`
`
`
`gaser-Inoluced
`"’ Plasmas
`and
`Applications:
`
`
`
`edited by
`
`Leon J. Radziemski
`Department of Physics
`New Mexico State University
`Las Cruces, New Mexico
`
`David A. Cremers
`Chemical and Laser Sciences Division
`
`Los Alamos Nationai Laboratory
`Los Alamos, New Mexico
`
`MARCEL DEKKER, iNC.
`
`New York and Base!
`
`ASML 1206
`
`ASML 1206
`
`

`

`
`
`Library of Congress Cataloging-in-Publication Data
`
`Laserwinduced plasmas : physical, chemical, and biological applications / edited
`by Leon J. Radziemski, David A. Cremers.
`p.
`cm.
`
`Includes bibliographies.
`ISBN 0-8247-8078-7 (alk. paper)
`1. Plasma engineering.
`2. High power lasers.
`II. Cremers,David A.
`TA2020.L37 1989
`
`620.044--dc20
`
`I. Radziemski, Leon J.,
`
`89-7883
`CIP
`
`This book is printed on acid~free paper.
`
`Copyright© 1989 MARCELDEKKER. INC. All Rights Reserved
`
`Neither this book nor any part may be reproduced or transmitted in any form
`or by any means, electronic or mechanical, including photocopying, microfilming,
`and recording, or by any information storage and retrieval system, without per-
`mission in writing from the publisher.
`
`MARCEL DEKKER, INC.
`270 Madison Avenue, New York, New York 10016
`
`Current printing (last digit):
`10 9
`8
`7
`6
`5 4 3
`2
`
`1
`
`PRINTED IN THE UNITED STATES OF AMERICA
`
`
`
`

`

`Contents
`
`Preface
`Contributors
`
`1 Physics of Laser-Induced Breakdown: An Update
`Guy M. Weyl
`
`1.1
`1.2
`1.3
`1.4
`1.5
`
`Introduction
`Creation of Initial Electrons
`Electron Growth in Gases
`
`Laser-Induced Breakdown of Solids and Liquids
`Concluding Remarks
`References
`
`2 Modeling of Post-Breakdown Phenomena
`Robert G. Root
`
`2.1
`2.2
`2.3
`2.4
`2.5
`2.6
`2.7
`2.8
`2.9
`2.10
`2.11
`2.12
`
`Introduction
`
`Creation of a Propagating Plasma
`Absorption Characteristics of Heated Gases
`Features of Propagating Plasmas
`One-Dimensional Laser—Supported Combustion Waves
`One-Dimensional Laser—Supported Detonation Wave
`One-Dimensional Laser-Supported Radiation Wave
`Transition Regions
`Radial Expansion
`Thermal Coupling
`Other Factors
`
`Summary
`References
`
`3
`
`Introduction to Laser Plasma Diagnostics
`Allan A. Hauer and Hector A. Baldis
`
`3.1
`3.2
`
`Introduction
`
`Introduction to Optical Diagnostics
`ix
`
`iii
`xi
`
`69
`
`69
`70
`72
`75
`77
`88
`92
`93
`95
`99
`100
`101
`101
`
`105
`
`105
`110
`
`

`

`
`
`
`
`x
`
`3.3
`
`Introduction to X—ray Diagnostics
`References
`
`4 Laser-Sustained Plasmas
`Dennis R. Keefer
`
`Introduction
`4.1
`Principles of Operation
`4.2
`4.3 Analytical Models
`4.4
`Experimental Studies
`4.5 Applications of the Laser-Sustained Plasma
`References
`
`5
`
`Inertialiy Confined Fusion
`Robert L. McCrory and John M. Soures
`
`'
`
`5.1 Historical Overview
`
`5.2
`5.3
`5.4
`5.5
`
`Laser—Fusion Scaling Laws
`Coronal Physics
`X—ray Generation by Laser—Produced Plasmas
`Laser—Driven Ablation
`
`5.6 Hydrodynamic Stability of Ablatively Driven Shells
`5.7
`Irradiation Uniformity Requirements
`5.8
`Implosion Experiments
`References
`
`6 Laser-Based Semiconductor Fabrication
`Joseph R. Wachter
`
`6.1 Aspects of Semiconductor Fabrication
`6.2 Applications of Lasers in the Semiconductor Industry
`6.3
`Research Areas
`6.4 Outlook
`References
`
`7 Spectrochemical Analysis Using Laser Plasma Excitation
`Leon J. Radziemski and David A. Cremers
`
`Review
`7.1
`7.2 Methods and Properties of Analysis Using Laser Plasmas
`7.3
`Analysis of Gases
`7.4 Analysis of Bulk Liquids
`7.5 Analysis of Particles
`7.6 Analysis‘of Solids
`7.7 Advances in Instrumentation
`
`Contents
`
`131
`161
`
`169
`
`169
`172
`182
`189
`196
`203
`
`207
`
`207
`
`211
`217
`224
`227
`
`239
`243
`251
`260
`
`269
`
`269
`276
`283
`290
`291
`
`295
`
`295
`296
`302
`306
`309
`313
`318
`
`

`

`Contents
`
`7.8
`
`Prognosis
`References
`
`8 Fundamentals bf Analysis of Solids by Laser-Produced
`Plasmas
`
`Yong W. Kim
`
`8.1
`8.2
`
`Chapter Organization
`Introduction
`
`8.3
`
`Phenomenology of Laser Heating of Condensed-Phase
`Targets
`8.4 Quantitative Spectroscopy
`8.5
`Intensity Measurements and Elemental Analysis
`8.6
`Summary
`References
`
`9 Laser Vaporization for Sample Introduction in Atomic and
`Mass Spectroscopy
`Joseph Sneddon, Peter G. Mitchell, and Nicholas S. Nogar
`
`9.1
`
`9.2
`9.3
`
`9.4
`
`9.5
`9.6
`9.7
`9.8
`
`10
`
`10.1
`10.2
`
`10.3
`
`Conventional Solid Sample Introduction for Atomic
`Spectroscopy
`Laser Ablation of Solid Samples
`Laser Ablation for Sample Introduction in Atomic
`Spectroscopy
`Relative Merits of Laser Ablation for Sample Introduction
`in Atomic Spectroscopy
`Laser Sources for Mass Spectrometry
`Applications of Laser Microprobe
`Applications of Laser Desorption and Postionization
`Conclusion
`References
`
`Current New Applications of Laser Plasmas
`Allan A. Hauer, David W. Forslund, Colin J. McKinstrie,
`Justin S. Wark, Philip J. Hargis, Jr., Roy A. Hamil, and Joseph
`M. Kindel
`
`Introduction
`
`Applications of Laser-Plasma-Generated X~rays and
`Particles
`
`Laser-Plasma Acceleration of Particles
`
`xi
`
`321
`323
`
`327
`
`327
`327
`
`330
`336
`341
`344
`345
`
`347
`
`347
`350
`
`353
`
`363
`365
`369
`372
`376
`376
`
`385
`
`385
`
`386
`413
`
`

`

`xii
`
`10.4 Laser-Pulsed Power Switching
`References
`
`Index
`
`'
`
`4
`
`Contents
`
`424
`432
`
`437
`
`

`

`
`
`4
`Laserir‘Sustained Plasmas
`
`Dennis Fl. Keefer
`
`Center for Laser Applications
`University of Tennessee Space Institute
`Tullahoma, Tennessee
`
`4.1
`
`INTRODUCTION
`
`Plasmas created by the radiation from focused laser beams were first ob-
`served with the advent of “giant pulse” Q-switched, ruby lasers by Maker
`et a1. (1963). These plasmas formed spontaneously by gas breakdown at
`the focus of a lens and were sustained only for the duration of the laser
`pulse. Plasmas were also observed to form on the surfaces of materials ir—
`radiated by high-power pulsed or continuous lasers and to propagate into
`the incident beam at subsonic or supersonic velocities. With the advent of
`continuous, high-power carbon dioxide lasers, it became possible to sustain
`a plasma in a steady—state condition near the focus of a laser beam, and the
`first experimental observation of a “continuous optical discharge” was re-
`ported by Generalov et a1. (1970). The continuous, laser-sustained plasma
`(LSP) is often referred to as a continuous optical discharge (COD) and it
`has a number of unique properties that make it an interesting candidate for
`a variety of applications.
`The laser-sustained plasma shares many characteristics with other gas
`discharges, as explained in detail by Raizer (1980) in his comprehensive re-
`view, but it is sustained through absorption of power from an optical beam
`by the process of inverse bremsstrahlung. Since the optical frequency of the
`sustaining beam is greater than the plasma frequency, the beam is capable of
`propagating well into the interior of the plasma where it is absorbed at high
`intensity near the focus. This is in contrast to plasmas sustained by high-
`frequency electrical fields (microwave and electrodeless discharges) that
`operate at frequencies below the plasma frequency and sustain the plasma
`through absorption within a thin layer near the plasma surface. This funda-
`mental difference in the power absorption mechanism makes it possible to
`169
`
`

`

`170
`
`Keefer
`
`generate steady-state plasmas having maximum temperatures of 10,000K or
`more in a small volume near the focus of a lens, far away from any confining
`structure. A photo of a plasma sustained by a laser beam focused with a lens
`is shown in Fig. 4.1(a): The 600 W Gaussian beam from a carbon dioxide
`laser was focused by a 191mm focal length lens into 2 atm of flowing ar—
`gon. Fig. 4.1(b) shows schematically how the plasma forms within the focal
`region.
`Continuous, laser-sustained plasmas have been produced in a variety of
`gases at pressures from 1 to 210 atm using carbon dioxide lasers operating at
`a wavelength of 10.6 pm and powers from 25 W to several kilowatts. Most
`of these experiments were performed in open air or large chambers with
`little flow, except for that provided by natural convection, but recent ex-
`periments by Gerasimenko et a1, (1983), Welle et a1. (1987), and Cross and
`Cremers (1986) have demonstrated that the LSP can be operated success-
`fully in a forced convective flow. Gas discharges that operate in a flowing
`environment have been called “plasmatrons” in the Soviet literature, and
`the laser-sustained plasma is often referred to as an “optical plasmatron.”
`These experiments have demonstrated that piasma conditions are strongly
`dependent on the position of the plasma within the sustaining beam, and
`that the plasma can be controlled 'ithin a wide range of conditions us—
`.
`.
`.
`.
`.
`1
`4:
`mg appropriate combinatiens of laser power, flew, and epticai configura—
`tion.
`
`The unique ability to sustain a plasma within a small, isolated volume
`at relatively high pressures and temperatures has suggested a number of
`potential applications for the laser-sustained plasma. Since the LSP can
`operate in pure hydrogen and the power can be beamed remotely, it has
`been proposed that the LSP could be used for high specific—impulse space
`propulsion. A number of papers have dealt with this application, and it was
`the subject of a review by Glumb and Krier (1984). Thompson et a1. (1978)
`described experiments in which laser energy was converted into electrical
`energy using a laser—sustained argon plasma. Cremers et a1. (1985) have
`suggested the LSP as a source for spectrochemical analysis and given some
`experimental results. Cross and Cremers (1986) have sustained plasmas in
`the throat of a small nozzle to produce atomic oxygen having a directed
`velocity of several km/sec for the laboratory study of surface interactions at
`energies and particle fluxes similar to those experienced by satellites in low-
`earth orbit. Other applications are suggested by analogy to other plasma
`devices including light sources, plasma chemistry, and materials processing.
`The physical processes that determine the unique characteristics of the
`LSP will be discussed in Sec. 4.2, and the theoretical analyses that have been
`used to describe the LSP Will be addressed in Sec. 4.3. Experimental results
`obtained will be presented in Sec. 4.4 and compared with the theoretical
`predictions. Sec. 4.5 will consider some possible applications.
`
`
`
`

`

`
`
`Laser-Sustained Plasmas
`
`1 71
`
`
`
`(b)
`
`(a) Photograph of a plasma sustained by a 600 W carbon dioxide laser
`Figure 4.1
`beam focused with a 191 mm focal length lens. (b) Schematic representation show—
`ing how the plasma forms within the focal volume.
`
`

`

`
`
`
`
`172
`
`Keefer
`
`4.2 PRINCIPLES OF OPERATION
`
`Plasmas that are created or sustained by lasers can be generated in a variety
`of forms, depending on the-"characteristics of the laser and optical geome-
`try used to generate them.“ High-energy pulsed lasers can generate plasma
`breakdown directly within a gas that results in a transient expanding plasma
`similar to an explosion. At lower laser intensities and longer pulse times,
`plasmas may be initiated at solid surfaces and then propagate into the sus-
`taining beam at supersonic velocities as a laser-sustained detonation (LSD)
`wave or subsonic velocities as a laser-sustained combustion (LSC) wave.
`These transient plasmas have been discussed by Raizer (1980) and will not
`be treated here. If the laser is continuous in output power and the optical
`geometry, flow, and pressure are favorable, then a steady-state LSP may
`be continuously maintained at a position near the focus of the beam. The
`intensity that is available from a continuous laser is insuflicient to cause
`breakdown in the gas, however, and an auxiliary source must be used to ini-
`tiate the plasma. A sketch of a steady-state laser-sustained plasma is shown
`in Fig, 4,1(b), The plasma may be sustained within a confining chamber to
`control the flow and pressure or in open air or a large chamber where the
`flow is determined by thermal buoyancy.
`In many ways, the laser—sustained plasma is similar to direct current or
`low—frequency electrodeless arcs and microwave discharges that are oper-
`ated in similar gases and at similar pressures. However, the LSP will gener—
`ally be more compact and have a higher maximum temperature than other
`continuous arc sources and can be sustained in a steady state well away from
`containing boundaries. A fundamental difference in the way in which en—
`ergy is absorbed by the plasma is responsible for these unique characteristics
`Of the LSP.
`
`4.2.1 Basic Physical Processes
`
`In a direct current (dc) arc or in an inductively coupled plasma (ICP), en-
`ergy is absorbed through ohmic heating produced by the low—frequency or
`direct currents flowing in the plasma. The electrical conductivity of an ideal
`plasma is given by (Shkarofsky et al., 1966)
`
`n62 U-iw
`
`0:71;.(112+w2)
`
`(41)
`
`where n is the electron density, e the electronic charge, In the electron mass,
`0.) the radian frequency of the applied electric field, 1/ the effective collision
`frequency for electrons, and i the square root of ~1. In the dc arc (w = 0),
`the currents are’transmitted through the plasma between electrodes and
`
`

`

`
`
`Laser-Sustained Plasmas
`
`_
`
`173
`
`the size of the plasma is determined by the size and spacing of the electrode
`and the confining boundaries.
`In the ICP, the currents are induced into
`the plasma from alternating currents flowing in a surrounding solenoidal
`coil. The arc is sustained, within a container that determines the plasma
`diameter, whereas the length of the plasma is determined by the length of
`the solenoid.
`
`The ICP operates at frequencies well below the plasma frequency
`
`w —- E: m
`1’- meo
`
`(42)
`'
`
`where 50 is the permittivity of free space. In this frequency range, the elec-
`tromagnetic field does not propagate as a wave within the plasma, but is
`attenuated as an evanescent wave (Holt and Haskell, 1965) over distances
`of the order of the skin depth
`
`a = ——-——
`
`(4.3)
`
`where c is the speed of light. Thus, the plasma is sustained by energy ab—
`sorbed within a small layer near its outer surface that produces a rather flat
`temperature profile within the plasma and limits the maximum tempera-
`tures that can be obtained.
`
`The frequency of the optical fields (28 THz for the 10.6 mm carbon diox~
`ide laser) used for the LSP is greater than the plasma frequency, and there-
`fore the incident laser beam can propagate well into the interior before
`it is significantly absorbed through the process of inverse bremsstrahlung
`(Shkarofsky et al., 1966). Since the focusing of the laser beam produced
`by a lens or mirror is essentially preserved as the beam propagates into the
`plasma, very large field strengths may be produced within the plasma near
`the beam focus. It is these large field strengths that lead to peak tempera-
`tures in the LSP that are generally greater than those obtained with either
`dc arcs or the ICP and make it possible to sustain a small volume of plasma
`near the focus, well away from any confining walls.
`Inverse bremsstrahlung is a process in which the plasma electrons ab-
`sorb photons from the laser beam during inelastic collisions with ions, neu—
`trals, and other electrons. The collisions between electrons and ions are
`the dominant process for the LSP and the absorption coefficient is given by
`(Shkarofsky et al., 1966)
`
`
`g 7rc ZnSOG 1—e-hw/kT
`“‘(ZT)
`kT (
`hw/kT >
`
`(4‘4)
`
`

`

`1 74
`
`Keefer
`
`where h is Planck’s constant divided by 2-7r, k Boltzmann’s constant, and T
`the temperature of the electrons. The factor G is the Gaunt factor and the
`factor nSO is given by
`
`
`
`115 _§n+nzzd e2 ,_
`0—3rfifi
`4”,
`
`"3
`
`27rm “2
`%T
`
`(4 5)
`'
`
`mm
`
`where Z is the ionic charge and 11+ the ion density. The Gaunt factor is a
`quantum mechanical correction to the classical theory, and extensive tables
`have been given by Karzas and Latter (1961). For the usual case where
`the photon energy is much less than the thermal energy (Fm << kT), the
`bracketed term in Eq. (4.4) is nearly independent of w, and the absorption
`coefficient is essentially proportional to the square of the wavelength.
`The size of the LSP will depend on several factors including the beam
`geometry, laser power, and absorption coefficient. The change in intensity
`of the laser beam as it propagates within the plasma is given by Beer’s law
`
`d1
`E=“M
`
`mm
`
`where s is the distance along the local direction of propagation. The absorp-
`tion length 1/01 is a dominant length scale for the LSP since it determines
`the distance over which the power is absorbed from the beam. For this rea-
`son, the dimension of the high-temperature absorbing portion of the plasma
`along the laser beam will be of the order of the absorption length. Although
`it is the absorption length that determines the length of the plasma along the
`beam axis, it is the laser beam diameter that determines the plasma diame-
`ter. The plasma expands to fill the beam cone where it is able to absorb
`power, then rapidly decreases in temperature outside the beam through
`thermal conduction and radiative loss mechanisms.
`
`The position of the LSP relative to the focal point is critical in determin-
`ing its structure and‘the range of parameters for which it can be maintained.
`When the plasma is initiated near the beam focus, it propagates into the
`sustaining beam and seeks a stable position. The position of stability will be
`located where the beam intensity is just sufficient that the absorbed power
`will balance the losses due to convection, thermal conduction, and thermal
`radiation. A number of factors combine to determine this position of sta-
`bility including the transverse profile of the incident beam, the focal length
`and aberrations of the focusing lens or mirror, the plasma pressure, and the
`incident flow velocity (Keefer et al., 1986; Welle et al., 1987).
`The power per unit volume that is absorbed by the plasma is given by
`
`P=M
`
`.
`
`

`

`
`
`
`
`Laser-Sustained Plasmas
`
`175
`
`where I is the local irradiance of the laser beam. Since I depends on the
`transverse profile of the incident beam as well as the focal length and aber—
`rations of the lens, these characteristics will influence the location within
`the focal region at which theminimum sustaining intensity is located. For
`example, for a small f/number"’lens, the intensity decreases rapidly with in-
`creasing distance from the focus and the plasma will stabilize near the focus.
`For a larger f/number system, the intensity decreases less rapidly and the
`plasma will stabilize at a- position further away from the focus. Indeed, for
`sufiiciently long focal lengths and high laser power, plasmas have been ob-
`served to propagate many meters (Razier, 1980) as “laser-supported com—
`bustion waves” at subsonic velocities.
`The detailed spatial structure of the plasma is determined by the interre-
`lations between the optical geometry of the sustaining beam, the pressure of
`the gas, and the flow through the plasma. At each point within the plasma,
`the temperature and flow must adjust to balance the power that is absorbed
`from the laser beam with the power lost through convection, conduction,
`and thermal radiation. The position in the beam relative to the focal point
`at which the plasma stabilizes is very important in determining the structure
`of the plasma that, in turn, determines the conditions of power, pressure,
`and flow for which a stable plasma can be maintained.
`Most of the early experiments with the LSP were carried out inside large
`chambers or in open air, where the flow through the plasma was determined
`by the effects of thermal buoyancy. Fixed focal geometries were used and
`the pressure and laser power were varied to define regions of power and
`pressure where it was possible to sustain the LSP in a variety of gases (Gen-
`eralov et al., 1972; Kozlov et al., 1979; Moody, 1975). These experiments
`indicated that there were upper and lower limits for both laser power and
`pressure at which the LSP could be sustained.
`Generalov et a1. (1972) suggested that the upper limit for power was a re-
`sult of forming the LSP with a horizontal beam. In this geometry, thermal
`buoyancy induces a flow transverse to the optical axis. The induced flow
`carries the plasma up and out of the beam when higher laser power causes
`the plasma to stabilize farther from the focus. They were unable to estab-
`lish an upper power limit when the experiment was operated with the beam
`propagating vertically upward. Kozlov et al. (1974) developed a radiative
`model for the LSP and explained the‘ upper power limit on the basis that
`the plasma must stabilize close enough to the focal point that the geomet-
`ric increase of laser beam intensity going into the plasma was greater than
`the loss of intensity due to absorption. They speculated that the failure of
`Generalov et al. (1972) to observe this limit in a vertical beam was due to
`rapid extinction and reignition of the plasma.
`It is clear from the experiments of Generalov et a1. (1972) that flow can
`have a large effect on the range of pressure and laser power that will support
`
`

`

`176
`
`Keefer
`
`a stable LSP. Plasmas sustained in the free jet issuing from a nozzle have
`been studied by Gerasimenko et a1. (1983) who measured the discharge
`wave velocity along the beam and ranges for the existence of a steady—state
`discharge. Recently, experiments have been conducted in confined tubes
`where forced convection dominated the flow (Welle et al., 1987). It was
`found that in addition to power and pressure, both the flow and optical ge-
`ometry of the beam have a profound influence on the characteristics of the
`plasma. It now appears that the earlier experimental results that defined re-
`gions of pressure and power for which the LSP could be sustained are valid
`only for the particular experimental geometry used to obtain them.
`When the plasma is ignited by an auxiliary source near the focal point,
`the plasma expands as it absorbs energy from the continuous laser beam and
`propagates into the beam with decreasing velocity until it stabilizes. The
`plasma becomes stationary at a point where the intensity is just sufficient
`that the power absorbed from the beam, given by Eq. (4.7), is balanced by
`the convective, conductive, and radiation losses. Since, in general, the in—
`tensity is not uniform across the beam, the plasma will adjust in size, shape,
`temperature, and flow to satisfy conservation of momentum and energy. If
`the flow through the plasma increases, then the thermal convection losses
`increase in the upstream region of the plasma and it must move toward the
`focus to a region of higher intensity in order to absorb enough power from
`the beam to compensate for the increased convective losses.
`Thermal radiation plays a significant role in determining the detailed
`structure of the plasma. Thermal radiation in the plasma occurs both as
`a result of bound~bound transitions, resulting in line radiation and absorp~
`tion, and free-bound and free-free transitions that result in continuum radi-
`ation and absorption. Over the optically thin portion of the spectrum, this
`radiation will not be strongly absorbed by the plasma or surrounding cooler
`regions and will simply escape from the plasma. Other portions of the spec-
`trum will be strongly absorbed, resulting in a transport of energy within the
`plasma. In the optically thick limit, this results in a diffusive energy trans-
`port that is similar to thermal conduction, but may be significantly larger.
`Detailed calculations of the LSP (Jeng and Keefer, 1986) indicate that this
`radiative transport is a dominant factor in the determination of the struc-
`ture and position of the LSP. In particular, it is the radiative transport that
`determines the temperature gradient in the upstream front of the plasma,
`thereby determining the position in the beam for which convection losses
`are balanced by absorption.
`The position of stability for the LSP also depends on the plasma pres-
`sure. The absorption coefficient is a strong function of plasma density, as
`seen from Eq. (4.4). If the pressure is increased and the absorption coeffi-
`cient increases, then the plasma can absorb more power from the beam and
`
`will move away from the focus to a lower intensity region in the beam. At the
`
`

`

`
`
`Laser-Sustained Plasmas
`
`177
`
`:Nw.my,mwmmwwrmwwVMWMWM”WWWWWMWWMWWK“M“....WWW.WMVWW..,...NW..
`
`
`
`same time, the plasma length along the beam decreases because of the de-
`crease in absorption length, but the diameter increases to fill the larger cross
`section of the beam. Thus, for the same laser beam conditions, a higher—
`pressure LSP will stabilize at a point farther away from the focal point and
`have a smaller length—to-diameter ratio than a lower—pressure LSP.
`Incident laser power, as well as the f/number and aberrations of the fo—
`cusing optics, will also influence the position at which the LSP stabilizes
`within the beam. From the foregoing discussion, it is clear that as the beam
`power is increased, the plasma will move up the beam away from the focal
`point. The distance that it moves is determined by the f/number (ratio of
`focal length to the beam diameter incident on the focusing element) of the
`optical system, since the rate of change in beam intensity along the optical
`axis decreases with an increase in f/number. Lens aberrations can also have
`
`an effect on plasma position (Keefer et al., 1986). In particular, when an an-
`nular beam from an unstable laser oscillator is focused by a spherical lens,
`it produces an annular prefocus region before reaching the focal point, and
`the intensity in this region may be sufficient to sustain an annular plasma.
`From the observations discussed above, it is clear that the position of
`the plasma relative to the focal point has a profound effect on the plasma
`characteristics. At the upper limits of stability for both laser power and
`pressure, it appears that the plasma becomes unstable when it moves too
`far from the focal point. This may be due to the fact, as proposed by Kozlov
`et al. (1974), that as the plasma moves sufficiently far away from the focus,
`the rate of increase of the beam intensity in the direction of propagation
`becomes smaller. Since the temperature of the plasma must increase as the
`beam propagates into the upstream edge of the plasma, the intensity of the
`beam must also increase. At some point, the decrease of the beam intensity
`due to absorption is greater than the increase due to focusing, so the plasma
`becomes unstable and extinguishes. Recent calculations by J eng and Keefer
`(1987a), however, indicate that there may exist local regions within the LSP
`where the beam intensity decreases as it penetrates the plasma.
`A considerable degree of control of the structure and position of the LSP
`can be gained through both optical geometry and flow, in addition to laser
`power and pressure. Utilization of these additional parameters makes it
`possible to successfully operate the LSP over a wider range of experimental
`conditions, enabling a wider range of potential applications.
`
`4.2.2 Plasma Characteristics
`
`Laser-sustained plasmas have been operated in a variety of molecular and
`rare gases at pressures from 1 to more than 200 atm. The resulting plasmas
`have characteristics that are similar to arc plasmas operated at similar pres-
`
`

`

`178
`
`Keefer
`
`sures, but the peak temperatures in the LSP are usually somewhat higher
`than those for the comparable arc. Radiation from the plasma can be a sig»
`nificant fraction of the total power input, and radiation transport plays a
`major role in determining-the structure of the plasma. Continuum absorp-
`tion processes are of particular importance in these plasmas since the power
`to sustain the plasma is absorbed through these mechanisms.
`The continuum absorption process involves both bound—free transitions
`(photoionization) and free-free transitions (inverse bremsstrahlung) in
`which photons are absorbed from the laser beam. The free-free transitions
`involve electron collisions with ions, other electrons, and neutral particles
`(Shkarofsky et al., 1966; Griem, 1964). The dominant absorption process
`for the LSP is through collisions between electrons and ions, and the absorp-
`tion coefficient for this process is given by Eq. (4.4), For the usual case in
`the LSP, Flu) << kT and the absorption is approximately proportional to the
`square of the laser wavelength. Due to this strong wavelength dependence,
`all of the reported experimental results for the LSP have been obtained us-
`ing the 10.6 ,um wavelength carbon dioxide laser. Since the length scale
`for the plasma is of the order of the absorption length, the length of the
`plasma and the power required to sustain it would be expected to increase
`dramatically for shorter wavelength lasers. Currently, the only other lasers
`.vux. VUAJVLALMV“L) rAuuAAAuv uLv LLIV LIJULUSUIL
`that are. likely candidatgg 1:0 sustain (‘nnfinnnnc nlacmae am Hm kxlr‘rnnnn
`or deuterium fluoride chemical lasers that operate at wavelengths of 3 to
`4 pm.
`Thermal radiation is one of the most important characteristics of the
`LSP. Thermal radiation lost from the plasma can account for nearly all
`the power absorbed by the plasma when the flow through the plasma is
`small and will account for a significant fraction of absorbed power even
`when the convective losses are large. The thermal radiation consists of
`continuum radiation resulting from recombination (free—bound transitions)
`and bremsstrahlung (free-free transitions) as well as line radiation (bound-
`bound transitions). Calculation of this radiation is straightforward,
`al—
`though rather tedious, when the plasma is in local thermodynamic equi-
`librium (LTE) (Griem, 1964). Local thermodynamic equilibrium is es-
`tablished when the electron collisional rate processes dominate the pro-
`cesses of radiative decay and recombination. When LTE is established
`in the plasma, the density in specific quantum states is the same as a sys-
`tem in complete thermal equilibrium having the same total density, tem-
`perature, and chemical composition.
`It should be emphasized that this
`does not imply that the radiation is similar to a blackbody at the plasma
`temperature.
`In general, the spectrum of the radiation from the plasma
`will have a complex structure consisting of the superposition of relatively
`narrow spectral lines and a continuum having a complex spectral struc-
`ture.
`‘
`
`
`
`

`

`Laser-Sustained Plasmas
`
`179
`
`The absorption coeflicient in the plasma depends on the wavelength, and
`for the ultraviolet portion of the spectrum below the wavelength of the reso—
`nance lines (transitions involving the ground state), the radiation is strongly
`absorbed by the plasma and the cooler surrounding gas. This results in a
`strong radiative transport’mechanism that is important in determining the
`structure of the plasma. Often, radiative transport for strongly absorbing
`gases is modeled as a diffusive energy transport similar to thermal conduc-
`tion. In the strongly ionized regions of the plasma, the radiative transport is
`many times larger than the intrinsic thermal conduction and is the dominant
`heat-transfer mechanism. This is especially true in the upstream region of
`the LSP where the temperature gradient is large, and radiation transport
`must offset the convective losses of the incident flow.
`
`In the longer wavelength region above the resonance transitions, the ab-
`sorption of the radiation by the plasma and the surrounding gas is much
`smaller. The absorption length for this radiation is often large compared
`to the characteristic dimensions of the plasma, and much of the radiation
`escapes. In this region of the spectrum, the plasma may be considered op—
`tically thin, and if the plasma is in LTE, then the escaping radiation can be
`used to characterize the temperature within the LSP (Keefer et al., 1986;
`Welle et al., 1987).
`The temperature within the plasma is far from uniform, as shown in
`Fig. 4.2. (The method used to obtain the experimental temperatures shown
`in Figs. 4.2, 4.4, and 4.10 is described in detail in Sec. 4.4.2). This figure
`shows an isotherm plot of the temperatures measured in an LSP sustained
`in 2.5 atm of argon by a carbon dioxide laser operating at a wavelength of
`10.6 pm. The plasma length and diameter, as determined by the 10,500K
`isotherm, are 11 and 4 mm, respectively. Note the steep temperature gradi-
`ents that exist in the upstream portion of the plasma and in the radial direc-
`tion near the limit of the laser beam. The temperature gradients in these
`regions are of the order of 106 K/m. In the upstream regions of the plasma,
`the direction of the convective energy transport is the opposite of that due to
`thermal conduction and radiation transport, and a strong temperature gra-
`dient develops to balance the convective losses with thermal conduction and
`radiative transport. The magnitude of the temperature gradient depends on
`the flow rate and increases with increasing flow. Strong radial temperature
`gradients develop near the edge of the laser beam where the available power
`decreases rapidly and are steeper near the focus where large conduction and
`radiation transport is required to balance the large powers absorbed from
`the beam. The peak temperature in the plasm