C. L. Tang, and G. F. Koster, J. Appl. Phys. 36. 2278 (1965); Also see, G. F. Koster, H. Statz, and C. L. Tang, J. Appl. Phys. 4oi*5 (1968). 22. A. E. Livingston, D. J. G. Irwin, and E. H. Pinnington J. Opt. Soc. Am. §2_t 1303 (1972). 23. W. L. Wiese, D. E. Kelleher, and D. R. Paquette, Phys. Rev. A6, 1132 (1972). 24. R. A. Hill, J. B. Gerardo, and P. C. Kepple, Phys. Rev. A£, 855 (1971). 25. P. Kepple and H. R. Griem, Phys. Rev. 173. 317 (1968). 26. E. W. Smith, J. Cooper, and C. R. Vidal, Phys. Rev. 185. 140 (1969). 27. Q. Boldt and W. S. Cooper, Z. Naturforsch. 19a. 968 (1964). 28. R. C. Elton and H. R. Griem, Phys. Rev. 135A, 1550 (1964). 29. Q. A. Moo-Young, J. R. Grieg, and H. R. Griem, Phys. Rev. A2, 1617 (1970). 30. H. R. Griem, Phys. Rev. 140A, 1140 (1965). 31. C. R. Vidal, J. Cooper, and E. W. Smith, The Astrophys J. Supplement, series ££, 37 (1973). . C M m H. R. Griem, Astrophys. J. 147. 1092 (1967). 33. A. B. Underhill and J. H. 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Creator Srivastava, Santosh Kumar (author)

Core Title Vacuum-Ultraviolet Plasma Spectroscopy On A Double-Arc With Measurements On Line-Strengths And Lineshapes; And On The Lowering Of Ionization Potentials

Degree Doctor of Philosophy

Degree Program physics

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Advisor Weissler, Gerhard L. (committee chair), Aklonis, John J. (committee member), Ogawa, Masaru (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-878726

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