LONG PATH LASER SPECTROSCOPY OF WEAK
SPECTRAL TRANSITIONS IN PLASMAS
A Thesis Submitted for the Degree of
DOCTOR OF PHILOSOPHY
In the UNIVERSITY OF LONDON
By
MARK PHILIP SYDNEY NIGHTINGALE
The Blackett Laboratory
Imperial College of Science and Technology
London SW7 2BZ LONG PATH LASER SPECTROSCOPY OF WEAK SPECTRAL TRANSITIONS IN PLASMAS
By
MARK PHILIP SYDNEY NIGHTINGALE
ABSTRACT
There has been much interest recently in spectral lineshapes,
especially in plasmas where charge particle broadening is important.
For the accurate measurement of such profiles, absorption
spectroscopy offers distinct advantages over other techniques but
requires the use of long optical paths (several metres or more) since,
typically, plasma opacities are extremely low.
A z-pinch plasma device has been used to generate a 10 metre
long plasma column and optical paths in this plasma exceeding one
kilometre have been achieved by the use of a multipassed CW dye
laser system. Such paths allow both the accurate measurement of
allowed line profiles over five orders of magnitude of absorption, and also provide the means of measuring weak features such as forbidden lines or continua.
Full electron density diagnostics have been performed using interferometry (over twenty-one metre paths) and these show considerable density oscillations during the plasma recombination phase whose origins and effects might have considerable importance in the use of plasmas as spectroscopic sources.
Results are presented for several long path absorption and
3 1 interferometric experiments. In Helium the 2p P - 3d 'D forbidden intercombination satellite on the 5876 A line-wing is fully resolved providing evidence as to its origin. In Hydrogen and Nitrogen, new values for continuum absorption are measured at various wavelengths and these are found to be considerably higher than accepted theoretical estimates. Finally interferometric measure- ments over 44 metre paths provide population estimates for the hydrogen first excited state and these are compared with computer collisional-radiative results.
Given these long paths, the possibility of measuring highly forbidden ionic ground state lines of astrophysical interest, such as the 5754 A [N II] line, is examined for transition probabilities in the range 1 - 0.001 per second, with the con- clusion that modifications to the z-pinch should allow such measurements to be made. 4
ACKNOWLEGEMENTS
I would firstly like to thank my supervisor, Professor
D.D. Burgess, whose encouragement helped so much when this project was proceeding slowly, and whose arguments forced me to remain critical and objective, even when the project was proceeding as planned. I would also like to thank him for obtaining the necessary funding, without which the experiments would not have been possible.
I also owe much gratitude to the rest of the Spectroscopy group at Imperial College, all of whom have offered help or advice at one time or another. Special mention must be made to Geof Kolbe whose experience of the ten-metre z-pinch and all matters electrical, was most useful at the start of this PhD,and also to technician
Peter Ruthven whose ability to machine spark gap sections at little advanced warning was most helpful. Finally, from college, I would like to thank the library and workshop services of the Physics Depart- ment under the supervision of Mrs B. Garton and Mr. R. Hobbs respectively.
Thanks are certainly due firstly to my parents, whose years of encouragement have got me this far; secondly to my sister-in-law
Margaret, who has found her way through the numerous English errors to type this thesis; and thirdly and most importantly of all, I would like to give special thanks to my wife Liz whose love, encouragement and support during the entirety of this work provided much needed inspiration.
Finally I would like to thank the Science Research Council for supporting me as a quota award postgraduate student for three years, and Imperial College for supporting me for a further seven months. Plate 1 -The Multipassing White Cell in Operation (1=823 64m.)
"Moreover, the z-pinch provides a long optical path in the
plasma two metres being entirely feasible."
D.D.Burgess (Space Sci. Revs. 13 , 493 (1972
"To carry nature lengths unknown before."
William Cowper (Beau's Reply) -6
INDEX
Page
Abstract 2
Acknowledgements 4
Index 6
Chapter 1 - Introduction
1.1 Summary 13
1.2 The Use of Plasmas in Experimental Atomic Physics 15
1.3 The Theoretical Background to Spectral Measurements in 16
Plasma Sources
1.3.1 Atomic Physics 16
1.3.2 Line Broadening Theory 18
1.3.3 Weak Features in Spectral Line Broadening Processes 18
1.3.3.1 Quasi-Molecular Satellites 19
1.3.3.2 Plasma Satellites 20
1.3.3.3 Forbidden Lines 21
1.3.3.4 Continuum Absorption 22
1.4 Techniques for Lineshape Measurement 22
1.4.1 Emission Spectroscopy 22
1.4.2 Absorption Spectroscopy 24
Chapter 2 - Laser Absorption in Plasmas
2.1 The Theory of Absorption 26
2.2 An Estimation of Likely Absorption Coefficients of Interest 27
2.2.1 Conditions in Existing Plasma Sources 27
2.2.2 Spectral Properties Required 29
2.2.3 Results 30
2.3 Plasmas Available for Long Path Absorption Measurements 32 7-
Page
2.A The Laser as a Background Source for Absorption Measurements 33
2.5 .Practical Limits for Absorption Spectroscopy over Long Path Lengths in Plasmas 35
2.5.1 Limits set by the Time of Flight of the Laser 35
2.5.2 Limits set by Atomic Saturation 35
2.5.3 Limits set by Laser Path Bending 37
2.5.A Limits set by Continuum Absorption 37
2.5.5 Limits set by Noise Levels 38
2.5.6 Limits set by Transition Linewidths 39
2.6 Conclusions AO
Chapter 3 - The Ten Metre Plasma Device and Previous Long Path Work
3.1 Introduction A1
3.2 Design A1
3.3 Previous History of the Ten Metre Plasma Device A5
3.3.1 Previous Diagnostic Measurements A5
3.3.2 Previous Absorption Measurements over Long Paths A8
3.3.2.1 Single Pass Measurements of Kolbe A8
3.3.2.2 Long Path Measurements of Playford A9
3.3.2.3 He I 23P - 33D 5876A Profile A9
3.3.2.A Hydrogen Balmer-Alpha Absorption Measurements 51
3.3.2.5 Hydrogen n=2 Level Population Measurement 5A
3.3.2.6 Conclusions 56
Chapter A - The Design of a Reliable Spark Gap for the Ten
Metre Plasma Device
A.1 Introduction 58
A.2 Requirements 58
A.3 Previous Designs 59
A.A Design 60 8
Page
4.5 Operational Experience with the Redesigned Gap 67
4.6 Further Improvements x 69
/
Chapter 5 - Apparatus used for Multiple-Pass Long Path Absorption Measurements and Technical Limits to Obtainable Path Lengths
5.1 Introduction 70
5.2 The 380A Ring CW Dye Laser 70
5.3 The Dye Laser Table 74 / 5.4 Optics for the CW Laser 74
5.5 The Multipassing Optical Arrangement 76
5.5.1 Requirements 76
5.5.2 Spatially Separated Multipassing Systems 77
5.5.2.1 Plane-Concave 78
5.5.2.2 Two Mirror Concave 78
5.5.2.3 Three Mirror Concave (White Cell) 79
5.5.3 Temporally-Resolved Multipassing Systems 81
5.5.4 Choice of Multipassing Systems 82
5.5.5 Path Lengths Obtained using Multiple Passing 84
5.6 Detection of Long Path'Laser Absorption 86
5.7 The Measurement and Recording of the Data 91
5.8 The Experimental Procedure 96
5.9 Limits to Long Path Absorption Spectroscopy 98
5.9.1 Experimental Limits 98
5.9.2 Theoretical Limits 100
Chapter 6 - Plasma Diagnostics
6.1 Temperature Diagnostics 102
6.1.1 The Maxwellian Electron Energy Distribution 102
6.1.2 Plasma Constituent Temperatures 103 9
Page
6.1.3 Existing Temperature Diagnostics on the Ten Metre Device 104
6.2 Electron Density Diagnostics 106
6.2.1 Emission Measurements 106.
6.2.2 Refractive Index Interferometry 107
6.2.2.1 Analysis of interferometer Traces 108
6.2.2.2 Other Contributions to the observed Refractive Index 110
6.2.2.3 Atomic and Molecular Contributions to the Measured 111
Refractive Index Change
6.2.2.4 Experimental Arrangement 115
6.2.2.5 Electron Density Diagnostic Results 116
6.2.2.5.1 Run A - MachZebnder Interferometry of Nitrogen Plasmas 116
as a function of Pressure
6.2.2.5.2 Run B - Michelson Interferometry in Nitrogen Plasmas 120
6.2.2.5.3 Run C - Interferometry at a Higher Bank Voltage 122
6.2.2.5.4 Run D - Interferometry at Various Off-Axis Positions in 124
a 0.15 Torr Nitrogen Plasma
6.2.2.5.5 Runs E, F - Electron Densities in Hydrogen and Helium Plasmas 126
6.2.2.5.6 Run G - 5145A Interferometry in Hydrogen, Helium and 126
Nitrogen Plasmas
6.2.2.5.7 Run H - Emission Measurements 132
6.2.3 Possible Explanations for the Electron Density Oscillations 132
6.2.3.1 Previous Observations 132
6.2.3.2 Radially Propagating Acoustic Waves 134
6.2.3.3 Persistence of Acoustic Waves 138
6.2.3.4 The Neutral Contribution to the Plasma Refractive Index 141
6.2.4 Elimination of the Density Bounces 142
6.3 Conclusions drawn from Diagnostic Measurements 143
Chapter 7 - Long Path Measurements of the He I 23P - 33D 5876A Profile
7.1 The He I 23P - 33D 5876A Far Wing Absorption Profile 145
7.1.1 Results 145 10
Page
7.1.2 Analysis 150
7.2 He I 5876A Line Centre Absorption Measurements 156
7.2.1 Experimental Results 156
7.2.2 Possible Saturation Mechanisms 158
7.2.3 Comparison of the Measured and Calculated He I 5876A Line 162 Centre Absorption Coefficients
7.2.4 Conclusions for the 5876A Line Centre Absorption Measurements 167
Chapter 8 - Long Path Absorption Measurements of the Far Wing of H-Alpha from 6400A to 6545fi
8.1 Results 170
8.2 Analysis of the Far Wing Absorption Measurements 172
8.2.1 Balmer-Alpha 172
8.2.2 Balmer-Beta ' 175
8.2.3 Lyman-Alpha 175
8.3 Molecular Absorption 176
8.4 Satellite Features 179
8.5 Continuum Absorption 180
8.5.1 Thomson Scattering 180-
8.5.2 Rayleigh Scattering 182
8.5.3 Free-Free (Inverse Bremsstrahlung) Absorption 183
8.5.4 Bound-Free (Photoionization) Continuum Absorption 184
8.5.4.1 Interferometric Measurement of Hydrogen Level Populations 185
8.5.5 Negative Ion Continuum Absorption 192
8.5.6 Conclusions for Continuum Absorption 193
8.6 Conclusions and Further Work 195
Chapter 9 - Absorption Measurements of Forbidden Lines in the Ground Configurations of Light Atoms and Ions
9.1 Introduction 197 11
Page
9.2 The Ground Configuration Structure of Light Atoms and Ions 198
9.3 Previous Observation and Calculation of Forbidden Lines 199
9.4 A review of Theoretical Calculations of Ground Configuration 206 Forbidden Line Transition Probabilities
9.5 Previous Experimental Measurements of,Ground Configuration 215 Forbidden Lines
9.6 The Optical Depths of Spectral Lines 218
9.6.1 Level Populations 219
9.6.2 The Normalized Lineshape Factor 220
9.6.3 Opacities of the Nil Forbidden Lines 222
9.7 Other Possible Sources of Absorption close to the 5754A 225
Forbidden Line
9.7.1 Atomic Absorption by NI and Nil 225
9.7.2 Molecular Absorption 228
9.7.2.1 Molecular Populations 228
9.7.2.2 Absorption by Molecular Resonance Transitions 230
9-7.2.3 Absorption by Molecular Lines of Wavelength close to 5754A 232
9.7.2.4 Conclusions for Molecular Absorption 234
9.7.3 The Quadratic Stark Effect on the [Nil] Forbidden Line 234
9.7.4 Continuum Absorption 239
9.7.4.1 Free-Free and Bound-Free Absorption by N and N+ 239
9-7.4.2 Free-Free and Bound-Free Absorption by N~ 242 9.7.5 Conclusions regarding the Feasibility of using Absorption 243 Spectroscopy to measure the Nil 5754A Transition Probability 9.8 The First Attempt at an Absorption Measurement of the Nil 246 5754A Forbidden Line
9.9 An Interferometric Measurement of Density Gradients present 250 within the plasmas used for long path absorption measurements
9.10 Path Bending 253
9.11 Conclusions for Absorption Spectroscopy in a Nitrogen Plasma 254
Chapter 10 - Conclusions and Further Work
10.1 Technical Achievements 256 12
Page
10.2 Diagnostic Achievements 257
10.3 Experimental Results and Conclusions 257
10.4 Further Work 259
10.5 Concluding Remarks 260
Appendix A - The Sensitivity and Accuracy of Long Path
Absorption Measurements
A1 Choice of Method 261
A2 Choice of Path Lengths 262
A3 An Example of Optimum Path Length Calculation 263
A4 Choice of Laser Power 264
Appendix B - The Refractivity of a Voigt Profiled' Atomic Transition
B1 The General Expression for a Voigt Profile 267
B2 The Far Wing of a Voigt Profile 268
B3 The Line Centre Absorption Coefficient for a Voigt Profile 269
Appendix C - Forbidden Transitions of Interest (of A>0.001s~1) 271
References 273 CHAPTER 1
INTRODUCTION
1.1 Summary
The use of spectroscopic techniques for the measurement
of otherwise unobservable quantities has long been established as
a most useful tool in experimental science. One such technique -
absorption spectroscopy - has proved invaluable in the measurement
of atomic properties in many sources, but until recently has rarely
proved usable in plasmas (despite the introduction of lasers as
background sources) due to problems concerned with the opacities of
atomic transitions, which under typical plasma conditions are very low
indeed. Spectroscopic measurements in laboratory plasmas are crucial,
however, since many plasmas, both terrestrial and astrophysical,
can only be measured spectrally, and the subsequent analysis relies on theoretical atomic, plasma and line broadening physics, much of which has not been fully experimentally verified. It will be shown in
this thesis that absorption spectroscopy can indeed be used on a plasma —6 —1 source and that weak transitions (of absorption coefficient 10~ -1 m~ )
are measurable.
The plasma is produced in a purpose built device (of which one new constructional detail is described)fand a commercial CW ring dye laser is used as the required background source. The length of optical path available within the plasma is greatly lengthened
(by more than two orders of magnitude) by the use of a multiple-pass optical system, which provides absorption path lengths of more than a kilometre, thus allowing the measurement of plasma absorption —6 —1 coefficients as low as 10" m~ for the first time.
Detailed electron density diagnostic results, obtained
by laser interferometry over 21 metres of optical path, are
presented, which show previously undiagnosed density oscillations
to be present in the supposedly quiescent plasma recombination
phase (which is current free). Possible explanations for these
bounces, and their likely influence on long path absorption measure-
ments, are discussed. 3 3 Measurements are also described of the Hel 2 P - 3 D
5876A profile, measured in absorption using path lengths of up to
1,200 metres, and considerable disagreements between theoretical and
measured line centre absorption coefficients have been found. In 3 1 addition the plasma induced 2 P - 3 D satellite has been observed,
and the mechanism for its existence verified.
Continuum absorption measurements in both hydrogen and nitrogen plasmas are described, which show that previously accepted theoretical values of the continuum opacity in such plasmas may be an order of magnitude too low.
Finally the possibility is discussed of using long path absorption spectroscopy for the first time in the measurement of transition probabilities of electric-dipole forbidden lines (of astrophysical interest) within the ground configurations of light ions.
An attempt to measure such a line has shown that the density bounces, observed during the diagnostic measurements, must be eliminated if the full sensitivity, offered by the available long paths, is to be realised. Simple changes to the plasma device, to be made within the near future, should eliminate these problems, and the measurement of the electric dipole forbidden lines should then be feasible.
1 .2 The Use of Plasmas in Experimental Atomic Physics
At any one time, one method of performing new and interesting physics is to use methods, or achieve conditions,that have not been previously obtainable (such as recent interest in V.U.V. and X-ray lasers). Plasma sources have therefore been of great interest in experimental atomic physics for many years for two reasons.
Firstly, there is a great need to measure well understood atomic processes in plasmas in order both to understand the plasma state itself (e.g. emission studies of hydrogenic line profiles) and also to diagnose plasma conditions in new plasmas (e.g. Thomson scattering as a temperature diagnostic).
Secondly, plasmas can provide species or conditions that are otherwise unobtainable in the laboratory. For instance, plasma conditions can now be regularly generated that accurately reproduce those conditions found in stellar interiors, thus allowing the theoretical background to the analysis of stellar spectra to be checked experimentally. In the work described in this thesis, a plasma device was used to provide both ions, and also atomic species with measurable populations within their excited states.
The use of plasmas for such purposes is not without problems however. Firstly, most plasma devices are pulsed, unlike many alternative atomic sources, and the rate of data aquisition is therefore poor. Secondly, the short plasma lifetimes can increase the effects of some experimental problems, an example being the low signal to noise ratios obtainable with plasma emission measurements.
Thirdly, the free electrons and high temperatures of plasmas introduce 16
further problems. High collision rates mean that many atomic
properties change sufficiently fast that they cannot be measured.
For instance, Burgess (1) shows that, for a hydrogen plasma of 15 -3 10 electrons cm at 10,000K, the high frequency of dephasing 11 -1 collisions (^10 s ) means that very high laser powers will be
required if coherent laser experiments are to be performed in
plasmas. In addition the time for a given perturber configuration
to change nsec.) is smaller, or comparable to, the level
de-excitation time for typical transition (1-800 nsec.) and so it
is impossible to selectively pump one perturber configuration by
pumping at a selected wavelength in the wing of a line profile.
Finally, the use of velocity-selective techniques, such as saturation
spectroscopy (as used by Hansh, Shahin and Schawlow (2)), is limited 5 -1
due to the high frequency of velocity-changing collisions (^5 x 10 s ).
The final problem with the use of plasmas in atomic physics
is that absorption measurements are severely limited by the low
optical depths of atomic transitions in typical plasmas. This is
further discussed in section 1.4.
1.3 The Theoretical Background to Spectral Measurement in Plasma Sources
Since this present research is concerned with experimental
measurements of atomic parameters and lineshapes, then the theor-
etical background discussed here will be restricted to atomic
physics and line broadening theory.
1.3.1 Atomic Physics
Spectroscopic techniques play a vital role in atomic
physics since:
(a) many atomic species can only be observed and measured spectrally, and (b) the accuracy of spectroscopic measurements often
surpasses that of all alternative techniques.
Both the theoretical and experimental branches of atomic
physics have undergone great changes in the last two decades.
For the experimental atomic physicists, the introduction of lasers
has greatly extended the range of feasible experiments. Research
topics of interest at the present time include:
(i) The use of recently developed laser systems for measure-
ments in the U.V. spectral region (and the development of lasers
capable of extending the range of available wavelengths into the
V.U.V. and X-ray spectral regions).
(ii) The use of highly stable lasers, of bandwidths less 13 than 1 kHz (corresponding to a resolution of 1 part in 10 ), for
very precise measurements of energy levels and their shifts.
(iii) The use of short laser pulses (of less than 20 psec
duration) in order to measure very fast atomic processes.
In addition, experiments not involving lasers, such as
photoelectron spectroscopy and those using synchrotron radiation
sources, have also made great progress in recent years.
Similarly theoretical atomic physics has been greatly
enhanced by the development of modern computers, both in the range and the accuracy of possible calculations. Atomic structure computations have now reached a highly sophisticated state, and, in many cases, such calculations have achieved superior accuracy to existing experimental data (an example is the theoretical work on forbidden line transition probabilities discussed in Chapter 9).
At the present time, the inclusion of configuration interaction and atomic level mixing in such calculations is thought to be well understood, but the introduction of many body theory to account for the effects of correlations still poses many problems.
1.3.2 Line Broadening Theory
The particular branch of atomic physics of relevance to
much of the work discussed in this thesis is the calculation and measurement of spectral lineshapes. Such profiles are of crucial
importance in atomic physics since they act as highly sensitive
probes of the environment surrounding the atom, and therefore form
the basis of many diagnostic techniques, especially when other forms of measurement, such as probes^are unusable. Over the last
two decades there has been a great increase in the extent and precision of theoretical line broadening calculations, extending to the model-microfield and ion-dynamic theories of Seidel (3) and
Lee (4). Such theories are of quantum mechanical nature and do not include classical approximations, such as the classical path and adiabatic approximations.
Experimental measurement of such profiles has not been so rapid, since many line profiles have proved difficult to measure
(as discussed later). Examples of measurements that have been made are: the observation of the dip in the line centre of Hytf by Burgess and Mahon (5); the measurement of assymetries in spectral lines, such as the Hyg measurement of Chotin et al. (6); and the accurate measurement of hydrogenic line profiles in the regions where neither impact nor quasi-static broadening will apply, such as by Grutzmacher and Wende (7), for comparison with unified broadening theories of
Vidal, Cooper and Smith (8) and Seidel (3).
1.3.3 Weak features in Spectral Line Broadening Processes
The majority of existing line broadening measurements have, for reasons discussed later, largely been confined to the central regions of line profiles of relatively intense emission lines. The aim of the research presented in this thesis is to use absorption
spectroscopy to extend the range of such measurements to include
much weaker spectral features, many of which may become strong under
different conditions.
Weak features are defined, for the present purposes, as
-2 -1
those resulting in absorption coefficients of less than 10 m ,
which can therefore only be measured, in absorption, by obtaining
path lengths of several metres or more. Such weak features include
forbidden lines arising from the breakdown of selection rules;
continua which provide the background plasma absorption; and the
general shape and structure of the far wings of spectral lines.
The study of such weak features is useful since it provides
information concerning the mixing of atomic levels, the effects of
correlations on atomic processes, and the effects of weak interactions
between an atom and its environment. In addition, such weak features
may not remain weak for all envisagable conditions - for instance
the forbidden lines discussed in Chapter 9 are very weak spectral
features in the laboratory plasmas of interest in this research, but are dominant emission lines in many spectra from low density 6 —3 ( NgOO cm ) astrophysical sources. Weak features of interest
include quantum mechanical interference effects, plasma polarization
effects, quasi-molecular satellites, plasma satellites, forbidden
lines and continua. The first two of these are not discussed here since they apply for plasmas whose densities are beyond the range of
those used in the experiments described later. The remaining topics are now discussed in more detail.
1.3.3.1 Quasi-Molecular Satellites
Stewart et al. (9) first proposed in 1973 that quasi- molecular satellites might be visible in the far wings of spectral lines. Preston (10) observed these satellites in the far wing of Lyman-alpha in a hydrogen/argon plasma, and Baker and Burgess (11) have performed such measurements at higher densities. The satellites occur due to. the perturbation of the atomic energy levels during the formation of a quasi (unbound) molecule between the emitter and a positive ion. The effect of the perturbing ion on the atomic energy level can be such that minima occur in transition energy level spacings as a function of the distance between the atom and the ion. The result is an enhancement of the line profile at that particular energy level spacing, and a satellite is therefore observed in the wing of the profile. There is a shortage of both theoretical and experimental data for such satellites and further experimental measurement should be possible using long path absorption spectro- scopy, providing that satellite absorption coefficients of more
—6 — 1 than 10 m can be achieved (corresponding to electron densities 16 3 of more than >10 cm" for Htf , as shown in Chapter 8).
1.3.3.2 Plasma Satellites
Satellites are present in the linewings of certain allowed lines containing forbidden components. These satellites arise where the forbidden transition becomes allowed, at a detuning + fiC0pfrom line centre, due to coupling between the radiation field and a plasmon of unit angular momentum and an energy tlU)p(as first predicted by Baranger and Mozer (12)). Similarly satellites occur at detunings of + 2Tl(j0pfrom allowed line centres due to the coupling of two plasmons with the radiation field (as described by Burgess (13)).*
The experimental observation of such satellites has proved difficult. Hildenbrandt and Kunze (14) have used laser-induced fluorescence to observe satellites near the forbidden component of o 14 • the Hel 4471A line in a plasma of electron density of 0.8 - 1.2 x 10 cm and Nee and Griem (15) have observed the + 2?Kji) satellites close to infra-red hydrogen transitions in a highly turbulent plasma.
Drawin (16) and Piel (17) have both discussed the possible confusion between such observed plasma satellites and possible molecular transitions present in the wings of atomic lines. A major problem in identifying the origin of an observed satellite is that existing measurements have been made in emission, with consequent poor signal to noise ratios. The technique discussed in this thesis should provide a far more accurate measurement of such satellites, and theoretical calculations (D. Spirit (private communication)) have shown that the satellites close to Hel lines should have absorption
-6 -1 lMt coefficients of more than 10~ m" , and will thus be measurable.
1.3.3.3 Forbidden Lines
There has been much interest in electric-dipole forbidden lines induced by the quadratic Stark mixing of atomic levels by the plasma electric field. An example is the measurement of Burgess and Cairns (18) of the Hel 4471A 2 P - 4 D allowed transition with 3 3 its 2 P - 4 F satellite, which confirmed the necessity for the inclusion of non-adiabatic ion dynamic broadening in the calculation of such lineshapes, as first predicted by Burgess (19) in 1970.
Such forbidden lines are of interest since they can be used for spectral diagnostic measurements of both laser-produced plasmas (such as performed in Ar XVII by Kikenny et al. (20)) and also 0 and B type stars (an example being Snijders and Underhill (21)).
Theoretical calculations for such lines include Barnard, Cooper and
Smith (22), and Mazure, Goldbach and Nollez (23). The former reference agrees well (^5%) with existing experimental results, but the latter paper agrees to only 20% accuracy, thus indicating that the model microfield method used by the authors was incorrect.
Given the increased accuracy and sensitivity of absorption spectro- scopy over long path lengths, it will be useful to measure such 22
forbidden lines, since the disagreement between existing theories is less than the accuracy of the existing experimental results.
Further electric-dipole forbidden lines, including those used in astrophysical diagnostic measurements, are described in detail in Chapter 9.
1.3.3.4 Continuum Absorption
One weak feature, of special interest to astrophysicists, is the value of the plasma continuum opacity as a function of plasma conditions. Such opacities are of considerable importance in the calculation of conditions within stellar objects, and the existing theoretical background to such absorption is supposedly well under- stood. Calculations for hydrogenic species (e.g. Menzel and Perkins
(24)) have been performed analytically, and those for non-hydrogenic species have been calculated using quantum defect theory (Peach (25)).
Existing experimental measurements have used emission spectroscopy, which, for reasons discussed later, leads to poor accuracy. The high accuracy and sensitivity of absorption spectroscopy over long paths will provide a more accurate measurement of continuum absorption coefficients, and results (which disagree significantly with existing theories) are given in Chapters 8 and 9.
1.4 Techniques for Lineshape Measurement
As previously discussed, many modern non-linear laser spectroscopic techniques, otherwise widely used in atomic physics research, cannot be used in typical plasmas due to the high collision rates. The remaining choice is between emission and absorption measurements.
1.4.1 • Emission Spectroscopy
For reasons that will become clear in Chapter 2, most lineshape measurements in plasmas have been made using emission measurements. The problems with this technique are (a) poor signal to noise for the measurement of weak features and (b) poor resolution.
(1) As an example consider a transverse emission measure- ment on the 17 cm diameter plasma column used for absorption measurements described in later chapters. Using a monochromator with a slit of 1 cm height imaged, using an f/10 lens, into the centre —6 3 of the plasma, then the volume of plasma observed is 7.2 x 10 m . It is shown in Chapter 8 that a typical hydrogen plasma of interest in this thesis has a number density of atoms in the n=3 level of 16 —3 6 x 10 m~ , and the total number of atoms in this level under 11 observation is therefore 4.3 x 10 .
The number of Hd transitions occuring in the volume per unit time is therefore -J D JL
= 8.7 x 1018s"1
These photons however are emitted into 471 steradians, and the number 14-1 emitted into the detection solid angle is therefore 1.1 x 10 s . Since He* has a linewidth of 2A (for the plasma conditions given above), and since a typical monochromator resolution is 0.1 A, then 12 approximately 5 x 10 photons reach the detector per second.
Assuming efficiencies for the optical system and the photo- multiplier of 60% and 5% respectively, the number of photoelectrons produced in the 0.5 JJS signal integration time (used in the absorption experiments described later) will be 7.5 x 10 . The line centre of the profile can therefore be measured to an accuracy due to shot noise of~0.4%. Using the Ho< profile described in Chapter 8, the estimated shot noise for a detuning of 6A (2.7 FWHM linewidths) is
9%, that for a detuning of 10A (4.5 FWHM linewidths) is 23%, and that for the theoretically predicted continuum (Chapter 8) is
80%. These figures confirm the conclusion given earlier, that
emission spectroscopy can be used for accurate measurement of the
central regions of allowed (strong) lines. When measurement is
required of weak spectral features, however, the accuracy obtained is
far worse. The Nil forbidden line of interest in Chapter 9 has a
transition probability of 1.1 s , an upper level population of
x 101 7 m 1 (at 10,000 K and 101 S electrons cm 1 ), and a linewidth of ~0.lA, and hence 8 D 1-09x10 m" Av -3 ,
This is 2 x 10 % of the equivalent value for the H o4 transition just calculated, and the number of photoelectrons that would be detected in
an emission measurement of the Nil forbidden line would therefore only be ^ 2 per us.
(2) The second major problem with emission measurements -4» is that of resolution. Although resolution as high as 10 A can be achieved, the signal levels obtained decrease linearly with increasing
-1 -2«
resolution, and a resolution of 10 to 10 A is typical if emission measurements of high (better than 10%) accuracy are required.
1.4.2 Absorption Spectroscopy
The alternative technique of absorption spectroscopy does not suffer from these problems. With the use of a laser as the required background source, shot noise can be negligible. The laser used in experiments described later produces v3 x 10 11 photons per -4» microsecond into a bandwidth of only 10 A. Assuming that the opacity being measured is approximately unity and that the combined optical and detection efficiency is 20% (as used later), then the number of photoelectrons detected in 0.5 us is 10 10 , resulting in a negligible 25
shot noise of ^10 _3 %. Obviously the optical depth may be sufficiently
high (10 or more) that shot noise could become important, but in
the experiments described later the optical depth is always less
than 3, and in any case can be reduced by reducing the optical path. -4,
The CW laser used has a bandwidth of less than 10 A, and
this is therefore the experimental resolution. It should be noted
that for laser absorption spectroscopy, both resolution and shot noise
are independent of the transition measured (provided T < 10) and
that weak spectral features can therefore be measured accurately,
unlike in emission spectroscopy.
The use of absorption spectroscopy has one problem, however, which has greatly limited its use in plasma spectroscopy. The equation
relating the optical depth and the percentage transmission is given in _3
Chapter 2, and shows that X must lie between 10 and 7 to be observ- able, if the limits in measurable transmission are 0.1% and 99.9%. It will be shown in Chapter 2 that absorption coefficients in plasmas —6 —1 are low (1-10 m~ ), due to low level population values and high transition linewidths, and long paths (0.5 - 108 metres) will therefore be required if such transitions are to be measurable.
Providing that these path lengths can be obtained, then laser absorption spectroscopy offers far higher resolution and signal to noise than the alternative of emission spectroscopy. The achievement of the required long paths is described in the following three chapters, and forms the main technical achievement of this thesis. CHAPTER 1
LASER ABSORPTION IN PLASMAS
2.1 The Theory of Absorption
In this chapter the main considerations in the application
of absorption spectroscopy in the visible spectral region to a plasma
source will be discussed. The starting point for such a discussion
must be the derivation of absorption coefficients..for likely trans-
itions, as a function of plasma parameters that are known,or can be
estimated.
For light of power Ie incident upon a medium of absorption
coefficient k , the transmitted power , after a length I is
given by T I,1 =1.f e" where X (the optical depth) * kdl
Mihalas (26) shows that the absorption coefficient for a transition
between a lower level j and upper level j , including absorption and stimulated emission, is given by
k = is* Nj$(v)Bjj -NjWv) Bjj 4tt where V is the transition frequency, R- and R« are the relevant IJ }\
Einstein B coefficients (defined in intensity units), Nj and Nj are the two level populations and 0(V) and W(V)are the normalized absorption and emission line shapes (for a laser bandwidth much smaller than the transition linewidth). For the cases considered later, it is valid to assume that the two lineshape factors are identical and Wv) is therefore replaced by
From Thorne (27) the Einstein B coefficients can be related to the transition Einstein A value where
which, when substituted into the expression for k., produces
The absorption coefficient for a given transition therefore depends on three quantities - the normalized lineshape function, the trans- ition probability and the level population densities. A measurement or theoretical calculation of the line profile and either of the other two quantities will therefore allow the third quantity to be obtained from absorption measurements. As an example, the population densities and lineshape function are related to measurable plasma parameters for the proposed Nil forbidden line measurement, as discussed in Chapter 9, thus allowing the transition probability to be measured for the first time.
2.2 An Estimation of Likely Absorption Coefficients of Interest
2.2.1 Conditions in Existing Plasma Sources
At present there exist a large variety of laboratory plasma 3 8 sources providing temperatures that range from 10 to 10 K and 7 25 -3 electron densities of 10 to 10 cm . The range of plasma conditions available for the individual plasma devices can be seen in Burgess (1) and, in order to estimate the possibility of performing absorption measurements in such plasmas, several of these plasma sources have been chosen as examples. (i) The tokamak, in which the plasma is heated using ohmic and neutral injection heating,and confined using a combination of toroidal and poloidal magnetic fields, has been of much interest in recent years as the basis for a possible fusion reactor.
Temperatures and electron densities have been achieved in tokamaks ranging from 106 - 108K and 1013 - 101Acm~3 respectively and, . for the purposes of a rough calculation of likely absorption co- efficients in such devices, a temperature of A x 108K, an electron 13 -3 density of 2.7 x 10 cm , and a neutral hydrogen density of 1.A x 9 -3
10 cm will be assumed (as described for the DITE Tokamak at Culham
Laboratory by Koopman et al. (28)).
(ii) D.C. Arcs, in which a plasma is continuously maintained in a stabilized discharge between two electrodes, achieve conditions of 5,000 T < 50,000K and 101A < N- < 1018cm"3 within plasmas of typical dimensions 0.1 - 5 m.m. For this calculation, the conditions achieved by Boldt (29), who obtained a temperature of 10 K, an electron density of 3 x 10 16 cm —3 and a neutral density of 6 x 10 17 cm—" 3 , will be assumed.
(iii) The recombination z-pinch used by the author produces temperatures ranging from 3,000K - 20,000K and electron densities 13 15-3 15 ranging from 10 - 2 x 10 cm with neutral densities of 5 x 10 16 3 5 - A x 10 cm" . The plasma is produced in a high current (~10 A) pulsed discharge which collapses (pinches) due to the interaction between the current and its own magnetic field. This compression produces rapid heating resulting in high temperatures and ionization of the filling gas. The resultant plasma expands as the current flow ceases, quickly filling the entire plasma vessel, and recomb- ination commences. It will be shown in Chapter 6 that the equilibri- ation times in such plasmas are sufficiently fast that within 30 us of the current pulse the plasma should be uniform throughout its entire volume. For the purposes of the calculation a temperature of 4 15-3 16-3 10 K, electron density 10 cm and atomic densities of 2.8 x 10 cm 15 -3 for hydrogen and 9.6 x 10 cm for nitrogen will be assumed.
2.2.2 Spectral Properties Required
To calculate an absorption coefficient using the equation derived in section 2.1, the transition probability, lineshape and atomic level populations are required. (i) For allowed visible transitions the transition probab- 6 8—1 ilities are typically 10 -10 s~ , but much smaller values arise for forbidden transitions, such as the Nil forbidden transition discussed in Chapter 9 which has a transition probability of only 1.1 s
The A-values used in the calculation are those given by Wiese, Smith and Glennon (30).
(ii) It will be shown in Chapter 9, that the normalized line shape factor at a transition line centre approximately equals the inverse of the HWHM linewidth (in frequency units). Such linewidths may be due to Doppler broadening and are obtained from figure 2, or alternatively are due to Stark broadening and are obtained from
Griem (31).
(iii) Of the required transition parameters, the level pop- ulations are the hardest to estimate, since they may deviate sign- ificantly from their LTE values. For the purposes of this calculation it will be assumed that for all cases considered the hydrogen n=1 level population equals the total hydrogen density. The n=2 level population values are then given by: assuming LTE for the D.C. arc; 11 -3 using the measured value of 5 x 10 cm (at 10,000K, as shown in Chapter 8) for the ten metre device; and using the value of 2 x 6 —3 10 cm" listed by Koopman et al. (28) for the DITE Tokamak (for the conditions listed earlier). BO
2.2.3 Results
Using the equation derived in section 2.1, the results obtained
for hydrogen line-centre absorption coefficients for allowed trans-
itions in the plasma sources discussed in the previous section are
shown in table 2.1 From the table it can be seen that the absorpt-
ion coefficients in the visible spectral region are sufficiently low
that over typical plasma lengths of a few centimetres for a D.C.
arc and a few metres for a Tokamak or z-pinch, the line centre opacity
will only be approximately unity. For weak transitions the absorption
coefficients will obviously be far lower. Table 2.2 contains the
absorption coefficients measured or estimated for the plasma source
used by the author (the ten metre plasma device) for several weak
transitions of interest. The values for the hydrogen continuum and
the He 5876A intercombination line are quoted from experimental
results presented in Chapters 7 and 8; the value predicted for the
Nil forbidden line is derived in Chapter 9; and that for the He 5876A
plasmon satellite was supplied by D. Spirit (private communication).
2 6" Table 2.2 shows that absorption path lengths of 10 - 10 metres will _3
be required for measurable optical depths (10 - 10) to be observable
for such weak transitions. Obviously such lengths are far greater _3
than the dimensions of laboratory plasmas (typically 10 - 10 metres),
and single-pass absorption measurements cannot therefore detect such
absorption. A multipassing design will be presented in Chapter 5,
however, that lengthens the available absorption length in a plasma
column by a factor of 120 (to over 1 km), and such measurements
therefore become feasible for the first time. For the allowed
transitions, this multiple passing design will allow the line profiles
to be'measured far into the line wing, an example being the He 5876A
profile, described in Chapter 7, which is measured out to a detuning of 50 linewidths. Table 2.1 Allowed hydrogen line-centre absorption coefficients
Plasma Conditions Absorption Coefficients (m )
_3 T(K) N (cm"3) H ex.(6562A) e N^ (cm ) HA (A861 A) Ly* (1215A) 13 Tokamak A x 106 9 6 6 A J 1.A x 10 9 x 10" 6.5 x 10~ A.2 x 10" 2.7 x 10 1 7 10* 2 6 Arc 16 1 x 10 12.7 3 x 10 3 x 10 6 x 10 5 10* z-pinch 15 6.1 0.6 10^ 10 2.8 x 1016
Table 2.2 Typical Absorption Coefficients for Weak Transitions of Interest in Recombining z-pinch plasmas
Transition Plasma Absorption ^ P(Torr) T(K) N (cm 3) Coefficient (m~ ) e
3 1 HeI5876A 2 P - 3 D 0.A5 6,000 2 x 1013 10-5
6 HeI5876A plasmon satellite 0.A5 6,000 2 x 1013 3 x 10~
H continuum at X = 6500A 0.A5 10,000 1015 10-3 -5 3 1 1 3 Nil 575AA 2p s - D 0.15 10,000 1015 10 32
2.3 Plasmas Available for Long Path Absorption Measurements
The need for kilometre path lengths imposes severe restrict- ions upon the plasma sources usable for these measurements. Arcs and vaccum spark plasmas have dimensions of less than 5 centimetres and, even with multiple passing, cannot supply the required path lengths.
Tokamaks may be sufficiently large, but table 2.1 shows that their low densities result in low absorption coefficients, even for resonance transitions. An important condition for the use of long absorption paths (discussed in section 2.5.3) is that any turbulence or density gradients present within the plasma must be low enough that the resultant refractive index gradients will not deviate the beam path sufficiently to prevent the multipassing cell from functioning.
Pinch sources used during their current phase and shock tubes are therefore unlikely to be usable. It will be shown in Chapter 3 that z-pinches can be built with column lengths of up to 10 metres and such plasmas should be sufficiently uniform during their recombination phase to allow long paths of 1-2 kilometres to be used. This combination of long plasma length and uniformity makes the recombining z-pinch the optimum source for plasma absorption measurements of weak transitions and, for the purposes of this chapter, a preview of the plasma parameters available with the z-pinch used by the author is presented in table 2.3.
Table 2.3 Summary of the Parametres of the Ten Metre Plasma Device
Length 10.84 metres (single pass) 3 1.2 x 10 metres (multiple pass) Diameter 17 cm Neutral Densities 9 x 1015 - 3 x 1016cm"3 Temperatures 3,000 - 15,000 K Electron Densities 1013 - 2 x 1015 cm"3 33
2.4 The Laser as a Background Source for Absorption Measurements
Lasers are used for three main reasons in plasma spectroscopy:
(i) the generation of plasmas, such as in the laser compres- sion experiments at the Rutherford laboratory and elsewhere.
(ii) the perturbation of plasmas in known ways, such as used by Burgess and Skinner (32) to measure electron collision rates using laser-induced fluorescence.
(iii) the probing of plasmas to measure atomic or plasma properties without perturbing the plasma conditions. Both the laser diagnostic and absorption results presented later belong in this final category.
Lasers have several advantages for the purpose of absorption spectroscopy:
(i) power - within the 0.5 us integration time used in the 8 experiments described later, lasers produce light levels of 10 - 14 10 photons. Shot noise in absorption measurements will therefore _3 be 10 % or less,and hence is negligible.
(ii) tunability - for line profile studies it is necessary to tune the laser throughout the profile, and hence dye lasers are used. Such measurements are therefore restricted to the available dye wavelength range of 3300A - 9000A.
(iii) bandwidth - it was mentioned in Chapter 1 that a low laser bandwidth will allow high resolution measurements to be made of spectral features that are narrower than the resolution of the detection system. It is shown in section 2.5.6 that typical line- widths are 50 mA or more and so a laser of bandwidth less than 10 mA is required.
(iv) divergence - in order to successfully align the multi- passing system discussed in Chapter 5 it is necessary to use lasers 34
of divergence of less than 2-3 mrad.
In all these respects laser sources are far superior to alternative background sources (such as arcs) for plasma absorption measurements. There are two laser systems most likely to provide the required wavelength resolution. Firstly, the pulsed laser system described in Burgess (1), which produces typically 30-50 kW in a
5-10 nsec pulse with a bandwidth of 5 mA. Alternatively a CW ring dye laser (such as the Spectra Physics 380A laser described in
Chapter 5) produces 20-500 mW continuously, with a bandwidth of less than 5 MHz (0.05 mA at the peak of Rhodamine 6G dye). Of these two, the CW laser was chosen since it is both simpler to align within the multipassing system, and also records data throughout the entire recombination phase (200 us), unlike the pulsed laser which measures data over a time of 5 ns per shot only. The main advantage of the pulsed laser - high power - is immaterial since the shot-noise obtained using the CW laser is negligible. The CW laser is described in detail in Chapter 5,but its properties of relevance to the discussion of the plasma device and multipassing system are given in table 2.4.
Table 2.4 Summary of 380A CW Dye Laser Parameters
Power 20 - 500 mW
No. of photons per microsecond 3 x 1011 (at 5876A and 100 mW)
Bandwidth <0.05 mA
Wavelength setting accuracy mA at present
Divergence 1.2 mrad 35
2.5 Practical Limits for Absorption Spectroscopy over Long Path Lengths in Plasmas
2.5.1 Limits set by the Time of Flight of the Laser
The ultimate limit for the maximum usable path length is set by the time of flight for the laser beam, which should not be longer than the time taken for plasma conditions to change appreciably.
The diagnostic results presented in Chapter 6 show that conditions during the plasma recombination phase change significantly (10%) over a timescale of 5-20 us, which corresponds to a path length of 1.5 -
6 kilometres. These path lengths are therefore the maximum usable with the present device. If further lengths are required than a slower decaying plasma must be used.
2.5.2 Limits set by Atomic Saturation
One limit on the laser power usable for such an absorption measurement is set by the possibility of saturating the atomic transition under observation. Burgess (1) quotes the laser power required for saturation (at the transition line centre) to be given by 8rchv Av r+A P- > . A . where A is the transition probability, is the upper state decay rate to the lower level (by all routes except stimulated emission) and Av is the transition homogeneous linewidth (for laser bandwidth less than AV ). For allowed transitions in the visible spectral 7 -1 region (with A~ 5x10 s ) in a plasma of electron density of approximately 1014- cm 3 (and hence ZW~0.A 1 GHz and Ir— ^1 0 9-s 1 ) the saturation power given by the above equation lies in the range 3 2 2 1-10 W/cm . For laser powers producing more than 0.5 W/cm into a bandwidth of less than 0.1 GHz,saturation may therefore occur, depending on plasma conditions (through T and Av ) and the laser
wavelength. Such powers are easily obtainable by both pulsed and
CW lasers and this question must be faced for each absorption measure- ment required.
If the absorption measurement is to be used to measure a
transition probability or a spectral lineshape,then the laser
power used must be significantly lower (< 10% say) than the power
required to saturate. The optimum accuracy will be obtained with
the laser power as close as possible to this limiting power, since
the errors due to plasma emission shot noise will then be mini- mized.
If the only intention is to observe a spectral feature above
the background absorption then the optimum accuracy obtainable is gained by using laser powers greater than the power to saturate,
as shown in Appendix A, where a laser power of an order of magnitude
larger than P^ is shown to be required to obtain close to the maximum accuracy possible.
2.5.3 Limits set by Laser Path Bending
One possible problem in achieving long (kilometre) path
lengths in pulsed plasma sources will occur if density gradients are present. The resultant refractive index gradients will bend the path of the laser beam, and, if the bending is sufficiently large, the laser will fail to reach the detector. An example is given in section 9.10
—6 — 1 and shows that a value for dn/dr of 1.47 x 10~ m results in a beam deflection of 0.18 m.m. over a path length of ~10 metres. This effect should be no problem in the recombining plasmas used for the absorpt- ion measurements described later, since these plasmas are presumed to be uniform (a point that will be further discussed in Chapters 6 and 9).
2.5.4 Limits set by Continuum Absorption
For a given absorption path length the limit in allowable 37
electron density in the plasma is given by the condition that
the free-free continuum must be optically thin at the laser wave- length (assuming that at high electron densities all other contrib- utions to the continuum opacity are small). The expression for the
free-free absorption coefficient is discussed in Chapter 8, and the
resultant expression for a hydrogen plasma at 10,000K and measured at 6000A is
1 48 kff(m ) = 3x10~ Ne(m3)
This is plotted in figure 1, and the electron densities required
to produce unit optical depth in the ten metre device over path
lengths of 1 kilometre (multiple passed), 10.84 metres (single pass)
and 17 cm (single transverse pass) are indicated. These show that
for long path absorption spectroscopy using optical path lengths of 16 3 1-2 kilometres, the limit in allowable electron density is~10 cm
2.5.5 Limits set by Noise Levels The shot noise that provides the limit for emission
experiments has been shown in section 1.4.2 to be negligible _3
(<10 %) for the laser used in the absorption experiments described
later. The limiting signal/noise ratio is therefore set by alternative
contributions to the noise: (i) Experimental limitations (discussed in Chapter 5) due
to laser stability and with airborne dust provide the present limits
to obtainable path lengths and also the major source of error (5-30%) -5. -1
for the weakest absorption coefficients measured ( |{/v7 x 10 m ).
(ii) Plasma emission is mostly filtered by the etalon detection
system described in Chapter 4, nevertheless there is still a remaining
emission signal requiring subtraction from the transmitted laser signal.
The problem here is the 20-30% shot noise of this emission signal - the Figure 1-Continuum Absorption in a Hydrogen Plasma (at 10000K) due to Free-Free Transitions at a wavelength of 6000 A.
Temperature 39
noise value being typically 0 - 3 mV in an emission signal
of 0 - 10 mV, compared to a transmitted laser signal of 20 - 500 mV.
The resultant noise on the detected trace is hence 15% at the lowest
laser signals,and drops to less than 1% at the highest powers - a
considerable increase in accuracy than for emission measurements.
This situation will improve further, when a planned 18 W Argon Ion
laser is used to pump the dye, thus allowing higher CW laser powers
to be obtained.
(iii) The digitizer recording system described in Chapter 5 is
prone to problems with excessive electrical pick-up whilst it is
recording. To prevent this, measurements are taken no earlier than
50 us after peak current, where the pick-up is negligible.
It should be noted that,given the wide range of optical paths
available using the multiple-pass system, it is possible to perform
measurements at an optimum path length for each point in the profile
and this is discussed in detail in Appendix A and Chapter 5.
2.5.6 Limits set by Transition Linewidths
It was stated in section 1.4 that the use of a laser back-
ground source of resolution < 5 mA is sufficient to resolve all line
profiles of interest. Assuming that the minimum width of any trans-
ition must be the Doppler width, then a FWHM linewidth is given by
Thorne (27) to be AX = 7-2x10"7Xy^ where T is the temperature and M the mass number. This is plotted
in figure 2, for the species used by the-author, from which it can
be seen that the present resolution of 5 mA is sufficient (< 10% of
transition FWHM) for temperatures of more than 2,000 K. 2.6 Conclusions
Several important conclusions have been reached in this chapter:
(1) Calculations show that absorption coefficients of —6 —1 interest are very low in plasmas (10" -1 m" ) and path lengths of a kilometre or more will be required if measurable optical depths _3
(10 - 10) are to be achieved. These low absorption coefficients arise since visible absorption lines not only occur between excited states, of low population, but also.have high linewidths.
(2) To obtain such long path lengths the plasma used must be uniform which greatly limits the plasma sources usable for such measurements.
(3) The use of a CW ring dye laser as the background source -3 means that shot noise will be negligible ('-10 %) and that the laser bandwidth (10 AA) will be much smaller than typical transition line- widths (0.1 A or more).
(4) Several limits may exist for the laser powers, path lengths and plasma conditions with which long path measurements can be performed. None of these limits however should prevent measure- ments over 1 km paths using the ten metre z-pinch .and 380 ring laser, whose properties are summarized in tables 2.3 and 2.4 respectively. 41
CHAPTER 4
THE TEN METRE PLASMA DEVICE AND PREVIOUS LONG PATH WORK
3.1 Introduction
As outlined in the previous chapters, the object of this work is to measure very weak absorption over long optical paths within a plasma. The range of plasma sources usable for such measurements has already been shown to be severely limited and so the plasma used by the author, produced by a high current capacitor discharge and described in detail in this chapter, is observed after the completion of the discharge when the resultant plasma should be 2 3 sufficiently uniform to allow optical paths of 10 - 10 metres to be used.
3.2 Design
The Ten Metre Plasma Device was designed and built in
1975 by D.D. Burgess and M. Eckart. The plasma is produced in ten one-metre z-pinch modules, as shown in plate 2. Each module consists of a central electrode with two outer electrodes with the plasma contained inside cylindrical pyrex walls of length 1.01 metres and internal diameter 17 cm. Current return bars are fitted out- side the plasma vessel walls, thus providing a low inductance cylindrically symmetric discharge, which is critically damped by a series of 0.75ft(+10%) high current resistors (manufactured by
Allen and Bradley Ltd.). The plasmas produced in the ten one- metre discharges should all be identical, .since if any one section provides a lower impedance than the rest (and hence draws more current), the extra current will cause faster collapse 42
in that section, the inductance will rise, and the current will
therefore drop down to the value in the other sections. Experiment- ally it has been shown by C.St.Q. Playford (private communication)
that the uniformity of plasma conditions in the ten sections is better than 5% at a time of 30us after the peak current.
The five two-metre sections (built 1 end-to-end') produce a total pinch length of 10.45 metres with plane end-windows, and
10.84 metres with the Brewster end-windows used for the long path absorption experiments. This design provides as long a plasma column as is feasible in this laboratory, and to extend the optical paths available to even longer lengths, the plasma device has been constructed with a 7 cm. aperture. This allows the optical system described in Chapter 5 to be used to multipass the plasma spatially up to 120 times (thus generating a kilometre path length).
One problem for absorption measurements in plasmas is the effect of any cold boundary layers close to the plasma vessel walls.
In this plasma device the absorption is measured within the central
7 cm. of the 17 cm. diameter plasma column and the laser will not
therefore pass through the cold boundary layer since Playford
(private communication) has shown not only that the boundary layer extends only 4 cm. in from the wall, but also that the central 7 cm. of the plasma is uniform (to 10% accuracy). The remaining boundary layers are due to possible cold end zones. The holders for the
Brewster end-windows extend the plasma out to 27 cm. beyond the end electrodes and these regions are unlikely to have the same conditions as the rest of the plasma during the initial current pulse. They should reach identical conditions to the rest of the plasma column, however, within several microseconds of the current ending, and it
appears likely that any cold end regions present after that time will 43
only have the same spatial extent as those regions measured
transversely by Playford (i.e. 4 cm. at each end).
The result is therefore two cold boundary layers of total
length 8 'cm. in a 10.84 metre plasma,which is therefore 0.7% of the
absorption length and unlikely to lead to problems for interpretation
of the measured absorption data.
A bank of 180 0.5uF low-inductance capacitors charged to
20 kV is switched through a single spark gap to provide the
discharge, producing a peak current of approximately 200 kilo Amps,
(since the plasma device has a total resistance of 0.074fjand a total
inductance (at the time of maximum compression) of approximately
130nH.) The current is monitored with a Rogowski coilfand the
resultant trace (reproduced in plate 7 ) shows the current to last
for 30us with a risetime (10% - 90%) of 2.5us, and a jitter of '~1us.
The electrical system used to trigger the plasma device
is shown in figure 3. An electrical circuit produces a 20 V trigger
pulse of 20 nsec risetime and negligible jitter and this is used
to trigger a Chelsea Instruments W14 Trigger unit. The 10 kV output
pulse from the W14 unit is boosted to 23 kV using a ferrite-cored 1:5
transformer and the resultant pulse used to trigger the auxiliary
spark gap. This gap discharges a 0.5uF 20 kV low-inductance
capacitor through an air-cored 1:4 transformer built by Kolbe (33 )
which produces the 80 kV pulse required to trigger the main spark
gap. The main capacitor bank is charged in • 17-seconds' to a voltage
of 20 kV, producing a stored energy of 18 kJ; an energy density within 3 the plasma of 18.3 kJ per m ; and an estimated lower limit of the
energy density within the main spark gap of 600 MJ per nP. This main
spark gap provided the most experimental problems during the period
of the present research and is discussed in detail in Chapter 4. 44
Plate 2 -The Ten Metre Plasma Device in Operation
5:1 (Ferrite-Cored)
20 kV JllOkV
:10MQ Main 90uF IL5QF Gap lOMft
Plasma Device :100kfi 0-5uF flOOkft
Figure 3 -The Trigger Circuit for the Ten Metre Plasma Device I
3.3 Previous History of the Ten Metre Plasma Device
The spark gap and capacitor bank used on the ten metre
plasma device were first built for the Maggi I bank at Aldermaston
in 1958, in which all the capacitors were individually switched.
From 1964 onwards the bank was used at Imperial College for
powering a Theta-pinch plasma device, with the Aldermaston switching
design still in use. When it was decided to build the ten metre
device, the Maggi I bank was used, but the multiple gap design was
presumed to be redundant and the master gap from the original
design was used as the single spark gap. The bank itself remains
as used at Aldermaston, but the spark gap has been replaced (see
Chapter 4), the triggering electronics have been rebuilt as described,
and the charging system has also been replaced (by Kolbe (33)).
The basic design of the multiple z-pinch device was
envisaged by D.D. Burgess in 1973 and constructed by M. Eckart who assembled the pinch, re-connected the bank through the single spark gap, and fitted the necessary damping resistors after diagnosing the undamped current oscillations. The second and third experimenters on this pinch were G. Kolbe and C. St. Q. Playford who, together with
D.D. Burgess, performed several diagnostic and absorption measurements of relevance to the work presented in later chapters, and their results are now discussed.
3.3.1 Previous Diagnostic Measurements
The two quantities of diagnostic interest in plasmas are the electron density and temperature. Playford and Kolbe have both measured electron densities for the ten metre device with a
0.45 Torr Hydrogen filling. Kolbe (33) used both a Fabry-Perot interferometric method and an H/3 lineshape measurement to obtain the electron density whilst Playford used a MachZehnder interferometer 15 3 Ne(10 cm ) 4a.0*45Torr Hydrogen Plasma 3? 20-5kV Bank Voltage Diagnosed by Burgess Kolbe and Playford (35)
1-
SO 150 200 25i 0 ToTimo e after Peak Current(us) 15 -3 Np(10 cm ) 4b. 0-5Torr Helium Plasma 3n 20-5 kV Bank Voltage Diagnosed by Playford 2- (private communication)
1-
50 100 150 200 250 Time after Peak Current(us)
Figure 4-(a)and(b)-Previous Electron Density Diagnostic Measurements performed on the Ten Metre Plasma Device. Temperature(K) 4c.0-45Torr Hydrogen Plasma 20000- 20kV Bank Voltage Diagnosed by Burgess Kolbe and Playford(35) 15000-
10000-
5000-
50 100 150 200 Time after Peak Currentlus) Temperature(K) 4d. 0-45 Torr Helium Plasma 200001 ^ 20kV Bank Voltage Diagnosed by Kolbe (private communication) 15000-
10000-
5000-
50 100 150 200 Time after Peak Current(us) Figure 4-(c)and(d)-Previous Temperature Diagnostic Measurements performed on the Ten Metre Plasma Device similar to that described in Chapter 6. The results are shown in
Figure 4. Playford (private communication) also measured the
electron density in a helium plasma of filling pressure 0.5 Torr and
a bank voltage of 20.5 kV, the result also being reproduced in
figure 4.
Kolbe (33) has also diagnosed plasma temperatures in
hydrogen and helium plasmas by measuring the spectral profile of
the Thomson scattered radiation produced during irradiation of the
plasma with a 200MW laser pulse from a Korad 1000 Ruby laser.
This experiment is further discussed in Chapter 6, and the results
obtained by Kolbe are shown in figure 4.
The conclusions of the diagnostic measurements preceeding
the author's work are therefore that the recombining plasmas generated in the ten metre device provide temperatures of
5000 K - 20,000 K and electron densities of 0 - 3 x 1015cm-3, where the electron densities are well diagnosed, reproducible and decrease mono.tonically. However, new diagnostic results obtained by
the author, that disagree with these conclusions, are presented in
Chapter 6.
3.3.2 Previous Absorption Measurements over Long Paths
3.3.2.1 Single Pass Measurements of Kolbe
Kolbe has used the single-pass plasma length of 10.45 metres to measure both the absorption line profile of Hy8 and also to perform a 'double resonance' collision rate measurement. He obtained the H^ profile using a flashlamp-pumped dye cell as a' back- ground absorption source. The transmitted beam was then sampled with a monochromator9 thus resolving the required linewidth of
FWHM 2A with an instrument resolution of 0.1 A. The profile was observed for detunings of up to two linewidths from line centre and compared with the existing theory of Seidel (3). The result was a 10 --20% disagreement in linewidth between that measured and the theoretical width as calculated using the measured electron
density - the profiles were not sufficiently accurate, however,
to be sure that this difference was real and more experiments for
Hp are already planned.
Kolbe and Burgess have also performed a 'double-
resonance' measurement of collision rates in a helium plasma, obtained by pumping the He I 2 P - 4 D 4471A transition with a pulsed dye laser and measuring the resultant changes in lower level population by probing the plasma with a C.W. dye laser tuned to the
He I 23P - 3% 5876 A transition (which shares a common lower level with the pumped transition). The result can be seen in
Burgess, Kolbe, Nightingale and Playford (34) and shows collision rates to be much lower than theoretically predicted.
3.3.2.2 Long Path Measurements of Playford
Using a multiple-pass arrangement discussed in detail in Chapter 5, Playford demonstrated for the first time in this plasma the feasibility of multiple-passing as a method of achieving long plasma absorption path lengths. His arrangement obtained a path of up to 180 metres within the plasma,and it was thought that
200 metres was likely to be the limit for this technique. Using this arrangement Playford performed two experiments, both of which are of importance for the work described in Chapters 7 and 8. 3 3 3.3.2.3 He I 2 P - 3 D 5876A Profile
Burgess and Playford (36) measured an absorption line profile of the He I 5876 A 2^ - 3 % line using a home-built CW dye laser and path lengths of : 10 metres over the majority of the profile, 140 metres for the far wing of the profile, and a 17 cm transverse path for the line centre points. The profiles for both wings for the transition are presented in Burgess, Kolbe and 50
Playford (35) and a more detailed explanation of the blue wing is given in Burgess and Playford (36). It is this blue wing which is of particular interest considering later results and it is reproduced in figure 5, where the profile refers to a time of
200us after the peak current.
1000 t= 200us. P= 0-5Torr V=20 kV
Predicted position 23P-3'D
Extrapolated' Lorentz wing (AA ) \ 01-
001 001 01 1 10 A A lA) Figure 5 - HeI5876A Profile (Blue Wing) published by Burgess and Playford(36)normalised to a path length of 140m.
Several points arise from this result:
1) The line profile is plotted on a log-log scale
and the wing should have a gradient of -2 in the region 0.1 A - lA where the profile is electron impact-broadened. Although the red wing
shows such a gradient, the blue wing certainly does not.
2) One cause of this blue-wing deviation is a feature
in the linewing at about lA- tentatively identified by Playford as the 2 7 P - 31 D intercombination line. Burgess and Playford (36) discuss possible reasons for the existence of this feature and conclude that the most likely reason is, as proposed by Burgess, due to charge exchange interactions.
3) Features can also be seen in both linewings at approximately the plasma frequency from line centre ( 3A) and
Burgess and Playford (36) discuss possible explanations for such structure, but fail to reach a firm conclusion.
These results are very interesting since the long paths have allowed measurements to be made further into the linewing
(40 linewidths), and with far higher precision, than previous
(emission) measurements. If the identification and mechanism for the intercombination line are correct then this measurement provides the first data (either experimental or theoretical) for charge exchange between excited states in He. In addition the anomalous line profile and far wing structure may provide the first evidence that existing line broadening theory may not completely describe line profiles at such high detunings. Numerous improvements to the experimental arrangement, described in Chapter 5, have allowed these results of Burgess and Playford to be considerably extended, and the improved results are presented in Chapter 7.
3.3.2.4 Hydrogen Balmer-Alpha Absorption Measurements
An absorption profile of the hydrogen 2—03 Balmer- alpha transition at 6562 A has been published by Burgess, Kolbe and
Playford ( 35). The original intention of this experiment was to measure this profile in the transition region between impact and quasi-static broadening (4 - 200 A from line centre), for comparison with the unified theories discussed in Chapter 1. Path lengths of up to 180 metres were therefore used for measurements at such J H« *io i 11 i i ii111 i i i 11.iii I I Till1 I I I I I . J c.r - in-'t n-Tf — BLUE WING EQUIVALENT B TIME AFTER FIRING a OPTICAL 'i- 70 MICROSECONOS OEPTH.r FOR n =10,scm'3 100 METRES i "•••t> e PATH *10
— PROFILES BY RW LEE V vi — VCS PROFILES 0 *10 •MOOEL MICROFIELO PROFILE V WITH OOPPLER
ELECTRON DENSITY (all theoriesUTCE 15 cm3 .10 OOPPLER TEMPERATURE (all theories)=14,OOOK ELECTRON TEMPERATURE (all rHEORi£s)s 10.000K
10 ' " ' I I I I I III I 1 I I mi 2 .10' .10" x10° xio «10 o SEPARATION FROM LINE CENTRE A A(A) Figure 6 Fi<* Profile (Blue Wing) published by Burgess Kolbe and Playford (35),showing high background Continuum Absorption in a 0-45 Torr Plasma
T FOR 100» PATH
0 1 2 3 4 5 6 7 fl 9 10 11 12 13 14 15 16 17 18 19 20 21 22 3 f (T„=0-5eVl (Ta=1-5eV) (Ta=1-85eVl NUONm' ) Figure 7 -Measured Continuum Opacity close to Fk* as Function of Electron Density (from Burgess Kolbe and Playford(35)) 53
large detunings. Also of interest was the line centre absorption
coefficient, since ion dynamic effects predicted by Lee (4 ) might prove important, and so measurements were taken transversely
and Abel-inverted to provide the required line centre data.
The blue wing of the absorption profile is shown in
figure 6 which shows a good agreement with the theoretical profiles
for detunings of 0.5 - 5 A from line centre, and there appears to
be little need for further experimentation for those wavelengths.
The line centre results provide an interesting comparison between
the two theories and clearly agree with the predictions of Vidal,
Cooper and Smith ( 8) and not those of Lee (4 ). For this present
thesis it was decided not to perform transverse measurements, but to
concentrate on the far wing of the profile where long paths are
required and where the most interesting questions arising from the
previous experiment apply.
Far into the linewing (15 A onwards) Burgess, Kolbe and
Playford's profile shows a continuum absorption coefficient of -3 -1
5±0.5 x 10 m , for a time of 70us after the peak current, which
is a factor of 50 higher than theoretically predicted (as discussed
in Chapter 8). This anomalous continuum absorption was further
analyzed as a function of time, and hence of electron density, and
the results are shown in figure 7.
It can be clearly seen that the measured anomalous continuum
opacity is linear with respect to electron density, a most suprising
result since the plasma temperature changes by a factor of 4 during
the times observed. Possible mechanisms for continuum absorption at
these wavelengths are discussed in detail in Chapter 8, but should
this observed linear dependence on electron density be true, then
this imposes severe limitations on the mechanisms applicable here. 54
Bound-free absorption (by both neutral hydrogen atoms and negative hydrogen ions ) and molecular absorption qre strongly dependent on plasma temperature; free-free absorption by electrons in the field of neutral hydrogen atoms depends inversely on the square root of the plasma temperature; and the corresponding free-free absorption with positive hydrogen ions depends on both the square of the electron density and also the inverse of the square root of the temperature.
Only absorption by Thomson scattering should be both linear with respect to electron density and independent of temperature, but this is shown in Chapter 8 to be five orders of magnitude too weak to explain Playford's measured continuum. In addition to these problems, the Hot profile measured by Playford contains structure below the continuum, a result which cannot be explained in any obvious manner.
It is crucial that this anomalous hydrogen continuum absorption coefficient is explained since such continuum absorption is important in theoretical radiative transfer calculations of conditions in stellar interiors. Further experimental results, of superior accuracy, are presented in Chapter 8, which show that
the continuum' is smaller than that estimated by Playford, but still far greater than the theoretically predicted value by over an order of magnitude.
3.3.2.5 Hydrogen n = 2 Level Population Measurement
The H«/ and H£ profiles already described have been used by
Burgess, Kolbe and Playford (35) to estimate the hydrogen n=2 level population as a function of electron density,and the result is shown in figure 8, which also includes the predictions of a theoretical calculation of this level population performed by Gohil
(private communication) using collisional radiative theory (and utilizing the measured plasma conditions). The experimental results 55
indicate a level population that increases slowly with increasing
electron density and disagrees markedly with the theoretical
population which predicts a minumum population at an electron
density of 6 x 101^cm~3,and rapidly increasing populations above
and below this value.
-3 N cm n«02
- Theory 12 10 » - He< + - H p»
10 11 10 14 ...14 -3. n (10 cm ) e
Figure 8 - Absolute na2 population deduced from Balmer-alpha wing opacity (using profiles of Vidal,Cooper and Smith) and from Balmer-beta line centre opacity, in comparison with collisional radiative theory predictions, (Reproduced from Burgess Kolbe and Playford (35)1
Given such deviations between theoretical and experimental
level populations, it is clear that a confirmation of these populations
by an independent experimental method will prove useful. In Chapter 8
an interferometric measurement of the level population is discussed
which confirms the existing experimental values, thus posing
questions as to the validity of the assumptions used for such 56
collisional-radiative theoretical calculations.
3.3.2.6 Conclusions
The diagnostic and absorption measurements performed on the ten-metre plasma device prior to the work presented in this thesis have been discussed in this chapter, and several important conclusions can be drawn:
1) The ten metre plasma device has been shown to provide a well-diagnosed plasma whose electron densities and temperatures change slowly over several hundreds of microseconds.
2) Absorption path lengths of up to 180 metres have been demonstrated and several absorption experiments have been performed using such path lengths.
3) One such long-path absorption measurement, a He I 5876A profile, has demonstrated the existence of an intercombination satellite feature which has been suggested by Burgess to be due to a charge-exchange process. Other features, that cannot be explained at present, have also been observed in the 5876 A far wing.
4) The continuum opacity close to Hot is anomalously high and varies linearly with electron density, a result which cannot be explained theoretically and which may have important consequences for radiative transfer calculations in hydrogen plasmas.
5) An experimental measurement has been made of the hydrogen n=2 level population and the results compared with the predictions of collisional radiative theory. The marked disagree- ment between theory and experiment suggests that basic atomic parameters, such as collision rates, used in the theoretical calculation, may be in error.
The absorption results discussed in this chapter have provided several interesting and important results. The existence 57
3 1 of the He I 2 P - 3 'D intercombination line, the anomalous
hydrogen continuum absorption, and the disagreement between
theoretical and measured level populations all provide unexpected disagreement with accepted atomic physics, and more extensive measurements are therefore required.
Much needed improvements to the experimental apparatus are described in Chapter 5, but this is preceeded by a description of a cheap but practical design for a high current spark gap.
At the end of Playford's research, the spark gap used by him failed completely, and a new gap was required before the further absorption and diagnostic results, presented later, could be attempted. 58
CHAPTER 4
THE DESIGN OF A RELIABLE SPARK GAP FOR THE TEN METRE PLASMA DEVICE
4.1 Introduction
The spark gap used to switch the capacitor bank for the
ten metre plasma device during the work of Kolbe and Playford failed
completely at the outset of the author's work. This chapter describes
the design of a cheap but reliable swinging cascade spark gap based on a design described by Fitch and McCormick (37).
Despite the advantages of switching high currents using multiple spark gaps (as discussed in Fitch and McCormick) it was decided that,since the capacitor bank was already cabled for a single gap, this design should be maintained.
4.2 Requirements
There were several important design requirements for the new spark gap:
1) The gap was required to hold-off the required bank voltage of 15 - 25 kV but, for each bank voltage, needed to be as close as possible to spontaneous firing since this leads to the minimum jitter.
A low jitter (<1us) is required since certain experiments (such as
Thomson scattering) require the triggering of laser flashlamps a long time ahead of the triggering of the spark gap. Typically it was found necessary to run the spark gap in order that it would spontaneously break down without triggering once every twenty shots, 2) The required flexibility in operating voltage ruled out the use of vacuum spark gaps such as those described by Hagerman and Williams (38), despite the advantages these gaps have of low 59
inductance and lack of shock wave damage. Instead it was decided
to adjust the spark gap breakdown voltage by using a pressurized gap, p containing 0-30 lbs/in of a suitable filling gas. The design was therefore required to be pressure tight.
3) The previous gap was time consuming to disassemble and the replacement design had to provide easy access for cleaning and maintenance and allow simple replacement of those parts most likely to wear. The design also had to be as inexpensive as possible.
4) In order to save re-cabling either the capacitor bank or the plasma device, the gap had to fit the existing cable connections from the previous gap. These are two 2'9" copper disks with 6" holes to fit the spark gap.
5) It was also required that the new gap must not change the inductance of the discharge circuit significantly, since this would invalidate the existing diagnostic results. As the previous gap had a far smaller inductance than that of the cables connecting it to the plasma device, this requirement became that the new gap should have as low an inductance as possible.
4.3 Previous Designs
Several designs for such gaps can be found in the literature.
Craggs and Meek (39) provide a useful general guideline to high- voltage design, especially for high current switching. James, Barns and Browning (40) describe a 5nH, 60 kV gap made with heavy alloy electrodes, for fast multiple switching, and this basic design is also used by Barnes et al. (41 ) . Goldman et al. (42) outline a multiple-gapped design for firing a 60 kV 96 kJ theta-pinch capacitor bank with a quoted jitter of 25 nsec, using gaps that are open to the air (and hence 'self-cleaning'). They use rolled steel for the electrodes, since this is described as producing less dust, and
their design is cylindrical with a central steel rod as the
trigger electrode and two steel disks as the outer electrodes.
Villeval'd et al (43) describe a more advanced version of this
gap using V4 - 40 Tugster Copper alloy electrodes to fire a
6 uF, 50kV, 750 kA bank with an inductance of ~15nH . Finally
Rout (44) provides a design for a corona triggered sealed spark gap used at Aldermaston, and this type of design has been described in reports from Aldermaston (J. Kilkenny - private communication).
4.4 Design
Considering the requirements listed previously, especially those of cost and simplicity, it was decided to design a simpler gap than those described, whilst maintaining some of their best features. A radial design, shown in figure 9 and plates 3,4 and 5, was chosen, the discharge occurring between two concentric electrodes 1/4 inch apart. This configuration was chosen with the intention of the discharge occuring around the ring and hence spreading the damage. Whether the discharge occurs around the entire ring each shot or whether it occurs at single points randomly spread around the ring on different shots is irrelevant: the resultant lowering of damage after a large number of shots is the same.
The outer electrode (marked E on figure 9) is a thick, solid copper annulus and connects directly to an upper copper disk (left over from the old gap). The inner electrode I is a mushroom-shaped piece of copper and is connected via the lower brass plate G to the lower copper disk from the old gap.
Triggering is performed by a piece of copper piping of diameter 61
Figure 9-The Spark Gap used on the Ten Metre Device (Cross-Section)
lGas in
Whitworth Bolts
- • c Ei
A. Top Pressure PlatetBrass) B. Trigger Connector(Brass) C. Trigger Support!RT.FE.) D. Top Insulator I PJ.F.E) E. Outer Electrode(Copper) F. Bottom Insulator (P.T.EE] G. Bottom Pressure Platet Brass) H. Centre Electrode SupportfBrass) I. Centre Electrode (Copper) J. Trigger Electrode(Copper) half-way between the inner diameter of the annulus and the outer diameter of the inner electrode, and this is held approx- imately 1/4" - 1/2" above the plane of the electrodes (and hence the discharge).The pipe is only 1/16" thick and so produces a large amount of field emission during triggering and the gap might well be acting as a Corona injection gap rather than the swinging cascade gap envisaged. Certainly the damage to this trigger ring is. not significant, suggesting that the main discharge misses it completely. This pipe is silver soldered onto a brass holding ring and this entire assembly J'is supported from above, using three spring-loaded pieces of studding which allow the height and orientation of the gap to be altered. Also silver soldered to the trigger assembly are three copper strips which carry the trigger pulse to the ring. This simple design for the trigger electrode is essential since it is this section which most rapidly wears. Fitch and McCormick (37 ) discuss various electrode materials and conclude that copper and brass are the best of the cheap metals available. For low cost and simple machining brass was originally chosen for the electrodes, but this was found to lead to excessive electrode erosion, and hence to a large amount of metallic spluttering onto the insulators, leading to insulator tracking and consequent destruction. Copper electrodes were therefore used instead, and have proved satisfactory.
For the insulation disks D and F 'Kite1 brand Tufnol was originally used due to its manufacturer's quoted 'resistance to tracking1, but was found to have the disadvantage, however, of cleaving easily due to the mechanical stresses during firing.
Because of this PTFE disks are now used as these have much greater strength against mechanical shock (indeed when the first spark gap with such an insulator eventually tracked down a bolt hole through the PTFE - the PTFE disk was so strong that the shock bent a 1/4" thick brass disk by first before the PTFE fractured !)
In order to minimize the inductance of the gap, the two lower insulator rings need to be as thin as possible and so are shaped to prevent tracking. The lowest insulator, ring F, provides insulation between the outer electrode and the bottom brass plate and the shape, which can be seen in figure 9 in cross-section, is a result of several refinements to prevent all possible routes for tracking. The middle insulator ring prevents the tracking from the outer electrode to the trigger assembly and is of much simpler design, as is the third PTFE ring C which simply supports the trigger assembly.
Three brass plates complete the major components of the spark gap. The lowest of these acts as both the lower pressure plate and also as the connection from the centre electrode to the lower copper disk. The middle plate B connects the trigger cable from the air-cored pulse transformer to the copper strips of the trigger assembly; and the top plate A acts purely as a pressure plate. Both the top and bottom plates have piping silver soldered to them for filling gas supply and exhaust, respectively.
Six nylon 1/4" diameter bolts hold the entire assembly together concentrically and are designed to withstand the necessary filling and shock pressures. In order to prevent tracking these bolts are smeared with silicone insulating grease where they pass through the lowest PTFE disk. After the design, it appeared simpler to hold the gap together by using a steel bar (left from the old Aldermaston gap), held in place by two 1" diameter pieces of steel studding, and the six nylon bolts are only used to hold the gap sections in position. Standard 3/8" diameter re-inforced tubing provides the gas supply and exhaust, and 1/8" diameter o-rings seal each joint ensuring that the gap remains pressure Plate 3- The Spark Gap for the Ten Metre Plasma Device (i) The Discharge Region Plate 4-The Spark Gap for the Ten Metre Plasma Device (ii) Open,Showing the Trigger Ring
ON U"1 Plate 5-The Spark Gap for the Ten Metre Plasma Device (iii)Assembled
ON 2 tight up to 30 lbs/in . This is important both to maintain hold-off voltage and also to ensure that oxides of nitrogen, produced during the discharge, are flushed safely out of the gap, by the filling gas, and into the fume cupboard.
As previously mentioned, electrical connections to the pinch and capacitor bank are made via the two large copper disks, see figure 9, which are attached to the outer electrode and the lowest brass plate by brass holding rings. These copper disks are therefore only 1" apart and so 12 Melinex sheets are interposed to prevent breakdown, with extra Melinex rings inserted where the brass holding rings reduce this gap to only 3/4".
4.5 Operational Experience with the Redesigned Gap
When this gap was first designed it appeared sensible to use Oxygen-free Nitrogen as the filling gas since its high ionization potential and non-corrosive nature appear ideal for such a purpose. In order to test the gap's relationship between breakdown voltage and filling pressure, the gap was initially used untriggered and simply charged up until breakdown. This P showed that a pressure range of 0 - 20 lbs/in should be sufficient to obtain the required voltage range.
After a few tens of shots, however, it was noticed that the breakdown voltage was slowly falling with each shot and only with excessive flushing of filling gas between each shot could the breakdown level be maintained. The gap was examined and, although no damage was observed, the gap did contain a large amount of a black deposit and a similar deposit was found in a filter installed in the gas exhaust line. Further shots with the O.F.N, filling produced similar results until eventually the Tufnol lower ring (this is before PTFE was used) tracked and was written off at
only 22 kV.
The identification of the black powder appeared important,
but simple chemical tests proved insufficient, and several sections
of the gap were therefore sent to the Analytic Services Laboratory
at Imperial College. The deposit was shown there to be fairly
pure carbon, which was presumed to be due to the distillation of
the Tufnol by heating in a pure nitrogen atmosphere, leaving the carbon filler behind. It was found that this problem could be eliminated, however, by the use of air for the filling gas, and since this change was made, no degradation of the insulator has been apparent, even after several thousands of shots. It was feared that the use of a filling gas containing oxygen might lead to rapid electrode erosion, but' this fear has proved unfounded.
Two explanations were put forward to explain the lack of a carbon deposit when using air. Firstly the carbon may still be produced but the oxygen present might oxidise it during each shot,
the resultant carbon dioxide being flushed out of the gap. If this is the case, however, the erosion of the insulator should be noticeable after a large number of shots - none is apparent.
A more likely explanation is that the oxygen reacts with the surface layers of the insulator, producing a protective layer for subsequent shots. The PTFE insulators, used at present, also show no problem when used with air filling and this combination has been used continuously ever since.
Using current traces like those shown in plate 7, taken with a Rogowski coil, the spark gap discharge has been shown to be reproducible with a delay of ~1us , with a risetime of 4.5 nsec and a jitter of less than 1 us» The design described in this chapter provides a simple
spark gap, capable of switching 200 kA but costing only £65 for
materials (late 1980 prices). At the time of writing, the
present gap has now operated untouched, and unopened, for 17 months
corresponding to an estimated 3,000 - 5,000 shots. With the
introduction of the 80 kV air-cored pulse transformer, the trigger
assembly has been raised above the plane of the discharge, and
consequently the wear of this trigger ring is considerably reduced.
It may well prove necessary soon to replace the inner electrode,
since the gap spacing is probably increasing due to electrode
erosion. (The screw-in centre electrode has been designed with this
possibility in mind.)
4.6 Further Improvements
Several improvements to the existing design are planned
for future spark gaps:
1) The connection of the copper strips to the middle brass plate is unsatisfactory and will be replaced with a much stronger holding ring with a thicker brass plate.
2) There is a danger with the present gap of widespread damage caused by tracking down the bolt holes present in the lower insulating disk (F). In future this set of bolt holes will be replaced by two sets of blind tapped holes, which should eliminate the problem entirely.
3) If a further decrease in jitter is required then the trigger ring can be split, the resultant U.V. flash accelerating the breakdown of the discharge. 70
CHAPTER 6
APPARATUS USED FOR MULTIPLE-PASS LONG PATH ABSORPTION MEASUREMENTS — AND TECHNICAL LIMITS TO OBTAINABLE PATH LENGTHS
5.1 Introduction
At the start of this present research it was clear that the apparatus used during Playford's absorption measurements required improvement if many weak spectral features of interest were to be observed. The single change in the plasma device has already been described in the previous chapter, and discussion of the numerous changes in the optical and electronic apparatus are now discussed.
5.2 The 380A Ring CW Dye Laser
For his long path absorption work, Playford built a CW dye laser pumped by a Spectra Physics 164 Argon-Ion laser. This CW dye laser, also used initially by the author, was similar to that described by Kogelnik et al. (45), and used a '3 mirror cavity with a
home-made dye jet, with a prism and an etalon providing the coarse and fine tuning respectively. Playford claimed in reference (35) to have obtained 50 mW output power at 6562A using Rhodamine 640, and 100 mW power at 5876A using Rhodamine 6G, but these values now seem dubious since later measurements by the author have failed to match such output powers. The linewidth of the laser was measured by the author,using a 3 cm. thick solid quartz etalon, to be 38 ±1 mA,corresponding to about thirty longitudinal modes.
Due to competition between these modes, the output power of Playford's laser varied appreciably, (up to 30% over timescales of the order of a microsecond). This significantly affected his absorption results, especially as he did not use a laser input reference monitor of the type described later in this chapter.
Fortunately the problems caused by the lack of power,
resolution and power stability of Playford!s laser were overcome
when, in 1978, it was possible to purchase the first commercial
ring dye laser to be sold in the U.K. This laser, the Spectra
Physics 380A Ring CW Dye Laser, duly arrived in mid 1979, and has
been used for all of the experiments presented in this thesis.
The 380A laser uses a vertical dye flow,producing a -1
200um thick jet moving at a speed of 26 ms , and is pumped with the
Argon-Ion 164 laser focussed to a 8um diameter spot. The CW ring
laser cavity is shown in figure 10,and is a four mirror ring cavity, with a Faraday-rotating uni-directional device ensuring lasing in one direction around the ring only.
+ Ar Laser Pump Mirror
Astigmatic Compensator photodjode •
OUJPUT Unidirectional Thin Scanning Birefringent M4 Beamsplitter Device Etalon Etalon Filter
Figure 10-The 380A Ring Dye Laser Cavity 72
Significantly higher output powers are therefore produced since there are no regions of unused gain as found in standing wave lasers. The extra power allows more efficient frequency selection, resulting in only one longitudinal mode lasing at any time, and a feedback loop
is used to maintain the output wavelength in one mode for long periods
(several hours).
Several devices are added to the 380A cavity to achieve the single frequency output. A birefringent filter of broad bandwidth (700 GHz) and a thin etalon of free spectral range 900 GHz provide the coarse and medium tuning respectively, and a low-finesse thick etalon (of free spectral range 76 GHz), the length of which is piezo-electrically controlled, allows the single frequency output to be tuned when necessary. The cavity also contains a beamsplitter- photodiode unit,which provides the required feedback signal,and two quartz galvoplates, which are rotated during the continuous tuning to maintain the cavity length, thus preventing 200 MHz cavity mode hops.
The output is horizontally polarized,and tunable across a range of 600 A with one dye filling (5650 A - 6250 A for Rhodamine 6G).
The powers obtained from this laser have been as follows: for wave- lengths between 5650 A and 6250 A,a filling of 1.44 grammes of
Rhodamine 6G in 1.5 litres of Ethylene Glycol has produced an average power of 300 mW (and a maximum of 700 mW) [using a 4W (all lines) argon-ion pump laser power] at the peak of the dye gain curve. For wavelengths between 6350 A and 6590 A,a filling of 1.33 grammes of
Rhodamine 640 and 1.08 grammes of Rhodamine 6G in 1.5 litres of
Ethylene Glycol has resulted in an average power of 50 mW at the peak of the dye gain curve [using an argon ion pump power of 3.2 W (all lines)]
- the low argon ion laser power quoted for this dye being due to problems with the pump laser during the period of usage of the red dye mixture. Unfortunately this red dye also had a lifetime of only
two to three weeks and the dye laser output power quickly dropped
from the maximum available. (Since the author obtained these results,
a new dye, D.C.M., has become available. This has been tested in
the 380A ring laser and provides a peak power of 75 mW at the dye gain peak using 2 W (all lines) of argon-ion pump power; lases from 6200 A to 6830 A; and has a lifetime of longer than six months.)
The method suggested by the manufacturers for tuning the laser is:
(i) The fine etalon is removed,
(ii) The Bi-refringent filter is tuned as close to the desired wavelength as possible.
(iii) The,Uni-directional device is tilted to tune the wavelength even closer to the required wavelength. This is necessary since this device contains an (unwanted) etalon.
(iv) The fine etalon is replaced and tuned to obtain the
76 GHz etalon mode closest to the desired wavelength.
(v) Finally the electronic etalon scan is used to scan to the desired wavelength.
This method appears satisfactory on paper, but has caused difficulties since the interaction between the fine etalon and the etalon contained in the uni-directional device introduces unpredictable wavelength hops in stage (iv). Because of this it has been found necessary to use a double-pass Hilger spectrometer as a coarse wavelength monitor.
When this laser was first run,the output wavelength jittered substantially (1 GHz over an hour) and it was found necessary to build a special table for the laser. 74
5.3 The Dye Laser Table
The basic material chosen for the anti-vibration table
top was alluminium honeycomb manufactured by Ciba-Geigy Ltd. 3
The type picked was Aeroweb 3003 with a density of 5.2 lb/ft ,
a cell size of 1/4" and a foil thickness of 2.5 thou. This
honeycomb does not include top and bottom surfaces and steel
'skins' were chosen for these, in order that magnetic mirror mounts
could be used on the table. A stainless steel top skin (Type 430
steel from Hanson Harrison Ltd.) was used to prevent surface rust,
together with a mild steel bottom skin, both of 12 guage thickness.
The similar coefficient of expansion of these two skins should
prevent problems with changing room temperatures. To bond the skins
to the honeycomb, Redox 410. Araldite was obtained from Ciba-Geigy.
This design provides a table top that is sufficiently light
to be lifted by one person but also highly rigid, with a very low
natural accoustic frequency to prevent ringing(and hence transmission
of vibration from the table supports to the laser). The table
supports consist of alternate concrete and polystyrene blocks
covered in aluminium foil (to prevent solvent damage to the
polystyrene) with car tyres on the top of these, to further reduce
vibration. Monitoring the laser output wavelength with a spectrum
analyzer shows an 'instantaneous' laser bandwidth of less than
10 MHz and a wavelength drift of 30 MHz in twenty seconds,and
200 MHz over two hours.
5.4 Optics for the CW Laser
For historical reasons the CW laser is operated in one laboratory,and its output beamed 16 metres to the plasma device in another. The optics required both to provide this beam path,and to monitor the laser output have been completely replaced during the 75 period of the author's work.
Firstly the optical system used for guiding the beam between the two laboratories suffered during Playford's research from a lack of stability. Playford's wall-mounted Dexion mirror mountings were scrapped,and replaced by optical benches bolted to the wall using heavy mild steel mounts, resulting in a beam deflection due to mirror vibration of less then 50 urad. Playford used aluminium-coated, microscope slides to direct the laser beam and these have now been replaced by X/1 0 mirror blanks (supplied by
Ealing Optical Ltd.) which have been coated for ^99.8% reflectivity
(at 45° incidence) for the wavelength range 5500 A - 6800 A (coated at Culham Laboratory coatings department) and mounted in standard three-point mirror mounts.
The 380A ring laser output properties that require continuous monitoring are the power, wavelength and bandwidth. The power is measured with a Spectra Physics 404 power meter to an accuracy of 5% (which is essential for adjusting the 15 degrees of freedom of the laser cavity during alignment for optimum power output).
The output wavelength is measured totO. 2A accuracy using a Hilger-Watts
D330 double-pass spectrometer, fitted with an eyepiece and fed with
4% of the laser output using a beamsplitter. Such a coarse wave- length measurement is essential, both for tuning the laser close to a desired wavelength, and also for monitoring the random mode hops that occur during fine tuning. This wavelength setting accuracy of +0.2 A (~20 GHz at 5876 A) is adequate for the continuum absorption experiments discussed in chapters 8 and 9 , but for many line profile measurements is insufficient, and a more accurate measurement is required. The trick used for the only high accuracy experiment presented, in this thesis (He I5876A profile discussed in Chapter 7) is to insert into the laser beam a Phillips LCK500 He lamp which 76
fluoresces when the laser is tuned to within + 1GHz (+10 mA)
of the 5876 A transition line centre.
Having set the laser to line centre, tuning can then be
performed by use of the fine etalon and the electronic scan. The
continuous tuning is monitored using a Spectra-Physics 470 spectrum
analyzer, of 2 GHz free spectral range, whose output is displayed on
a Tektronix 555 oscilloscope. (This spectrum analyzer also provides
the monitor for the laser bandwidth, with a resolution of 10 MHz).
Using this method, detunings of up to 350 GHz have been used with
an accuracy of +1 GHz. .
The remaining optics required for the experiments discussed later are: the interferometer used for electron density diagnostics,which is discussed in Chapter 6, and the multipassing mirror system discussed in the following section.
5.5 The Multipassing Optical Arrangement
5.5.1 Requirements
The most important development of the absorption system was the design and building of an improved multiple pass optical arrangement providing greater optical lengths than the 180 metres achieved previously. The requirements of such a design are simple:
(i) The system must multipass the laser beam a useful number of times in such a way that the number of passes can be simply changed across a wide range. Once any number is set then the path length must remain constant for several hours without re-alignment.
(ii) The most crucial requirement is that, at any setting, the exact number of passes within the multipassing system must be easily measurable. Without this knowledge the measured opacity cannot be analysed to provide the absorption coefficient. (iii) The CW laser beam has a divergence of~1 mrad., and after forty metres the laser beam will have a diameter equal to that of the end windows, resulting in a loss of laser intensity.
Obviously to obtain more than 40 metres of path re-focussing must be provided by the multipassing optics.
(iv) The system must be simple to align and focus - the mirrors have to be more than 10.5 metres apart and only one can be viewed at any one time. An alignment or focussing routine of any complexity will therefore be impossible for one person to operate.
Given these requirements there are two basic designs for such a system - one using a spatial method of beam separation, the other using temporal separation.
5.5.2 Spatially Separated Multipassing Systems
In this system the mirrors are aligned such that, at some plane in the cavity,all of the beams are separated spatially, and can be counted to measure the path length. The simplest method of achieving this is to design the cavity such that the beam is always re-focussed onto the mirror at one end each pass so that the individual foci are separated. Three such methods have been used and are shown in figure 11.
Both Plane Rad.R Rad.R Rad.R
(i)Plane-Concave (ii)2 Mirror Concave (iii)3 Mirror Concave Figure 11-Spatia l Multipassing Designs 5.5.2.1 Plane-Concave
This is the system used by Burgess and Playford (35,36 ) for long path measurements on H-alpha and He 5876A, using the old
CW dye laser. A plane mirror was used at the input end, with an
18 metre mirror at the other end, both being aluminium coated with quartz overlay. The result was an ellipse of points on the plane mirror providing the measurement of the multipassed length. There were two problems however. Firstly the cavity did not re-focus every traversal since an 18 metre concave mirror was used with a mirror spacing of only 12 metres. The result was a mixture of spot sizes of up to a centimetre diameter on the plane mirror, which limited the possible number of passes countable. A second problem was that changing the path length was not straightforward, since the angle that the input beam entered had to be such that, after
the required number of passes, the beam struck the exit point. To change the cavity length, this input angle required changing - a
two mirror realignment. A dielectric coated version of Playford's mirrors, used in an identical design, confirmed these problems and showed that 100 - 200 metres was the maximum length obtainable with
this system due to the problem with spot size.
5.5.2.2 Two Mirror Concave
This design is the basis for that used by the author
and has been used by several previous workers. Salour (46), who
was designing a system to delay short laser pulses, provides a
general review of this system, where his work follows from two
papers by Herriot et al. (47,48). in the first of these, they
describe such a cavity with the mirror spacing varied, and show
that the resulting elliptical spot pattern on the input mirror will
emerge from the input hole if the ratio of cavity length to mirror 79 radius is an exact integer. In their second paper these authors describe a 1,000 pass cavity using 7.5 cm. diameter 10 m. radius of curvature mirrors. They improve on their previous paper, firstly by using a third mirror outside of the cavity to reintroduce the output beam back into the cavity, resulting in a second ellipse of spots displaced from the first, and secondly they use astigmatic mirrors to produce new spot patterns such as Lissajous figures, of which excellent photographs are reproduced. It must be noted that their quoted lengths were obtained without such problems as windows in the beam path and so would be very much reduced if used in the present work. The design described by Herriot et al. might well have been useful for the long path absorption cell if it had not been for the requirement of changing the path length easily. With this arrangement a change in; path length would mean changing the mirror spacing - an inappropriate procedure for re-alignment in the present case. Instead a variation on Herriot et al's cavity was used.
5.5.2.3 Three Mirror Concave (White Cell)
In reference (36) Playford's multipassing arrangement is described as a White Cell. This is not true since White used a three mirror confocal cavity as can be seen in his original paper (49).
The confocal design of his multipassing cavity ensures that the laser is refocussed onto the input mirror each double-pass, but one of the mirrors is now split into two halves which greatly simplifies the operation of such a system. To describe its operation consider figure 12 and plate 6.
On the left is the input mirror, on the right the two halves of the second mirror. The laser enters the cavity at one of the two notches on the input mirror (marked IN(o)), with a diameter of 2 m.m., and is directed onto mirror 2A (which is on the same side of the system Mirror 1 Mirror 2A Mirror 2B
0UT(120) 80 40 IN(0) O 0 0 f
2O0 6O0 10O0
Figure 12-Spot Patterns for Three Mirror (White Cell) Multipassing Cavity
V
0 .» • 0*.
Rate 6 - Observed Multipassing Cavity Spot Patterns axis as the input notch) producing a 10 - 20 m.m. spot on this mirror.
Mirror 2A is then tilted to return and focus this beam to a 2 m.m. spot on mirror 1 diagonally opposite the input position (marked
20 on the diagram). Mirror 1 is then aligned so that the beam returns to mirror 2B and again forms a 10 - 20 m.m. spot. Finally mirror 2B is aligned to focus the beam down to a 2 m.m. spot on mirror 1 at a position (marked 40) horizontally displaced from the input spot.
The entire process is repeated, producing no extra spots on mirrors 2A and 2B, but two extra spots for each quadruple pass on mirror 1. After an integral number of quadruple passes (3 shown in figure 12) the beam strikes the output notch (marked OUT (120)) and exits from the cavity. To change the cavity length, all that is required is to tilt mirror 2B about its vertical axis and the two rows of spots on mirror 1 will move, thus increasing or decreasing the path length undergone before the beam exits from the cavity.
This is the same design used by White (49) in which he obtained 56 metres of path with 90 passes using 62.5 cm. radius mirrors. A similar design was used by Howard et al. (50) for infra-red absorption spectroscopy in which they obtained 68 passes with 10" diameter mirrors of 22 metre spacing. In both of these cases conventional light sources were used, since lasers had yet to be discovered.
5.5.3 Temporally-Resolved Multipassing Systems
So far the designs considered have been those in which the low divergence and high powers of lasers have been used to obtain and measure multiple passes.by separating the individual beams. The availability of lasers of very short time duration provides a second alternative. A 5 nsec laser pulse (for instance) occupies a length of only 1.5 metres and a known optical path can be provided by introducing the pulse into a multiple pass cavity, and extracting it after a known length of time (and hence path length, since the velocity of light in the plasma is well known).
This pulse length of only a few metres,removes the problem of inter- ference between succesive passes, but results in two basic problems - firstly the difficulty of switching the laser into and out of the cavity with an accuracy of perhaps 50 nsecs.; and secondly the problem of lowering the cavity losses so that the resultant shot-noise does not dominate the expected absorption.
Such a system has been considered by Kolbe (private communication) using a nitrogen-pumped dye laser, and switching the laser pulse with Pockels cells and a 'Brewster plate' beam- splitter. The losses in these switching components, however, would limit the paths available to 200 metres and so a combination of this system and a White Cell design has been suggested, where the temporal switching system is required every 8 passes. This would allow path lengths of 1 km. to be obtained before the losses become too large.
5.5.4. Choice of Multipassing Systems
From the arguments presented in section 5.5.2 it was clear that the three mirror design was the most suitable multiple pass design of those using spatial separation. The remaining choice was therefore between this three mirror design and the temporally separated system, the relevant differences being:
(1) The CW laser was fully working at the start of this research, and was of proven ability with respect to beam divergence, beam stability and single mode nature, etc. . Although the nitrogen- r pumped dye laser was working, it had not been tested over long paths, and results from other experiments with the laser showed problems
with the ratioing and differencing of input and output beams
(possibly due to the various component modes of the pulsed laser
producing different spatial beam profiles on succesive shots). The
CW laser is single mode and does not suffer from such problems.
This possibility of differencing input and output signals is crucial
if very small absorption, such as that proposed for the Nil
forbidden line experiment proposed in Chapter 9,, is to be measured.
(2) The basic difference between the two lasers is the
difference in timescale. The pulsed laser lasts typically for
5 nsec., which is ideal for the switching in the temporally
resolved system, but leads to absorption data at only one time
in the discharge per shot. This means that a vast number of shots must be taken in order to use the variety of conditions provided by the use of a recombining plasma. This problem does not apply for
the CW dye laser, and one scan of the line profile provides data at all times of interest. An extra advantage provided by the continuous output of the CW laser is the possibility of reducing noise on the detected laser signals by averaging over times shorter than the time for plasma conditions to change significantly,but longer than pulsed laser timescales.
(3) The CW laser has a low bandwidth 10 MHz) and hence a long coherence length (~10 metres) which provides the possibility of enlarging the scope of long path experiments to include inter- ferometry.
(4) The pulsed dye laser has the advantage of a much larger wavelength range, since it operates from 3600A to 7500A, compared to the CW laser range of only 5600A to 6800A (using the existing pump laser).
(5) Another significant advantage of the pulsed laser is that it is simple and relatively inexpensive. The CW laser, 84
on the other hand, is expensive in terms of capital, maintenance and running costs.
All other problems with the CW laser absorption system, such as dust, vibration, etc., apply equally to both systems, and are discussed later.
Considering those points, it was decided to continue the use of the CW dye laser for the ultra long path work, despite its high running cost, and to use a three mirror White Cell multipassing cavity design.
5.5.5 Path Lengths obtained using Multiple Passing
The three mirror multipassing cavity chosen to provide the required long absorption paths uses 3 inch diameter, \ inch thick mirrors, cut to 11.94 metre radius by I.C.O.S. Ltd.,and coated for
> 99.95% reflectivity for a wavelength range of 5000A - 7000A
(at normal incidence) by Culham Laboratory.•Originally the mirror blanks used were constructed of standard glass, but the coatings quickly degraded, and hard crown glass blanks were used instead.
The mirrors are mounted in purpose-built adaptors which in turn are mounted on commercial mirror mounts supplied by Unimatic Engineering Ltd.
(allowing 2 arc-sec precision adjustment). The input mirror was originally placed on a precision screw slide in order to provide an accurate adjustment of the distance between the mirrors, but this was found unnecessary as an inaccuracy of several centimetres in the setting of the mirror spacing was found to have little effect on the spot pattern.
The first test of the mirrors took place in position around the z-pinch,' but without the end-windows present, resulting in paths of up to 140 passes (1.5 kms. in the plasma device). This arrangement proved that the arguments concerning the alignment of such a system were indeed correct, since this system was aligned by one single
person and once aligned,the path length could be changed by the
movement of one mirror mount control only. Even greater path
length was generatedf when an extra plane mirror was inserted to
reflect the output beam straight back down its path in the multi-
passing system. The output of this arrangement was separated from
the input using a beam splitter and, although unusable at that time because of problems with beam movement, showed that paths of more
than 268 passes (e.g. path length in pinch'" 2.5 km) are possible.
The use of the White Cell,without end-windows present,provided a measurement of the losses at the mirrors. For a path of 100 passes a 2 mW input produced a 1.3 mW output, corresponding to 65% trans- mission for 99 mirror reflections, i.e. 0.4% loss per reflection.
This loss is higher than expected,but still acceptable, as shown by the path lengths achieved.
At this point the Brewster windows built by Playford were inserted and the path length obtainable dropped to only 60 passes
(630 m). Examination of these windows showed firstly that they were not optically flat by any means, leading to lensing over such large paths. A second problem was that the end-windows were angled at
45° and not Brewster's angle - leading to the high losses in transmitted intensity. To overcome this, brass holders were machined at Brewster's angle,and 5" thick, 6" diameter Optical crown glass
(type 524593) windows of flatness (suppled by Ealing Optical
Ltd.) were fitted using silicone rubber cement. The two windows were rotated to produce minimum reflection losses, and the pair orientated at 180° to each other leading to a plasma length of
10.84m. + 0.01m.
With these in position, White Cell paths of 140 passes
(1518 metres in pinch) were obtained, although a maximum usable path 86
(for reasons discussed later) was found to be 110 passes (~1200 metres).
Repeating the loss measurement showed that after 72 passes (i.e. 71 mirror reflections and 288 end-window faces) an input power of
19 mW produced an output power of 0.4 mW. This is a transmission of 2.1% and, using the previous figure for mirror losses, gives a value for the end-window loss of 1 .2% per face. This is surprisingly high and is thought to be due to a film of dirt that forms quickly on the inside of the windows. These results, with special reference to achievable sensitivity and signal/noise levels, will be discussed further in section 5.9 after a description of the detection system used.
5.6 Detection of Long Path Laser Absorption
It was shown in section 2.1 that, in order to measure an absorption coefficient Ky, the three quantities required are the incident laser intensity 1(0), the transmitted intensity .1(1) and the length I , since
k -1 HO) K- ( Id)
The measurement of I has already been discussed, and it is the measurement of the two intensities that is important here.
In Playford's experiments, only the transmitted signal was measured and the oscilloscope time base was therefore set sufficiently high that the signal level at late times, where there was no absorption, provided the value of the input laser power. This did however introduce several problems. Firstly, this measurement could not account for high frequency (~10 kHz) fluctuations in dye laser output power; secondly it assumed that these late times did indeed correspond to zero absorption (which was only judged to be true by the fact that detected signals were constant at these times); and thirdly the use of such a long timebase compressed those times of real interest,
where the absorption took place, to the first two or three
centimetres of the oscilloscope trace - thus lowering the accuracy
with which they could be measured (e.g. the use of 100us /div as
a timebase must surely introduce a reading error of +^us , which is
not trivial). The experimental arrangement will therefore require
two detectors of CW laser light of 0 - 50 mW power. The vast majority
of spectroscopic experiments in the visible spectral region use
photomultipliers for such detection because of their useful linearity,
sensitivity and time response. Since the photomultiplier is so
sensitive to unwanted wavelengths then a dispersive device, usually
a monochromator, is inserted. In this experiment, however, the laser
11 intensities of interest were high (3 x 10' photons per us for instance)
and the signals required reduction to avoid saturating the photo-
multiplier, for which there were several options:
(i) A neutral density filter could have been placed before
the detector - this would simply have wasted photons and increased
the shot noise on the trace.
(ii) The photomultiplier tube voltage could have been
reduced but this would have required voltages of less then 300 - 400V
and the photomultiplier tube would be non-linear at..these voltages.
(iii) The method used by Playford was to reduce the laser
signal by reducing the slit width of the monochromator. This wasted
photons and also introduced a problem which, for the longer paths,
was a crucial design point for the detection system. If the laser
beam was partially obstructed,after it first entered the plasma
(such as by the slit on a monochromator),the noise content of the
detected signal rose dramatically. This was thought to be due to
rapid changes in the beam's radial intensity distribution, resulting
in a fluctuating detection signal unless the entire beam area 88
reached the detector. It was therefore crucial that, once the input and,absorption laser beams had been split, no aperture be allowed to cut either of the beams, and the use of monochromator slits to control the .photomultiplier signal was therefore impossible.
Another important problem with this combination of photomultiplier and monochromator was that the monochromator throughput was only
30% - 50%,and a typical photomultiplier efficiency was.only 5%, resulting in a low signal/noise ratio of the photomultiplier output due to shot noise.
It was decided therefore to use large area photodiodes as detectors. Such diodes have sufficiently large area (1 cm., diameter) that they do not aperture the beam; they can take continuous laser powers of tens of milliwatts without saturating; and have high efficiencies (— 60%) thus reducing the shot noise dramatically. A first attempt used Radio Spares large area photodiodes together with J.F.E.T. operational amplifiers. These diodes were cheap but suffered from high leakage current, high capacitance (and hence ringing) and one of the diodes developed a fault after only two weeks. The replacements were United Detector
Technology Pin 10 photodiodes, whose characteristics are shown in
Table 5.1. They are of Schottky barrier type and so require a reverse bias voltage.
Table 5.1 - Characteristics of U.D.T. Schottky Barrier Photodiodes
responsivity at 6000A = 0.26 A/W (-55%) capacitance with 50V reverse bias = 175 pF dark current = 0.5 uA break down reverse bias = 100 V active area =3.14 cm2
These proved ideal, with such a large active area that a lens was added before the diode in order to increase the area of diode used to sample the laser, thus reducing both errors due to localized
variations in diode sensitivity, and also the effects of any high-
intensity spots in the laser beam. The low capacitance and high
breakdown voltage of these diodes is essential for good time
response,and the low dark current is negligible compared to the
values of signal expected. The diodes were found to have much
better reproducibility and better agreement with the-quoted
characteristics than the Radio Spares diodes, and so were used for
all the following experiments.
Without further amplification, the signals from these
diodes would be immeasurable and so extra amplifiers were added.
To achieve this several variations of a simple J.F.E.T. operational
amplifier were tried resulting in the circuit shown in figure 13.
Figure 13 -Laser Detection Circuit-
The operational amplifier is a type 351 J.F.E.T. and is powered by _+ 15V encapsulated mains power supplies. The 45V reverse- bias for the diode provides a good risetime,and the 5KfJresistor to earth ensures a usable fall time. The 10K<^)potentiometer is used to 90 balance the amplifier against D.C. drifts and the 1 KQ feedback resistor provides adequate gain,with a sufficiently small time- response. The resistor and 100 pF capacitor were found necessary to prevent signal oscillations when the amplifier output was fed to 20 - 30 metre signal cables used for connection to the computer (described later).
With this circuit a total half width - half maximum response time of less than 500 nsec. was produced but with a 10% bounce 1us after the main pulse when the long signal cables were used. Since the plasma conditions change appreciably in 5 us
(or more), this time response is quite adequate. By observing the light from a Chelsea Instruments 3021 stroboscope, the time responses of the two photodiodes were proved to be identical, and the CW dye laser was used to show both detector outputs to be linear (to better
than 2%) for laser powers (at 5876A) of 28 uW - 5.6 mW (producing output signals of 5 mV - 1 V).
These diodes are superior to photomultipliers in area and sensitivity, and are adequate with regard to linearity and
time-response. The final problem is therefore the removal of the unwanted plasma emission. As previously described, monochromators are not suitable because of possible aperture and throughput problems.
Three alternative methods were therefore tested:
(1) A Grubb Parsons filter of bandwidth 24A centred at
5876A.
(2) The filter in (1) with an extra 140um etalon
(3) The 140urn etalon used in tandem with a 3um etalon.
With these}the results shown in Table 5.2 were obtained. 91
Table 5.2 Comparison of Wavelength Filters Filter System Laser Transmission Plasma Emission (at 5876A) Transmission *
(1) Grubb Parsons Filter 70% 17% (2) Grubb-Parsons Filter & Etalon 65% 10.4% (3) Tandem Etalons 67% 6.3%
* Plasma emission measured at 50us after peak current in 0.15 Torr N2 plasma.
The results show that the tandem etalons provide the optimum combination of laser transmission with plasma emission reduction.
It was quickly discovered that light could reach the photodiodes from the plasma by reflections within the room, and so the detectors and etalons were enclosed in a light-tight hardboard box,as shown in figure 14.
5.7 The Measurement and Recording of the Data
Two output signals were produced by the photodiode detectors and these had to be recorded separately for later analysis.
Even without the plasma present, the two diodes produced different output signals, due to the different losses present in the input and transmitted beam paths, and some method of balancing these two signals was required. To achieve this, the two signal cables were both terminated with identical 10 kfi cermet multiturn potentiometers.
The potentiometer terminating the cable carrying the higher signal was then adjusted so that the signals recorded, in the absence of absorption, were identical. The most accurate method of performing this was to use a Tektronix 7000 series oscilloscope containing a type 7A13 Differential Comparator plug-in with the potentiometers set for a null difference signal (accurate to + 1mV).
Some of the experiments described later were recorded 92
using an oscilloscope and no further equipment was required. The long path absorption measurements, however, were recordedt directly onto computer using two transient digitizers. The digitizers and computers were run in the laser room (hence the use of long signal cables) and a Telequipment oscilloscope was therefore used to monitor the photodiode output signals close to
the diodes themselves,in order that mirror adjustments and etalon
tunings could be performed to provide maximum signals. Tektronix
7912 AD and R7912 digitizers were used to record the data and the signals were fed to a Tektronix CP 4165 controller and stored on floppy disc. This use of a computer for signal recording and storage has several major advantages:
(a) This arrangement provides a better trace reading accuracy (_+0.25% of full-screen for both vertical and horizontal directions) than the use of polaroid for photographic storage
(+1% of full-screen).
(b) With this system wasted shots can be erased and the disc space re-used.
(c) The waveforms recorded on floppy disc can be mani- pulated by the computer for: subtraction of zero levels; averaging of signals; and, most usefully here, the ratioing of two traces.
(Previously these calculations would have been done by measuring the
trace,at each time required,with a ruler and using a calculator. This
is very time consuming and the information provided by the variety
of available plasma conditions is greatly reduced. )
The full detection system was tested,in the absence of
any plasma absorption,by the use of varying neutral density filters.
200us long digitizer traces were recorded,after the necessary signal
balancing,and the measured and theoretical absorption compared for
each shot. The result was an agreement between experiment and theory to within 2% for an apparent opacity range of 0 - 6. The absorption,
experiments described later never measure higher opacities than this
and the detection and recording systems therefore work as required.
„ The experimental arrangement, shown in figure 14,
includes a Motorola 510 photodiode, coupled to a 2N918 transistor amplifier, the combined unit having a risetime of 0.6us, using a
3 metre-long signal cable terminated in 420Q. This diode measures the plasma emission,and is used as the trigger pulse for a Tektronix
7623A storage oscilloscope whose GATE pulse starts the unit used to delay and trigger the digitizers. The storage oscilloscope is also used to show various traces of .interest, such as the pinch current trace taken with a Rogowski coil. The delay is necessary since high electrical pick-up and emission at early times would otherwise mean an insensitive setting for the digitizers. The use of a delay - 50us for hydrogen and helium,and 80us for nitrogen- allows observation for long periods (50 - 280us), where the signals do not change vastly, and the digitizers can be set to a sensitive scale.
The 7912 AD programmable digitizer uses its own plug- ins (nos. 7A16P and 7B90P) and the R7912 digitizer uses standard
Tektronix plug-ins which allow a choice of options. In appendix
A it is shown that in order to measure the opacity to the highest accuracy then
(a) For an opacity of more than 0.69 the input and output intensities should be recorded (input/output method).
(b) For an opacity of less than 0.69, the most accurate results are obtained by recording the input intensity together with the difference in input and output intensities using the Tektronix
7A13 (Differential Comparator) plug-in ( the input/difference method). Digitizer 1
7603 Oscilloscope 10k Q Potentiometers Trigger Pulse and Photodiode Outputs Laser Double Pass Monochromator
555 Oscilloscope
Figure 14-The Experimental Arrangement used for Long Path Absorption Measurements (i) The Laser System and the Computer vO Trigger Pulse and
Figure 14-The Experimental Arrangement used for Long Path Absorption Measurements (ii)The Plasma Device ,Multipassing Cell and Detection System 5.8 The Experimental Procedure
The multiple-passed laser absorption experimental apparatus has now been discussed in full in this chapter, and the resultant arrangement is shown in figure 14. When used for the absorption measurements presented later in Chapters 7,8 and 9,
the procedure for each shot was:
(i) The laser was tuned to the desired wavelength using the tuning procedures described in section 5.2.
(ii) The Telequipment oscilloscope was then used to set the tandem etalon system for maximum laser transmission,and also used to adjust the long path mirrors for the highest signal levels with the lowest noise content.
(iii) Returning to the laser laboratory, the 10 Kftpotent- iometers were then balanced to produce a null voltage on the 7603 oscilloscope and the digitizers armed.
(iv) After the firing-of one shot the laser beam was blocked and a second shot taken (after the necessary two minute wait), with the etalons, digitizers and potentiometers untouched, in order to measure the plasma emission present in the first shot.
In later computer analysis, this emission background was subtracted, and the two resultant laser signals were ratioed to obtain the optical depth. After dividing by the plasma length in order to obtain the absorption coefficient, the resultant traces were stored on floppy disc for the subsequent averaging of several (up to 8) shots for each wavelength in the profile.
Typical results for such an analysis are shown in figure 15 which shows 'raw data' for the input, output, corresponding emission, opacity and absorption coefficient traces for one absorption shot. Digitizer 40- 1-75- Noise
0 50us ' ' 250us (i)Input Laser Signal (ii)Emission Content of (i) mV
2-5
0 1 r 50us 250us (iii) Out-put Laser Signal (iv)Emission Content of (iii) t WKflif1) 2-73-1 3-5i
1-37 1-75
0 T 1 1 1 0 i 1 1 1 50us 250us 50us 250us (v)Optical Depth over780-48m. (vi)Absorption Coef.
Figure 15-Digitizer Traces and resulting Optical Depth and Absorption Coefficient Traces for a detuning of 71GHz from He 15876A Line Centre,measured over 780-48m. 98
5.9 Limits to Long Path Absorption 'Spectroscopy
5.9.1 Experimental Limits
Before this present long path arrangement was developed, the experimental limit to path length, and hence accuracy and sensitivity, appeared to be due to mirror losses and a lack of beam focussing. Given the improved mirror reflectivities, the more precise optical design used, and the superior detection system, it has been seen that these limits no longer hold and that new limitations have arisen.
Firstly, the beam vibrates very slightly for random periods, producing a movement in the final output spot of up to
5 m.m. This causes up to a 10% fluctuation on the measured output intensity for path lengths of over 400 metres. The origin of the vibration remains unknown, although it has been positively identified as arising from the laser or from the beam path between the laser and plasma. At present the most likely explanations are possible air currents or air-borne dust within the laser cavity causing slight deviations (estimated to be less than 0.1 mrad) in the lasing direction. This vibration results in a percentage error in the opacity measurement equal to the 0 - 10% error of the output intensity measurement when the input/output method is used. The problem intensifies, however, when the input/difference method is used for optically thin absorption measurements. For this method the percentage error in the opacity can become very high (up to 30%) for the lowest absorption coefficients measured, and this problem certainly provides the lower limit to measurable f\ — 1 absorption coefficients at approximately 2 x 10" m~ ( T=0.002 over 1 km).
Two more problems arise for path lengths of greater than
800 metres. Firstly, the losses at the plasma end-windows are suprisingly high due to a film of dirt which greatly lowers the 99
transmitted laser powers. The second problem is a 1-5 MHz noise present on the difference signal whose amplitude varies with path length as shown in figure 16.
% Noise 10" - 8- 6- 4- 2- 0- 60 80 100 No of Passes Figure16-HF Noise on Out-put Signal as a function of Length This noise was first thought to be due to problems with the measure- ment of the entire spatial structure of the beam, but the insertion of two beam diffusers before the photodiode showed no decrease in this noise content. Instead the noise is now thought to be due to dust in the laser beam in those sections of the multipassing arrange- ment lying outside of the plasma. Dust free conditions to be installed around the end-windows and multipassing mirrors in the near future should reduce this problem.
Finally there is also a possible problem of vibration reaching the long path mirrors due to insufficient vibration isolation of the tables supporting the mirrors. New commercial table tops, similar to the home-made top described in section 5.3, have now been ordered to replace the existing tables, and these will be bolted directly to a main building supporting wall, which will provide a significantly more stable structure than the existing one.
To summarize, the dominant experimental limit to the generation and use of long paths is set by an unidentified beam vibration, which limits the path at present to 1200 metres. 100
5.9.2 Theoretical Limits
Given that a range of path lengths from 17 cm. (transverse measurement)to K2km. has been demonstrated, and that a powerful laser background source is in use, then consideration must be given to the possibility that there might be an optimum path length to use to obtain the highest accuracy for each point in a line profile.
Applying the condition that the percentage error of the measured opacity should be a minimum, then the arithmetic to calculate the optimum path length is presented in Appendix A.
An example of such a calculation, where the plasma emission is the dominant contribution to the error, is included,showing an optimum opacity of 1.8 for the conditions used. For several of the experiments described later these conditions are typical and path lengths producing opacities of 1-2 were used. Table 5.3 shows the results for typical signal to noise values obtained,as a function of lengthTfor unit opacity measurements with a CW laser of 50 mW introduced into the multipassing system, using the input/output method.
Table 5.3 - Typical signal to noise values obtained for unit opacity absorption measurements using a 50 mW CW laser
Path Detected Noise on signal (mv) ' Resultant Length (m) Signal (mV) Shot noise* Dust Shot noise* Signal (5.6mW=1 V-) on laser Losses on to signal emission Noise signal
10.8 1000 3x10~6 1 3 250 108 1000 4x10"6 4 3 143 434 313 6x10"3 9.9 3 30.5 870 16 2x10~3 0.9 3 4.1 1200 10.7 1x10~3 0.9 3 2.7
* Shot noise for signal integrated over 1 us The signal to noise values listed show that 3% accuracy is obtainable for path lengths of up to ^400 metres. The accuracy drops with increasing path length reaching 10% accuracy for a path length of
600 metres and 37%at a path length of~1.2 km. The low accuracies obtained at the longest path lengths (>800 m.) result primarily from the high end-window losses discussed earlier and it is this problem, together with that of beam wander, that must be solved if absorption coefficients of less than 10"^ m~1(requiring path lengths of >10 metres) are to be observed. 102
CHAPTER 6
PLASMA DIAGNOSTICS
The plasma parameters required for the analysis of an absorption measurement are the densities and temperatures of the various constituents. It has been shown by Kolbe and Playford
(as discussed in Chapter 3) that the recombining plasmas generated in the ten metre device are only partially ionized when run with filling pressures of around 0.5 Torr. The only plasma constituents present therefore are neutral atoms, electrons and singly charged ions, since molecular populations (discussed in Chapters 8 and 9) are assumed negligible. The electron and ionic number densities must be equal due to charge conservation, and the neutral density is therefore the known atomic filling density minus the ionic density. In order to establish all the plasma constituent densities therefore only the electron density requires measurement.
The relationship between the temperatures of the various plasma constituents cannot be treated so trivially, and a more detailed examination of equilibrium is required.
6.1 Temperature Diagnostics
6.1.1 The Maxwellian Electron Energy Distribution
In order for the temperature of a plasma to have any meaning at all, the electron energy distribution must be Maxwellian.
Wilson ( 51 ) shows that this will be so if the electron-electron equilibriation time tQO, given by Spitzer (52 ) to be
T (where In A is tabulated ee by Spitzer) 103
is negligible compared to:
(i) the energy decay time for energy losses from the plasma, which is of order tens of microseconds for the plasmas used here;
(ii) the energy heating time of the pinch, which is approximately equal to the current risetime (1 us);
(iii) the particle containment time, which is also approximately equal to the current risetime. I C _3
For a temperature of 10,000 K and an electron density of 10 cm the expression for igg results in a value of 4.4 x 10 s, and the electron energy distribution should indeed be Maxwellian.
6.1.2 Plasma Constituent Temperatures
It will be advantageous for diagnostic purposes to know whether the temperatures of the electronic, ionic and neutral plasma constituents are equal, since if they are, a measurement of one will provide the others. For them to be equal, the relaxation times between the constituents should be less than the time for plasma conditions to change appreciably. Having obtained the electron- electron relaxation time tgg given earlier, the other relaxation times are given by m; J r r T F . — 10 FR- mG ee ei" MG ee ni i
18 3 and the results for 10,000 K and N^ = 10 cm" are given in table 6.1
The results of electron density diagnostics (presented later in figures 23, 24 and 25) show that plasma conditions change over 3/2 timescales of 5-20 us, and given the Te /Ne dependence of , none of the equilibriation times should rise above 5 us under envisaged plasma conditions. It therefore appears that the equilibriation between all constituents should be sufficiently fast that all the constituents will be at the same temperature. 104
Table 6.1 - Theoretical Equilibriatlon Times Between Plasma Constituents at 10,000K and 1QT5 electrons cm-3 (from Spitzer)
Equi.libriation Time (s) Hydrogen Helium Nitrogen
11 -11 11 Electron-Electron 4.4 x 10" 4.4 x 10 4.4 x 10~ -9 -9 -9 Ion-Ion 3.8 x 10 7.1 x 10 1.9x10 -7 6 Electron-Ion 3.4 x 10 1.2 x 10" 8.4 x 10"8 -8 Neutral-Ion 4.2 x 10 7 x 10~8 2.1 x 10~8
Finally it should be noted that LTE only applies, between
the higher atomic excited states for the plasma conditions antici-
pated. This is not a problem, however, since the analysis presented
later is independent of equilibrium assumptions (except for the
Nil forbidden line theory developed in Chapter 9, for which LTE
is assumed.)
6.1.3 Existing Temperature Diagnostics on the Ten Metre Device
Many spectroscopic methods of temperature diagnostics,
such as measurements of the black-body profile in the infra-red
spectral region, continuum emission and line intensity measurements,
have been used in the past (as discussed by Huddlestone and
Leonard ( 53 )), but these have now been superceeded by superior methods.
The most powerful existing method of plasma temperature measurement is the Thomson scattering of high power laser light by the free electrons - the spectral distribution of the scattered light providing the temperature. Extensive reviews of this technique have been published, such as Evans and Katzenstein (54),
De Silva and Goldenbaum ( 55) and Sheffield (56 ), which discuss both the theoretical background to the scattering process and the experimental difficulties encountered in such measurements. Such Thomson scattering has been used on the ten metre plasma device by Kolbe to obtain temperatures (shown in figure 4 and described in Chapter 3) in hydrogen and helium plasmas, and these temperatures will be used in the analysis of long path absorption experiments described in Chapters 7 and 8.
The author attempted to make use of the apparatus, built by Kolbe, in order to measure the corresponding temperature for nitrogen plasmas generated in the ten metre device (required for
Chapter 9). This attempt failed, however, since insufficient signal/noise level was obtained for the resultant profile to be analyzed.
The first possible explanation put forward for this lack of scattered light, was that the electron density might be lower in the nitrogen recombination plasma than for corresponding times in the hydrogen and helium plasmas. This possibility illustrated the need for electron density diagnostics and these are described in section 6.2 .
A second possibility was that the nitrogen plasma might be optically thick at, or close to, 6943A due to nearby NI and
Nil atomic transitions. A Chelsea Instruments 3021 stroboscope was therefore used as a background source for transverse absorption measurements, across the entire range of wavelengths used in the scattering experiment. No absorption was detected, thus setting an upper limit on the absorption coefficients at these wavelengths of
0.1 m (leading to negligible absorption of both the input laser and the scattered light).
The major problem encountered in these experiments (both by Kolbe and the author) was the very low scattered signal to background ratio., which was typically 0.5-4. Even for the hydrogen and helium diagnostics the accuracy obtained was poor, • 106 and it is therefore intended to repeat these measurements as soon as possible, using improved techniques now being developed on another plasma device at Imperial College.
A final plasma temperature diagnostic, of special interest in this present research given the available long absorption paths, is the measurement of the Doppler profile of an absorption line in which the collisional linewidth is negligible. This is clearly not capable of the spatial resolution of Thomson scattering measurements, since the absorption is measured along the entire optical path, but in the uniform plasmas used in this present research, such a lack of spatial resolution is irrelevant. This particular technique will be of special importance for the nitrogen plasma, since the Nil forbidden line (discussed in Chapter 9) has a negligible collisional width compared to its Doppler width of
60 - 150 m/L A Gaussian fit to the measured lineshape will therefore provide the plasma temperature at all times in the recombination phase, a possibility which will be shown to be attractive in the discussion of the electron density diagnostic results, described in the following sections.
6.2 Electron Density Diagnostics
6.2.1 Emission Measurements
Since the Thomson scattering results suggested that the ten metre device run with a 0.45 Torr nitrogen filling might achieve only low electron densities during the recombination phase, it was decided to measure the plasma emission spectrum close to 6943A where several Nil lines might be present. The device was run with both 0.45 and 0.6 Torr of nitrogen, at a bank voltage of 20kV. The emission was measured with a Monospek 1000 mono- chromator equipped with a Hamamatsu R928 photomultiplier, with 107
the signal cable terminated in 5.6 kQ, corresponding to a
1 us time resolution. The signal levels obtained were extremely low and it was found necessary to use 80 urn mono- chromator slit settings, resulting in a spectral resolution of only 0.8A.
The monochromator was tuned from 6940A to 6973A, and the Nil lines at 6941.8A and 6970.6A were visible on the resultant spectrum for all times between 30 us and 100 us after the peak current, thus confirming the prescence of a signif- icant electron density. Also observable was the NI 6945.2A line and a calculation, based on the assumption of Boltzman level population ratios, suggested a plasma temperature of 11,000 ± 3,000K for the observed times. The signal to background value was very poor for these results (~2) and more accurate conclusions were therefore impossible.
There exist a variety of spectral electron density diagnostic techniques such as line broadening and line ratio measurements (as described by Griem( 31 )). The length of plasma provided by the ten metre pinch, however, makes an alternative technique - refractive index interferometry - capable of far higher accuracy than any of these spectral techniques. In addition this interferometric technique does not require a knowledge of the plasma temperature and can thus be used for the nitrogen plasma.
6.2.2 Refractive Index Interferometry
First used by Dolgov and Mendel'shtum in 1953 ( 57 ) for a spark discharge, this method has become (since the advent of lasers) one of the most widely used methods of electron density measurement in plasmas, and several useful reviews have been written, such as Alpher and White (58 ),
Lochte — Holtgreven ( 59 ) and Jahoda and Sawyer ( 60 ). The plasma refractive index contribution from the
free electrons can be calculated to high precision, for a
frequency (jl) much greater than the plasma frequency 00p, given by
The resultant dispersion relation for transverse
electromagnetic waves, with no magnetic field present and
ignoring collisions, is shown in (60 ) to be
and hence the refractive index is given by
This refractive index therefore varies linearly with changing electron density, and an interferometric measure" ment of its change during the plasma recombination will there- fore allow the electron density to be derived.
One extra contribution to the measured fringe pattern arises from the fluctuating phase difference between the two interferometer arms due to mirror vibrations. The fringes produced by these vibrations, however, have a periodic time of
200 us - 1 msec and can thus be distinguished from the faster changing electron density fringes.
6.2.2.1 Analysis of Interferometer Traces
The traces were analyzed by finding the time late in the recombination (180 - 300 us) where the fast-changing plasma fringes merged with the slower "building" fringes. This time was then assumed to correspond to zero electron density, and densities at earlier times were then found by counting fringes back from this zero fringe time. During the initial current pulse a time should have been reached where the electron density was maximum. The fringes seen at earlier times than this would be due to plasma heating, and could have been used to confirm the peak value of the electron density. This proved impossible for the ten metre plasmas, however, since the interferometer fringe contrast was immeasurable until 20 us after the peak current, presumably due to absorption or beam refraction.
In order to relate the electron density to the measured fringe pattern, consider the MachZehnder inter- ferometer shown in figure 17.
^ / Defector
I / £ Laser ' Plasma Device(NeJ)
Figure 17-The Mach-Zehnder Interferometer
Assuming that the interferometer is aligned to produce interference fringes at the detector, then, as the electron density N changes by Af\J , the refractive index V £ changes by Ane( where 2 Ancl= - AN. e
2 2ME£<>U) This changing refractive index will produce a change in phase
AO, over a plasma length I , given by
A0 = 2rr Anjl) dl X jo
I = e2X ANtDdl JO ©
2 vtceitu:O ® and, since a change in phase of 2TT will produce one inter- ferometer fringe, the number of fringes detected AF will be given by
2 AF = jfA ANe(l) dl 8TC^£-o M„T/ ^ o I = 4-47x10~16A ANJl) dl
Hence the electron density at a time I" , Ne(t") , can be calculated by counting the number of fringes FH-), observed between that time and the zero fringe time, from the relation 5 Njt) = mxii F(t) m-3 where the assumption has been made that the pinch is of uniform electron density, so that Njljldl can be equated to Nc(t.)xl Jo As an example, the expression for Nfi(t) shows that 15 -3 an electron density of 10 cm measured over 10 metres using a He/Ne laser will produce 3 fringes. The fringe pattern should be measurable to 1/4 fringe accuracy, which implies an accuracy in electron density estimation of 8%, under these conditions.
6.2.2.2 Other Contributions to the Observed Refractive Index So far one major assumption made in this analysis is 111
that no other changes in refractive index, comparable to that due to the free electrons, occur within the plasma and that all other sources of refractive index change over much slower timescales than the plasma lifetime. There are however several alternative contributions to the refractive index for which these assumptions might not be valid.
One possible problem is that the sound wave produced by the discharge might travel through the floor to the tables supporting, the interferometer mirrors, which might set these mirrors vibrating at a sufficiently high frequency that the resultant fringes would change over timescales comparable to those of the required free electron fringes. Results presented later, with both inter- ferometer arms aligned through the plasma, show no such vibration- induced fringes.
6.2.2.3 Atomic and Molecular Contributions to the Measured
Refractive Index Change
In addition to the electronic contribution to the refractive index discussed so far, there are three sources of changing refractive index within the plasma of atomic and molecular origin.
(1) During the plasma lifetime, atomic, ionic and molecular number densities will change due to recombination and association processes. Should the resultant changes in refractive index be comparable to that of the changing electron density, then the measured interferometer fringe pattern will lead to an incorrect estimate of the electron density. The atomic species of interest in this chapter are hydrogen, helium and nitrogen and for these species, three methods have been used to estimate the likely atomic and molecular contributions to the 112
refractive index:
(a) Kaye and Laby ( 61 ) list the refractive indices
and for H2, N2 He at S.T.P. and a wavelength of 5893A.
(b) The required atomic refractive indices were
calculated from the expression (Thorne (27))
n-1 = 4-47x10"16N V kM Y(X-XJ)
where No is the ground state population and fj , Aj are the resonance oscillator strengths and wavelengths. These were
obtained from Wiese et al. (30) for bound resonant transitions,
and the data for continuum resonant transitions was obtained by
using the highest continuum wavelength, with an oscillator
strength obtained by using an f-sum rule. This method provided
data for H, He, He+, N and N+.
(c) Allen ( 62) provides values for the polariz-
ability Zi , measured at visible wavelengths, for H, He and N,
from which the specific refractive index (n-1 /Natomic^
given by 2T1>:
The results provided by these three methods are
shown in Table 6.2, and the values listed can be used to estimate
the changes in refractive index during recombination and association.
For every recombination of an electron and an ion the
-28 ~3
change in electronic specific refractive index is 1.28 x 10 m
at 5893A. The resultant changes in atomic specific refractive
index are shown in table 6.3, from which it can be seen that
the contribution to the change in refractive index due to the
atomic species is small (~3.5%) compared to the electronic
contribution. 113
Table 6.2 Molecular, Atomic and Ionic Specific Refractive Indices at 5893A
Species Specific Refractive Index (m~ )
(a) S.T.P. Gas (b) Atomic (c) Polar- Value Used Calculation izability Here
30 30 HI 4.9 x 10~30 4.2 x 10~ 4.5 x 10~ HII 0 30 30 H2 5.1 x 10" 5.1 x 10~ 30 30 Hel 1.34 x 1CT30 1.34 x 10" 1.38 x 10" 1.34 x 10-30 31 Hell 2.83 x 10" 2.83 x 10~31 -29 30 NI 7.1 x 10~ 8.5 x 10~30 1.1 x 10 * Nil 3.4 x ID"30 30 29 3.4 x 10" 29 N2 1.1 x 10" 1.1 x 10"
Table 6.3 Specific Atomic Refractive Index Change during Recombination
Recombination Specific Refractive Index Change (m_3),due to change in Atomic Density, at 5893A
HII —» HI 4.5 x 10"30 -30 Hell —• Hel 1 .06 x 10 J -30 Nil —*-NI 5.1 x 10
Another source of changing refractive index, not usually con-
sidered in estimating the accuracy of interferometric plasma diagnostics,
is that resulting from association. Soon after the completion of the
current pulse, the plasma will be composed entirely of atoms and ions at typical plasma temperatures, but eventually the plasma must become a molecular gas at room temperature. If the change in refractive index produced during this complete association is comparable with
14 -3, that of the electron densities of interest (10 cm ), then the association may introduce inaccuracies into the analysis of the inter- ferometer traces. The estimated changes in refractive index during 114
complete association in hydrogen and nitrogen plasmas are given in table/6,4, and the electron densities required to produce the same change in refractive index are given for comparison.
Table 6.4 Change in Refractive Index during Association at 5893fi
Association Pressure (at room Change in Refractive Index Equivalent temp, of 3Q0K) (assuming complete assoc- change in iation) N (cnT3) e
8 U HI—>H2 0.45 Torr -5.5 x 10" +3.7 x 10 8 U NI—»*N2 0.15 Torr -2.9 x 10~ +2 x 10
Table 6.4 shows that for both gases, the change in refractive index during association is sufficient to produce a large error in the positioning of the baseline (zero fringe) for the fringe counting in the diagnostic experiments. This effect, however, will only be important should a significant fraction of the total association have taken place by the time that the zero fringe is estimated to occur. In Chapters 8 and 9 the likely molecular populations within the hydrogen and nitrogen plasmas are estimated, and the populations present at the zero fringe times (diagnosed later) are shown in table 6.5, along with the resultant error in electron density.
Table 6.5 Likely errors in Electron Density measurement due to Refractive Index changes during Association
Plasma Time of Last Theoretical % of Error in Observed Molecules Assoc- Electron Fringe (us) iated at this time Density (cm~3)
13 0.45 Torr Hydrogen 195 14 5.2 x 10 0.15 Torr Nitrogen 240 10 2 x 1013
Table 6;5 shows that this effect should not be a problem since the resultant error in baseline corresponds-to only a quarter of.a fringe in the diagnostic experiments described later in this chapter. (2) A second changing atomic contribution to the measured
plasma refractive index will occur if spatial variations in atomic
density are present. The plasmas used for the present work are
observed during their current free recombination phase and should be
uniform. This contribution to the changing refractive index should
therefore be negligible.
(3) The final atomic source of changing refractive index is
due to variations in atomic level populations in the lower levels of
transitions with wavelengths close to the interferometer laser wave-
length. Jenkins ( 63) has shown this effect to be negligible for
helium plasma measured at 6328A (as measured later), and in section
6.2.2.5.2 and Chapter 8, experimental results are presented which
show that nearby atomic transitions in hydrogen and nitrogen plasmas
have negligible effects on the interferometer fringe patterns.
The molecular population calculations presented in Chapters
8 and 9 show that likely molecular densities within the plasma are 13 -3
sufficiently low (~10 cm ) until very late times (170us onwards)
that refractive index contributions due to nearby molecular trans-
itions will be negligible.
6.2.2.4 Experimental Arrangement
Attention is confined in these diagnostics to interferometry
using continuous lasers, and pulsed laser interferometric techniques will not be discussed. Such interferometry was first used by Ashby
and Jephcott ( 64) who used a Fabry-Perot interferometer and a
He/Ne laser(operating on both 3.39 and 0.63 urn wavelengths) and measured their electron density by feeding the 3.39 urn interferometer
output back into the laser cavity, and monitoring the change in output
phase via its effect on the 0.63um emission from the laser. The length
of plasma of interest here, however, prevented the use of the two wavelength feedback technique since the number of fringes produced.
would have been too large. Playford used a Fabry-Perot interferometer for such diagnostic measurements on the ten-metre plasma (as described in
Chapter 3). The diagnostics presented by the author, however, have all involved MachZehnder and Michelson interferometer arrangements, since the Fabry-Perot arrangement leads to an Airy fringe pattern, which is insensitive to small changes in refractive index between the fringe peaks. Since the exact interferometer arrangements used in each experiment vary, they will be discussed individually for each run. It will be shown in Chapter 9 that the use of the ten-metre plasma device as a source of nitrogen ions is of particular interest and therefore interferometric electron density results were first carried out for a nitrogen plasma.
6.2.2.5 Electron Density Diagnostic Results
6.2.2.5.1 Run A - MachZehnder Interferometry of Nitrogen Plasmas as a function of Pressure
In order to measure the electron densities in nitrogen plasmas the CW ring dye laser was tuned to 5876A. The MachZehnder arrangement shown in figure 18 was used, the laser beam being focussed to the input end of the plasma device and aligned along the central axis of the plasma. The output from the Motorola 510 Photodiode was fed into the Tektronix 7623A storage oscilloscope which was triggered by the 20 V pulse used to initiate the firing of the z-pinch. One oscilloscope plug-in monitored the plasma current using a Rogowski coil and this was used to reference all fringe patterns to the time of peak current. Problems were encountered with the amount of plasma emission detected by the photodiode, and so a Grubb Parsons 1" diameter N.B. type 2 filter, coated for 5876A and of bandwidth
24A, was inserted to reduce this emission to an acceptable level.
The end-windows used were those built for long path measurements by
Playford and resulted in a plasma length of 10.85 metres, with a
1 - 2% error in length due to possible cold regions close to the end-windows. At 5876A the measured fringe pattern was therefore 14 -3 due to an electron density of 3.51 x 10 cm per fringe.
Results were taken at filling pressures of 0.025, 0.05,
0.1, 0.2 and 0.4 Torr of nitrogen (all with 20kV bank voltage) and, for each of these, traces were taken on various time-bases ranging from 5us/div. to 200us/div. Also taken were shots of the absorption for one pass down the plasma. Both the interferometric and absorption results were most surprising, the traces showing reproducible reversals, as shown in figure 19 and plate 7. It was noticed that there was a loss in fringe contrast between pairs of reversals with a corresponding peak in the single pass absorption trace.
The interpretation put forward to explain this behaviour was that the reversals corresponded to times at which the electron density decay changed direction (i.e. bounced), and that the loss in fringe contrast occurred when the electron density was rapidly increasing, thus suggesting that the peaks observed in the absorption trace were due to beam refraction. The fringe pattern was therefore counted back from the zero fringe as previously described, but the direction of electron density change reversed at each reversal point, as shown in figure 19 (taken from the 0.15 Torr nitrogen plasma measurement of Run B).
The use of multiple shots per time-base setting allowed all such reversals to be identified, and was helpful in the identification of the last electron density fringe where confusion with the mirror vibration fringes was possible. Because of this possibility, the electron densities obtained from all the interferometric runs are quoted to an accuracy of a quarter of a fringe.
Analysis of these traces, including the bounces, showed an electron density which, at a given time, increased with filling pressure up to pressures of 0.1 - 0.2 Torr and then remained approx- imately constant for further increases in pressure. The period between Laser VjQtWn 70%N ^ * \JOO°/o
Plasma
30% M 100%^: ^100% Screening Filter i —Pinhole i + Lens i i _ _ JJPhptodiode ! Figure 18 -Mach-Zehnder Interferometer used for Electron Density Diagnostics
18M.^100% 12M.*F«100%
Plasma
100%^ filter i —Pinhole • --Lens i 1 uPhotodiode < I 1 *100% Laser Screening Figure 20 -Michelson Interferometer used for Electron Density Diagnostics Measured Fringe Pattern
I I I. I m ^AlWAl \ / A» \ / \ i VA v | r \ y V\ I \h \v 1 Y> ] . 1 T 1 100% Laser Transmission 1 1 1 1 1 1 1 1 1 1 : i i i Plasma Emission i i \ « 1 i i 1 1 ' i \ i I V y\ 1 I ^ i 1 1\ V^ h i ' 1 « 1 nsities J Diagnosed felejctronD * i ' \ ! i i i \ 1 1 \ 1 1 \ 1 /\ !i i \ I / !\ i i \ 1/ l \ i \i/ i \ ' ! i
I I I I Time After Peak Current
Figure 19-Interpretation of Observed Fringe Pattern, Laser Transmission and Plasma Emission for a Typical Plasma in terms of Density Bounces 120
bounces was found to increase with increasing filling pressure ranging from 25 - 35us at a pressure of 0.025 Torr to 70us at
0.4 Torr. Although the results were consistent, it was difficult to interpret the last fringe at several pressures and so the experiment was repeated with a more sensitive interferometer design.
6.2.2.5.2 Run B - Michelson Interferometry in Nitrogen Plasmas
The Michelson interferometer design shown in figure 20 was used to provide double the optical path length used in Run A, thus doubling the accuracy of the diagnostic measurements. It was decided that the electron density results obtained for pressures of less than
0.1 Torr and more than 0.3 Torr were unlikely to be of great interest, since the maximum electron density (and hence Nil density) was of prime importance, and Run A suggested that this should occur at a filling pressure of ~ 0.2 Torr.
The two 4% beamsplitters allowed the emergent double- passed beams to be recombined and the two curved mirrors approximately refocused the laser at the input end, hence raising the detected intensity. The CW ring dye laser was again tuned to 5876A which, with the double-passed length of 21.7 metres, produced one fringe per 14 -3 electron density of 1.75 x 10 cm •
Results were taken with nitrogen filling pressures of 0.1,
0.15, 0.2, 0.25 and 0.3 Torr (all with 20kV bank voltage) and the results for 0.15 Torr are shown in plate 7, in which the high reproducibility of the fringe patterns can be clearly seen. The electron densities deduced from this run are shown in figure 23 and are discussed after the presentation of run G.
Two variations of the interferometry were attempted at a filling pressure of 0.1 Torr of nitrogen. Five shots were taken with a wavelength variation from 5853A - 5899A, and no significant change (i) Superimposed Current Traces (Taken with a Rogowski Coil)
^m *A WBmV (a) 5us/div. J^H(bl10us/div. S HSiBm "M(c)20us/div. BBB(d)50us/div. B (ii) Interferometer Traces
Plate7-Oscilloscope Traces for Electron Density Diagnostic Measurements in 015 Torr Nitrogen Plasma (measured over 21-7metres at 5876A) 122
in the fringe pattern was noticeable. The expression for the refractive index close to an absorption line is given by Thorne ( 27 ), for a detuning AX from line centre, to be
n-1 « 2-23x10~16Njfj Xj AX where the absorption line has a wavelengthXj , an oscillator strength fj , and a lower level population Nj. This lack of change in the observed fringe pattern over a variation in wavelength of
40A showed that no atomic transitions of wavelength close to 5876A were responsible for the measured fringe patterns. The resolvable change in fringe pattern was 5% (say) which, for an immeasurable change in refractive index over 40A, suggested a minimum detuning to the nearest atomic line, providing a significant contribution to the refractive index, of ~ 800A. Transitions, in the visible spectral region occur between excited states of low population - 10"^ of ground state population), and hence the refractive index for such transitions at 800A detuning will be negligible compared to that of the resonant transitions , discussed earlier. .
The second variation attempted was to record a trace with a changed bank voltage. Definite changes in fringe pattern were observed, and it was therefore decided to examine this electron density dependence of bank voltage further.
6.2.2.5.3 Run C - Interferometry at a Higher Bank Voltage This run utilized the same experimental arrangement as Run B with the laser still tuned to 5876A, the z-pinch run with a bank voltage of 24kV and results taken at filling pressures of 0.1, 0.2 and
0.3 Torr. The resultant electron densities are shown in figure 21.
When these results are compared with those taken at 20kV (shown in figure 23), it can be seen that for a higher bank voltage, the time between bounces decreased whilst the height of the bounces increased. 123
Electron Densities(10^cm~
Times(us)
Figure 21-Diagnosed Electron Densities for 24kV Nitrogen Plasma measured over 217metres at 5876A This suggested that the higher plasma electron densities and
temperatures produced using a higher bank voltage (44% increase in
bank energy) increased the frequency of the bounces. This agreed
with the results from Run B which showed a decrease in bounce
frequency with increasing filling pressure (and therefore decreasing
plasma temperature).
One possible explanation was that a radially propagating
wave of neutral or electron density might be converging onto the
plasma axis, thus causing the observed bounces in electron density.
In order to test this off-axis measurements were made.
6.2.2.5.4 Run D - Interferometry at various off-axis positions in 0.15 Torr Nitrogen Plasma
For this experiment the CW laser was run with a Rhodamine
640/Rhodamine 6G mixture and was tuned to provide fluorescence in a
Phillips Cd bulb at 6438.9A, with . a power of 80mW. Playford's angled end-windows were replaced with plane windows on to which were taped paper masks, allowing the beam to be set 0, 1, 2, or 3 cm off-axis with an accuracy of ± 2 m.m.
Using the results from Run B, it was decided that 0.15 Torr was the optimum nitrogen filling pressure for maximum electron density, and the off-axis scan was therefore taken at this pressure only, with a 20kV bank voltage. With an interferometer length of
21.3 m. and a laser wavelength of 6438.9A the fringe pattern corr- esponded to an electron density of 1.63 x 101Acm~3 Per fringe and the off-axis electron densities obtained are shown in figure 22.
The results show evidence of electron density gradients across the centre 3 cm. of the plasma during the bounces (indicating that the peaks observed in the absorption traces in Run's A and B are probably due to refraction during the bounces). The traces measured at 2 and 3 cm. off-axis positions show a slight lengthening of each 125 Electron DensitiesdO^crn^)
Figure22-Diagnosed Electron Densities at various distances from the plasma axis for the 0-15Torr/20kV Nitrogen plasma measured over 21-3m. at 6439A 126
bounce which is compatible with the idea of a radially propagating wave which would register twice on these traces. The difference in time between the two peaks of one bounce on the 3 cm. off-axis trace would be 3/1? of the bounce period which is barely resolvable.
The density gradients appeared small and so were ignored during the remainder of the diagnostics (but returned to in Chapter 9). Given the significance of the bounces , it was decided to re-measure the fringe patterns for hydrogen and helium plasmas since no such oscillatory behaviour was previously diagnosed by Playford and Kolbe.
6.2.2.5.5 Runs E, F - Electron Densities in Hydrogen and Helium Plasmas
For these experiments it was decided to simplify the experiment by replacing the CW laser with a Spectra-Physics 124 He/Ne laser. Results were taken for filling pressures of 0.15, 0.3 ,0.45 and
0.6 Torr in hydrogen, and 0.15, 0.3 and .0.45 Torr in helium, and the results are shown in figures 24, 25 and discussed after run G. With this length and laser combination the -fringe patterns obtained corresponded 14 -3 to 1.66 x 10 cm per fringe.
Again it was found that the fringe pattern was difficult to interpret at late times due to building fringes, and that fringe contrast was lost at times earlier than 25us. In order to measure these times more clearly then it was decided to use single-pass interferometry at a lower wavelength.
6.2.2.5.6 Run G - 5145& Interferometry in Hydrogen, Helium and Nitrogen Plasmas
For these measurements the Spectra Physics 164 Argon-Ion laser was used at threshold power (in order to prevent lasing on multiple longitudinal modes) and results were taken for various time-base settings for:
(i) Hydrogen - 0.15, 0.3, 0.45 and 0.6 Torr pressures
(ii) Helium - 0.15, 0.3 and 0.45 Torr pressures
(i-ii) Nitrogen - 0.1, 0.15, 0.2, 0.25 and 0.3 Torr pressures Electron Densities(10^cm3)
Figure 23-Diagnosed Electron Densities as a function of Pressure and Time for the Ten Metre Plasma Device run with a Nitrogen filling and a 20kV Bank Voltage (10-65m. 14 -3 Electron Densities(10 cm ) (a)0-15Torr Playford and Kolbes result 150 200 (d) 0-6 Torr 200 250 Time(us) 24-Diagnosed Electron Densities as a function of Pressure and Time for the Ten Metre Plasma Device run with a Hydrogen filling and a 20kVBank Voltage (10-65m. (c) 0-45 Torr Time(us) Figure 25-Diagnosed Electron Densities as a function of Pressure and Time for the Ten Metre Plasma Device run with a Helium filling and a 20kV Bank Voltage. (10-65m. Runs A, B, E and F. Using all of the results, the best fits to the data were estimated, and these final results are shown in figures 23, 24 and 25. The nitrogen electron densities are as described in the previous sections with the bounces occurring with a frequency that decreases with increasing pressure. The results in hydrogen show similar bounces at early times and again the frequency of these oscillations decreases with increasing pressure but with a frequency that is far higher than for nitrogen. The electron density reaches a maximum at a pressure of 0.45 Torr, and it is this pressure that will be used in the absorption results presented later. Also shown on the 0.45 Torr trace is the result obtained by Playford and Kolbe. There is excellent agreement between the two results for the times between 70us and 130 us with a slight (half fringe) disagreement at later times. The main disagreement occurs before 70 us, where the bounces become apparent in the present results. Further examination of Playford and Kolbe's oscilloscope traces showed that the bounces were indeed present for their measurements, but were apparently ignored. (It should be noted that no absorption data has been published for times earlier than 70 us.) In helium the maximum electron density was observed at a filling pressure of 0.45 Torr which will therefore be used in the absorption experiments discussed later. Again bounces were present, with a similar bounce period to that observed in the nitrogen plasmas. When these recent results for helium were compared with Playford's earlier diagnostics (for 0.45 Torr He plasma) there were vast differences (as indicated in figure 25). Playford did not diagnose any bounces to occur, and again an examination of his original oscilloscope traces showed them to have been present. Another major difference between the two results was that Playford's densities were 14-3 approximately 5 x 10 cm higher than the author's results for late Relative Intensity Time(us) Relative Intensity Figure 26 -Broadband Plasma Emission Measurements .132 times (>200 us). The present interferometer traces showed no fringes later than about 200 us, and further interferometric measurements, looking especially at these late times, have still failed to observe more fringes. The conclusion reached is therefore that the electron density does decay to zero at around 200 us and that Playford's results are anomalously high, presumably due to a mis-interpretation of the building fringes present on his traces. This means that the electron densities in helium used in Playford's publications (34,35,36) are seriously in error. This error has no effect, however, on the conclusions drawn in those papers, since the methods of analysis used were independent of electron density. 6.2.2.5.7 Run H - Emission Measurements The final experiment connected with the electron density measurement was to examine the plasma emission in search of bounces in the emitted intensity. Broadband emission measurements using a photodiode were made for 0.15 Torr nitrogen, 0.45 Torr hydrogen and 0.45 Torr helium plasmas and the results are shown in figure 26. The emission traces appeared very similar to the electron density results already shown. The main difference was a large emission peak present in helium stretching from 60 - 800 us and reaching a peak value of 20% of the main plasma emission peak. This is probably due to emission from the 23P - 33D transition at 5876A which 3 increases late in the discharge due to overpopulation of the 2 P 3 level due to the metastable 2 S level. The emission measurements clearly confirm the existence of- the electron density oscillations, and explanation of their origin is clearly required. 6.2.3 Possible Explanations of the Electron Density Oscillations 6.2.3.1 Previous Observations In an attempt to explain these bounces, earlier work performed on a smaller plasma device was examined. Firstly, Jenkins ( 63 ) .133 ran a 75 cm long z-pinch with argon, hydrogen and helium fillings and observed similar electron density oscillations. Secondly, Burgess, Dangor and Jenkins ( 65 ) measured the filling pressure dependence of the maximum electron density obtained in both Jenkins1 z-pinch and a second z-pinch. They found that the electron densities achieved peaked with filling pressure at a critical value of Pc. They suggested that the electron density oscillations were only seen for filling pressures greater than Pc,and showed that the 75 cm z-pinch only developed a shock for pressures below Pc. This work was continued by Mahon ( 66 ) who ran the 75 cm pinch; and observed electron density oscillations in argon and nitrogen plasmas. She presented theoretical analysis of a critically damped cylindrical pinch discharge for which she predicted shock velocities, compression ratios and times for maximum compression (all of which agreed with experiment to a factor of 2) as a function of filling gas pressure. She discussed the possibility of the bounces being due to a propagating shock wave left after the initial compression, and concluded that, although the idea of a propagating wave was correct, in fact the wave was of an acoustic rather than shock nature. She assumed that the presence of such an acoustic wave indicated that the plasma must be providing acoustic amplification for the wave to propagate for such a length of time, and considered two possibilities. Firstly, the D'Angelo recombination instability., in which the electron density and temperature dependence of the recombination coefficient can be such that differences in electron density between two regions (e.g. in a wave) might increase. Secondly, Ingard ( 67 ) has shown acoustic amplification to be present above a critical electron density. The first of these mechanisms only applies for a plasma in which the electron temperature is far higher than the ionic temperature, and is therefore ignored here. The second mechanism is discussed further later. 6.2.3.2 Radially Propagating Acoustic Waves In order to identify the nature of the acoustic disturb- ance present, Mahon (66 ) derived the dispersion relation for such waves and showed three independent modes to be present: (i) The ordinary neutral sound wave, obeying the dispersion relation U)= kc , in which there is attenuation due to thermal conductivity, viscosity and wall losses, and in which all three components of the plasma oscillate in phase. (ii) A second mode,which is a degenerate ion-acoustic mode, where the electrons and ions move in phase. Mahon states that this mode has a decay length of only one acoustic wavelength and so ignores this term. (iii) The final mode is a degenerate electron oscillation with a wavelength of one Debye length,and again Mahon ignores this as it should be heavily damped. The question is whether a neutral sound wave can produce the observed electron density bounces, and, in order to estimate this, the two possible types of acoustic oscillation should be considered: (i) A propagating acoustic pulse moving at the neutral sound ma be speed Cn Y present where , _ /YMh1 v^ir for a neutral species of temperature Tp and atomic massMp. Such a wave of increased neutral density (and hence electron density) will result in oscillations in the axial electron density, with a frequency VT given by .135 . £n_ _ [W T" D where D is the plasma diameter. (ii) The alternative mode of oscillation is due to an acoustic standing wave. In the case of the ten-metre plasma device the wave must be cylindrically symmetric and the mode with wavelength equal to twice the plasma diameter is forbidden for such a longitudinal oscillation. The fundamental mode is therefore that with a wavelength of approximately two thirds of the plasma diameter and hence has an oscillatory frequency Vs where V = L£N_ FMEL 5 2 20 V4D Mn It will be shown later that the damping for acoustic oscillations is proportional to the square of the acoustic frequency and it is only necessary therefore to discuss the fundamental standing mode. Given the different bounce frequency between these two modes, it is possible to differentiate between them by comparison with the measured diagnostic results. For all three species measured y will be 1.67, and the measured bounce periods in the hydrogen and helium plasmas can be used to predict plasma temperatures for comparison with Kolbe's measured values. The results are given in table 6.6, which shows the measured bounce times in the two plasmas, and table 6.7, which shows the two derived temperatures together with Kolbe's measured temperatures. Table 6.6 Measured Bounce Times in Hydrogen and Helium Plasmas Plasma Bounce Time (us after peak current) 1 2 3 4 5 0.45 Torr H2 15+1 27±1 41 ±2 55+2 72+3 0.45 Torr He 22+1 45±2 68+2 100+5 - Table 6.7 Temperatures derived from Bounce Times given in Table 6.6 Plasma Bounces Period (us) Average Time (us Temperatures (°K) after peak current) Propagating Standing Kolbe (Theoretical) (Theoretical) (Experimental) 1-2 12+2 21 14,500+5,000 6,450+2,000 18,000+2,000 0.45 2-3 14+3 34 10,700+4,600 4,750+2,000 15,500+2,000 Torr 3-4 14+4 48 10,700+6,000 4,750±2,700 14,000+2,000 H 2 4-5 17+5 63.5 7,300+4,300 3,200±1,400 12,500+2,000 0.45 1-2 23+3 33.5 15,800+4,100 7,000+1,800 15,000+2,000 Torr 2-3 23+3 56.5 15,800+4,100 7,000+1,800 13,700+2,000 He 3-4 32+7 81 8,200+3,600 3,600+1,600 11 ,700+2,000 Table 6.8 Bounce times and periods in 0.15 Torr nitrogen plasma Bounce Bounce Period (us) Average Time in Period (us) 30 75 128.5 184.5 CUJN Plasma Temperature (K) Figure 27- Predicted Bounce Period for a17cm. diameter Plasma Column as a function of Temperature Figure 28-Plasma Temperature in the 0-15 Torr/20kV Nitrogen Plasma as diagnosed from the observed Bounces It can be seen from Table 6.7 that, despite the high errors in the derived temperatures (the percentage error in temperature is twice that of the bounce period), the temperatures derived by assuming a standing wave are inconsistent with the measured values. The propagating wave, however, is in moderate agreement with Kolbe's results and it is therefore assumed that the observed oscillations are due to the propagation of a cylindrical acoustic pulse. Given this explanation of the observed bounces, it is therefore possible to use the observed bounce period in all three gases, and at all filling pressures, to estimate the plasma temperatures, since the relationship shown in figure 27 applies. The 0.15 Torr nitrogen plasma (of 20kV bank voltage) is of interest for absorption measurements discussed in Chapter 9. The measured bounce periods for this plasma are given in table 6.8, and the relationship shown in figure 27 has been used to provide the required plasma temperature, the results being shown in figure 28, as a function of time. Figure 28 shows that the temperature in the nitrogen plasma, used for later absorption measurements, is comparable to that measured previously for hydrogen and helium plasmas. Figures 4 and 28 are therefore used as the temperature diagnostic results for hydrogen, helium and nitrogen plasmas in the analysis of the long path absorption measurements presented in Chapters 7, 8 and 9. 6.2.3.3 Persistence of Acoustic Waves The persistence of these neutral waves (presumably generated in the post-pinch expansion) with such little damping requires analysis. Two types of damping are present in the pinch. Firstly that due to heat conduction and viscosity leading to an —c(X amplitude decay e where (from Kinsler and Frey(68 )) .139 <* - I m + x(Y-i) " 2PoC3 \ 3 . 2-3o)2T) 3 2p0c Putting in values in this expression for o< using the lowest standing wave frequency V5 (which presumably will be the lowest frequency component of the propagating acoustic pulse predicted) suggests a damping loss of.8 - 10% per oscillation which is significantly smaller than observed (25 - 75%). Presumably the second loss mechanism - wall loss -, which is more difficult to treat mathe- matically, is responsible for the majority of the damping. One more complication discussed by Mahon is that acoustic amplification as described by Ingard (67 ) may be important. This paper has been followed by three others by Ingard and Schulz, and the four of them will be referred to as I (67 ), II (69 ), III (70 ) and IV (71 ). Oscillatory behaviour in otherwise quiescent plasmas has been seen before: Stickler and Stuart (72 ) noted a kink in a D.C. discharge at discrete modulation frequencies; Berlande et al.(73 ) observed electron density and emission oscillations in helium and neon afterglow plasmas (in a rectangular discharge); and Wojaczek (74 ) has observed emission oscillations due to externally applied acoustic waves. Ingard I considered the equation of motion for the neutral plasma component and demonstrated the existence of a source term Sq in the acoustic wave equation given by h . 3 )h r.T .3/ 7 where F1 is the unpeturbed neutral pressure and ^^p the electron- .140 neutral collision cross-section. He then considered a neutral density pertubation ANp due to an acoustic oscillation which in turn produced an electron density perturbation ANq where 6 (with a corresponding change in ion density). He showed that this density perturbation could act as a source in the wave equation result- ing in acoustic amplification, and derived an expression (used by Mahon) to predict a critical electron density below which acoustic amplification would not occur. Using this expression, and changing the result to account for the lowest acoustic mode having a wave- length of 2D/3 (and not D as used by Ingard), produced the critical electron densities for the ten metre plasma shown in Table 6.9. Table 6.9 Critical Electron Densities in the Ten Metre Plasma above which Acoustic Amplification can occur Species Pressure (Torr) Critical Electron Density (cm ) 14 H 0.45 3.4 x 10 13 He 0.45 9 x 10 13 N 0.15 7 x 10,J The critical densities obtained are lower than the observed densities at which the bounces vanish, but are of the correct order, and the ratios between the three critical densities shown agree with the experimental ratios. It therefore appears possible that acoustic amplification may well be present for the propagating neutral wave observed. In papers II, III and IV Ingard and Schulz further develop these ideas, especially the possibility that the three plasma constituents might oscillate slightly out of phase, resulting in slight charge separations. They suggest that the amplification arises due to electron-atom collisions. In the absence of the • acoustic wave the energy transferred in such collisions simply increases the neutral kinetic energy. With the presence of the wave, however, some of this collisional energy is transferred to acoustic modes, resulting in wave amplification. An alternative explanation, put forward in IV is that the acoustic disturbance distorts the balance between charge diffusion and ionization. 6.2.3.4 The Neutral Contribution to the Plasma Refractive Index In the analysis of the electron density traces it was assumed that the atomic density within the plasma remained constant and that the entire measured refractive index change was therefore due to the changing electron density. If these bounces in refractive index are indeed due to propagating neutral waves then the assumption about atomic density is incorrect, and both contrib- utions to the changing refractive index must be taken into account during the bounces. Since 'n"1'fotal = + where (n-1)a|.oC Naf- = ANaf and (n-1)elo the change in refractive index An during a bounce is therefore given by An = AANgj.+BANe For propagating neutral waves the relationship between the two changing densities has already been given and therefore: An = / ANgj.+ B]ANe \T£ I As an example the hydrogen 0.45 Torr plasma with an observed bounce at 40 us can be considered. At this time the unperturbed densities 22 3 21 3 are Na(. = 2.8 x 10 m" and Ng = 1 .35 x 10 m- . From section 6.2.2.3 -30 ?ft ^ A = +4.5 x 10 ancj g = -1.48 x 10 m and hence 29 An = 5-5x10" ANe and the diagnosed electron density bounce will therefore be three times higher than shown in figure 24. Such a procedure could be carried out for all bounces on all of the electron density traces, but absorption results presented later are restricted to late times (70 us - 240 us) where such bounces are small. The exception is the nitrogen plasma used, and this is discussed in further detail in Chapter 9. 6.2.4 Elimination of the Density Bounces It will be seen in the following chapters that these bounces can cause severe problems when long optical paths are required. Whatever the origin of the bounces, and whatever their damping mechanism, it is most likely that reducing the plasma vessel diameter should reduce their effect. This will increase the natural frequencies supported by the plasma and the damping of the propagating wave will therefore increase (as the square of the decrease in tube diameter). The lower diameter will also lead to a lower period between successive wall reflections and wall losses will therefore increase. One extra advantage of the lower tube diameter is that the existing bank energy will be discharged into a smaller plasma volume, presumably leading to increased ionization and higher plasma temperatures, which will thus increase the range of plasma conditions available for long path absorption measurements (an example is that higher electron densities and plasma temperatures would greatly increase the expected Nil forbidden line absorption coefficients of interest in Chapter 9). .143 The existing tube diameter of 17 cm should be capable of being reduced to 12 cm without moving the plasma boundary layer into the central 7 cm diameter region in which the absorption measurements are taken.' • A second method of reducing the effects of such bounces is to diffuse the acoustic waves. The cylindrical geometry of'the plasma device leads to a focusing of the waves on the plasma axis, and simple diffusers should considerably reduce the effects of such waves by randomizing the acoustic wave front along the plasma length. Two possible methods of achieving this are: firstly to introduce random variations in the diameter of the plasma vessel, and secondly to insert partially reflecting flat plates into the plasma volume. A combination of both methods should eliminate the bounces and work should start soon on testing these methods by utilizing a two-metre section of z-pinch. The problems with such oscillatory electron densities will be returned to in Chapter 9. 6.3 Conclusions drawn from Diagnostic Measurements New diagnostic experiments have been attempted, with the ten-metre plasma device being run for the first time in nitrogen. Several major conclusions have emerged: (i) Thomson scattering measurements have been attempted on the nitrogen plasma but without success due to low electron densities present in the 0.45 Torr plasma observed, combined with high back- ground plasma emission. (ii) Interferometric electron density measurements have been performed with increased sensitivity using a double-pass Michelson 13 3 arrangement capable of an accuracy of 5 x 10 electrons per cm . Measurements have been made over a wide range of conditions in hydrogen, helium and nitrogen plasmas. .144 (iii) The results show density oscillations to be present in all plasmas examined, and these are thought to be due to a cylin- drical acoustic wave propagating at the neutral sound velocity. (iv) These density oscillations have been used to estimate the temperature of the nitrogen plasma used for absorption measurements. (v) The diagnostic results presented here in a hydrogen plasma are in good agreement with most of the results obtained earlier by Kolbe and Playford. For a helium plasma, however, there are very large discrepancies between the present and previous results, the present results superceeding the previous (less rigorous) ones. (vi) Using the results presented in figures 4, 23, 24, 25 and 28, the available range of plasma temperatures and electron densities used for absorption measurements are tabulated in table 6.10. Table 6.10 Plasma Temperatures and Electron Densities achievable with the Hydrogen, Helium and Nitrogen Plasmas used in Absorption measurements _3 Plasma Temperature Range (°K) Electron Density Range(cm ) 15 0.45 Torr Hydrogen 4,000 - 18,000 0-1.5x10 15 0.45 Torr Helium 8,000 - 18,000 0-1.0x10 15 0.15 Torr Nitrogen 7,000 - 16,000 0-1.0x10 CHAPTER 7 LONG PATH MEASUREMENTS OF THE Hel 23P-33D 5876A PROFILE The plasmas provided by the ten metre device, diagnosed as described in Chapter 6, were used to study a number of weak spectral features over path lengths of up to 1200 metres. The first experi- 3 3 ment described is a measurement of the He 2 P-3 D 5876A line profile, which follows from the tentative experiment performed by Playford (described in Chapter 3). The experimental results for this profile fall into two sections - a measurement of the far wing, including a forbidden line, and a measurement of the line centre profile. 7.1 The Hel 23P-33D 5876A Far Wing Absorption Profile 7.1.1 Results The apparatus for this experiment was that described in Chapters 3, 4 and 5 and shown in figure 14. Path lengths of 43.4 - 1214.1 metres were used, with the CW laser run in Rhod- amine 6G, and the plasma device run with a bank voltage of 20 kV and filling pressure of 0.45 Torr of helium. As described in Chapter 5, a Phillips lamp was used to tune the laser to within 1 GHz of the transition line centre, and detunings of up to 350 GHz (4A) were then obtained, as previously outlined, to an accuracy of +1 GHz (+10 mA). For detunings of up to 160 GHz, the input and output signals were recorded since optical depths of more than 0.69 could be achieved with the available path lengths. The limit in accuracy was therefore due to dust and plasma emission. For detunings of greater than 160 GHz, however, the input/difference method .146 3 k(10 m) k(10'3iii1) (a)80us (b)120 us 200 300 . 200 300 Detuning(GHz) Detuning (GHz) ktlO'm1) k(10"3d, (c)160us 12 (d)200us 4 I I ' T" 200 300 100 200 300 Detuning(GHz) Detuning(GHz) k(10"3m1) (e) 240 us 23 P- 31 D Satellite Predicted At 99-6GHZ 200 300 Detuning(GHz) Figure 29-The He I 5876A Far Blue Wing Absorption Profile measured in a 0-45 Torr Plasma over Long Optical Paths! 40-1200lnT~ (i) Linear Plot .147 1 Loglklnf1)) Loq(k(m" )) (a) 80 us •2 t (b)120us -2-5 -3- i fa "V i -3-5" v -3- •full -4- -3-5- I i 1- »—• ' i' 'i 30 50 100 «200v 300 3H0 5-+0 iJo 200' 300 Detuning(GHz) Detuning(GHz) Log(k(m"1)) Log(k(m"1)) "2(c)160us (d)200us I . -2++t T+ -2-5- V, \ ( -2-5- Vv -3- V V| 3-5- 1 lf 4 h miL -3-5:: ' 30 50 100 200 300 30 50 1(Jo 2&0I0iLr.0 Detuning(GHz) Detuning(GHz) Log(k(m"1)) (e) 240 us G radiant=-2- -3-5+ 30 50 .100 200 300 Detuning (GHz) Figure 29-The Hel 5876A Far Blue Wing Absorption Profile measured in a 0-45 Torr Plasma over Long Optical Paths(40-1200m.) (ii) Log-Log Plot .148 (discussed in Chapter 5) was used, and the errors increased (to -10-30%) due to beam movement at the longer paths used ( >800 metres). Initial results showed large absorption peaks at times corresponding to those electron density bounces occurring before AO us after the peak current. The delay unit was therefore set for 50 us and results recorded for times between 50 us and 250 us after peak current. The results for times of 80 us, 120 us, 160 us, 200 us and 2A0 us are-presented in figure 29, which shows measurements of the blue wing of the profile, for detunings from 31 GHz - 3A0 GHz (0.35ft - 3.9ft), and the results are plotted on both linear-linear and log-log plots. The latter plot shows quite clearly the Lorentzian ( AV~2 ) allowed wing,with the forbidden component clearly super- imposed upon it at all times. Obviously this profile replaces that of Playford since it measures the expected Lorentzian profile far more accurately. The second comparison between these results and the preceeding ones concerns the apparent far-wing satellite in Playford's profile at a detuning of approximately 270 GHz (3ft). In this (more accurate) profile no sign of such a satellite is seen and a further examination of Playford's data suggests that his satellite may have been due to errors in only three data points. Given the reasonable fit to a Lorentzian allowed wing, the profile was used to estimate the underlying wing at the line- centre of the forbidden component as a function of time, and this is shown in figure 30. This underlying allowed wing was then subtracted from the measured data at the forbidden line-centre detuning to obtain the forbidden line-centre absorption coefficient shown as a function of time in figure 31. Finally, these two quantities were ratioed and the result is shown in figure 32. The ratio obtained is approximately constant from 80 us to 2A0 us .149 14 3 1 ' TKa(1fi m" ) 1-2- / 1-0- 0-8- 0-6- / / 0-4- y / 0-2- 0 0 50 100 150 200 2 50 Time(us) Figure 30-The He5876A Allowed Line Absorption Coefficient-at the Intercombination Line Detuning 1-2 3 1 kf(10" m" ) 1-0- 0-8- 0-6- 04- 0-2- 0 0 50 100 150 200 250 Time(us) Figure 31-The He 5876A InFercombination Line Centre Absorption Coef. 0-9 T Af/ 0-8 1 k: J 0-7- * . : 0-6- 0-5- 0-4 0 •50 # 100 150 200 250 Time(us) Figure 32- The He 5876A Intercombinafion Line Centre to Underlying Allowed Wing Absorption Ratio ranging from 0.57 - 0.76 and does show some oscillatory structure, which may well correspond to the electron density bounces, but the comparison is unclear since it was impossible to obtain definite identification from the interferometric results of electron density bounces after 100 us. 7.1.2 Analysis Consider the He 2p, 3d energy levels shown in Table 7.1, using data from Moore ( 75 ) Table 7.1 Helium 2p and 3d energy levels Level Energy (cm ) 3 2p P? 16.9081.11 3 2p 169081.19 3 2P J>0 169082.19 186095.90 3d ,"3,2,1 3d D 186099.22 At a temperature of 5000K (for instance) the FWHM Doppler width is 12.9 GH3 and several of the possible transitions occurring between the levels shown will be unresolvable. The resultant spectrum is shown in Table 7.2, where the detunings are measured from the allowed line main component. Table 7.2 Helium 2p - 3d Transitions Transition Detuning (GHz) 3 3 Allowed Main component 2p PQ - 3d 0 3 3 ' ' Allowed Fine component 2p Po - 3d D^ -31.2 Forbidden Main component 2p3p - 3d^D 99.6 3 2,1 1 2 Forbidden Fine component 2p P - 3d D 68.A The measured absorption profile (figure 29) shows the maximum .151 forbidden line absorption to be at a detuning of 96+iGHz. When a Doppler profile was fitted to the forbidden line profile, the detuning of the transition line centre was found to be 100+2GHz, which agrees very accurately (to within 1/4 of the profile HWHM) with 3 1 the theoretical 2p P - 3d D intercombination line detuning. A calculation of the spectral line shifts expected for the electron densities present was carried out, using line shift data for Hel 5876A given by Griem ( 31 ), which showed that such shifts would be very small «0.5 GHz) for the conditions diagnosed. The conclusion is therefore that the interpretation of the observed 3 1 satellite as the 2 P - 3 D intercombination line is indeed correct. There may well be a fine structure component of this intercombination line at a detuning of 68.4 GH?. Unfortunately this line would be 8 times weaker than the observed line and would not be visible amongst the scatter of points of the allowed wing at that detuning. When the previously discussed improvements to the experimental apparatus have been completed, it is hoped to resolve this line. It will be shown in section 7.2 that the He 5876& allowed profile close to line centre deviates considerably from the theoretically expected shape and the peak absorption value measured is very uncertain. Because of this it was impossible to compare the forbidden and allowed line centre absorption ratios, and instead the ratio of absorption coefficients of the forbidden and allowed profiles both measured at the forbidden line detuning were considered. At its line centre the forbidden line has an absorption coefficient k^ shown in Chapter 2 to be given by — • 8tc lowerf Avd 9| .152 where Af is the fobidden transition probability, N^^gp^ is the number, density for the transition lower level and Av^j is the Doppler HWHM. It'is shown in Appendix B that the allowed line has an absorption coefficient at the forbidden line detuning AVf of k^ where where AVQ is the allowed transition collisional (Stark broadened) width. Since both transitions share a common level the ratio becomes 1/2. 2 kf_ _ rc Avf Aa g^ ka " AvdAvcAagUa which, for this particular pair of transitions, becomes kf _ 7-7x10% k a " Avd Av 8 1/ But Avd= 1-09 x10 T(°K) 2 Hz (Thorne (27 )) 12 3 Avc= 1-Bx10' NG(m" K Hz. (Griem (31 )) and hence 18 3 /2 Af = 2-1Bx10- Np(m" )T{°K) ^ ka Using the absorption coefficient ratios, electron densities and temperatures shown in figures 32, 25 and A respectively, this forbidden line transition probability has been calculated for all times between 80 us and 200 us and the result is shown as a function of electron density in figure 33. The result is a straight line given by C A(s1) = bNP(m"3) -d He2 P-3 D 5876A FORBIDDEN LINE TRANSITION PROBABILITY VERSES ELECTRON DENSITY — TRANSITION PROBABILITY (104 SEC"1) x BEST FIT 10 3 1 AF = 1-29 x10" Ne (cm ) S" —I 1 _1_ 0 10 20 30 40 ELECTRON DENSITY (1014 CM"3) where b = 1.295+0.012 x 10"16 C = 0.99+0.01 d = 70s"1 In the paper by Burgess and Playford ( 36 ) it was sug- gested that this electron (or ion) density dependence of the forbidden line could be due to the charge exchange reation: He(23P) + hv He* (33D) + + He + He* (33D) He (31D) + He where the asterisk indicates a virtual state, as indicated by the diagram: The forbidden line cannot be induced by the Stark mixing of atomic levels, as occurs for the AL=0, + 2 forbidden lines, since the Stark perturbation is spin-independent and therefore cannot mix states of different spin. Although the electron density dependence of the intercombination line could be explained by the line being induced by electron collisions, such electron-induced effects are well known in line broadening theory and lead to broad enhancement of the. entire allowed line profile and not to a local enhancement at the detuning at the intercombination line centre as observed here. Since electronic collisions cannot reproduce the observed feature, then the measured dependence on electron density must show that the process involves the He+ ion, of which the charge exchange reaction shown in figure 34 is the likely mechanism. The cross-section <5|. for the entire process (excitation to virtual state plus charge exchange) can be estimated by A - NHe+ kvHJ i* -J'mea| n Ne kcWl L. JIi mean where V|_|g+ is the ion velocity, and the square brackets indicate that the average is taken over the ion velocity distribution. Using the measured transition probability dependence on electron density then °cvHe+ = 1-29x10"16m3s"1 and hence oj. = 1-29x10 ,/5y ? V 2k 2kTT = 2-0x10"18T( K)J/2 m2 -20 2 and 0T. therefore ranges from 1.7 - 2.8 x 10 m for the temperatures present in the plasma used. No theoretical or experimental work has ever been published concerning a charge exchange reaction involving a virtual excited state, and this absorption measurement has therefore provided the first cross-section estimate for such a process. In order to test this explanation for the satellite, several further experiments should prove useful. (i) An identical satellite should be observable over long 1 1 absorption paths in the wing of the Hel 2 P - 3 D 6678A line due to the inverse charge exchange reaction suggested for the 5876A line. (ii) The 5876A far wing profile should be measured whilst 3 3 the Hel 2..P - 4 D 4471A allowed transition is pumped with a pulsed dye laser. This pumped transition shares a common lower level with both the 5876A allowed transition and the proposed inter- combination line. Should the observed satellite be due to the 3 1 2 P - 3 D transition, then the satellite to underlying wing ratio will remain unchanged during pumping. These two methods should provide the final confirmation that the observed satellite is indeed due to the proposed inter- combination transition. 7.2 He I 5876A Line Centre Absorption Measurements 7.2.1 Experimental Results A measurement of the He I 5876A transition line centre absorption coefficient appeared useful at one point in the analysis of the observed intercombination satellite. Playford ( 76 ) has shown that the two fine structure components have absorption -1 -1 coefficients of approximately 7m and 0.9m at a time of 200 us after the peak current. Since it was'decided not to attempt further side-on measurements (with subsequent Abel-inversion), then the minimum plasma length available was 10.84 metres. This ruled out the possibility of measuring the main component which would have an optical depth of ~76 over this length (at 200 us), but the weaker component was just measurable with an opacity of ~9»5 at this time. A measurement of this component was therefore attempted using the CW laser run with Rhodamine 6G, and using a single axial laser pass within the z-pinch, which was run with a 0.45 Torr He filling pressure. A first attempt at measuring this weaker component showed a significantly lower absorption coefficient (0.4m at 200 us) than obtained by Playford, and so more extensive measurements were Mm1) Detuning(GHz) Figure 34-The He I 5876A Line Profile measured over 10-84m. in a 0-45 Torr/20kV Plasma performed, including some across the main component line centre. The results obtained for times of 80, 120, 160, 200 and 240 us are shown in figure 34 and are most surprising. At a time of 200 us, where comparison can be made with Playford, the main component is 15 times lower than the earlier measurement and its lineshape is curiously flat. In addition the ratio of the two components changes from 2.4 to 0.91 over the times measured. The differences between the experimental measurements of Playford and the author are: (a) Path length - there is no understood mechanism by which the longer path length used by the author (up to 64 times that used by Playford) could cause the observed effects. (b) Laser, power - the ring laser has a power of 5 to 20 times greater than that used by Playford. (c) Laser bandwidth - the CW ring laser has an instant- aneous bandwidth of less than 10 MHzj which is far smaller than the 2.6 GHz (0.03A) bandwidth of Playford's laser. 7.2.2 Possible Saturation Mechanisms Given the flat shape of the observed lineshape, it appeared likely that saturation of some form was occurring close to line centre. The measurement of the linearity of the detection system has already been described (section 5.7) and proved the apparatus to be linear up to an optical depth of at least 6 (twice the peak opacity measured in this line centre experiment). It was presumed therefore that the saturation was due to a physical process and not problems with the apparatus. Attention was there- fore turned to the possibility of the atomic transition being saturated, given (b) and (c) above. Burgess ( 1 ) states that the necessary condition for such saturation is that the stimulated radiative transition rate should be greater than the sum of all other transition rates between those levels. In the absence of collisions, this condition becomes that the stimulated transition rate must be greater than that for spontaneous emission, and the minimum power for saturation at the transition line centre f^ is given by p _ 8ruhv3Av s~ c2 where Av is the larger of the homogeneous linewidth or the laser bandwidth. Inserting typical values for the He I 5876A transition, and assuming a homogeneous linewidth of 0.1 GHz- (corresponding to an 14 -3 electron density of approximately 10 cm ), then 2 Ps 0.5 W/cm' as the laser bandwidth- This calculation does not include collisional depopulation of the transition upper level, and when this is included, the equation for the saturation power becomes p _ 8nhv3Av IjT+Ajj S~ r2 Aij where fy is the downward decay rate for the transition upper level. Skinner ( 77) shows Py for 5876A to be 109 at an electron 14-3 density of 10 cm which, since the transition A-value is rj i 7.1 x 10 s" , raises R. by a factor of 15 from the value given above. As the electron density is raised then this minimum power for saturation rises as the square of the electron density (since Py and AV both linearly dependent on Ne). At a time of 80 us 14 -3 after the peak current, when the electron density is 3.6 x 10 cm , 2 2 the predicted saturation power is therefore ~10 W/cm . One extra contribution to the required saturation power is the effect of velocity-changing collisions. The laser band- width is far lower than the transition linewidth of interest, and the saturation under discussion involves the laser saturating a small subset of the total atomic population with zero velocity component in the direction of laser propagation. Collisions that change atomic velocities and therefore remove pumped atoms from this subset, and replace them with unpumped atoms, will therefore act as a further source of depopulation of the transition upper level and will therefore need to be added to the ( [7. +A-- ) factor IJ IJ in the equation for f^ . For a neutral helium gas the rate of velocity changing collisions is approximately given by the total rate of atomic collisions R^ where NHe In the 5876A line centre absorption experiment described the CW ring laser output was 200mW of which less than 40mW reached the plasma for the single pass measurements. The average diameter of the beam inside the plasma was approximately 5 mm, 2 corresponding to a power density of only 0.2 W/cm . At times later than 200 us, where there is negligible electron density present, this power might possibly be sufficient to saturate the transition. For the earlier times, however, this power is orders of magnitude too weak to explain the observed anomalous line centre absorption and atomic saturation does not seem to be responsible. A test of this conclusion was performed, by measuring the line centre absorption coefficient at a fixed time after peak current (200 us) as a function of laser intensity, and the result is shown in figure 35. Despite a change in laser power of a factor of seven, little change in absorption coefficient was observed - the value remaining constant at 0.3 m to within 20%. If the transition was saturated the measured absorption coefficient would have tended to zero as the power was raised. This confirms that the anomalous line shape is not due to atomic saturation. Absorption Coefficient(m^) 0-4t 0-3 11 * * 0-2-- 0-1- 0 1 2 3 4 CW Laser Power(mW) Figure 35-The HeI 5876A Line Centre Absorption Coefficient measured at 200us as a function of Laser Power 7.2.3 Comparison of the Measured and Calculated HeI5876ft Line Centre Absorption Coefficients The HeI5876ft main component line centre absorption coefficient can be calculated from the measured far wing absorption data discussed in section 7.1.1. Consider that section of the profile for which the lineshape is Lorentzian due to Stark broadening. It is shown in Appendix B that the absorption coefficient k(Av) at a detuning Av in this region is related to the line centre absorption coefficient kQ of a line with a Doppler broadened core by k(Av) = kyAVc Avd 2 tp2 Av where AVQ and Avj are the collisional and Doppler widths given in section 7.1.2. The value ofkQ for the 5876ft transition is therefore given by 108xJ0—k(Av)Av^ k m N>-3)TfK) and the values calculated using the diagnosed electron densities and temperatures are shown in figure 36. Using these values the 3 3 total population densities of the 2 P^ and 2 P^ levels (the trans- ition lower levels) have been calculated using the expression, given in Chapter 2, .2 l 8nV 9l Avd The resultant lower level population rises exponentially from 10-3 12-3 1.5 x 10 cm at 100 us to 10 cm at 180 us, thus confirming that the transition lower levels are populated by the metastable 3 2 S level. (Although calculations were not performed for times later than 180 us [since the accuracy of the electron density results was poor after this time] it was clear from the observed Line Centre Absorption Coefficientlm'1) 60t Measured Absorption Coefficient Predicted Absorption Coefficient 0-1 0-01 120 130 140 150 160 170 0-00110 0 110 120 1 30 140 150 160 1 70 . Time(us) r- Time(us) Figure 36-HeI 5876 A Line Centre Absorption Coefficients Figure 37-Comparison of Measured and Predicted Predicted from Far Wing Measurements Hel 5876A Line Centre Absorption Coefficients OS UJ 3 absorption that the 2 P population peaks after 222 us and decays slowly over several hundreds of microseconds). The predicted and measured line centre absorption values are compared in figure 37 from which it can be seen that the lowering of the measured absorption increases exponentially with time, stretching from 0.22 at 100 us to 0.0035 at 180 us. The predicted line centre absorption coefficient and the diagnosed electron densities and temperatures have been used to predict the theoretical Voigt profile and this is compared with the measured data point's, for the central 70 GHz of the profile at a time of 160 us, in figure 38. This shows that the two profiles clearly disagree strongly close to line centre, and that the measured profile is indeed very flat for the central 12.5 GHz. As expected the profiles agree well (within 10%) beyond a detuning of 60 GHz. The final anomaly observed in the measured absorption profiles shown in figure 34, is that the ratio of the two fine structure components changes with time, which is inexplicable since the ratio should be 0.125 at all times (since the temperature 3 is sufficient that the three 2 P levels should be populated in the ratios of their statistical weights). The measured fine structure component line centre absorption coefficients are shown in figure 39, and their ratio in figure 40 (which includes estimates of the likely error bars at four times). The results indicate a ratio that varies from 0.45 +0.1 at early times to 1.06 +0.1 at late times. This clearly disagrees with the theoretically predicted constant value of 0.125, which is a most curious result. Absorption Coefficient(m"1) Profile Predicted 104 from Measured Far Wing Absorption 14 The Measured Profile t—*—*—£—£—. -1 10'+ 102l -3 10 10 20 30 40 50 60 70 Detuning(GHz) Figure 38-A Comparison of the Measured and Predicted HeI5876A Line Profile for a time of 160us 166 Absorption Coefficient(m"^) 0*4+ The Main Component 0-3.+ The Fine Component 0-2+ / * * / 0-1 o-H* 80 • 100 120 140 160Time(ust. , ),18 0 Figure 39-Measured Line Centre Absorption Coefficients for the Fine Structure Components of the HeI5876A Transition Ratio (fine/main) 1-2t '-Typical: Error Bars- 0*84 0*4+ Theoretical Value of 0-125 0 80 100 120 1 40 160 180Time(us)200 Figure 40-The Ratio of the Two Measured Fine-Structure Components - as a Function of Time .167 7.2.4 Conclusions for the Line Centre Absorption Measurements Of all the experiments discussed in this thesis, this was the simplest and most straightforward since it involved a measure- ment of a high absorption coefficient using a single-pass absorption path length, with the CW laser operating at a wavelength close to the peak output of the Rhodamine 6G dye. The results obtained are therefore most surprising, and no obvious explanation can at present be put forward, although several possible mechanisms can be discounted as follows. . (i) Saturation of the atomic transition was ruled out . in section 7.2.2. 3 (ii) Deviations from thermal 2 P level population ratios could explain the changing ratio between the two fine structure absorption coefficients, but cannot explain the deviation between the measured and predicted profiles shown in figure 38. (iii) The CW laser resolution is sufficient to resolve the 3 1 2 P - 3 D intercombination linewidth of ~7GHz, and a lack of resolution cannot be responsible for the flat nature of the central region of the observed profile. (iv) Possible laser-induced emission is unlikely to explain the measured effects, since the predicted line centre absorption coefficients suggest that the CW laser should be absorbed within a few centimetres of entering the plasma. Any emission will therefore occur from a small volume of plasma, at a distance of approximately 12 metres from the detectors, and the measured signal would be negligible compared to the emission from the remainder of the plasma. (v) One possible explanation is that the CW laser might possibly be mode-locked which might lead to atomic saturation. The bandwidth of the laser has been measured to be less than 10 MHz, however, and the pulsetime of each mode-locked pulse would be more than 100 nsec which would have been detected during early long path measurements, when a photomultiplier detector was used. (vi) One possible error in the analysis used to predict the line centre absorption coefficient is that the collisional width AVQ might be larger than the Stark broadened widths used so far. The expression for the transition natural width, given in Thorne ( 27 ), shows that this width should only be 8MHz; resonance 3 broadening will be negligible since transitions between the 2 P levels and the ground state are forbidden; and Camm and Copley ( 78 ), have shown that Van Der Waal's broadening should be responsible for less than a 10 MHz width at these densities. The total alternative collisional width is therfore ~15 MHz which corresponds to the Stark 13 -3 width produced by an electron density of only 10 electrons cm Before a time of 180 us therefore, such collisional broadening will therefore have negligible effect on the results so far obtained. (vii) A possible explanation of the observed behaviour would be if the photodiode detectors were producing a very slowly decaying current after the disappearance of the laser signal during the total absorption. The measured line centre opacity of ^3.8 over 10.84 metres would require a current flow of only 3% of that occurring before the laser signal disappeared. This 3% current flow cannot,however, explain the fact that for detunings between 15 and 20 GHz, the measured absorption value is less than the peak measured value of ~ 0.38, despite the predicted absorption still being an order of magnitude larger than the measured value. Despite the simplicity of this experiment, the observed absorption still cannot be explained. The immediate future work must be to re-measure the existing data for verification, and to obtain higher accuracy. One useful experiment will be to measure the dependence of the line centre opacity as a function of absorption length, since this might well provide useful information concerning the mechanism responsible for the observed effects. Should this effect be verified, the theory of absorption by highly optically thick media may well require futher investigation. '170 CHAPTER 8 LONG PATH ABSORPTION MEASUREMENTS OF THE FAR WING OF H-ALPHA FROM 64Q0A TO 6545ft The hydrogen continuum opacity measurements reported by Burgess, Kolbe and Playford (35) (described in Chapter 3) indicated an anomalously high continuum absorption value in the far wing of Hd , and it was decided therefore to remeasure this far wing absorption using the improved multipassing system described earlier. 8.1 Results The plasma device was run with a 20 kV bank voltage and 0.45 Torr hydrogen filling pressure, and the multipassing cavity was used to provide path lengths ranging from 44 to 173 metres close to the line centre and 478 metres (44 passes) for the far wing measurements. This low number of passes for the weak far wing absorption measurements was necessitated by the low output power of the CW laser at these wavelengths (as discussed in Chapter 5). The experimental arrangement was as shown in figure 14, and the digitizers recorded data for plasma times of between 50 us and 250 us. The problems with wavelength accuracy were negligible in this experiment, since the ±0. 2ft error, introduced by the use of the double-pass spectrometer used to measure the wavelength, was quite sufficient, given a transition linewidth of 1—2ft. Figure 41 shows the measured absorption coefficient for detunings from 2-100ft for a time of 70 us after the peak current. This time is the only one for which Playford published data, and his results are included on the figure for comparison with the more recent ones. The two sets of data agree very well (to within 10%) for the detuning range of 2.8—10. 6ft, and Playford's measured absorption / Figure 41-A Comparison of the H* Blue Wing Absorption Profile measured by Playford and the Author 70us after fhe Peak Current in a 0-45 Torr Plasma 1 2 5 10 20 50 100 Detuning(A) coefficients at detunings of 7.24, 10.7 and 14.1 A agree very well with the author's profile, despite disagreeing significantly with that of Playford. Beyond 15A, however, there is considerable disagreement between the two sets of data (factor of 5) in the value of the continuum absorption coefficient, and Playford's anomalously high continuum is therefore reduced (but to a value which is still inexplicable, as further discussed). Given the superior experimental arrangement used by the author, and Playford's three points that agree with the new profile .172 and not his own, it appears reasonable therefore to suggest that these new results completely supercede and replace those of Playford. No explanation of the difference between these two sets of data is obvious and none can be put forward without further details of Playford's methods of absorption, wavelength and path length measurement. Discussion of Playford's observed linearity between his continuum opacity and electron density is given later. Figure 42 shows the results of the new wing absorption measurement for times of 100 us, 150 us and 200 us, (where only those points with detunings of more than 15A have been plotted) and indicates a flat absorption plateau for all the times presented, extending from 15A to 150A. Although some possible structure might be present in these traces, there is little firm evidence that such structure is not simply due to experimental error, and the few mechanisms capable of causing such structure are discussed (and discounted) later. 8.2 Analysis of the Far Wing Absorption Measurements There are several absorption mechanisms which might explain this measured far wing data, and these clearly require detailed examination. The first mechanism of interest is atomic absorption, of which only three possible transitions will be important at these wavelengths. 8.2.1 Balmer-Alpha Mihalas ( 26) shows that the transition region between electron impact and quasi-static broadening applies between the detunings: ( V = the electron thermal velocity, C_ = ththee starstarkk coefficient) Abs.Coef.dO V) 16t (a)100us 12 8- 4- Theoretical Continuum + H<*QuasiStatic Wing 0 0 40 80 i5o ~16 0 Abs.Coef.(1ff4m1) Detuning(A) 12 (b) 150 us I I 8 i I i i 1 I1! 4 1 0 0 40 80 120 160 Defuning(A) 4 1 Abs.Coef.(10" m ) (c) 200 us 8- i11 • 4- i - J 0 0 40 80 120 160 Detuning(A) Figure 42-Hydrogen Continuum Absorption measured between 6400A and 6545 A in a Hydrogen Plasma of filling pressure 0-45 Torr .174 V2 10 ,/1 and AX. = ie. (ile = 1-29x10" NQ(m-3)r3. /22 A 1 CTt \4e.m The upper transition region limit AX U is set by the condition that, for quasi-static broadening to apply, the frequency detuning must be greater than the frequency spread associated with the finite duration of the perturbation. The lower transition region limit AXj is given by the condition that, for impact broadening, the upper limit on the perturbation time of the atom by a charged particle is set by the condition that the perturber must lie within the Debye. sphere. Inserting the plasma conditions applicable to the absorption traces shown in figure 42 into the expressions for AX u and AX | , produces the results shown i-n table 8.1. Table 8.1 Transition Region between Impact and Quasi-Static Broadening for times of 100, 150 and 200 us in 0.45 Torr Hydrogen Plasma Time (us) AXj (A) AXU (A) 100 3.2 207 150 1 .9 115 200 0.4 69 It can be seen in Table 8.1 that the majority of the measured points lie within the transition region, and hence a quasi-static profile i may not apply. The unified theory of Vidal, Cooper and Smith (8 ), however, predicts that the AX5/2 quasi-static profile does indeed .apply for detunings higher than 8A to an accuracy of 25% (at 10,000K), and this profile was therefore used in>the required analysis. The AX5/2 profile, together with the theoretical continuum absorption coefficient (derived later), was used to predict the far wing applicable for a time of 100 us, using the measured absorption coefficient at 11.1 A for normalization, and the result is shown in figure 42. Clearly the theoretical profile does not fit the results, and Ho< absorption is not responsible for the anomalous profile. 8. 2.2 Hydrogen Balmer-Beta It was shown in Chapter 2 that, for the conditions of interest here, H^ has a line centre absorption coefficient of ~10% of that of Hot . The linewidths for Hot and are comparable, and the wavelengths shown in figure 42 17-154A from He* line centre and 1548-1685A from Hyg line centre. Considering the relative line centre opacities and detunings, the contribution to the observed absorption from H/S must be far lower than that of Hot, and therefore cannot explain the anomalously high absorption. 8.2.3 Hydrogen Lyman-Alpha It is shown in Appendix B that the absorption coefficient kc in the Lorentzian region of a line profile is given by: k -iL.Hu.^.AN, . C STt^Av2 1 (where AV^ is the collisional HWHM) = 1-88x# ^ Av2 for Lyman-alpha, using the A value provided by Wiese, Glennon and Smith (30 ), and assuming that Nj = total hydrogen density. Griem ( 31 ) gives the electron impact HWHM to be 14 -3 = 0.9 GHz per 10 electrons cm And hence the Lorentzian wing section of the profile is given by 3 . ..25 Ne(#cnf ) kc =1-7x10 Av2 This absorption coefficient is assumed to apply out to the detuning corresponding to the minimum detuning for the transition region (discussed in section 8.1.1), which, for Lyman-alpha, occurs at a value .176 2 14 3 1/2 AX( = 4-4 x 10 ' Ne(10 cm" ) A Beyond this detuning it is assumed that the quasi-static profile applies. Tfte values forAX^, the absorption coefficients at these detunings, and the resultant absorption coefficients at 6560A, are all given in table 8.2, for the times used in figure 42. Table 8.2 Absorption Coefficients close to Ho< due to Lyman-alpha for the times of 100, 150 and 200 us after peak current Time after peak 14 3 kjfm-l) 1 current (us) Ne(10 cm" ) atAXj k6562(m" ) 100 6 0.11 68.4 2.7 x 10'7 -8 150 2.2 0.065 71 .9 9 x 10 200 0.1 0.014 70.4 1.5 x 10~8 The absorption coefficients at 6560A, shown in table 8.2, are clearly negligible compared to those observed. 8.3 Molecular Absorption Diecke (79 ) shows that molecular hydrogen transitions stretch across the entire range of wavelengths observed, and might therefore account for the high absorption measured. The visible hydrogen molecular transitions take place between excited states, the lowest of which is ~90,000 cm above the ground state. Mayer and Mayer (80 ) provide the expression for the molecular partition function Qmolec where: Qmolec = Qvibronic x Qelectronic . For kT << Energy of first excited state Qelectronic « ground state statistical weight (= 1 for H2 ) and Qvibronic = 1 1 1 4 cX wexe + —+ -4 + u u 2 (1-eu) 21 6 u2 £Be(e -1) Be(e -1) 0J hc where e and g = M Table 8.3 Hydrogen Molecular Partition Functions T( K) Qmolec 14,000 328.1 12,000 236 10,000 162.2 8,000 104.8 6,000 61 .9 4,000 31 .9 2,000 12.6 The excited states are not metastable (except for the lowest triplet level which is sufficiently close to the singlet levels that its population will be close to its L.T.E. value) and the populations can be estimated by using Boltzman's law 9exNc eXP -exc Nexc=« H? kT J 1 + -1 For the first excited state ( of energy 91,700 cm above the ground state) the vibronic state with the highest population has quantum numbers v=0 and j = '""itf 2Bphc and hence * 9 = 2 +1 exc i/2Bghc ' Using the molecular Saha equation to predict H2 densities as a function of temperature produces the results shown in figure 43. Typical molecular line centre absorption coefficients for 6500A were calculated using the expression derived in Chapter 2, 7 -1 assuming a transition probability of 10 s and Doppler broadened lines (Stark broadening for molecules is very small), and the results are shown in table 8.4. Temperature! K) Figure 43-Predicted Molecular Population in a Hydrogen Plasma of 0-45 Torr Filling Pressure (assuming LTE) Table 8.4 Molecular Absorption Coefficients for 0.45 Tor-r Hydrogen Plasma (assuming L.T.E.) Temperature (°K) Absorption Coefficient (m~1) at 6500A 12,000 5.5 x 10~7 10,000 2.5 x 10~7 -8 8,000 5.4 x 10 -9 6,000 3x10 4,000 0 Despite the approximations involved in the calculations, table 8.4 shows that the molecular absorption is most unlikely to be respons- ible for the observed absorption. .179 8.4 Satellite Features Another possible explanation for the high far wing absorption observed is the presence of a large number of satellite features. The first mechanism for such a series of satellites is due to the formation of the H-H+ quasi-molecule (as discussed in Chapter 1). Stewart, Peak and Cooper (81 ) have calculated the absorption coefficient Tor such satellites in the wings of Lyman-alpha, where W = *(v)nHnH+ and showocjy) to be 1for Lyman-alpha satellites. Assuming that a comparable value of cx(v) will apply for He* satellites (i.e.c*(v) = 10~^8m8) and using a population of the 17 -3 hydrogen n=2 level of 5 x 10 'm (section 8.4.4.1) with an H+ ion density of 5 x 1020m~3, an absorption coefficient of 2.5 x 10~8m~1 is obtained. This is 4 to 5 orders of magnitude weaker than that required to explain the observed absorption. [It should be noted that such satellites have only been previously observed at higher electron densities (101^ - 1018 cm"3) where k^+is correspondingly higher]. A second possible mechanism for a series of far wing satellites is due to the plasmon satellites discussed in Chapter 1. Since Hoc is an allowed transition with a degenerate forbidden component, plasmon satellites can occur at detunings of ±2ntlDp where Dp is the plasma frequency and n is an integer. The peak absorption of such a satellite is proportional to the underlying allowed wing, however, which scales as AXS/2 . In addition Burgess ( 13 ) has shown that such plasmon satellite absorption varies as the square of the satellite detuning from the forbidden component (at the HcC line centre). The resultant spectrum for such a series of plasmon satellites if therefore proportional to AX"3 - a variation that .180 decreases even faster with detuning than the quasi-static H 8.5 Continuum Absorption Having failed to explain the observed far wing absorption by atomic and molecular transitions and satellites, the only remaining possibility is continuum absorption, to which there are a variety of contributions, discussed individually in the following sections. In order to test this possibility, the traces for detunings of 15 - 150 A have been averaged using the computer, resulting in the continuum absorption, shown in figure 44 as a function of time. Using the hydrogen electron density results, shown in figure 4a, this measured continuum absorption can be plotted as a function of electron density, and the result is shown in figure 45 . Figure 45 shows a non-linear electron density dependence which disagrees with Playford's continuum result. It must be noted, however, that all of Playford's values for the continuum absorption are significantly higher than those obtained here, and the conclusion must be that the linear dependence on electron density observed by Playford is due to the mechanism responsible for Playford's absolute values being anomalously high. There are several contributions to the theoretical continuum absorption and these are discussed in the following sections, with the results summarized in section -8.5.6. 8.5.1 Thomson Scattering The first contribution to the continuum absorption is that due to Thomson scattering of the laser light by the free electrons. The cross-section for this process CT. is constant at .181 Absorption Coefficient(10~V1) Time(us) Figure 44 -Measured Hydrogen Continuum Absorption between 6400A and 6545A as a function of Time Absorption Coefficient(10"\"1) 14+ Electron Density! 1014cm"B) Figure45- Measured Hydrogen Continuum Absorption between 6400A and 6545Aasa function of Electron Density —PR P a value of 6.7 x 10" m , and the absorption coefficient is kj. where kt = Vt 9 14 3 1 = 6-7x10" Ne(10 cm" ) m" The resultant absorption is shown in figure 53 , and discussed in section 8.5.6. 8.5.2 Rayleigh Scattering The bound electrons in the plasma can also scatter, with a cross-section 0"p(v)y (for frequencies much higher than the transition frequency Vy for the i - j transition) where / 1 r V^ 0"fr (v):i;j = fjjCij Tt y74 ij resulting in an absorption coefficient kp given by kr = I^My where the summation is over all atomic levels,of population Nj . The population and frequency terms in the expressions for kp and CTp(V)jj result in the scattering for transitions in the visible region being typically two orders of magnitude weaker than that for resonant transitions, and hence only resonant transitions need be included in the calculation of kp. For the neutral atoms, Nj approximately equals the atomic density (given the low ionic and excited state populations), the highest resonant wavelength for hydrogen is 1215a (with f„ = 0.42), and the resultant absorption coefficient is therefore 4 x y 13 -R which is negligible compared to kj. for Ng^TA-XlO Cm and can therefore be ignored. Finally consider the contribution to Rayleigh scattering from the molecules present within the plasma. The molecular resonance transitions are at sufficiently low wavelength that jj A 1 and,since molecular f-values are typically small (<<1), then 0" (V)• * FOR molecules must be smaller than 0"J . Since the r ij t molecular number density (shown in figure 43 ) is small compared to the electron density (shown in figure 24) until very late times ( > 180 us) then absorption due to molecular Rayleigh scattering must be smaller than Thomson scattering until late times, and can therefore be ignored. 8.5.3 Free-Free (Inverse-Bremsstrahlung) Absorption Another possible explanation for the observed continuum is the absorption produced during inverse-Bremsstrahlung by the free electrons within the fields of positive hydrogen ions. The method used to calculate the required absorption coefficients for such transitions, first derived by Menzel and Perkins (24 ), is to extend the theory of absorption between bound levels into''the continuum, using imaginary quantum numbers. Menzel and Perkins derived the expresssion for the free-free absorption coefficient averaged over a Maxwellian electron energy distribution) k„ = 1 Ui t tit G„N2 ffe ff 4 3 4lT£ 3V-J c•h(2n:mk) -/ 2 t1/2 where G^ is the free-free Gaunt factor and is approximately unity. Inserting values for the constants, and using a wavelength of 6500A, produces an absorption coefficient of N (1 )2 k - 3-87x10-6 * °y ."I " T('K)1/2 and this is shown as a function of time in figure 53 , and discussed in section 8.5.6. The values obtained using this equation have been checked with those given by Stilley and Callaway (82 ) and Peach ( 83 ), and agree to within 30% for the plasma conditions of interest, which is sufficient accuracy for the present purpose. 8.5.4 Bound-Free (Photoionization) Continuum Absorption Again using imaginary quantum numbers, the absorption due to bound-free transitions can be calculated in an analagous fashion to the free-free absorption, and Thorne (27 ) ..quotes the required absorption coefficient k^ to be given by kbf„v»lvlN" where n^ is the lowest level for which photoionization can occur at the wavelength under consideration, and Np is the population density of the nth level. °*p(v) is given by cx (v) = iitk4 jl. f—L- q, *nlV) 3VT ch6 UrcsJ nV bn Gth ^ is the bound-free Gaunt factor for the n level and is approximately unity. The lowest four hydrogen energy levels, and their corresponding photoionization edges, are given in Table 8.5 (ignoring ionization potential depression which is less than 0.1 ev ), which shows that rij = 3 for the wavelengths of interest. Table 8.5. Photoionization Edges for Hydrogen Levels n Ep (eV) X-Ep (eV) Max Photoionization \ (A) 1 0 13.6 914.1 2 10.2 3.4 3656.3 3 12.1 1 .5 8232.6 4 12.8 0.85 14625. Since c*^ and Np both decrease with n , only the n=3 and n=4 levels will be included in the summation used to obtain the absorption coefficient, which, at a wavelength of 6500A, becomes .185 N ^ N4 c19 3 m,- 1 k. ,= 2-78x10 243 + 1024 Clearly an accurate knowledge of the two level populations is required, which is not a trivial problem since recent fluore- scence measurements by Burgess, Myerscough, Skinner and Ward ( 84 ) have shown that theoretical level populations can be in significant error. To obtain estimates for the two populations, an interferometric level population measurement was therefore carried out. 8.5.4.1 Interferometric Measurement of Hydrogen Level Populations Consider the anomalous dispersion , at a detuning AX from an atomic transition, given by Thorne (27 ) to be 4fijNi n = 1 + o 9 AX 16TI e.mc . 9jNij xk 6 = 1 + 2-24x1()1 .^"-(Nj- |nj) where Ay and fy are the transition wavelength and oscillator strength, Nj and Nj are the lower and upper level populations respectively, and the contributions to n from all other atomic lines have been assumed to be negligible. For the given equation to apply, AX must be much larger than the transition HWHM linewidth but sufficiently small that the profile is Lorentzian (i.e. of section 8.2.1). An interferometric measurement of n~1 for a known AX will therefore provide the population function (Nj ""(^i/9j) Nj) and hence, given a theoretical model for ^i/Nj,, the level populations can be determined. Apart from this atomic contribution to the refractive index,-there is also the contribution from-the free electons, (already used in Chapter 6 to provide the electron density). Measurements must therefore be taken at two detunings from the atomic transition line centre, the difference in measured refractive index providing the population function. The hydrogen n=2 level population has already been measured by Burgess, Kolbe and Playford ( 35 ) (as described in Chapter 3) using absorption measurements of Hoc at 6562A, and it is this transition that is of interest, using the CW dye laser, for this alternative method. The use of an interferometric technique provides distinct advantages for the measurement of excited state populations. The analysis of absorption measurements requires detailed knowledge of the transition lineshape and thus requires either a large number of measurements across the entire profile, or alternatively measurements at one point in the profile combined with theoretical lineshapes and accurate plasma diagnostics. The interferometric method, however, only requires that the detuning from line centre remains within the limits already discussed, and that the change in refractive index due to the atomic transition be measurable. The accurate measurement of the contribution to the plasma refractive index from the atomic anomalous absorption is enhanced by the availability of multiple passed interferometer path lengths. Since the atomic refractive index varies as AV' , and the absorption _ r\ as (in the Lorentzian wing of the profile), then absorption of the laser beam by the plasma at one detuning can be eliminated by moving to a higher detuning whilst simultaneously lengthening the optical path within the plasma to maintain the number of fringes. Because of the electron density bounces it was found necessary to perform these interferometric measurements on the blue wing of the atomic line, where any atomic contribution to the plasma refractive index would necessarily have increased the number of fringes. Measurements on the profile red wing would have lead to problems of interpretation during the bounces, since it was not clear whether the atomic refractive index also bounced or not. The experimental arrangement used is shown in figure 46 . The plasma device was run at 20 kV with a 0.45 Torr hydrogen filling pressure and the oscilloscope was triggered 4 us before the current peak (measured using a Rogowski coil). The interferometer was demonstrated to achieve interference with equal path lengths in both arms of up to 820 metres (76 passes), but level population measurements were restricted to path lengths of 44 metres (4 passes) since this lead to a usable number of fringes. Results were taken for detunings of -46.7 A and -2. 4S, with an accuracy of 0.2A. The latter detuning is higher than the He* HWHM (1.1 A at 101^ electrons cm-3), and lower than the minimum transition detuning (given in section 8.1) for electron densities 14 -3 greater than 3 x 10 cm t Laser Storage Oscilloscope Figure 46-The Multipass Interferometer used for Anomalous Dispersion Measurements of the Hydrogen n=2 Level Population .188 Although the detuning used may be sufficiently large that the Lorentzian profile used in the preceeding analysis may not apply for times later than 150 us, the results should be approximately correct. The resultant fringe patterns were recorded on polaroid film and analyzed as described in Chapter 6 for the electron density diagnostics. The resultant fringe difference for the two wavelengths was then used to predict the level population function using the Hoc oscillator strength given by Wiese, Glennon and Smith ( 30 ), and the results are shown as a function of time in figure 47 and as a function of electron density in figure 48 . The population function clearly lasts for 300 us after the peak current and peaks at 70 us. Before this time bouncing is present at times that correspond to electron density bounces — further evidence that a neutral density perturbation is involved. This population function was compared with the results of a computer collisional-radiative code developed by Gohil ( 85 ), which used collision rates given by Johnson ( 86 ) and produced the results for the n=2, 3 and 4 populations and the (^2/g^) N^) population function shown in figure 49 . A comparison of the author's measured function and that calculated by Gohil (using measured electron density and temperature values ) is plotted in figure 50 . Despite high errors in the theoretical points (due to high temperature errors), there is clearly considerable disagreement between theory and experiment. This experimental conclusion therefore agrees with that of Burgess, Kolbe and Playford ( 35 ) and shows Gohil's theoretical calculation to be in error. This is presumably one more proof that the rates used in such computer calculations may be incorrect. Given the absence of a more accurate method of calculating .189 Figure 47 -Measured Hydrogen Level Population Function in the 0-45Torr Plasma as a function of Time Electron Density(1(rcm ) Figure 48-Measured Hydrogen Level Population Function as a function of Electron Density .190 Population (cm ) (i)n=2 1013l 1-2 Temperature(eV) Populafionlcirf3) _ (ii)n=3 •1011| 1010f 9 10 + 10' 0 0-4 0-8 1'2 Temperature (eV) Electron -3 Density(1014cm"3) Populationtcm ) (iii)n=4 a - 10 1011 + b - 8 c - 6 10 10 d - 4 9 10 1 e - 2 8 F - 1 10 0-4 0-8 T2 Temperature(eV) rf3) (iv)N2-|N3 c ba T2 Tem'perature(eV) Figure 49 - Theoretical Hydrogen Level Populations for a Plasma of 0-45 Torr Filling Pressure,as a function of Temperature and Electron Density, predicted by Gohil (85} .191 11 3 (N2-^N )(10 CM~ ) 3 + 3 • Measured (Full Line) 24t I Computed by GohiKDotted Line) 16- Error Bars in Computed Function due to \ Errors in Diagnosed Temperatures \ 8- \ -V 0 40 60 80 100 120 140 160 T80 Time after Peak Current(us) Figure 50 - A Comparison of the Measured Hydrogen Level Population Function and that Computed by Gohil(85) for a Plasma of 0-45 Torr Filling Pressure 10 -3 PopulationdO cm ) 8 . 80 120 160 200 Tjme after Peak Current(us) Figure 51 - Hydrogen Level Populations used in the calculation of the Bound-Free Continuum Absorption Coefficient for the 0-45 Torr Plasma .192 N^ andN^, Gohil's /N2 and N^/N^ ratios were assumed to be correct and were used with the measured ( N 2 ""(^2/9^) N^) values to predict N- and N. , the results being shown in figure 51 . Using J 4- these population values, the required bound-free absorption coefficient k,. was calculated,and the results are shown in figure 53 and discussed bf in section 8.5.6. 8.5.5 Negative Ion Continuum Absorption Two major contributions to the continuum absorption are due to the presence of the H~ ion which has an ionization potential of only 0.754 eV and thus produces both free-free and bound-free continua throughout the entire visible region of the spectrum. Geltman ( 87) has published a theoretical calculation of the cross-section 0j_M_ for the bound-free absorption process, bH —21 2 which has a value of 3.56 x 10 m at 6500A. The corresponding free-free absorption cross-section has been calculated by Geltman ( 88 ) and Stilley and Callaway ( 82 )» of which the latter's values are used here, due to their higher accuracy ( 3%). Stallcop ( 89) calculates the free-free absorption coefficient but uses a Saha code to obtain the neutral hydrogen ground state population. For the present purposes Stilley and Callaway's free-free absorption coefficient is used and the neutral hydrogen ground state population is derived by assuming it to be equal to the hydrogen atomic filling density. The resultant free-free absorption coefficient is shown in figure 53. Using the previously diagnosed electron densities and temperatures, a Saha code was run to provide the N^j- densities, required for the bound-free absorption calculation, and the results are shown in figure 52, the error bars shown being due to the errors in the temperature diagnostics. Using these N^-densities and Geltman's cross-section the bound free absorption coefficients were calculated and these are shown in figure 53, and are discussed in the'following section. H"Density(1010crn3) Figure 52-The Theoretically Calculated Negative Hydrogen Ion Density present in the 0-45 Torr Hydrogen Plasma' (assuming LTE) 8.5.6 Conclusions for Continuum Absorption The previous sections have outlined the methods used to estimate the various contributions to the continuum absorption for a wavelength of 6500A. The results are summarized in figure 53, which includes the averaged experimentally measured continuum values, presented earlier in figure 44 . From the graph it can be seen that the total theoretically predicted continuum is a factor of 6-11 times too low to explain the measured values. At the present time no explanation for this anomalously high continuum is obvious. The two major contributions to the theoretical continuum are due to bound-free absorption by neutral hydrogen atoms and negative hydrogen ions. For the neutral bound- free absorption to be responsible for the observed continuum at 1.94 Figure 53 COMPARISON OF MEASURED AND THEORETICAL HYDROGEN CONTINUUM ABSORPTION COEFFICIENTS 6415 A -6545 A FOR 0-45 TORR HYDROGEN PLASMA -3 10 EXPERIMENTAL RESULTS TOTAL THEORETICAL 10* H~BOUND-FREE o UJ IO5 H BOUND-FREE CL CC O CO 00 A O -7 UJ 10 HFREE-FREE -8 10 THOMSON SCATTER 60 80 100 120 140 160 180 TIME AFTER PEAK CURRENT (JJS) I 80 us (for instance) the N^ population would need to be 7.3 x 'l011cm~3. However, the (^-(^/gjhU) population has already 11-3 been measured to be 5.25 x 10 cm at this time, and the required N^ value would therefore result in anN^/^ value of 0.86 which is eight times that predicted by Gohil which is conceivable but •• unlikely.' For the H~ bound-free absorption to be responsible for the observed continuum at 80 us (for instance), then either the H~ population would need to be 65 times higher than that calculated using a Saha code; or alternatively the plasma temperature would need to be 2800°K, which is far outside of the possible error in diagnosed temperature, and therefore most unlikely. 8.6 Conclusions and Further Work In this Chapter, an experimental measurement of the far wing of the hydrogen Balmer-alpha transition has shown the existence of high continuum absorption in the wavelength region of 6400A to 6546A. Although numerous possible mechanisms have been proposed to explain the measured values, all have been examined in detail and found to be too weak to explain the magnitude of the observed absorption. Several further experiments are therefore required: (i) It will be useful to repeat the existing experiment, over the same range of wavelengths, but with far more data points. Although a structured linewing , due to satellite or molecular features,has been shown to be unlikely, this possibility should be ruled out. (ii) Measurements must be made at wavelengths beyond those so far attempted. With the existing CW dye laser, wavelengths as low as 5700A can be simply achieved, and the use of the argon-ion laser with specially coated multipassing mirrors, should extend measurements into the blue. (iii) Finally it will prove useful to perform more temper ature diagnostics, of far higher accuracy than those obtained previously. Although it has been shown that errors in the existing temperatures cannot explain the observed absorption, more accurate temperatures would allow more precise comparison between measured and theoretical continua and population values. 197 CHAPTER 9 ABSORPTION MEASUREMENTS OF FORBIDDEN LINES IN THE GROUND CONFIGURATIONS OF LIGHT ATOMS AND IONS 9.1 Introduction In the previous two chapters, experiments were described in which the multipassing system described in Chapter 5 was used to obtain path lengths of up to 1,200 metres in order to measure absorption in the far wings of hydrogen and helium spectral lines. The -4 -1 -1 ' absorption coefficients measured ranged from 2x10 m to 0.3 m , but these are well above the lowest measurable with the available path lengths. Given the maximum path length available of 1,200 metres, and a minimum detectable absorption of 0.1 - 0.2%, the minimum absorption —6 — 1 coefficient resolvable should be approximately 0.8 - 1.6 x 10~ m~ , which is considerably lower than that observed so far. Given this high sensitivity, the measurement of the transition probabilities of certain forbidden lines of astro- physical interest becomes feasible for the first time. These lines occur within the ground configurations of light atoms and ions, and are due to magnetic-dipole and electric-quadrupole transitions (electric-dipole transitions being forbidden by selection rules). The transition probabilities are therefore 8 to 11 orders of magnitude lower than for allowed lines, and it will be shown that the full sensitivity of the present experimental arrangement will be required if these lines are to be observed. In this chapter the possibility of measuring these lines will be discussed in detail. After a discussion of the atomic structure of the relevant species, a review of the astrophysical, theoretical and experimental history of these transitions is presented. Attention is then focussed on the most promising line 1 1 for measurement with the existing apparatus, the [Nil] D- S 5754A line (of A-value 1.1 s ), and problems with the measurement of such a line are analyzed. Results are then presented of an attempt at the measurement of this line, and the results are discussed. 9.2 The Ground Configuration Structure of Light Atoms and Ions Several major lines in the spectra of gaseous nebulae remained unclassified for considerable time , during which it was even suggested that they might be due to a new element called Nebulium. It was Bowen ( 90) who first suggested that these lines might be due to forbidden transitions within atomic ground config- urations . 2 Consider the configuration p , which applies for Nil and OIII. The theoretical energy levels can be calculated to a first approximation by assuming Russell-Saunders coupling (Russell and Saunders ( 91 )) and it is simple (Condon and Shortley ( 92 )) to 3 1 1 show that this configuration consists of three terms P, D, S, 1 1 split by the electro-static interaction, with spacings ( S- D): 13 3 ( D- P) of 3:2. The spin-orbit perturbation then splits the P 3 3 3 3 3 level in the P2, P, Pq states with a splitting of ( P2- P1): 3 3 ( P.j- P ) = 2:1. Consider now the measured enegy levels as shown in figure 59 . The measured splittings are: (1S-1D):(1D-3P) = 1.13:1 instead of 1.5:1 3 3 3 3 and ( P2- P1):( P1- Pq) = 1.67:1 instead of 2:1 1S. 32687-1 cm"1 3063 A 575A-8A. 1s22s22p2 (A=0-034s ) 6548lTTD2 153157 CJ 6583-6A , , j(A=0-003s-1) ^> 0,49-1,131-3 cm1 Figure 54-Transitions within the NH Ground Configuration There are clear deviations from pure Russell-Saunders coupling, which are of importance for the forbidden lines indicated on the diagram, 1 3 since they indicate a mixing of the Sq and Pq levels and the 1 3 D^ and P^ levels. This allows weak magnetic dipole transitions to occur, as discussed in the following section. 9.3 Previous Observation and Calculation of Forbidden Lines Forbidden lines have been of interest ever since selection rules for electric dipole radiation indicated the presence of metastable levels, from which radiative decay can only occur by magnetic dipole or electric quadrupole radiation. Theoretical predictions and, to a lesser extent, experimental measurements of such lines have been published frequently and a useful review article has been published by Garstang ( 93 ). The nature of forbidden line radiation was investigated experimentally for electric quadrupole radiation between 2 S and 2 D levels in sodium and potassium by Segre and Bakker ( 94 ),and for magnetic dipole 2 3 1 radiation using the 6p P - Sq transition in Lead by Niewodnic- zanski • ( 95 ). Most magnetic dipole transitions are intercombination 2 3 3 lines^although a few others have been measured,such as the 6p P - P^ transition in Bill (Cole ( 96 )), or those between Zeeman components 200 2 of the same level such as the 2s S^^ m = +1/2 to m = -1/2 transition measured by Lamb (97 ). In addition to such laboratory measurements, there have been a large number of forbidden line observations in astrophysical sources. Bowen (98 ) has pointed out that in many cases, forbidden lines have provided the most accurate values for the energy levels concerned since allowed transitions for these levels lie in the far U.V. and V.U.V. spectral regions. Plasma induced forbidden lines have also been observed,such as the forbidden lines in He,as.seen by Burgess and Cairns (18 ) and Mahon et al. (99 ), which are induced by the plasma microfield, and have been described theoretically in detail by Burgess (19 ). These lines have been seen in astrophysical spectra and are of use in stellar diagnostics, as described in Chapter 1. The ground configuration electric dipole forbidden, transitions in light species, of interest in the present work were originally seen in astrophysical spectra and first explained by Bowen (90 )t who suggested that their upper states might be low lying metastable levels, and proved that the known energy splittings for the ground configurations of suitable atoms predicted wavelengths of the correct order of magnitude. His identification was confirmed in the laboratory by McLennan et al. (100) who observed the 5577A [01] line (of A-value 1.3 5~ ) in -an electrical discharge tube,and later by Le Blanc et al. (101) in a similar fashion. The astrophysical connection of the lines, however, lies not only in their original identification, but also in their use as diagnostic tools for the analysis of interesting astrophysical bodies. Because of the low atomic and electron densities in 2 4-3 gaseous nebulae (10 -10 cm ), the collisional depopulation of the upper levels of these transitions is reduced to such an extent that .201 even the most highly forbidden radiative decay will dominate alternative collisional decay. These ground state transitions are therefore amongst the brightest lines from such objects, since their upper level populations are far higher than those of the allowed lines, which lie at higher energy among the excited states. Obviously the ratios of two such forbidden lines from the same species will depend on the relative A-values (assumed known) and the relative upper level populations. This population ratio will depend on temperature (i.e. Botzman distribution) at the higher nebula densities or on collision rates at the lower nebula densities. Observations of such line ratios can therefore provide diagnostics for temperatures, electron densities, atomic densities or relative atomic abundances depending on the particular lines observed and the conditions within the nebula. A typical use of forbidden lines in astrophysical diagnostics can be seen in Zeippen et al. (102), in which an 01 intercombination line at 1356A is used to show that oxygen abund- ances may be less than theoretically predicted in several objects. The uses of such lines to provide densities and temperatures is described in Seaton and Osterbrook (103) for calculations concerning OIII , and more generally in Seaton (104),where the use of many such lines from one source is used to provide an estimate of the accuracy of such calculations and indicates the problems with attempting to fit one 'electron density and temperature to such objects. More problems are discussed by Schull and McCray (105), who examine the results of forbidden line measurements in Quasars and Seyfert galaxies, and show that the ratios obtained may be significantly altered by radiative pumping due to high radiation fluxes in these objects, as originally proposed by Burgess (106). .202 They calculate results for OIII and show that,without including the radiative pumping,, an anomalously high electron density could be deduced from the ratio measurements. Closer to earth these forbidden lines are of considerable interest in the study of the upper atmosphere, due to their presence in aurorae. Several books and articles discuss the use of such lines in auroral studies, such as Bates (107) and McCormac (108). The Nil 5754A line,of interest later in this chapter, has been seen in auroral spectra by Dufay (109) and this line is discussed in the article by Bates. All of these spectral diagnostics by astrophysicists and meteorologists require a knowledge of the A-values of the spectral lines used, a requirement which has resulted in a vast number of theoretical transition probabilities calculations. These have used increasingly sophisticated approximations for the atomic wave-functions and dipole or quadrupole operators, and have achieved increasingly better agreement with the measured energy level spacings. The starting point for such calculations, as described by Aller (110) or Condon and Shortley ( 92), is the Poynting vector of classical physics, Taken with Maxwell's equations and the classical operators Electric dipole vector operator Electric quadrupole dyadic operator Magnetic dipole vector operator . this gives the individual Poynting vectors: .203 CK . M D-D -(D-Ir) Ir ed 32TX2e r2 ( N ck eq, (9-jr)-(Q-jr)-(irQ-ir)(irQ-ir) JT " 128Tt2e;r2 _ ck4 2 -md M-M - (M-ir) 32TC2e r2 where jp is the unit vector a distance I r| from the origin in the direction ofN. - The change to a quantum mechanical description is achieved by using the appropriate quantum mechanical operators for D , (3 and M in the above equations where (it should be noted that the definition of M will be further discussed later). The classical equations can then be modified (Condon and Shortley ( 92)) to calculate the rate of emission of energy (over a sphere of large radius) to be: 3 4 Ied = !6e_v y N( 3. .4 2 IMD N^JMLK^JMLMI^'J'M')! 3c3e and since I(*J-«J) = N (<>J ) A ) hV 3 3 then Aed(<*j.tfjj = J_ 16KJLyKo,jm|0|«'j'm'>| ZJ + I L—, A. M') = JL 8TrV^|Mm|QKjV)|2 2J+1 C, 5C _ 5nc £0 m>m' = 2JJ ^ri<«JMLM|«'J'M')|2 3hc £, rn,m' Putting typical values in these equations, to estimate the relative magnitudes of the three terms, shows (Aller (110)) A : A s 8 ed V md « 1:5x10 : Bx10 . This shows that, in general, electric quadrupole and magnetic dipole transition probabilities are 5-10 orders of magnitude lower than for electric dipole transitions and, since the line opacities are proportional to the transition probability, the opacities of forbidden lines are correspondingly 5-10 orders of magnitude lower. From these expressions for the transition probabilities the selection rules for each type of radiation can be derived and these are summarized in Table 9.1 (from Corney (m)). Rules 1 - 3 arise from matrix element symmetry principles and are exact, whereas rules 4-6 are only approximate. Rule 4 arises directly from 3, when the states involved can be described by one single electron configuration, and rules 5 and 6 arise only for pure LS coupling. Note that the An=0 rule applies to magnetic dipole radiation since the matrix elements ofM vanish if there is Table 9-1 Selection Rules for Atomic Transitions Changing Quantity Electric Dipole Magnetic Dipole Electric Quadrupole 1 1. J AJ=0,±1(0A0) . AJ=0,±1(0f0) AJ=0t±1,±2 (0H),V /2,0M) 2. m Am=0 +1 Am = 0,±1 Am = 0,±1,±2 3. Parity Change No change No change 4. I At= ±1 Al=0,An=0 Al=0,±2 5. S AS= 0 AS = 0 AS = 0 6. L AL=0,±1 (0^0) AL=0 AL=0,±1,±2((W*(),0tM) .206 a change in electron configuration. These then are the equations for the required transition probabilities for the three prominent .classes of radiation, together with the selection rules that apply to them. Attention will now be given to the various attempts to calculate transition probabilities for the magnetic dipole and electric quadrupole cases of interest. 9.4 A Review Qf Theoretical Calculations of Ground Configuration Forbidden Line Transition Probabilities The first important attempt to calculate these transition probabilities was by Bartlett (112) who treated electric quadrupole lines by mixing ground state wavefunctions (due to lack of pure LS coupling) and obtained A-value ratios. In a similar way Stevenson (113) used perturbation theory to predict line strengths in [OIII] and [Nil]. This work was continued by Condon (114), who used the approach quoted in Aller (110) and Condon and Shortley ( 92 ). The breakdown of LS coupling was expressed by a slight mixing of 13 13 3 D„ and P and also S and P wavefunctions (the P„ wave- 2 20 o o 1 function remaining pure). Using the measured level splittings listed earlier (measured from V.U.V. spectroscopy), the mixing constants were calculated and from these, the AS = 1 , AL =1 magnetic dipole matrix elements were calculated. Note that without this wave- function mixing, these magnetic dipole transitions would be forbidden. The AS =1 and A S=0, A J=2 electric quadrupole lines depend on calculations that are not so simple. Such calculations involve the evaluation of the integral s = -e r2R2(2p) dr O and this requires accurate radial wavefunctions R(2p). Magnetic dipole .207 transition probabilities on the other hand, do not contain such an integral and can be calculated from the experimentally measured level splittings (but with a recently discovered problem outlined later). Using Hartree self-consistent wavefunctions, Condon obtained -1 several transition probabilities, including the value of A ±.1.7s for the [Nil] 5754A line. (A useful review of Condon's calculations and results has been published by Bowen (115)). Pasternack (116) continued Condon's work, but with hydrogen-like wavefunctions plus the appropriate screening constants. He obtained a transition probability for the 5754A line of 2.2s~ , but obtained a closer agreement with later theories for his magnetic dipole line calculations. He concluded by suggesting that the problem, especially for electric quadrupole calculations, was the omission of configur- ation interaction. Shortley et al. (117), who examined the p2, p3 and p^ ground state configurations, again calculated the mixing of the ground state terms, and discussed the possibilities of inter- ference between the electric quadrupole and magnetic dipole radiative amplitudes for transitions in which they are of comparable magnitude. One of their results was to calculate the intensity ratio 2 I(4S3/2 - D5/2) (3728.9A) r = in Oil 2 I(4S3/2 - D3/2) (3726.2A) to be 1.64,whereas the experimentally measured value from astro- physical observation was 0.49. Aller et al. (118) included further interactions in their Hamiltonian, such as spin-spin and spin- other-orbit interactions, which become important since they affect the transition probability in first order, whereas the larger spin- 208. orbit interaction contributes in second order only. With these additions they calculated the above ratio r and obtained a value of 0.58 - a vast improvement on the previous result although they suggested that newer (unpublished) astrophysical results showed an even lower measured ratio of 0.38. A similar approach was used by Garstang (119), who 2 calculated Marvin interaction matrices to fit the p energy term spacings. He used the experimentally measured term spacings in his calculation, with the hope of partially accounting for configuration interaction effects, and obtained transition probabilities from CI to FV using self-consistent wave functions, including a value for [Nil] 5754A of 1.08s" . (Note that this was not an analytical treatment of configuration interaction). Garstang 's next paper (120) 3 continued this work with the [SII] 3p transitions when the spin-spin and spin-other-orbit effects were less important. He also showed that in NI and Oil, better agreement between theoretical and experi- mental level spacings was obtained if exchange effects were included in the wave functions. Yilmaz (121 ) used hydrogen-like wave functions, with a perturbation expansion method, which included electron-electron correlations, but no configuration interaction. He obtained a _ 1 transition probability for the [Nil] 5754A line of 1.35s~ , together with a value of 1.08s using Hartree-Fock calculations. In 1951 Naqvi published his thesis (Harvard University), which included many forbidden line transition probability results, but this was not available for reference. Estimates of his results can be made, however, from the similar work of Froese (1229 who used Hartree-Fock wavefunctions and obtained a result for [Nil] 5754A of 1.24s"1. .209 Further extensions were added by Nicolaides and Sinanoglu (123) who used non-closed-shell many-electron wave functions, already developed in three previous papers concerned with transition probabilities for allowed lines. Correlation effects, including configuration interaction, both for ground and excited states, had been found to produce significant effects for these allowed lines, and the calculations also proved that the problem for the inclusion of configuration interaction was that those interacting configurations which affect the energy level positions are not the same as those that affect the transition probabilities. These authors pointed out that previous forbidden line calculations, using independent-particle central-field models, suffered both by ignoring changes in the central field from term to term within the ground state, and also because of the lack of electron correlations. They believed that their calculations accounted for both of these failings, and suggested up to 30% changes in transition probability values, with a final accuracy of 5%. They obtained an [Nil] 5754A A-value of 1.082 s . The uses of such calculations can be seen in a second paper by these authors (124) in which their values for [01] transition probabilities corresponded to changes in certain stellar oxygen abundances of 20% to 30%. More recently there are two series of theoretical calcul- ations which still yield significant further changes to these transition probabilities. Both of these series are based upon the work by Eissner and Nussbaumer (125), in which a Thomas-Fermi non- relativistic computer program for atomic structure calculations was developed. The program has been modified by Nussbaumer (126) for 2 use in.calculating transition probabilities in the CIp sequence, using a Thomas-Fermi-Dirac type potential with configuration inter- action. He obtained an [Nil] 5754A value of 1 .12- 1.54 s"1, depending on which convergence condition was used, and agreed, in general, to within 5% with the results of Nicolaides and Sinanoglu. Further extensions were developed by Nussbaumer and 2 Rusca (127), in which more calculations for the CI p sequence were performed because: (i) previous calculations ignored relativistic effects, other than spin orbit interaction. (ii) Energy levels for the higher ionized members of the 2 p sequence were then more accurately known. (iii) Mason and Bhatia (128) had found significant differences from previous work for Mg VII, Si IX, S XI and Fe XXI. Nussbaumer and Rusca treated the relativistic corrections as the final perturbation,and included configuration interaction for eleven configurations. The 1s, 2s and 2p levels were calculated, using adjustable Thomas-Fermi potentials, and the 3s, 3p, 3d levels (used in the configuration-interaction caculation) calculated using hydrogenic potentials, the mixing constants being obtained by 2 3 1 1 minimizing the energies of the 2p , P, D and S terms (as for Nussbaumer and Storey(129))• They used a computational adjustment developed by Zeippen (130) (discussed later), to utilize the measured term splittings in the perturbation Hamiltonian, and obtained approximately 5% changes for the lower ionized species and more for higher species, concluding that more configuration interaction was unlikely to significantly affect the transition probabilities. For [Nil] 5754A they obtained a value of 1.12 s~1. One of the most recent calculations was that performed by Baluja and Doyle (131) in which they improved on the work of Nussbaumer and Rusca by:(1) including the relativistic effects of spin-orbit, spin-other-orbit and spin-spin, Darwin and mass 2.11 correction terms in their Hamiltonian;(2) by using elaborate configuration interaction wave functions derived by Balujajand (3) by performing 'ab initio' calculations without adjustment variables within the program. They confined their calculations to OIII and obtained results that agreed to 3% with Garstang (93 ), and to 8% with Nussbaumer and Rusca (127). The second of the recent series of such calculations starts with work by Dopita et al. (132), who used a line ratio in NI to predict electron densities in nebulae, but found that the ratio did not agree with the astrophysically observed value. This re-introduced the [Oil] 3729A/3726A ratio r, previously discussed by Shortley et al. (117), Aller (118) and Seaton and Osterbrook (103). For this ratio the currently accepted astrophysically observed value is 0.35, whereas the closest theoretical value at that time was 0.43. Both lines in the ratio contain both magnetic dipole and electric quadrupole contributions, and for the 3729A line the electric quad- rupole term contribution dominates but for the 3726A it is the magnetic dipole term. The majority of calculations so far described, have been concerned with the electric quadrupole transition probability, since the previously described radial integral provides the majority of the problems. For this reason previous calculations assumed that the problem with this ratio lay with the 3729A electric quadrupole / transition probability. However, Zeippen (133) used the SUPERSTRUCTURE program developed by Eissner and Seaton (134), with the intention of including the fullest treatment of configuration interaction, together with configuration-interaction type wavefunctions (based on the scaled statistical model potential of Eissner and Nussbaumer ( 125)) and included Breit-Pauli terms in the Hamiltonian. Much of the detail is included in Zeippen's thesis (130), including details .212 of 'semi-empirical' tests performed, both to determine which extra configurations should be included in such calculations, and also to use the measured energy level splittings to adjust the program para- meters to increase the accuracy of the calculations. His result was a ratio r of 0.42 which was still too high, and he concluded that the inclusion of more configurations in the calculation should have negligible effect. At the end of this paper, however, the alternative possibility, that the problem might be due to the transition operator used, was discussed, and Zeippen showed that the magnetic dipole operator might well require reconsideration. This idea was developed further in Eissner and Zeippen (135) who claimed then that the most accurate measurement of the [Oil] ratio in question was 0.36 +0.02 (Miller - private communication 1971). Their answer to the puzzle was to expand the magnetic dipole operator beyond the first order expression M = u_ (L + 2S) used B up to then, using an expression derived by Drake (136) (which is too lengthy to describe here). The wavefunctions used by Eissner and Zeippen were similar to those used in previous papers but with two versions used (one including nine configurations in the configuration interaction expression,and the other with two) in order to test whether further configuration interaction was likely to have much effect. The results of these calculations were very interesting, since they significantly altered the transition probability for the magnetic dipole line. It was found that some of the extra relativistic terms in the expanded magnetic dipole operator (which are of order 2 2 Z CX lower than the first order expression used previously) affect the transition probability in first order, whereas the first order magnetic dipole operator in fact affects the transition probability in second order. The result is that, for the 3729X line, the extra terms in the magnetic dipole operator produce a contribution to the transition probability of similar magnitude to the first order term but of opposite sign, which reduces the 3729A magnetic dipole transition probability by 3 - 4 orders of magnitude. This in turn reduces the value of the line ratio to 0.35, which is in far better agreement with the measured value. This idea was further used in two more papers; Zeippen 3 (137) looked at the NI 2p series and showed that these higher order magnetic dipole operator terms become less important for higher ionized species; and finally Mendoza and Zeippen (138) analyzed the 3 3p series and suggested that these species might provide transitions of use in astrophysical diagnostics. These then are the important papers detailing the theor- etical development of ground configuration forbidden transition probabilities in light species. It should be noted that little mention has been made of calculations of such lines for heavier atomic species (that would not be usable in recombining plasma form). Obviously vast improvements have been made since the original ideas of Bartlett, Stevenson and Condon and are still being made as shown by the recent results of Baluja and Doyle and also Zeippen, Eissner and Mendoza. It now appears that the atomic wavefunctions may be as accurate as possible, with the inclusion of configuration inter- action, and the problems with the electric quadrupole radial integral might well be solved. However the recent work of Zeippen et al. has shown that the magnetic dipole operator requires further work and perhaps a similar question will arise with the electric quadrupole operator for transitions such as the [Nil] 5754A transition examined here. The most comprehensive lists of wavelengths and theoretical .214 transition probabilities can be seen in Wiese et al. (30 ), Cheng et al. (139) (for Lithium to Fluorine isoelectronic sequences) and by Fawcett (140) for higher ionization stages. Before moving on to experimental considerations it should be noted that the analysis presented later is principally concerned 1 1 with the 5754A N [II] S - D line. The theoretical calculations for this line, mentioned in the previous papers, are summarized in Table 9.2 Table 9.2 Calculations of the N [II] 5754A 1S - 1D Theoretical Transition Probability _1 Author (s) Method of Wave Function Result (s ) Calculation Condon (1934) Hartree 1 .7 Pasternack (1940) H-like 2.2 Naqvi (1951) - 1 .08 Garstang (1951) H-like 1 .08 Yilmaz (1955) H-like and electron- electron correlations 1.08-1.35 Froese (1966) Hartree-Fock 1 .24 Nicolaides and Mang electron + correlations Sinanoglu (1971) + config. int. 1.082 Nussbaumer (1972) Thomas Fermi-Dirac + 1 .12-1.54 config. int. Nussbaumer and T.F.D. + C.I. + 1 .12 Rusca (1978) relativistic It can therefore be seen that all the results are consistent but that 10% - 20% disagreement is present between the various theories, with later results suggesting perhaps 5% accuracy about a mean value (used -1 in the later calculations) of 1.1 s Having thus discussed the vast theoretical literature for .215 such transitions, attention will now be turned to the much smaller collection of papers concerned with their laboratory measurement. 9.5 Previous Experimental Measurements of Ground Configuration Forbidden Lines Attention will be restricted here to those experiments in which forbidden line transition probabilities have been measured, and those in which wavelengths alone were measured will be omitted. Useful reviews of the existing methods of transition probability measurement are given by Corney (141) and Foster (142) where the methods used for allowed transitions include the measurement of: (i transition upper level lifetimes (ii Van der Waals or resonance broadened line profiles (iii anomalous dispersion (iv polarization rotation (v resonance fluorescence (vi emission intensity values (vii Absorption values There are several problems for methods (i) to (vi)when applied to the measurement of highly forbidden lines in plasmas. Lifetime measure- ments (i) require that there be no cascading into, and collisional depopulation out of, the transition upper level. For the lines of interest these conditions rule out: direct observation of emission decay (Holzberlein (143)); delayed coincidence methods (Bennett (144)); cascade coincidence methods (Nussbaum and Pipkin (145)) and phase shift measurements (Brewer et al. (146 ))• Similarly beam-foil (Kernahan et al. (147 )) and time-of-flight methods (Van Dyck et al. 7 (148)) would require impractical beam paths of 10 metres. The measurement of Van der Waals or resonance broadened .216 profiles (ii) is. also impossible since these broadening mechanisms are negligible, for such weak transitions, compared to the Doppler broadening process. Anomalous dispersion methods (iii) (such as the hook method of Marlowe (149)) and polarization rotation methods (iv) (such as that of Seka and Curzon (150)) will also be impossible for the measurement of forbidden lines with such low transition probabil- ities. Resonance fluorescence methods (v) including: the Hanle effect (Barrat(l51 )); level-crossing spectroscopy (Colegrove et al. (152)); and optical double-resonance methods (Brossel and Bitter (153)) would be impossible given both the electric field and the high collision rates- present in the plasma. Emission spectroscopy (vi) can be ruled out in plasmas since the low transition probabilities will result in negligible emission intensities when compared to the plasma background emission. The only remaining technique is therefore absorption Spectroscopy (vii), and it is this that is described in this chapter. Previous measurements of these forbidden lines have involved emission studies in low density atomic sources, and measurements have been restricted to 01 lines so far. The first emission method that has been used, involves the simultaneous measurement of a forbidden line intensity I and the transition upper level population Ny since: (with I corrected for solid angle, etc.) McConkey et al. (154) used a • TT-shaped discharge tube run with* a 20:1 He:02 mixture to measure the 6364A, 6300A, 5577A and 2972A line ratios in 01,and from .217 these obtained transition probability ratios to an accuracy of 15% - 20%. Their method was improved by McConkey and Kernahan ('155), where a similar discharge was run and. the 5577A [01] forbidden line K * / 1 "3 1 was measured with the 1218A 2p S - 2p 3s P allowed line (from which the forbidden upper level population was estimated by assuming Doppler broadened lineshapes). This produced an estimate of the 5577A [01] line transition probability of 1 s compared to theoret- -1 -1 ical calculations of 1.28 s and 1.44 s (Omholt). There were several problems, however. Firstly the forbidden lines were barely observable in emission; secondly the measurement assumed a uniform discharge, which was dubious and thirdly (and most importantly) the A-value of the V.U.V. 1218A allowed line, used to measure the required upper state population, was only known to 50% accuracy thus introducing a 50% inaccuracy into the forbidden line transition probability. McConkey and Kernahan suggested that this error might even be as high as 70%, but a later publication by Corney (156) suggested that recent work by Olt had reduced the upper level population error to 30%. More of such measurements were given in McConkey et al. (157) and Kernahan and Pang (158),which suffered from the same problems. The second experimental method used is that presented by Corney and Williams (159). They used a pulsed stationary discharge in an oxygen/inert gas filling mixture, and measured the lifetime of the 01 5577A line, by direct observation of the exponential decay, to be 0.76 seconds (and hence the transition probability to be 1.31 +0.005 s ). This method was previously used with astrophysical observations by Omholt (160), Stoffregen and Debolm (161 ), and Kvifte and Vegard (162), all of whom measured the same lifetime from changing auroral conditions -1 and obtained A-values of 1.3 - 1.4 s , although obviously of lesser .218 accuracy than Corney and William's experiment. In Corney and William's case, the errors were due to diffusion to the walls and collisional deactivation. They included a detailed analysis of these problems in their paper, and accounted for them in their results by measuring the lifetime as a function of buffer gas pressure. The problems with this method were (a) It required estimation of the collisional decay of the upper level which might be uncertain,and (b) It could only be used for neutral species, since the electrons present in an ionic source would lead not only to a very high collisional 6 9-1 deactivation rate (10 -10 s ), but also to the lifetime of the ionic —6 —3 species being small (10 -10 sec.) compared to the atomic lifetime of _2 interest (10-1 sec.). This completes the list of previous experimental measurements of ground configuration forbidden lines. Looking at the theoretical results, it might be suggested that, since the theoretically calculated transition probabilities have been improved so many times, the existing theoretical values are sufficiently accurate and that no experimental verification is required. It must be remembered, however, that only one accurate measurement of such a transition in a neutral species has ever been performed, and that no measurements have ever been made for ionic transitions. Using long path absorption spectroscopy, it is therefore intended to perform the first measurement of such a forbidden line transition probability in an ionic species, with sufficient accuracy to allow comparison between the various theoret- ically derived values. 9.6 The Optical Depths of Spectral Lines It was shown in section 2.1 that the absorption coefficient K for an atomic transition is given by .219 •)2 k = A_ In order to'estimate the likely absorption coefficients of forbidden lines within the plasmas generated in the ten metre plasma device, it is .necessary to estimate the normalized lineshape factor the transition level populations Nj and Nj in terms of the known plasma parameters of electron density and temperature. Tabulated values of X,A, gj and gj will then allow the absorption coefficient to be calculated. 9.6.1 Level Populations One of the major problems encountered by the.previous workers who have attempted to measure such forbidden transitions, is the problem of estimating Nj and Nj . A typical example is that of Kernahan and Pang ( 158) who measured an 01 forbidden line and used simultaneous measurements of allowed lines to provide the necessary level populations. This method required the accurate knowledge of the allowed transition probabilities, which proved to be the limiting accuracy of the entire experiment. Clearly if the ten metre plasma column is to measure neutral forbidden lines then measurement of such level populations will also be a problem. The situation is far simpler, however, if measurements are made of forbidden lines for singly ionized species since the ion density equals the (known) electron density by charge conservation (since the plasma is less than fully ionized, and the amount of doubly charged ions present should be negligible). The electron density has been accurately measured, which therefore means that the total ion densities can be accurately known. Having obtained the total ion density, the individual pop- ulations of the terms of the ground configuration are. needed. Consider 220. the case of Nil. At the temperatures and densities of interest, the populations within the excited ion configurations are typically five or six orders of magnitude lower than the ground state, and it is therefore valid to assume that the total ground configuration population can be equated to the total ion density. The individual populations can be calculated using Boltzman's law, since radiative rates between the terms are negligible compared to the collision rates, due to the low transition probabilities. A PET computer program was used to calculate the required Nil populations as a function of-temperature and the results are shown in Table 9.3. Table 9.3 Theoretical Nil 2p 2 Relative Term Populations as a function of temperature assuming LTE T(°K) Partition Relative Populations Function 3P A> 2 V \ 14,000 9.99 0.1 0.3 0.49 0.103 3.5x10~3 12,000 9.72 0.1 0.31 0.51 0.082 2.0x10"3 10,000 9.44 0.11 0.32 0.52 0.058 9.5X10~A 8,000 9.18 0.11 ' 0.32 0.53 0.035 3.0x10"^ 6,000 8.94 0.11 0.33 0.54 0.014 4.3x10"5 4,000 8.74 0.12 0.34 0.55 2.3x10~"3 8.7x10"7 The required populations Nj and Nj for a given time are therefore given by the relevant figures in Table 9.3 multiplied by the measured electron density for that time. 9.6.2 The Normalized Lineshape Factor There are two types of line broadening, likely to be respons- ible for the normalized lineshape factor (i) Pressure Broadening (Homogeneous) Included in this category are those contributions to the lineshape resulting from the absorber's interaction with its surrounding particles. Detailed mathematical treatment, and discussion of the various approximations used for each type of interaction will not be given here, but can be found in Cowley (163), Mihalas (26 ) and Griem (164). For the case of the Nil forbidden lines, the situation is relatively simple. The dominant broadening mechanism is Stark broad- ening and Griem ( 164) tabulates such linewidths. Although the required forbidden lines are not included in the tables, their line- widths can be estimated since the linewidth W is given in wavelength units by 1+7. w «x n X where fl is the principal quantum number of the transition upper level and X the transition wavelength. Griem provides widths for several Nil lines, and three of these are shown in table 9.4 for an electron 15 -3 4"\2 density of 10 cm . Then A. behaviour of the linewidth appears to be correct from the lines chosen, with^/n^X = 1.1 x For the 5754A forbidden transition the predicted linewidth is therefore -5 15-3 x 10 times the Electron Density (10 cm ), which is negligible compared to the Doppler width for likely electron densities. Table 9-4 Stark Widths of Nil Lines at Electron Density of 1015cm"3 (from Griem (164)) Line Linewidth (A) Wavelength (A) w/n4X2 3 3 5 -12 2p P - 3s P 4 x 10" 671 1.1 X 10 3 3 3 -12 3p D.- 4s P 3.5 x 10" 3,378 1.2x10 1 1 3 -1 2 3p S - 4s P 6.8 x 10~ 5,104 1.0x10 .222 (ii) Doppler Broadening (Inhomogeneous) The second contribution to the lineshape is due to the relative motions of the collection of absorbing atoms. Thorne (27 ) shows the Doppler broadened lineshape to be given by 2 2 2 I = I. exp[ - C (AV) /V« ] * SJW resulting in a FWHM linewidth of AX'. in wavelength units of • 7 AX'=^F^ = 7-16X10 x/jZ M d Inserting typical valuesfdr the Nil 5754A forbidden line, the FWHM linewidth at 10,000 K is therefore 0.1lA, which is clearly far larger than the pressure broadened width. Assuming therefore that only the Doppler contribution to the normalized lineshape requires consider- ation then where A is given by the normalization POTF 0(v) dv = 1 which means that re A M h'2 A = x, 2TI kT " Avd where is the Doppler HW^M linewidth in frequency units. Hence at the line centre of a Doppler broadened transition in nitrogen 9.6.3 Opacities of the Nil Forbidden Lines Given the required level populations and normalized lineshape .223 functions, the required absorption coefficients can now be calculated. The various Nil forbidden lines available for measurement are compared 15 -3 in Table 9.5, in which an electron density of 10 cm and a temper- ature of 10,000 K have been assumed, using A-values and wavelengths given by Wiese et al. (30 ). Table 9.5 Theoretical Nil Ground Configuration Forbidden 15 -3 Absorption Coefficients at 10,000K and N =10 cm Transition Wavelength(A) A-value (s ) Absorption Coefficient (m'1) 1 1 -5 D - S 5754.8 1 .1 1 .56 x 10 3 3P - D1 6583.6 0.003 6.8 x 10"7 3P - D1 6548.1 0.001 2.6 x 10~6 3P - 's 3063.0 0.034 6.8 x 10~7 The results show that all of the lines should be detectable at these plasma conditions (given path lengths of up to 1,200 metres). The 5754A line is clearly the strongest of the set of lines and is therefore the one of most interest for the rest of this chapter. Using the theory developed so far the theoretical absorption coefficient of the 5754A line can be calculated for the ten metre plasma column, using the measured electron densities (figure 23) and the expected plasma temperatures (figure 28) for the plasma device used with 0.15 Torr nitrogen filling. Putting values for this transition into the equation derived in Section 9.6. 23 1/ k = 2-75x10" TCK)" 2[Nr5Nj] and this is plotted as a function of time in figure 55. The result of the theoretical calculation is a measurable absorption coefficient .224 Absorption Coefficienf(106m~1) 24- The Present Minimum Detectable Value 120 160 200 Time after Peak Current(us) Figure 55-The Theoretically Predicted Nil 1 D-n 1S 5754- Forbidden Line Peak Absorption Coefficient for a Nitrogen Plasma of 0-15Torr Filling Pressure and 20kV Bank Voltage (i.e. greater than the minimum detectable absorption value Qf —6 — 1 1.7 x 10" ID ) for times between 40 and 170 us, reaching a peak -5 -1 value of 2.1 x 10 m (i.e.T^0.025 over 1,200 metres) at 50 us. At this time the line should be ten times stronger than the minimum —6 —1 resolvable absorption coefficient of 1.7 x 10~ m" , and the line should therefore be observable to beyond four HWHM linewidths from line centre. Given the necessary use of the input/difference method (discussed in Chapter 5) for the measurement of such a weak optical depth, then the likely inaccuracy of such a measurement may be as high as 30%. The introduction of a new, more powerful, argon-ion laser in the near future, will raise the output powers available from the CW laser considerably (up to 1-2 watts) which will therefore .225 raise the accuracy of these measurements, since the present limit in accuracy is set by shot noise on the detected plasma emission. It should be noted that saturation of the forbidden line will not be a problem since the power required to saturate FJ. was shown in Chapter 7 to be given by 3 p ^ 8Tihv Av ir. / A ) •s ^3 VV For the forbidden transitions Av (the transition homogeneous linewidth) is 102 - 103 lower than that for He I 5876$, but (ly/Ay) is 106 - 109 higher, due to the low A-values of these transitions, and the powers required to saturate are 10^ - 1019 higher than the 100 W/cm2 discussed in Chapter 7 , and saturation will therefore be no problem with the existing laser. One problem that might prevent the measurement of such lines is the possibility of the absorption from such lines being dominated by other absorption due to atomic, molecular or continuum absorption, and this is now discussed for 5754A in more detail. 9-7 Other Possible Sources of Absorption close to the 5754$ Forbidden Line 9-7.1 Atomic Absorption by NI and Nil These calculations include both the atomic resonance transitions,and also those between excited states producing wavelengths close to 5754$. For all the lines included, the lineshapes are assumed to be Lorentzian and the absorption coefficient at a detuning Av is therefore given by (Appendix B): >2 9,I AVC K^A. JL AN, C 8*2 9, I AV2 A Lorentzian lineshape, however, only applies for a detuning Av smaller than the plasma frequency AVp , beyond which the transition to .226 quasi-static broadening (with a lineshape proportional to AV7/4 for such lines) occurs. The procedure used for such lines is there- fore to use the Lorentzian expression to calculate the expected absorption coefficient at Av=Avp, and then to use the quasi-static profile to obtain the absorption coefficient for 5754ft. The five resonance and two nearby transitions used to calculate the expected atomic absorption are shown in Table 9.6, which includes the necessary atomic parameters for use in the absorption coefficient equation. The AVC listed were obtained from Griem (164 ) and apply 15 -3 for an.electron density of 10 'cm • , and a temperature of 10,000 K. For alternative plasma conditions, it is approximately correct to simply change AVr linearly with electron density. Using the parameters given in Table 9.6, the plasma cond- itions diagnosed earlier have been used to provide values for AVp » k(AVp) and k(5754ft) for the 0.15 Torr nitrogen plasma, and the expected values fork (5754ft). are shown in figure 56, where the required level number densities have been given by: the electron density for the Nil resonance line; the total atomic density for the NI resonance lines; and level populations for the two non- resonance transitions using Boltzman's law. Although the use of this law is not valid, since LTE will not apply for these levels, the calculation should be correct to within a factor of two or three,' which is sufficient. The results show that atomic absorption should remain an order of magnitude lower than the predicted forbidden line absorption for all times. Since the atomic absorption comes from lines of considerable detuning from 5754ft, then the absorption will not change measurably across the forbidden line profile. The atomic absorption will there- Table 9.6 Parameters for atomic transitions most likely to provide absorption close to 5754$ 1 Species Transition X(«) A-value (s~ ) AVc(GHZ) 2 3 4 S NI Resonance 2s 2p -2s2p 1135 2.3 x 108 3 0.16 3 2 NI Resonance 2p - 2p 3s 1200 5.4 x 108 3 0.15 2 2 NI Excited 2p 3p - 2p 6s 5817 3 x 105 1 .5 5.3 2 3 Nil Resonance 2p - 2s2p 645 1.1 x 1010 0.33 0.25 2 3 Nil Resonance 2p - 2s2p 1085 5.7 x 108 1 .67 0.25 2 3 Nil Resonance 2p - 2s2p 916 1 .8 x 109 1 0.25 Nil Excited 2p3s - 2p3p 5731 1 .5 x 106 0.6 0.3 .228 Absorption Coefficient(m^) .Jhe Predicted Forbidden Line Absorption NI ResojiaDC^Absorption Nil Resonance Absorption NI 5817A Transition 120 160 200 Time after Peak Current(us) Figure 56-The Predicted Absorption Coefficients at 5754A due to Atomic Absorption in a Nitrogen Plasma of 0-15 Torr Filling Pressure and 20kV Bank Voltage fore contribute to the background absorption, and will not be a problem, 9-7.2 Molecular Absorption 9.7.2.1 Molecular Populations In order to calculate the molecular absorption due to both N2 and N2 , it is necessary to estimate the likely populations of the two species within the plasma. Both have high dissociation energies, and therefore might be present at sufficiently high concentr- ations that two problems might arise: (a) Either species might provide sufficient absorption at 5754A to dominate the forbidden line absorption. Time after Peak Current(us) Figure 57- Theoretical N^ and N* Populations in the 0-15 Torr Nitrogen Plasma as a function of Time (assuming LTE) (Molecular Filling Density = 4-8x1015cm~3) (b) A significant N* density (compared to the electron density) will prevent the equality of the Nil and electron densities, used in the forbidden line analysis. To estimate the two populations as a function of time, two sources of information were used. Loftus and Krupenie (165 ) contains a vast collection of theoretical and experimental data for both N2 and N*, and provides tables of the molecular parameters required in the following calculations. Secondly, a computer program (EXIT 6), written by Judith Flagg of Harvard University (1967) provided the required populations (assuming LTE), and the results for a nitrogen plasma of 0.15 Torr filling pressure (i.e. total nitrogen atomic 15 -3 density of 9.66 x 10 cm ) are shown in figure 57 . The calculations show that the N* population will be less than 0.1% of the Nil density for all times, and the equality used in the forbidden line analysis is therefore valid. Using the populations shown, the expected absorption coefficients can now be calculated using the equation derived in section 2.1 and assuming that the molecular lines are Doppler broadened. 9.7.2.2 Absorption by Molecular Resonance Transitions There are two series of resonance transitions likely to provide significant absorption at 575AA in N2- Firstly the Lyman- Birge-Hopfield series aTTg—X^Xg which produces wavelengths as high " 'AT- as 2600A ( V =27 — V=15 ). Loftus and Kruperie Ci 65 ) list the 1 3 TTg level to have a lifetime of approximately 100 us and an A-value 4 -1 of 10 s is therefore used. Assuming that the transitions of importance for calculating far-wing absorption are those occurring from the lowest vibrational level (producing a wavelength of approximately 1960A), and also assuming that the entire N2 population lies in this lowest vibrational level (an overestimate for this order of magnitude .231 calculation), then the absorption coefficient has been calculated. The redults obtained indicated a maximum absorption coefficient for -15 -1 the times of interest of only 7x10 m , using a likely overestimate of 0.1 GHz forfhe collisional linewidth. Despite the approximations used in this calculation, the ten orders of magnitude difference between the forbidden line and the molecular absorption coefficients show that this resonance series will have negligible effect on the forbidden line measurements. The second N^ resonance series of possible importance is A3R+ V1R+ the Vegard-Kaplan A X 2_g forbidden series of upper state lifetime 1.9s and with a maximum wavelength of 5300A. The differences in wavelength and transition probability mean that this series should have an absorption coefficient at 5754A of only 20% of the Lyman- Birge-Hopfield series already discussed, and should also therefore be of negligible importance. The resonance series of greatest importance for N* is the v 2c-* n 2c-* ' " 1st Negative X Z- — D series whose V=1 to V = 5 band has a 3 / bandhead of 5754.4A (in air), the bandhead corresponding to the J =8 , J =9 transition. Lofthus and Krupenie list the transition probability 4 -1 for this band to be 7.9 x 10 s , and with the-absorption coefficient calculated using the usual equation, then the line centre absorption coefficient for the single transition is given by (assuming Doppler broadening) k5754 = 1 x 10"21 T( K'1/2 N(fn"3)lnwer m"1 In order to calculate this absorption coefficient it as assumed that the level populations are given by Boltzman's law and hence n N(JJ = -2I±I- exp[-E(J )/kT] NN + V 2 .232 where the required partition function is listed in Table 9-7. Table 9.7 Nitrogen Molecular Partition Functions calculated using EXIT 6 Temperature (°K) Partition Function N2 14,000 13,308 59,200 12,000 9,405 42,604 10,000 6,470 29,270 8,000 4,215 18,847 Using the total N* density shown in figure 57, the relevant lower level population density for this transition has been calculated and the resultant absorption coefficient is shown in figure 58. The results show that this transition will be insignificant compared to the predicted forbidden line until after 130 us, after which it will contribute to the background absorption. 9.7.2.3 Absorption by Molecular Lines of Wavelength close to 5754ft The closest N* molecular transition wavelength to 5754ft is due to the first negative series, discussed in the previous section, and no other N^ molecular absorption should be important. The closest N^ molecular transition to 5754ft is due to the O + 3 y " ' 1st Positive A Zy—B Zg(V=8—V=12) band which Loftus and Krupenie (165 ) list as having a band origin at 5742ft (air) and a band head at 5755.2ft (air). The quantum numbers of the transitions occurring at the forbidden line wavelength are not known since the simple calculation of molecular wavelengths fails for this level, (see Tanaka and Jursa (166 )) due to perturbation of the B ^ZN 5 + / / Y level by the nearly ZG ( N(S )+N(S )) level (Loftus and Kruperie (165 ))• Assuming therefore that the transition occurring at the forbidden line is Time after Peak Current(us) Figure 58 - The Estimated Absorption Coefficient close to 5754 A due to the Nq X2I* - B2!* series for the Nitrogen Plasma of 0-15 Torr Filling Pressure 1 Absorption Coefficientlm"1) Figure 59- The Estimated Absorption Coefficient close to 3 5754A due to the N2 A IjfrB?Ug (V =8 -v=12) series for the Nitrogen Plasma of 0-15 Torr Filling Pressure .234 that corresponding to the peak intensity for the entire band, which u occurs for the transition with lower level quantum number Jfpg^ where j n _ /' kT max" V 2Bghc then the lower level number density is given by (assuming LTE) N . N2 NLOWER~(2W1» ^EXPT-EJ'/KT] NO < // Using the partition functions listed in table 9.7, and the J^gx values given by the above equation, then ^lower 136611 calculated as a function of time. Lofthus and Kruperie (165) list the transition 4 -1 probability for this line to be 6.5 x 10 s , and the absorption coefficient equation has been used to predict the absorption due to this band at 5754A,"the result being shown in figure 59. The graph shows that this molecular line will produce insignificant absorption at 5754A until after 130 us after the peak current. 9.7.2.4 Conclusions for Molecular Absorption Approximate calculations have been presented in the previous sections of the likely absorption coefficient at 5754A due to trans- itions in N2 and N*. For all the transitions considered, no absorp- tion is likely to be a problem for forbidden line measurements taken within the first 130 us after the peak current. At later times two series of molecular lines may be present, which will lower the accuracy with which measurements can be made, especially if the"Nil Doppler profile is to be used to provide the plasma temperature. 9.7.3 The Quadratic Stark Effect on the [Nil] Forbidden Line The next problem concerning the measurement of the 5754A line, is the possibility of an electric dipole contribution to the line being induced by Stark mixing of the atomic levels of opposite parity by the electric charge distribution within the plasma. .235 Obviously if the contribution is significant the line profile will still be interesting but the [Nil] transition probability will not be measurable. A useful treatment of the Stark effect is given in Condon and Shortley ( 92 ) in Chapter 17* which shows•the atomic Hamiltonian to be H = H0-egz (H. = the unperturbed Hamiltonian) where second order perturbation-theory must be used for non-hydrogenic species since the first order effect vanishes. The result is that an unperturbed level becomes slightly mixed with nearby levels of the same J, MJ but of opposite parity, Consider the Nil ground configuration together with the 3 nearest excited configuration of opposite parity, the 2s2p , which is approximately 134,000 cm above the ground configuration as shown in Figure 60. 2s2p3 [e;elf 1R From Wiese et al. ( 30 ) -1 Level c* : E = 15316 cm = 5 -1 e> : E = 32687 cm = 1 -1 leveU f : E = 166766 cm ; = 3 1: 5754^ = 1.08s"1 2s22p2/leveMl/ Transition A 2: 746A A = 1.6 x 109s"1 3: 660A H - 1.1 X 10As~1 Figure 60-Quadratic Stark Mixing of the NH Ground Configuration From first order perturbation theory the wavefunctions for levels o( and fi are changed from their unperturbed values |o4) and |/60) to new wavefunctions by the mixing with state yfdue to the quadratic Stark effect.where ^ ;<".L ERLOY-M2' <«L = <«L- and similarly for In order to calculate the induced electric dipole transition probability between ok and ft due to the mixing, the matrix element is required which, using the derived expressions for and | 4 ) is L/J2-M2VJERLO <8jerl/8><<* ler IO iSfHt^M lerl »0>< HJerl 4X yjerl 0 'WW Gf the four terms included in this expression, the first includes the matrix element and the last contains the matrix element (tfleH ^ , both of which are zero. The result is therefore < lerI £ > = I <<*Jerltf.>aierl4> Ji^L.Ji-8 "V E -E, L T * s 0 Now for this case • J, = 1,and IJl^ = o for one of the possible transitions. .237 Taking the.complex conjugate of each side of the equation and multiplying produces 2 2 2 l<*lerls>l = |l l -.2 1 + 1 Now,in order to calculate these squared matrix elements consider the definition of the transition probability for electric dipole radiation Aij = -JMTl i.e. I Also required is the average electric field strength which, for this calculation, is taken to be the Holtzmark normal field strength given by : _ _E_ f /3 9 3 2 f-f = 3-75x10 Ne(m ) /3 Vnf1 >0- 2E Finally the energy term is required, which is obtained from the given energy levels 1 1 + = 5x1035 J"2 E-E E -E and therefore .238 3-55 xlO"47^/^ = (3-7Bx10"9N^3 )2x5x1035x(3-55x1047)2 where A^j^ is the required induced electric dipole transition probability. The result is therefore 32 3 4/3 1 A* $ = 1-73 x 10 Ne(m ) s which is plotted in figure 61 as a function of time, using the diagnosed electron densities for the 0.15 Torr nitrogen plasma. From the graph it can be seen that the peak value of A^a occurs -3 at 50 us with a value of 1.7 x 10 . This process will therefore -A, -1 Induced Transition Probability(10 s ') Time after Peak Current(us) Figure 61-The Estimated Stark-Induced Electric Dipole Transition Probability for the Nil 5754A Transition in the 0-15 Torr Nitrogen Plasma .239 be negligible. Should this measurement be attempted on a different plasma of higher electron density, then this process may become important, contributing 1% of the total transition probability at 16 —3 an electron density of 2 x 10 m . 9.7.4 Continuum Absorption Continuum absorption has already been discussed in detail in section 8.4 for a hydrogen plasma, and results obtained in that section will be quoted here without further derivation. If the relevant nitrogen wavelengths and oscillator strengths are inserted into the equation given in section 8.4 for the Rayleigh scattering cross section, it can be shown that this process will again be negligible compared to the alternative process of Thomson scattering. It was shown in section 8.4.1 that the absorption coefficient due to Thomson scattering is independent of the atomic species present within the plasma, and the absorption coefficients due to this process for the —7 —1 —8 —1 0.15 Torr nitrogen plasma will lie between 10" m~ and 10" m~ (as shown for the hydrogen plasma in figure 53 ) and can therefore be ignored. The remaining continuum absorption processes of interest are bound-free and free-free absorption by N, N+ and N~. 9.7.4.1 Free-Free and Bound-Free Absorption by N and N+ The basic theory for these two continuum absorption processes is that given in sections 8.4.3 and 8.4.4 for the hydrogenic case. Corrections to the hydrogenic results have been developed in a series of papers by Peach ( 83 ), (167 ), ( 25 ) and (168 ). The simpler question of the free-free continuum absorption was covered in Peach ( 83 ), in which the required cross-section was developed using a central field model and extrapolated quantum defect theory. The result is a free- free absorption coefficient for a non-hydrogenic species expressed as the hydrogenic coefficient plus a correction term where KFF = KRR • KRR N H Correction and results are tabulated for a variety of species, including nitrogen. The second and third papers by Peach ( 167, 25 ) extend the earlier work to the calculation of the bound-free continuum of N using a similar theoretical procedure, and again hydrogenic and correction absorption coefficients are calculated. These results are further extended to include bound-free absorption by N+ in the fourth paper (168 ). The predicted continuum absorption is shown in figure 62 for the 0.15 Torr nitrogen plasma, for a wavelength of 5800A, where the diagnosed electron densities and temperatures have been used to calculate the absorption coefficients from Peach's cross-sections. The bound-free calculation does not include the possibility of continuum structure due to N+ levels. Le Dourneuf et al. (169 ) and Zeippen et al. (170) have calculated ground state photoionization cross-sections, and, using this data, it appears unlikely that such structure will be important at 5754/L Figure 62 shows that the free-free absorption should be negligible, for all times, compared to the predicted forbidden line absorption. The bound-free absorption coefficient, however, is larger than the forbidden line and will cause severe problems for its measurement. At times of 50 - 80 us, where the forbidden line absorption is largest, this bound-free continuum will be 2 - 3 orders of magnitude larger than the predicted forbidden line and observation of the line will probably be impossible. For times of later than 120 us, however, the continuum/forbidden line ratio drops below 20 and the observation of the line appears feasible. Absorption Coefficient(m^) lound-Free Absorption 10"4. Predicted ' Forbidden Line ^Absorption Free-Free Absorption 120 160 200 Time after Peak Current(us) Figure 62-The Predicted Absorption Coefficients in the 015 TorrNitrogen Plasma due to Continuum Absorption by Neutral Atomic Nitrogen Absorption Coefficient(m^) 10- 4 Predicted Forbidden Line Absorption 10"61 Free-Free Absorption 8 10' Boun^j-Free Absorption 40 120 160 200 Time after Peak Current(us) Figure 63-The Predicted Absorption Coefficients in the 0-15 Torr Nitrogen Plasma due to Continuum Absorption by the Negative Nitrogen Ion 8 3 NN-(10 cm ) 120 160 200 Time after Peak Current(us) Figure 64-The Predicted N" Density (assuming LTE) for the Nitrogen Plasma of 0-15 Torr Filling Pressure .242 This problem with free-bound absorption arises from the low electron density and high temperature of the 0.15 Torr nitrogen plasma used. With the decreasing of the plasma vessel diameter in the future, it may well prove possible to obtain useful electron (and hence Nil) densities using higher filling pressures, and thus lower temperatures. The electron density and temperature dependence of the forbidden line absorption are compared with the temperature and neutral atomic density dependence of the free-bound continuum.later. The pressure of 0.15 Torr is used in this present work, since absorption measurements presented in section 9.8 were completed before the nitrogen plasma temperatures, given in Chapter 6, were deduced. For future work the optimum filling pressure and bank voltage should be found in order that this problem can be reduced. It should be noted that the bound-free continuum absorption is highly dependent on temperature, its value changing by ~20% per 100°K at 10,000K. Given that the temperatures used in these calculations are only estimates given by the measured bounce periods, it is quite likely that the predicted bound-free continuum may well be a large overestimate, and this problem may be drastically reduced. It therefore appears that an attempt at the forbidden line absorption experiment will be useful at this stage, even if only to measure the continuum absorption value. 9-7.4.2 Free-Free and Bound-Free Continuum Absorption by N~ Two more possible sources of continuum absorption at 5754A are due to the presence of the N~ ion. Consider first the free-free absorption. John and Williams (171 ) have published absorption cross-sections for this process and, using the measured electron densities and temperatures and equating the neutral atomic .243 density to that given by the filling pressure, then the results shown in figure 63 have been obtained. The calculation of the bound-free continuum absorption coefficient requires the N~ population to be known. Fraga (172) 4 3 suggests that this ion has an unbound ground state, ( 2p P2 1 0 1 0.2 ev above the NI ground state, which explains the zero electron affinity measured for nitrogen. Hotop and Lineburger (173) point 4 1 out, however, that the first excited state 2p D^ is bound,since 3 2 it lies 0.2eV below the 2p D_ . level in NI. Using this 0/d, Sid/0 energy, and assuming LTE, the N" density can be calculated as a function of time, using the Saha equation and the measured electron density and temperature, and the result is shown in figure 64* Boldt (29 ,174) has.used a wall-stabilized arc to measure continuum emission in oxygen and nitrogen plasmas and, assuming LTE, he has obtained cross-sections for negative ion bound-free absorption for -22 2 these two species. His value for the N ion is 9 x 10 m at 5754A and, using the estimated N~ ion densities shown, the bound-free absorption coefficient has been calculated and is shown in figure 63 • The results show that neither of these processes should prevent the required measurement. 9.7.5 Conclusions Regarding the Feasibility of using Absorption Spectroscopy to Measure the Nil 5754A Transition Probability The preceeding sections have considered the possible measurement of the Nil 5754A electric-dipole forbidden line transition probability for the first time, using long path absorption spectro- scopy. Several conclusions have been reached: (i) The predicted forbidden line absorption coefficients, corresponding to the plasma conditions generated in the ten metre device, are sufficiently large that the transition probability .244 should be measurable to an accuracy of 30% or better over a path length of 1.2 kilometres. (ii) Several possible alternative sources of absorption at 5754ft have been investigated. Those sources resulting in absorp- tion coefficients that are small (< 10% of that predicted for the forbidden line) are shown in table 9.8, and the sources of signif- icant absorption (> 10% of forbidden line) are shown in table 9-9. It has been shown that the largest contribution to the absorption at 5754ft is due to bound-free absorption from excited states in neutral atomic nitrogen, and that the predicted value for this absorption (shown in figure 62 ) is a factor of between 5 and 100 higher than that predicted for the forbidden line for the 0.15 Torr nitrogen plasma. Table 9.8 Trivial contributions to the total absorption coefficient at 5754ft (k < 10% of Nil forbidden line) Absorption Described in Section NI Resonance 9.7.1 Nil Resonance 9.7.1 NI 5817ft 9.7.1 Nil 5731ft 9.7.1 N^ Resonance 9.7.2.2 + N2 Resonance before 130 us 9.7.2.2 3 3 U N2 A Zy-B TTg before 130 us • 9.7.2.3 Quadratic Stark Induced Electric Dipole 9.7.3 Free-Free with N 9.7.4.2 Free-Free with N+ 9.7.4.1 Bound-Free by N~ 9.7.4.2 Bound-Free by N+ 9.7.4.1 .245 Table 9.9 Significant Contributions to the total Absorption Coefficient at 5754$ (k > 10% of Nil forbidden line) Absorption Described in Section + N2 Resonance after 130 us 9.7.2.2 3 3 N2 A Z^"B TTg after 130 us 9.7.2.3 Bound-free by N 9.7.4.1 (iii) Given the known electron density, neutral density,and temperature dependence of the forbidden line and bound-free absorption coefficients, it is possible to predict those plasma conditions required for an optimum measurement of the 5754$ forbidden line. Since the forbidden line absorption coefficient is given by 1 k«NeT" /2eXp[-E1 /kT] then it might at first appear that both the electron density and the temperature should be as high as possible for the required optimum measurement. The bound-free absorption coefficient for neutral nitrogen, however, is proportional to both populations of excited atomic levels and to the neutral atomic density. Since these excited levels are of far higher energy above the ground state (>100,000 cm'1) than the lower level of the forbidden line (15,320 cm'1), then the increase in bound-free absorption due to an increase in temperature is far larger than the corresponding increase in forbidden line absorption. The optimum plasma conditions for the measurement of the forbidden line will therefore be: (a) High electron (and hence ion) density (b) Low neutral density which, taken with (a), suggests that the percentage ionization of the plasma should be high, the upper limit to the allowable ionization being given by the condition that the NIII density must be negligible compared to the Nil density (i.e. plasma must be less than 80% ionized). (c) As low a temperature as possible is required in order that the forbidden line can be observed above the neutral bound- free continuum absorption background. In future work, it is intended to investigate the variation of plasma conditions obtainable with various filling pressures and bank voltages used in the ten metre device, with the intention of achieving the maximum forbidden line to background value. For the purposes of the present research it was decided to attempt a forbidden line measurement using the ten metre plasma device run with a 0.15 Torr nitrogen filling pressure. The total absorption coefficient, predicted earlier in this chapter, suggests that the majority of the absorption observed will be due to bound- free absorption by neutral atoms, and the absorption should vary -1 -1 from 10 m at 50 us (measurable to ~-0.7% accuracy using a 100 _5 metre path) to 10 at 180 us (measurable to -^30% accuracy over 1.2 kilometres). At early times (40-80 us) the Nil forbidden line absorption coefficient will be less than 1% of that due to bound- free absorption and will therefore be immeasurable. At times later than 150 us, however, the forbidden line will contribute more than 20% of the total absorption coefficient and should be observable. Even if the absorption measurement cannot resolve the forbidden line it should serve as a test of the predicted bound-free continuum absorp- tion. 9.8 The First Attempt at an Absorption Measurement of the Nil 5754A Forbidden Line The experimental arrangement used for this measurement was .247 identical to that used for the measurements of the Hel 5876A far wing described in Chapter 7, with the CW laser run with a Rhodamine 6G filling, the multipassing system used to provide absorption lengths of up to 1,200 metres, and with the plasma device run with a 20 kV bank voltage and 0.15 Torr nitrogen filling pressure. When results were first recorded it was found that very large absorption peaks occurred at those times corresponding to electron density bounces. Those measured before 80 us were suffic- iently large that they required the digitizers to be set at insensitive voltage settings such that the far smaller absorption coefficients at times later than 80 us became difficult to measure. A delay of 80 us before the digitizers were triggered was therefore introduced, and results confined to times between 80 us and 280 us. One moderately large absorption peak did occur in this range of times at 110 us and this is visible in figure 66. The forbidden line profile was measured at seven wave- lengths, spaced at 5 GHz (0.06A) intervals, with the forbidden line (of FWHM linewidth of 10 GHz) expected in the centre of this range. The results showed no observable forbidden line, but a higher continuum than predicted was observed. As an example the absorption coefficient -4 -1 measured at 180 us was 2.1 +0.4 x 10 m compared to the total -5 -1 predicted value for this plasma of 1.4 x 10 m - a disagreement of 15 +3. The experiment was therefore repeated to provide a more accurate continuum absorption measurement. More data was taken close to 5754A, and similar measurements were taken at 5940A, 6000A, 6208.2A and 6440A ( all measured to +0.2A) and the results are shown in figure 65, for a time of 180 us after the peak current. The error bars obtained are somewhat high (+20%) but the _ / 4 Absorption Coefficient(10 m") 2-4 \ 20- 1 N <• 1-6- 5754A 3 1-2- X 0-8- 0-4- ^Theoretical Value(Peach(.168)) 0 5600 5800 6000 6200 6400 660Q, Wavelength(A) Figure 65-Nitrogen Continuum Absorption Measured 180us after peak current in the 0-15 Torr Plasma -4 -1 Absorption Coefficient(10" m" ) •Predicted by Peach(168) -Measured 160 200 240 280 Time after Peak Current(us) Figure 66-Measured Nitrogen Continuum Absorption at5754 A for the 0-15 Torr Plasma as a function of Time .249 absorption is high at all wavelengths thus suggesting that absorption due to nearby atomic and molecular transitions is unlikely to be responsible. Peach III (168) has shown that the bound-free absorption coefficient for neutral nitrogen atoms,for wavelengths between 550Oft and 6600ft,varies with wavelength as X-3 Assuming that the measured absorption is due to this process, then, using the -4 -1 absorption coefficient of 2.1 +0.4 x 10 m , measured at 5754ft and 180 us;as normalization, the wavelength dependence of the absorption coefficient is plotted in figure 65, from which it can be seen that the measured absorption does appear to scale as X-3. As a comparison between the measured and predicted continuum absorption, the traces taken at 5754ft have been averaged and the resultant variation of measured absorption with time is shown in figure 66, with the predicted absorption (due to bound-free and mole- cular transitions) included. At times later than 120 us, the measured continuum is clearly far larger than theoretically predicted, presumably due either to the temperature being higher than estimated in Chapter 6 (a temperature of ^11,000 K would be required at 180 us), or to overpopulation of the excited states (by a factor of 14.3 at 180 us). Whatever the mechanism responsible for this high continuum absorption, the forbidden lines cannot be measured using the 0.15 Torr nitrogen plasma in the ten metre device,as presently used. After 150 us, the continuum absorption is sufficiently high that the forbidden line absorption would be small (5%) compared to the error in the measured continuum absorption. In order to perform measurements at these late times,the plasma conditions must there- fore be varied to increase the forbidden line/continuum background .250 absorption ratio (as discussed previously). Before 150 us, absorption measurements were prevented by the large absorption peaks present at those times corresponding to electron density bounces. It therefore appeared feasible that refractive index gradients might be present within the plasma (due to the bounces) and that beam refraction might therefore be occurring at these times. An experi- mental measurement of possible refractive index gradients was therefore attempted. 9.9 An Interferometric Measurement of Density Gradients present within the plasmas used for long path absorption measurements A similar experimental arrangement was used for this measurement as that used for the off-axis electron density measure- ments described in Chapter 6, except that both arms of the inter- ferometer were placed within the plasma. The plane end-windows were used (providing a plasma length of 21.7 metres) and results were taken with 0.15 Torr nitrogen, 0.45 Torr hydrogen, and 0.45 Torr helium plasmas (all with 20kV bank voltage), with the CW laser tuned to 5876A for the measurements in nitrogen and hydrogen, and to 5857A for those in helium. For each filling the interferometer was first aligned with the two arms at +3 cm and -3 cm off of axis. The results were most satisfactory, with no fringes visible, thus confirming the symmetry of the bounces. The interferometer was then run with the two arms at 0 and 3 cm from axis, and the measured refractive index differences between these positions are shown in figure 67 , the dotted lines on each trace showing the axial refractive indices described in Chapter 6. In the hydrogen and helium plasmas the gradients were very small after 50 us, and then only occurred during the (n-1) (i)The Nitrogen Plasma Filling Pressure = 0-15 Torr Bank Voltage = 20kV 150 200 250 . Time after Peak Current(us) (n-1) 3x10 (ii)The Hydrogen Plasma Filling Pressure = 0-45Torr Bank Voltage =20kV 2x10"'.. 150 200 250 Time after Peak Current(us) (n-1) 2x10"7- (iii)The Helium Plasma \ W Filling Pressures 0-45Torr 1 Bank Voltage = 20 kV 10:1 \ 1I ^\ r\ \ t V \ /V / \ \ F ^ O \ 0- \A JX -P- 0 50 100 150 200 250 Time after Peak Current(us) Figure 67-A Comparison of the Measured Axial Refractive Index (Dotted Line) and the Difference in Refractive Index Measured between the Axis and 3cm. off of the Axis (Full Line) for the three Plasmas used for Absorption Measurements .252 peaks of electron density bounces. In the nitrogen plasma the effect was far more pronounced,with refractive index gradients present at all times. The gradients are presumably the result of the radially propagating accoustic wave as it converges onto the plasma axis. The perturbation in neutral density (and hence that in electron density) will increase as the wave approaches the axis. The differing persistence of these gradients in the three plasmas is more puzzling. One possibility is that the propagating accoustic wave leaves high densities in its wake,and that these take varying times to dissipate. Alternatively the propagating neutral pulse may be of different width in the three'gases, being sufficiently wide in the nitrogen plasma that its effects on axis for each pulse are still apparent when the following pulse arrives. It is unclear at present which mechanism is responsible for the persistence of the gradients., but it will be shown in the following section that they may be responsible for the observed anomalous absorption peaks. These persistant refractive index gradients in the nitrogen plasma introduce one last problem. As described in section 6.2.2.2, the electron density diagnostics presented in Chapter 6 require that no changes in atomic density occur within the plasma. During the bounces this assumption breaks down, and the measured fringe pattern contains an atomic contribution which is calcuable only if the electron density present in the absence of the bounce is known. For the nitrogen plasma, however, the density gradient persists for all times measured, and the electronic and atomic contributions to the total refractive index cannot be separated. The unfortunate conclusion is therefore that the electron densities shown in Chapter 6 .253 are in error. Obviously this problem follows directly from the presence of the radially propagating accoustic wave discussed in Chapter 6, and the methods for its elimination, discussed then, are therefore increasingly important. 9.10 Path Bending The likely, explanation for the large absorption peaks observed for all three gases during the bounces, is that the high refractive index gradients present bend the beam path. If the beam is sufficiently deviated then some or all of the laser light will fail to reach the detector, and an apparent absorption will be recorded. In order to estimate such effects, use is made of the standard ray equations. If the beam is at a distance z parallel to the axis, and travelling at an angle to the axis, in a radially symmetric refractive index gradient dn/dr, then de-= 1_ dn dz n dr and and therefore dj; _ 1 dn dz2 " n dr Obviously to proceed further, a model is required for the exact form of the refractive index gradient, and the approximation used here is that this is given by n(r) = n(0) 1 + MR 2 (since this is the simplest solution for the above equation). Assuming the boundary conditions are that the beam is injected into .254 the cavity at a radius T0 and parallel to the axis, then the resultant equation for path radius T is: r = ToCoshlVA'z) The beam therefore diverges and, if the gradients are sufficiently large, will strike the plasma vessel wall and total absorption will therefore be recorded. As an example consider the 0.15 Torr nitrogen plasma. At a time of 110 us (corresponding to an electron density bounce) then n(3 cm) - n(0 cm) = 4.41 x 10"8 therefore A~10 4 and the deflection.after 10.84 metres, of a beam incident 3 cm from the plasma axis, will therefore be 0.18 m.m., and hence,over a single pass,the beam will not deviate sufficiently to cause any problems. With the high optical lengths produced by the multi- passing cavity, however, the net deflection might be sufficient that the beam might catch the edge of a mirror or end-window,and an apparent absorption will be measured. Given the small diameter of laser spot produced at the input end of the multipassing cell, then once the beam starts to catch an edge in the cavity, only a slight increase in deviation will be required for the beam to be totally blocked. This behaviour is certainly compatible with the absorption recorded during the electron density bounces,in which very sharply rising absorption peaks are seen, and this is therefore the most likely explanation for the observed peaks. 9.11 Conclusions for Absorption Spectroscopy in a Nitrogen Plasma In this chapter, a forbidden line of astrophysical interest .255 has been described, and its measurement using long path absorption spectroscopy discussed. Experimentally, it has been shown that, for the plasma used at present, this forbidden line measurement is impossible due to high continuum absorption and beam deflection. It has also been shown that the presence of refractive index gradients within the nitrogen plasma has invalidated the electron density diagnostics described in Chapter 6. Such a problem does not apply for the hydrogen and helium plasmas used for the experiments described in Chapters 7 and 8, and the results presented there still apply. The explanation for the high measured continuum is unclear at present, but the most likely explanation is that of bound-free absorption by neutral atomic nitrogen. Obviously the re-building of the plasma device to eliminate the bounces is crucial if the possibility of measuring the weak Nil forbidden line is to be realised. Once the plasmas obtained are uniform, then a variety of filling pressures and bank voltages should be used to produce those plasma conditions^ resulting in:the highest forbidden line to background continuum absorption ratio. One method of achieving this will be to work with a far higher percent- age of the NI atoms ionized. The limit to the allowable percentage ionization is probably 80%, since above this value the NIII density will become significant (>1% of Nil density) and the equality between the electron and Nil densities, used in the analysis of the forbidden line transition probability, will break down. Finally, once the plasmas available are such that the 5754A forbidden line has been measured, then there exist a large number of such astrophysically interesting lines, and these are listed in Appendix C. CHAPTER 10 CONCLUSIONS AND FURTHER WORK 10.1 Technical Achievements In order that weak spectral features could be measured in a plasma using absorption spectroscopy, several items of experimental apparatus required design or development. The results obtained have been far better than envisaged at the start of this thesis, since path lengths of more than 200 metres were then unproved. The development of the experimental apparatus required was discussed in Chapters 3, 4 and 5 and the general achievements outlined were: (i) The design of a replacement spark gap for the ten metre plasma device which fulfilled all of the switching require- ments for the capacitor bank. (ii) The installation of the Spectra Physics 380A CW ring dye laser. (iii) The rebuilding of the laser monitoring and detection equipment in order that the full sensitivity of the experimental arrangement could be realized. (iv) The building of a three mirror multipassing cavity capable of providing absorption path lengths within the plasma of more than a kilometre for the first time. Simple changes to the apparatus, discussed in Chapter 5, 1 may well allow even longer paths (2 - 3 km) to be achieved, and a new Argon-ion laser (producing 18W all lines and 3W UV power) should extend the range of available dye laser wavelengths down to 4000A and increase the available dye laser powers toWatts. 10.2 Diagnostic Achievements The diagnostic measurements performed on the ten metre plasmas used for absorption measurements were discussed in Chapter 6. The accuracy of the temperature diagnostics so far obtained has been poor, but equipment soon to be used with these plasmas should improve this. The electron density interferometric diagnostics have provided the most surprising results of the entire thesis. The sensitive arrangement used, capable of detecting electron densities 13 -3 as low as 2 x 10 cm , has shown the existence of previously undiagnosed electron density oscillations in the supposed quiescent recombining plasma. These are now thought to be due to the presence of a radially propagating acoustic wave, and, using this conclusion, nitrogen plasma temperatures of interest have been estimated. 10.3 Experimental Results and Conclusions The results of long path absorption and interferometric experiments, discussed in Chapters 7, 8 and 9, have shown the available long paths to permit measurement of absorption coefficients -5 -1 as low as 8 x 10 m (to 30% accuracy) and that higher absorption -3 -1 coefficients (10 -10 m ) can be measured to an accuracy of better than 1%. In the Hel 5876A profile measurement, the variation in available path lengths was used to observe the profile over orders.of magnitude of absorption, and out to 50 linewidths from line centre. .258 The conclusions obtained during the experimental measurements were that: (i) Multiple pass plasma absorption spectroscopy offers a useful technique for the study of highly excited atomic levels, ionic species and the behaviour of atomic properties within a plasma environment, and that this technique is of greater sensitivity and accuracy than the alternative method of emission spectroscopy. (ii) Ground configuration electric dipole forbidden lines, of astrophysical interest, within light ions (such as Nil) should be measurable given kilometre absorption paths. This will provide the first measurement of the transition probability of these lines. (iii) Radially propagating acoustic disturbances are present within the plasma, producing refractive index, absorption and emission peaks. These acoustic waves are unwanted since they produce refractive index gradients and thus, at present, prevent the measurement of the Nil forbidden line described in Chapter 9. Modifications to the plasma device should eliminate this problem. (iv) The satellite feature seen on the wing of the He I 2p3P-3d3D 5876ft profile has been confirmed to be the 2p3P-3d1D intercombination line. The transition probability of this satellite has been shown to be linearly dependent on electron (or ion) density, which is compatible with the proposal that this line occurs via a charge exchange reaction. (v) Continuum absorption values in both hydrogen and nitrogen plasmas have been shown to be higher than theoretically estimated, and possible explanations for this have been discussed in Chapters 8 and 9. (vi) Anomalously low absorption coefficients have been measured close to the line centre of the He I 5876ft transition. No explanation for this curious behaviour is obvious at present and further work is certainly required. (vii) Experimentally measured level populations have been obtained which disagree with the results of a collisional radiative code, as discussed in Chapter 8. 10.4 Further Work The experiments described in this thesis have produced more questions than answers, and several further experiments are therefore planned. (a) The plasma device must be rebuilt to eliminate the density oscillations. (b) Temperature diagnostics must be performed to an accuracy of better than 5% in all species, since the poor accuracy of existing results prevents firm conclusions being drawn in the analysis of some of the measured absorption data. (c) Given the changes in (a), the optimum plasma for Nil forbidden line measurements should be identified, and the measurement re-attempted. (d) The hydrogen and nitrogen continua require confirmation at further wavelengths, and with a higher accuracy than that obtained so far. Given more accurate temperature diagnostics, then firmer conclusions concerning the mechanisms responsible for these anomalous results should be possible. (e) Similarly, the accurate temperature diagnostics will allow a more accurate comparison between measured and theoretical level populations. (f) Playford's transverse measurements of the He I 5876$ line centre absorption coefficient should be repeated using the CW ring laser, for comparison with the existing line centre data (taken over 10.84 metres). (g) Further 5876A line centre absorption measurements are required using the 10.84 metre plasma to obtain more accurate anomalous line centre profiles, in order that the mechanism responsible might be identified. (h) More data should be obtained for the He 5876A inter- combination line, since a more accurate Doppler profile should provide the plasma temperatures as a function of time. Two further experiments that can be used to confirm the identification of the intercombination line are firstly a double resonance experiment in which the forbidden line absorption is monitored during pumping of a second transition, and secondly an observation of a similar satellite in the wing of the He I 6678A transition. 10.5 Concluding Remarks These then are the conclusions arising from the experiments performed so far,and the further experiments suggested by those conclusions. The work presented has proved that long path laser absorption spectroscopy in plasmas is a useful, sensitive and flexible technique for measurements of quantities of interest in atomic physics. The apparatus developed has allowed this technique to be used close to its limiting sensitivity and accuracy (as discussed in Chapter 2), and improvements now planned should allow this plasma/laser system to be used as a facility for a wide range of spectroscopic experiments. APPENDIX A THE SENSITIVITY AND ACCURACY OF LONG PATH ABSORPTION MEASUREMENTS A.1 Choice of Method In order to measure the optical depth X then either the output intensity or the difference between the output and input intensities can be measured, these two quantities being related to the input intensity I and the optical depth X by I| = - input/output method T = IQ(1- e" ) - input/difference method Assuming that the lowest percentage error in optical depth (Ax/x) is required, and that the errors in I0 are far smaller than those in I, and I , , A I, and A I, respectively , then the errors produced I • I D by the two methods are given by: AI, m= - 1* '(I I,xjntyio ) At \ _ AId T d (I0-Id)ln(I0/(I0-Id)) and hence I AT) _ AI( 1' y^ = If the errors Al^ and Alj are due to shot noise or excessive plasma emission, then AI ^ = Aand the two methods are equally valid. One major problem for the measurement of low optical depths using the longest path lengths is that the ultimate limit in absorption measure- ment is due to trace reading accuracy. Even using the transient digitizers the recorded traces (output and difference signals) can only be read to a maximum accuracy of 1 part in 1024. For this error therefore AI, ALD and and the ratio is > 1 for > Io/2 for I, <1/2 i.e. when reading accuracy limits the measurements, then the input/output method should be used for measuring more than 50% absorption (i.e. T ^ 0.69); and the input/difference method should be used for less than 50% absorption ( T<0.69). A.2 Choice of Path Length Given the range of available path lengths (10.84 - 1,200 metres in 43.4 metre steps), the possibility of using an optimum path length for the measurement of a given optical depth arises. Assuming that the percentage error in optical depth (Au/T), due to errors in or , is required to be a minimum then this optimum path length can be calculated as follows, (i) Using the input/output method since AT _ AIi tT I Ind^IJ then d_/Ax_\ = iTaI] _ _d(AIi\ dl \ T I - T H "dl\ I( / which is zero when AI optimum which can be re-written as -1 . 1 dl = + 1 optimum, ^ k A!, (ii) Using the input/difference method since At _ Aid x (I0-I )ln(I0/(I0-I ) AI then _d/Ax\ _ I d/ d \ AI, dl 1 x ) " x d LHll0-ld) KI0-Id)J which is zero when Al /(I -Id) = d 0 optimum^ d which can be rewritten as -1 rdi'AId' optimum^ = + 1 KAL Hence, given a knowledge of the dependence of AI [ or/\ on the absorption length, the optimum length for a given absorption coeffic- ient measurement can be calculated. A.3 An Example of an Optimum Path Length Calculation t Consider the use of the input/output method to measure T from I | and IQ . Assuming that the error in IJ , AI[ , is given by three terms ]/ ALJ = 2 + .264 where Sq = constant noise (such as due to shot noise on plasma emission) a>| = shot noise a2= percentage noise (such as reading accuracy) Substituting the equation for AI ^ into the equations for the optimum absorption length then a a 1/2 _ Q * ll[ + a2I[ aQ 4^(2)12 As a numerical example consider this measurement with the following values: 9Q = 2 mV of shot noise on plasma emission 3-j = negligible shot noise (see Chapter 1) a2 = 5% reading accuracy Hence for a typical input signal of I0 = 200 mV then xopt = 1+5e"V which has the solution TQpj- = 1.82, and therefore Ij = 32.4 mV and At/I = 6%. This analysis can in principle, be carried out for all measurements, but most of those performed required 1 < X < 2 .and so, where possible, the absorption length was adjusted to keep between these limits. A.4 Choice of Laser Power For absorption measurements of transition probabilities and lineshapes then the choice of laser power is straightforward. Providing the laser does not reach a power that will significantly perturb the atomic energy level populations (i.e. Of Chapter 7), then the laser power should be increased as far as .265 possible, to minimize the errors due to«shot noise on the plasma emission, etc. If the only measurement required is the wavelength of a spectral feature, however, then the condition of lack of saturation is unnecessary, and the achievement of higher accuracies by using higher laser powers than those required to saturate must be considered At low powers ( IQ«I^ > where Ig is the intensity required to saturate the atomic transition (as given in Chapter 7)) then the absorption coefficient is a constant with a value kQ . At high powers ( Ie ) Skinner ( 77) has shown that the absorption coefficient becomes WS / and hence, using the full expression for k , the percentage accuracy of absorption measurements becomes A1) LI AYIS+IJEXPTWIIS+I.)] X f " Wo at low intensity this becomes k l At \ _ AIie ° C^* 1 Y I Mo Io which is the standard small signal result, , and shows that higher accuracies are obtained as IQ is raised. As higher powers, the minimum value for At/t is At] AL min 0 5 J —06 as o and AX/X reaches within 10% of this minimum value when JLLLO = 0-9 I o I0*9IS Hence the accuracy of the observation of spectral features can be increased by using higher powers than those required to saturate, but the accuracy tends to a limit for IQ»I .267 APPENDIX B THE REFRACTIVITY OF A VOIGT PROFILED ATOMIC TRANSITION B.1 The General Expression for a Voigt Profile The complex refractivity n for a Lorentzian lineshape close to the atomic line is given by: n= n-ik where n-1 = -9jI AjjXjJ Jj (Vj;-V!J ) (N- gLM.. ) Q 3 2 l l' y 9 z 9 J i 32TT [(vt -vr+Avc ] J and g A X Av, _ j l ij (Nj-gjNj) 9 2 2 2 i 8tc [(v..-v) +Avc ] where the subscripts j and j refer to the lower and upper transition levels respectively, and AVr is the collisional HWHM linewidth. To convert to a Voigt Profile then let 2 (n- n.-2i-n-)/j! \'2 exp[-rnv/2 kT] dv [ 1 9j J i gj J (2nkT/ and let V- -v(1 In order to ease the arithmetic let 2_ MV; y 2kT g. 9j X;, F = (M.-ZLM-)— -^oA A- 9 T9j 8Tr2 ji v - VjJj Avc x =• j a = Ava AVJ where A\/j is the Doppler HwIm width, given in Section 9.6.2 The expressions for K and n-1 therefore become ,2 k = Fa 2 2 dy AV, -.4 (x-y) +a y n-1 = —3 (x-y) e" dy J (x-y)2 + 2a -06 B.2 The Far Wing of a Voigt Profile Consider the far wings of such a profile where X^a O6 (X-Y)E-Y^ dy = -V4 (x-y)2+ a2 (x-y) e'dy -OD '-OD Providing then this integral 'equals' ^IL X and similarly e y -dy =_ Sk (x-y)2 + a2 '-od Hence in the far wings of a Voigt profile = 9j XyAjj 'Nj-|Nj) 9i 32 tt3 Av gj X-jAji Avc g. and k = / -J-y 7 (N: - =LNs ) 9j 8tc2 Av2 1 gj J Thus in the Lorentzian wings of the profile both the absorption and the refractive index are given by the same expressions as those that apply in the absence of the Doppler contribution to the profile. B.3 The Line Centre Absorption Coefficient for a Voigt Profile It was shown in Chapter 9 that the line centre absorption coefficient for a Doppler broadened line is given by 9j_ XjjAjj j_ 9j V 9i 8tc3/2 Av/N' 9j" j1 In the absence of a Doppler contribution to the lineshape the line centre absorption coefficient would be = fii^ji jl(n.-£ln., °c 9j qtc2 Avc ' 9j j' The inclusion of Doppler broadening in a lineshape therefore lowers 1/2 the line centre absorption coefficient by a factor of but leaves the far Lorentzian wing unaffected. The Line centre absorption coefficient kG is therefore related to an absorption coefficient K.. measured a detuning Av .270 from line centre by Av2 ko = 'v AvcAvdJ APPENDIX C Forbidden Transitions of Interest (of A> 0.001s ') (Data from Aller (110 ) ) Species X(A> Ats"1) Type of Transition e = electric quadrupole m = magnetic dipole Nil 5754.8 1 .08 e Nil 6583.6 0.003 m, e Nil 3063.0 0.034 m Nil 6548.1 0.001 m, e 01 5577.4 1 .34 e 01 2972.4 0.07 m 01 6300.2 0.005 m, e 01 6363.9 0.002 m, e Oil 7319.8 0.11 m, e Oil 7318.6 0.061 e on 7329.9 0.1 m, e on 7330.7 0.061 m, e on 3726.2 0.002 m, e CI 4621.5 0.0026 m SI 4506.9 0.01 e SI 4587.0 0.33 m Sil 6589.7 0.003 e Sil 6526.9 0.036 m PI 5332.4 0.099 m, e PI 5339.7 0.04 m, e • FII 4157.5 2.1 e FII 4789.5 0.044 m, e FII 4869.3 0.014 m, e SII 4068.6 0.32 m, e SII 4076.4 0.13 m, e PII 7869.5 2.9 e PII 4669.5 0.223 m cm 3675.0 1 .28 m OIII 4363.2 1 .6 e OIII 5006.8 0.021 m, e OIII 4958.9 0.007 m, e Nelll 3342.9 2.8 e Nelll 3868.7 0.2 m, e Nelll 3967.5 0.06 m, e C1III 5517.7 0.002 m, e C1III 5537.6 0.006 m, e Fill 5721 .1 0.028 m, e Fill 5733.0 0.05 m, e SIII 6312.1 3.6 e AIII 7135.8 0.32 m It must be noted that there are more transitions than these listed,but that others either have wavelengths outside of the range of output from existing dye lasers, or else occur in highly ionized species (Z >3),which will require a different plasma source from that used in this present research. .273 REFERENCES 1. 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