edited by '
`
`Leon 3., Raoiziemeiii
`Department of Physics
`New Mexico State University
`Las Cruces, New Mexico
`
`oavid A Cremere
`Chemical and Laser Sciences Division
`Los Aiarnos National Laboratory
`Los Aiarnos, New Mexico
`
`MARCEL DEKKEP, INC.
`
`New York and Base!
`
`
`
`
`
`ASML 1006
`
`ASML 1006
`
`

`
`
`
`Library of Congress Cataloging-in-Publioation Data
`
`Laser-induced plasrnas : physical, chemical, and biological appllcations/ edited
`by Leon J. Radziemski, David A. Cremers.
`I p.
`cm.
`Includes bibliographies.
`ISBN 0-824$/«8078-7 (alk. paper)
`.1. Plasma engineering.
`2. High power lasers.
`II. Cremers,DaVid A.
`TA202.0.L3’7 1989
`
`1. Radzieméki, Leon .I,,
`-
`
`620.044»-dc2O
`
`89-7883
`CIP
`
`This book‘ is printed on acid-free paper.’
`
`Copyright © 1989 MARCEL DEKKER. 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 IOOI6
`
`Current printing (last digit):
`l0 9
`8
`7
`6
`5
`4 3
`2
`
`I
`
`l’RIN'1‘I3D IN THE UNITED STATES OF AMERICA
`
`

`
`Corrie rite
`
`Preface
`b Contributors
`
`1
`
`i’hysics of Laser‘-Induced Breakdown: An Update
`Guy M. Weyl
`
`1.1
`1.2
`1.3
`1.4
`1.5
`
`'Introduc1;ion
`Creation of initial Electrons
`Electron Growth in Gases
`.Laser~lnciuced Breakdown of Solids and Liquids
`Concluding Remarks
`References
`
`2
`
`‘Modeling of I:’ost-Breakdown Phenomena
`Robert G. Root
`
`'
`
`'
`
`lntro<;luction_
`2.1
`Creation of a Propagating, Plasma
`2.2
`2.3. Absorption Characteristics of Heated Gases
`2.4
`- Features of Propagating Plasmas
`2.5
`One—Dimension.al Laser—Supportecl C3ombust‘io'n Waves
`2.6
`O'n—e~Dimens’ional Laser—Sup_porteCi Detonation Wave
`2.7
`One~1I}.imen.sional Laser-Supported Radiation Wave
`2.8
`Transition Regions
`2.9
`Radial Expansion
`2.1.0 Thermal Coupling
`2.11 Other Factors
`'
`2.12 Summary
`References
`
`.
`
`.
`
`’
`
`_
`
`iii
`xi
`
`1
`
`1
`3
`8
`36
`58
`59
`
`69
`
`69
`70
`72
`75
`77
`88
`92
`93
`95
`.99
`100 ,
`101
`101
`
`3
`
`Introduction to Laser Plasma Diagnostics
`Allan A. 1'ia’u.er and Hector A. Baldis
`
`3.1
`3.2
`
`1
`Introduction
`Introduction to Optical Diagnostics
`
`ix
`
`2
`
`105
`
`105
`110
`
`

`
`
`
`x
`
`3.3
`
`Introduction to X-ray Diagnostics
`References
`
`4 Laser«Sustainecl Plas"nms
`Dennis R. Keefer
`
`A
`
`_
`
`Introduction
`4.1
`Principles of Operation
`4.2
`Analytical Models
`4.3
`4.4‘ Experimental Studies
`4.5
`Applications of the Laser~Sustained Plasma
`R-eferences
`
`5
`
`Inertially Confined Fusion
`Robert L. McCrory and John M. Soures
`
`5.1
`5.2
`5.3
`5.4
`5.5
`5.6
`5.7
`5.8
`
`Historical Overview
`Laser~l7usion Scaling Laws
`Coronal Physics
`X.~ray Generation by Laser~l’rocluc.ed Plzgtsinas
`Laser-Driven Ablation
`it-Iydro<;lynam:ic Stability of Ablmively Driven Shells
`Irradiation Uniformity Requirements
`Implosion Experiments
`6
`References
`
`6 Laser-Based Semiconductor Fal.>ricati(.)n
`
`Joseph R. Wachter
`
`Contents
`
`1371.
`161
`
`169
`
`169
`172
`182
`189
`196
`203
`
`207
`
`207
`211
`217
`224
`227
`239
`243
`251
`260
`
`269
`
`'
`6.1 Aspects of Semiconductor Fabrication
`6.2 Appflcations of Lasers in the Semiconductor Industry
`6.3
`Research .Areas
`6.4 Outlook
`References
`
`269
`276
`283
`. 290
`291
`
`'
`
`7 Spectmchemical Analysis Using Laser" Plasnm Excitati()n
`Leon J. Radzietnski and David A. Cremers
`
`I
`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 Analysisof Solids
`7.7
`Advances in Instrumentation
`
`295
`
`295
`296
`302
`306
`309
`313
`318
`
`

`
`
`
`Contents
`
`7,8
`
`Piiognosis
`References
`
`8 Fundamentals of Analysis of Solids by L836!‘-Pl‘()(ll.!C€d
`_ Plasmas
`Yong W. Kim
`
`8.1
`8.2
`8.3
`
`Chapter Oi'gan.izaitioi1
`Introduction
`l’hen'onnenolog,y of Laser Hcatitig of Condcnsecl~Phase
`Tmgetss
`_
`8.4 Quantitative Spectroscopy
`8.5
`lntetnsity Measure1nent.s and Elemental Analysis
`8.6
`Summary
`References
`
`A
`
`A
`
`9 Laser Vaporization for Sample introcluction in Atomic and
`Mass Spectroscopy
`'
`Joseph Sneddon, Peter Mitchell, and Nicholas S. Nogar
`
`9.4
`
`9.1
`
`9.2
`9.3
`
`C‘.onventio‘na.l Solid Sample Introduction for Atomic
`Spectroscopy
`Laser Ablation of Solid Samples
`Laser Ablation for Sample Introduction in Atomic
`Spectroscopy
`V
`Relative Merits of l....aser Ablation for Sample introduction
`in Atomic Spectroscopy
`Laser Sources for .Mz.is:; Spectrometry
`9.5
`9.6 Applications of Laser Mic.i.'oprobe
`9.7 Applications of Laser Desorption and Postionization
`9.8
`Conclusion
`References
`
`'
`
`10 Current Newv Applications of Laser Plzisnieis
`Allan A. Haiier, David W. Fors.lunti,‘Colin J. McKinstrie,
`Justin S. Wark, Philip J. l.-l.a1‘gis, Jr., Roy A. H£lI1“lll, and Joseph
`M. Kindel
`
`Introduction
`10.1
`10.2 Applications of Laser-Plas’ina-Generated X~rays and '
`Particles
`i.,21S€3I'*Pl‘ZlSITl21/\CCCl€?'I‘21llOIl()fPEll‘iiCl(iS
`
`110.3
`
`_
`
`3
`
`.
`
`A
`
`V
`
`.
`
`xi
`
`321
`323
`
`327
`
`327
`327
`
`330
`336
`' 341
`344
`345
`
`347
`
`347
`350
`
`35 3
`
`363
`365
`369
`372
`376
`376
`
`385
`
`385
`
`386
`413
`
`

`
`
`
`xii
`
`10.4 Laser»-Pulsczd Power Switching
`Refcarences
`
`Index
`
`'
`
`“
`
`V
`
`Contents
`
`424
`432
`
`437
`
`

`
`
`
`4
`
`Laeenfiustained Plasmas
`
`Dennis R. Keefer
`
`Center for Laser AppIz'ct1ri0n.s'
`Um'ver.s'ily of Terzneswe Space Irzmmte
`Tliillahorrza, Tenztessee
`
`4.1
`
`INTROEJUCTIO N-
`
`Plasrnas created by the iiacliation from focused laser beams were first ob»
`served with the advent of “giant pulse” Q-switched, ruby lasers by Maker
`et al. (1963). These plasmas t‘ormed.spontaneously by gas breakdown at
`the focus of a lens and were sustained only for the duration of the laser
`pulse. Plasnias were also observed to form on the surfaces of materials in
`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, highwpower carbon dioxide lasers, it became possible to sustain
`a plasma in a steadywstate condition near the focus of a laser beam, and the
`first experimental observation of a “continuous optical discharge” was re—
`ported by Generalov et al. (1970). The continuous, laser~sustain.ecl 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 laserusustained 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 brernsstrahlung. Since the optical frequency of the
`sustaining beam is greater than the plasma frequeiicy, 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 eiectcrodeless 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 rnakes it possible to
`
`169
`
`

`
`
`
`
`
`
`
`1'70
`
`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 191 mm 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 1-0.6 um 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 al. (1983), Welle et al. (1987), and Cross and
`Cremers (1986) have demonstratedthat 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 plasma conditions are strongly
`dependent on the position of the plasma within the sustaining beam, and
`that the plasma can be controlled within a wide range of conditions us~
`ing appropriate comb.inati.ons of laser power, flow, and optical configura~
`tion.
`V
`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 H
`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 al. (1978)
`described experiments in which laser energy was converted into electrical
`energy using a laser-sustained argon plasma. Cremers et al. (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.
`
`

`
`
`
`Lemerfiusiained Plasnwas
`
`171
`
`(b)
`
`(2)) 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.
`
`

`
`
`
`
`
`1 72
`
`Keefer
`
`4.2
`
`I’;‘2'{INC§l’LES
`
`0P}33RATICfN
`
`Plasmas that are created or sustained by lasers can be generated in a variety
`of forms, depending on the Tcharacteristics of the laser and optical. geo.me~
`try used to generate them: Highenergy pulsed lasers can generate plasma
`breakdown directly within a gas that results in a transient expanding plasma
`sirnilar to an explosion, At lower laser intensities and longer pulse ti mes,
`plasmas may be initiated at solid surfaces and then propagate into the sus~
`taining beam at supersonic velocities
`a laser~sustained detonation (LSD)
`wave or subsonic velocities as a ltasensustainecl combustion
`wave.
`These transient plasmas have been discussed by Raizcr (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 steaciy~state LS? may
`be continuously maintained at a position near the focus of the beam. The
`intensity that is available from a continuous laser is insuihcient 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.l.(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 lasetwsustained plasma is similar to direct current or
`lovwfrequency electrodeless arcs and microwave discharges that are open
`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 Flrticcsses
`
`In a direct current (dc) are or in an inductively coupled plasma (ICP), en~
`ergy is absorbed through ohmic heating produced by the low~i’requency or
`direct currents flowing in the plasma. The electrical conductivity of an ideal
`plasma is given by (Shl<arofsl<y et al., ’.l_966)
`‘
`
`7282
`
`“s” 7;;
`
`—~i
`
`y
`
`(‘W
`
`where n is the electron density, e the electronic charge, In the electron mass,
`0.) the radian frequency of the applied electric field, 2/ the effective collision
`frequency for electrons, and i the square root of ml. in the do arc (to m 0),
`the currents are transmitted through the plasma between electrodes and
`
`

`
`haaervfiustalned Plasmas
`
`.
`
`‘W8
`
`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 frorn alternating currents flowing in a surrounding solenoidal
`coil. The arc is sustainedgwithin a container that determines the plasma
`diameter, whereas the length of the plasma is determined by the length of
`the solenoid.
`The [CF operates at frequencies well below the plasma frequency
`
`‘neg
`WP” (#23)
`
`1/2
`
`4
`
`
`
`<4“)
`
`where 60 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
`
`5 =.~. —w—5——~
`/2__2
`W1) W
`
`(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 fiat
`temperature profile within the plasma and limits the tnaximum tempera~
`tures that can be obtained.
`The frequency of the optical fields (28 THz for the 10.6 pm carbon diox~
`ide laser)»usec1 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
`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 LS? and the absorption coefficient is given by
`» (’Sh1<:arofsky et al., 1966)
`
`M We 2nS0G 1~e””“”‘T
`aM(tu)
`lcTm< Ftw//cT
`
`>
`
`(411)
`
`

`
`
`
`
`
`1°74
`
`Keefer
`
`where h is Planck’s constant divided by 27¢, k Boltzmann’s constant, and T
`thetemperature of the electrons. The factor G is the Gaunt factor and the
`factor nS0 is given by
`
`16n,+nZ2i
`YLSOW: 3
`171203
`
`62
`47reO
`
`Zvrm 1/2
`3/CT
`
`-
`
`(4.5)
`
`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 (hm << kit’), the
`bracketed term in Eq. (4.4) is nearly independent of (U, and the absorption
`coefiicient 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 coefiicient. The change in intensity
`of the laser beam as it propagates within the plasma is given by Beer’s law
`
`d1
`.3; M ~—aI
`
`(4.6)
`
`where sis the distance along the local direction of propagation. The absorp~
`tion length 1/0: 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 till 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 LS1’ relative to the focal point is critical in determin-
`ing its structure andthe 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 star»
`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 at
`
`t
`
`(4.7)
`
`

`
`Laser-ésuetalned 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 the minimum sustaining intensity is located. For
`example, for a small f/nuinbeflens, the intensity decreases rapidly with in~
`creasing distance from the focus and the plasma will stabilize near the focus.
`For a larger f/nurnber system, the intensity decreasesless rapidly and the
`plasma will stabilize at a position further away from the focus. Indeed, for
`sufficiently 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 al. (1972) suggested that the upper limit for power was a re»
`sult of forming, the LS1’ 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 LS? 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 al. (1972) that flow can
`have a large effect on therange of pressure and laser power that will support
`
`

`
`
`
`
`
`
`
`1 76
`
`Keefer
`
`a stable LSP. Plasmas sustained in the free jet issuing from a nozzle have
`been studied by Gerasimenko et al. (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 LS1’ co uldbe 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 sutficient
`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 ilow 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~bour1d 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 LS1’ (Jeng and Keefer, 1986) indicate that this
`radiative transport is a dominant factor in the determination of the struc-
`ture and position of the LS1’. 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 l...E.~3P also depends on the plasma pres“-
`sure. The absorption coetiicient; is a strong function of plasma density, as
`seen from Eq. (4.4). If the pressure is increased and the absorption COCffi*
`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
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`same time, the plasma length alcmg 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-»cliameter ratio than a lower-pressure LS1’.
`incident laser power, as well as the i’/number and t=ili>crrations of the fo-
`cusing oyptics, will also iniiluence 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 cleterminerl by the f/number (ratio of
`focal length to the beam dianieter 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 efiect 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 stiflicient to sustain an annular plasma.
`Front the observations discussed above, it is clear that the position of
`the plasma relative to the focal point has a profound ciiect 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
`er. al. (1974), that as the plasma moves sutticiently 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 extingnishes. Recent calculations by Jeng and Keefer‘
`Q98”/a), however, indicate that there may exist local regions within the LSP
`where the beam intensity decreases as it penetrates the plasma,
`A co.ns.iderable degree of control of the structure and position of the LS1’
`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 LS1’ over a wider range of experimental
`conditions, enabling a wider range of potential applications.
`
`4.2.2
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`iflasma. Charac’teristi<:s
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`Lase'r»-sustained plasmas have been operated in a variety oi’-nnolecular and
`rare gases at pressures ifrorn 1 to more than 200 atm. ”I"he resulting plasmas
`have characteristics that are similar to arc plasnias operatccl at similar pres~
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`Keefer
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`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«
`niiicant fraction of the total power input, and radiation transport plays a
`major role in deteraztiningthe 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~i'ree 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, hw <<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 nm 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
`that are likely candidates to sustain continuous plasmas are the hydrogen
`or deuterium fluoride chemical lasers that operate at wavelengths of 3 to
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`4 am.
`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~t'ree transitions) as well
`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) (Griern, 1964). Local therniodynarnic 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.
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`Plasmas
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`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 (tra_nsitions involving the ground state), the radiation is strongly
`absorbed by the plasma and the cooler surrounding gas. This results in a
`strong radiative ltransport"ni.ecl1anism that is irnportant 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 plasm.a,'and much of the radiation
`escapes. In this region of the spectrum, the plasma maybe 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 run. The plasma length and diameter, as determined by the 10,50OK
`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 10“ K./tn. 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 tem'p'erature gradient depends on
`the flow rate and increases with increasing ilow. Strong radia