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A study of laser plasma interactions in a cylindrical cavity McKenna, RossAllan D. 1990

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A S T U D Y O F L A S E R P L A S M A I N T E R A C T I O N S IN A C Y L I N D R I C A L C A V I T Y By Ross Allan D. McKenna B. Sc. (Honours Physics), Dalhousie University, 1987 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF PHYSICS We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1990 © RossAllan D. McKenna, 1990 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada Date DE-6 (2/88) Abstract A CO2 laser system delivering a 12 J pulse with a FWHM of 2 ns on target was developed to serve as a driver for studies of laser plasma interactions within a cylindrical cavity. The system consisted of a hybrid oscillator, followed by an amplifier chain, and it achieved its design goals of delivering an intense CO2 pulse, Gaussian in time and space, with a high contrast ratio on a reliable basis. The targets in which the plasma was produced consisted of small rectangular plates of lucite, with holes drilled through one of the long axes. The holes were 350 /zm to 600 /xm in diameter, and 10 mm in length. These dimensions allowed the laser beam, focused at the entrance of the hole, to produce sufficient intensity on the inner walls of the cylindrical cavity for plasma formation, while allowing the beam, with a waist diameter of 100 fim at the focus to deliver most of its energy within the cavity. The beam propagated via multiple reflections from the plasma through the cavity. Diagnostics were performed on the beam transmitted through the target. Streak cam-era images were collected of the intensity of visible emission from the plasma along the axis of the target. Anomalous results were obtained with respect to the reproducible ob-servation of maximum visible light emission from regions at the far end cavity from where the laser beam is injected. Another unforseen but interesting result was the small diver-gence of the beam transmitted through the cavity. Prehminary models were developed to attempt to explain the observations. ii Table of Contents Abstract 2 List of Tables 6 List of Figures 7 Acknowledgements 9 1 Introduction 1 1.1 Motivation 1 1.2 X-ray Lasers 2 1.3 Filament ation 6 1.4 Diagnostic Experiments 7 1.5 Outline of the Thesis 9 2 Theory 12 2.1 Introduction 12 2.2 Ablation 12 2.3 Plasma Expansion 13 2.3.1 Fluid Equations 13 2.3.2 Thermal Expansion 16 2.3.3 Ponderomotive Force 19 2.4 Beam Propagation in a Plasma 19 2.4.1 Dielectric Properties of a Plasma 19 iii 2.4.2 Diffraction and the Geometrical Optics Limit 21 2.4.3 Absorption and Emission 23 3 The C 0 2 Laser System 27 3.1 Introduction 27 3.2 Details of the Components 27 3.2.1 The Hybrid Oscillator 27 3.2.2 2 ns Pulse Generation 31 3.2.3 Backscatter Protection 32 3.2.4 The Preamplifier 32 3.2.5 The 3-Stage Amplifier 35 3.2.6 The Lumonics Amplifier 36 3.2.7 Triggering and Timing Control 36 3.2.8 Minimization of Parasitic Oscillations and Pre-Pulse 37 4 The Target 39 4.1 Parameters Influencing Target Design 39 4.2 Target Fabrication 40 4.3 The Target Chamber 41 4.4 Positioning of the Target 42 5 Experimental Diagnostics and Results 48 5.1 Introduction 48 5.2 Transmitted Beam Results 49 5.3 Optical Emission from the Plasma 52 6 Discussion and Analysis of the Experimental Results 68 6.1 Introduction 68 iv 6.2 Transmitted Beam Energy 68 6.3 Transmitted Beam Divergence 70 6.4 Visible Light Emission along the Axis 72 7 Conclusions ^6 Bibliography 78 v List of Tables Fractional energy transmission through cylindrical cavities vi List of Figures 3.1 Schematic diagram of the hybrid oscillator 29 3.2 Overview of the amplifier chain 34 4.1 The target and its positioning system 41 4.2 The target chamber 43 4.3 A plot used to determine the focal plane 46 5.1 Measurements of transmitted beam energies through 400±50 fim cavities. 50 5.2 Measurements of transmitted beam energies through 550±50 um cavities. 51 5.3 Images of damage patterns formed on (A): Mylar, (B,C): thermal paper, and (D) B-10 foil located 6-8 cm behind the target 53 5.4 Optical system for streak camera observation of visible light emission along the cavity axis 55 5.5 Streak camera image of the cavity in focus mode 57 5.6 Streak camera image of an intensionally misaligned shot 59 5.7 Streak camera image of the visible light emission from a 550±50 fim di-ameter cavity. 60 5.8 Typical shot-to-shot variations of the visible light emission from the cavity. 61 5.9 Reversal of the maximum emission peak from the back of the cavity to the front in successive shots 62 5.10 Streak camera image of visible light emission dominated by peaks at the back of the cavity. 63 5.11 Streak camera image of emission with the lumonics fired 65 vii 5.12 Fast, high resolution image of visible plasma emission dynamics 66 5.13 High speed streak camera image of plasma emission dynamics 67 6.14 Ray tracing simulation of incident beam intensity (A), and corresponding streak image of visible emission (B), for a 400±50 um diameter cavity. . 73 6.15 Ray tracing simulation of incident beam intensity (A), and corresponding streak image of visible emission (B), for a 550±50 /zm diameter cavity. . 74 viii Acknowledgements I would like to thank my supervisor, Dr. Jochen Meyer, for his guidance and support. I also wish to extend my thanks to fellow students Abdul Elezzabi, Roger Chin, Michel Laberge, and Peter Zhu for many diverse conversations that were at times entertaining and at others educational, and sometimes even both. Al Cheuck was always there when the electrical or electronic systems started smoking, or when a part needed to be obtained from San Jose, California by roughly 5 P.M. Hubert Houtman provided sage advice on laser systems, and perhaps more importantly, insight into the particular quirks of the components used in this laboratory. Jack Bosma instructed me in the mysteries of the student machine shop, allowing me to make all of the parts that we could not afford, or could not wait to be shipped from Katmandu, Nepal. Special thanks are extended to my family, to Suzanne Saatchi, to the gang at Physsoc, and to the Triumf summer students of 1988 for their moral support and constant encouragement. Mention should also be made of the Natural Sciences and Engineering Research Council of Canada (NSERC) which funded my first two years of study through the Post Graduate Scholarship program. Finally, I wish to dedicate this work to the memory of my wife, Ann, for her love, for her inspiration, and for the many lessons she taught me in life. i x Chapter 1 Introduction 1.1 Motivation Considerable interest exists in the study of laser plasma interactions within closed ge-ometries. The absorption of energy from the laser by a plasma tends to produce large temperature gradients and consequently strong pressure forces within the plasma. In the absence of opposing forces, these pressures tend to lead to expansion of the plasma, and rapid loss of particles from the area of interest. Magnetic confinement, which in the case of laser plasmas usually takes the form of a solenoid about the laser beam axis, can provide such a force. However, in the case of high density plasmas the magnetic field strengths required to provide confinement become technologically unfeasible. Closed ge-ometries, typically parallel plates, cylinders or spheres, take advantage of the collision of plasmas expanding from opposing walls to maintain high density plasmas over long time scales within the cavities they form. In addition, the geometries can be tailored to pro-duce desired plasma density gradients, for such purposes as beam focusing, or radiation waveguides. Unfortunately, while such geometries solve many problems in terms of applications, they present considerable difficulties in terms of the interactions that take place within the cavities. Experimentally, the simple fact that the geometry is closed resticts the freedom to probe the plasma. The conditions produced by a laser plasma prohibit the probes from being located within the cavity, and thus observation is retricted to detection of radiation 1 Chapter 1. Introduction 2 emitted by, or scattered from the plasma. This radiation, however, is impeded by the same walls that confine the cavity. As a consequence, probing is usually accomplished by introducing openings in the cavity, introducing possible distortions of the results, as the observations are made in regions where the plasma may freely expand. Theoretically, such plasmas present such problems as steep gradients in temperature and pressure, plasma-wall interactions, early plasma formation, and high laser intensities. In addition, the geometries often do not permit modelling in one, or sometimes even two dimensions, and thus require expensive two and three dimensional computer models. The considerable potential of the applications nevertheless requires that these obstacles be overcome. The remainder of this chapter discusses in some detail the applications in x-ray lasing schemes, and in the dynamics of plasma filaments that provided motivation for the study of the particular closed geometry examined in this work, a cylindrical cavity with the laser beam axis parallel to the cylinder axis. It concludes with a description of some of the previous efforts to perform experiments on laser-plasma interactions in a cylindrical cavity. 1.2 X-ray Lasers Since the development of the maser in the early 1950's [1], efforts have been made to extend amplified stimulated emission of radiation to shorter and shorter wavelenths. The-oretical schemes to produce lasing in the x-ray region were published as early as 1965 [2]. X-ray lasing schemes rely on two basic mechanisms to produce population inversion. One method relies on collisional excitation of an optically forbidden transition to pump a long lifetime metastable upper state, a method which was first suggested by Vinogradov et al in 1975 [12]. An alternate technique employs then recombination pumping scheme discussed by Gudzenko et al [2]. Recombination pumping is produced in a highly ionized Chapter 1. Introduction 3 plasma during the cascade of electrons down through the excited states following the recombination into a high lying level. In general, the transitions involve progressively increasing energy gaps, and as a result increasing radiative transition probabilities. Since the population of a given energy level is inversely proportional to its decay probability, this results in successively decreasing level populations until the ground state is reached, and as a consequence, population inversions are produced. Reabsorption of the radi-ated energy can reduce the inversion. Collisions can equilibriate the inversion, and as a consequence such inversions can only exist when conditions are far from equilibrium. Thus recombination schemes must provide rapid cooling of the plasma, either through radiative loss, adiabatic expansion cooling, or heat transport to a thermal sink. Fur-thermore, the need to minimize collisional equilibrium effects imposes an upper limit on the plasma density that can be utilized. Some advantages that recombinative pumping possesses over collisional pumping are the efficiency of conversion of pump beam energy to x-ray energy, and the fact that the lasing wavelength decreases relatively rapidly with increasing charge of the atomic core Z of the lasing species. Attempts to translate theoretical x-ray lasing schemes into experimental systems showed slow progess during the 1970's, with some observations of population inversions [4,3], but no clear demonstrations of gain media. Jacoby et al made the first report of gain in the x-ray region in 1981 [5] for the hydrogen-like carbon ion (C VI) recombination pumped Balmer-a transition (Ha) at 182 A. The targets were carbon fibres, 2 pm to 6 pm in diameter, irradiated by a Nd glass laser system producing a pulse of up to 10 J and of 180 ps duration focused to a line 2 mm long by 40 pm wide. A gain length product of <5 was quoted, based on comparisons of the H Q emission measured along the target axis to that measured transverse to the axis. The paper that stimulated considerable interest in the field of x-ray lasers was the Chapter 1. Introduction 4 demonstration by Matthews et al of amplified spontaneous emission (ASE) from neon-like selenium produced by a collisionally excited population inversion of the 2p53p and 2p53s levels at 206.3 A and 209.6 A (J = 2 to 1) [6]. The targets were foils of 1500 A thick Formvar, on which a 750 A layer of Se was vapour deposited. The foil was driven to explosion by green light (A = 0.532 um) focused along a line as long as 2.2 cm by 200 fim in width, with a typical incident intensity of 5xl01 3 W/cm2. Once again, gain was determined by measuring the ratio of axial to transverse x-ray emission. A gain coefficient of 5.5 ± 1.0 cm - 1 was calculated for both lines. The lasing schemes discussed so far allow free expansion of the plasma lasing medium, leading to rapid depletion of the plasma density, and allowing little control of the cooling rate, a critical parameter in producing inversion. As a result, gain conditions in such systems last for only a very short time. These drawbacks led Suckewer et al to develop a lasing scheme which used a strong solenoidal magnetic field to confine the plasma, for which they published results in 1985 [7]. The lasing transition was the same one in C VI used by Jacoby et al. The target was a carbon disk illuminated on its flat surface by a 300 J, 75 ns FWHM pulse from a CO2 laser. The plasma was confined radially by a magnetic field of approximately 90 kG. In addition, a thin carbon blade was attached to the disk, parallel to the plasma column, which served to produce a more uniform plasma along the axial direction, as well as to provide additional cooling of the plasma via heat transport. Gain values were determined by comparison of the emission line intensities for lasing and non-lasing transitions along the axis of the plasma column, and transverse to it. The gain product was detemined to be 6.5, with an estimated length of 1 cm for the region of significant gain. This technique was significant not only in its use of plasma confinement, but in the fact that the required intensities of 5xl01 2 W/cm2 put x-ray lasing studies within the reach of many laser facilities worldwide. Chapter 1. Introduction 5 The first report of x-ray lasing in a closed geometry, and one of the primary mo-tivations for this study, was published by Lin et al in 1988 [8,9]. The transition they studied was between the energy levels ls3p 1 P 0 and ls4p 1 P 0 of Mg XI at 154.6 A. The target consisted of Mg microtubes, 100 pm in diameter, and 200 pm in length, with a lateral jet nozzle with a neck 30 pm wide along the length of one side. The end of the tube opposite to the one through which the laser beam was focused was blocked with magnesium foil. A 10 J, 250 ps FWHM laser pulse, with a wavelength of 1.06 ^m, was focused to a spot size of 60 pm. at the entrance of the tube by an f/1.5 aspherical lens, and illuminated the inner walls of the cavity through multiple reflections, with an aver-age intensity of 3.5xlO13 W/cm2. The objectives of high density (ne ~ 3xl0 2 ° cm -3), and population inversion were achieved. Diagnostics, however, could only be performed on the side blowing plasma plume, and from an oblique angle, on the entrance to the tube. Such restrictions meant that a gain coefficient of 27 cm - 1 could only be indirectly deduced from measuring the spectral lines of the 4 —> 1 and 3 —> 1 transitions. Recent experiments by Miura et al [10] have demonstrated x-ray lasing in a system even more closely related to that studied in this work. The lasing transition was once again the carbon VI 3d-2p transition at 182 A, but this time pumped by a CO2 laser producing a 400 J pulse with a FWHM of 50 ns. The target was a 0.2 ^m thick parylene (C8H8) foil at the edge of a 30 pm thick paralene hollow cylinder which measured 3 mm in diameter and 3 mm to 12 mm in length. A 0.5 mm wide rectagular window running most of the length of the cylinder allowed the measurement of transverse x-ray emissions. A peak intensity of 4xl01 2 W/cm2 was produced by a 500 pm spot focused on the foil by a spherical mirror (f = 3 m). Radiation scattered by the foil illuminates the inner walls of the cylinder, producing a plasma column. The thickness of the foil is determined such that a desired plasma density is reached when burn-through of the foil occurs, allowing the density to be controlled to produce maximum gain. The remainder of the laser pulse Chapter 1. Introduction 6 heats the plasma as it expands into the centre of the cavity, while radiation loss and heat transport to the walls provide the rapid cooling required for population inversion outside the central region. Comparison of ASE along the axial and transverse directions of the plasma column produced a gain length product of up to 2.4 for the 12 mm long target. A subsequent paper by Daido et al [11] has modelled this system, and proposed high-Z impurity doping of the target as a means of achieving gain coefficients of the order of 5 cm - 1. Thus although no attempt was made to measure population inversions in this study, the closed cylindrical geometry, and as a consequence, the laser-plasma interactions within the cavity, closely resemble those produced in configurations that have demon-strated x-ray lasing. It is hoped that by better characterizing the interactions involved, opportunities will be presented to optimize the gain and the divergence characteristics of such a system. 1.3 Filamentation Filamentation has recently received considerable attention as it is perceived as a poten-tial threat to the feasibility of using short wavelength (A ~ 0.25 urn) lasers to directly drive target compressions for inertial confinement fusion [13]. Filamentation arises when a small perturbation in the laser beam intensity profile generates a perturbation in the plasma density, either directly via the ponderomotive force or indirectly via enhanced heating and subsequent expansion [14]. Self focusing then arises, as a local minimum in the refractive index is produced at the centre of the density perturbation. This focus-ing further enhances the intensity perturbation, producing a feedback loop. The high intensities of light within the filament can locally exceed the threshold for parametric Chapter 1. Introduction 7 instabilities such as stimulated Raman scattering (SRS) and stimulated Brillouin scat-tering, and may be a source of suprathermal electrons. The focusing and scattering processes result in nonuniform irradiation of fusion targets, possibly enhancing fluid in-stabilities, and reducing target compression. Suprathermal electrons lead to preheating of the target core, and further limit maximum compression of the target. Experimen-tally, interferometry and shadowgraphy can not distinguish between filamentation and the effects of hot spots in the laser beam. Evidence of filamentation in laboratory plas-mas is typically indirect, arising from structure in x-ray photographs and in images of backscattered light and the second harmonic emission. The conditions within the cylindrical cavity examined in this work are believed to resemble those in the filamentation process, particularly at late times when the concave plasma density profile produced has restricted the laser beam width to within a few pm of the target axis. Furthermore, the axial scale lengths (several mm) resemble the long scale length plasmas envisaged for reactor conditions. 1.4 Diagnostic Experiments As was mentioned above in the discussion of x-ray lasers, diagnostics of the laser plasma interactions in cylindrical cavities has usually been quite limited. In an attempt to address this issue, Cunningham and Weber conducted a series of experiments that they reported in 1988 [15,16]. Hollow micro cylinders, constructed of Al, Cu and Au, were illuminated by 80 ps FWHM laser pulses at a wavelength of 1.05 pm, directed through a longitudinal entrance slit. The targets were 1 mm in length, with a slit width of 75 pm, and internal diameters of 200 pm to 300 pm. Laser pulses perpendicular to the target axis, with typical energies of 1.5-3.0 J were focused by an f/2 spherical lens to a focal spot of 80 pm, or by a cylinrical lens to a 500 pm long line focus, and entered the Chapter 1. Introduction 8 target through the slit. Nomarski-type interferometry along the axis probed the temporal and spatial development of the plasma density. A pinhole imaging x-ray streak camera provided temporally and spatially resolved observations of x-ray emission. A miniature crystal spectrometer allowed space-resolved spectral measurements of the x-ray emission. The major drawback of these observations is that most of the measurements were made with a spot focused laser beam, perpendicular to the target symmetry axis, to provide the intensities required to fully ionize the high-Z plasmas produced by ablation from the target walls. As a consequence, the dynamics in the evolving plasma are perhaps only an approximation of those in a closed cylindrical geometry. Additional studies were carried out by C. Stockl on the interactions produced by a frequency doubled Nd-glass laser injected along the symmetry axis of small gold capillary tubes [17]. Preliminary experiments were conducted by focusing the laser beam between two parallel plates separated by 0.3 - 1.5 mm, and observing the x-ray emission with a pin-hole camera and an x-ray streak camera, both viewing the plasma between the plates from locations perpendicular to the beam axis. The targets used in the cylindrical cavity experiments were gold capillaries, 200 jum and 700 u in diameter and 2-12 fim in length. Laser pulse energies were typically 8 J in energy with a FWHM of 3 ns. Measurements were made of the laser light transmitted through the target as the length of the target was varied. For some of these experiments a 30 ps, 200 mJ laser pulse was used. Observation of the x-ray emission along the axis of the targets was made with a pin-hole camera, using calibration values for the film to determine absolute intensities of emission. Time resolved measurements of the x-ray pulse were made with an x-ray photodiode. Slit-camera images recorded the intensity of x-ray emission as a function of angle. X-ray emission perpendicular to the laser axis was obtained by drilling holes in the tube walls 100 fim. in diameter at 1 mm intervals along the target. The x-rays emitted were imaged by a pin-hole camera, with a grating fitted in the hole, to provide Chapter 1. Introduction 9 observations of the intensity distribution along the axis as a function of wavelength. These results, published while this work was being prepared, provide some basis of comparison with the observations presented in this thesis. 1.5 Outline of the Thesis The remainder of this thesis is presented as follows. Chapter 2 describes the theoretical principles underlying the plasma dynamics and laser-plasma interactions that are studied in this work. The discussion progresses es-sentially along the time-line of plasma development in the cavity. Thus, the first topic discussed is the ablation of material from the wall of the cavity, and the subsequent ionization of this material to form a plasma. As it is the effects of collective plasma mo-tion that are diagnosed in this thesis, the plasma dynamics are then described in terms of a fluid model. Simple models of thermal expansion early in the development of the plasma, when the laser is treated primarily as a heat source, are presented, and com-puter simulations of similar geometries are referenced. The ponderomotive force, which arises from steep gradients in the electric field of the laser beam is then introduced. This force plays a dominant role in the dynamics of the plasma at later times, as the plasma converges toward the symmetry axis. These discussions permit a theoretical description of the development of the plasma profile in time. This description forms a background for the analysis of beam propagation through the plasma, and radiative emission from the plasma, the quantities that were diagnostically measured in this thesis. A theoretical description of beam propagation in the plasma forms the remainder of the chapter. One of the cornerstones of this thesis was the development of a high-power, short pulse laser system. This system was required to provide the complete ionization of the plasma ions, and rapid heating and cooling of the plasma needed to simulate x-ray lasing Chapter 1. Introduction 10 conditions, as well as the steep gradients of the electric field perpendicular to the symme-try axis characteristic of filamentation. Such a system was designed and constructed, and Chapter 3 forms a description of this system. The core of the system was built around an amalgamation of the best components of two previous laser systems. The new system achieved its design goal of improved reliability over the old systems, which were in a state of repair much more often than they were performing experiments, and often misfired when they were in use. Additional improvements desired and produced were a better contrast ratio for the beam pulse provided by a dual Pockels' cell arrangement, and the elimination of tri-n-propylamine, a carcinogenic arc suppressant, from the amplifiers. Once a laser system had been developed to produce the plasma and drive the laser plasma interactions, targets had to be fabricated to provide the cylindrical cavities in which the interactions were to be studied. The factors influencing the design of these targets, as well as details of the construction process, are provided in Chapter 4. This chapter also includes description of the target chamber used to house the target during experimentation, and the positioning system which provided the precise alignment of the target required to pass the laser beam through the cavity along its symmetry axis. Once the required components had been acquired or constructed, the thesis program progressed to the experimental stage. The results obtained from these experiments are presented in Chapter 5. The data obtained from transmitted energy measurements, as well as the observations made of the transmitted beam divergence, and the visible light emission from the plasma are compiled for easy interpretation. A brief description of the diagnostic techniques is also included. Chapter 6 presents the interpretations and analysis made of the experimental results. The transmission measurements are compared to theoretically expected values for ab-sorption for assumed plasma behaviour. The transmitted beam divergence observations are considered in terms of focusing properties of plasma density gradients, and diffraction Chapter 1. Introduction 11 limits on effective cavity diameters. The visible light emission observations are discussed with respect to assumed sources of emission, and analyzed on the basis of theoretical considerations, and computer generated ray tracing simulations. Chapter 7 concludes the thesis with a summary of the interpretations made about the experimental results. It also provides suggestions for further work to be done, and possible improvements on methods.se Chapter 2 Theory 2.1 Introduction As was suggested in the first chapter, the theoretical description of plasmas produced by laser ablation from a solid, and the interaction of a laser beam with that solid, is required to understand, and to provide analysis of the diagnostic results collected from experiments conducted in this thesis. The theory presented in this chapter outlines the production of a plasma by a laser beam incident on a solid surface, and the subsequent development of the plasma in the presence of a laser beam. It also examines the propagation of a laser beam in such a plasma. The chapter concludes by discussing the dominant mechanisms for absorption and emission of radiation by the plasma. 2.2 Ablation Laser radiation incident on a solid surface is absorbed, and for intensities > 109 W/cm2, a thin layer of the surface is sublimated, and expands from the surface at high velocity [18]. For intensities in the vicinity of I ~ 1010 W/cm2 the expanding gas is ionized, and a plasma is formed. Such plasmas are typically opaque to the laser radiation near the solid surface, and as a consequence, any further ablation of material from the solid surface occurs only via heat transport through the plasma. Once the initial ionization occurs, subsequent growth of the ionization is assumed to occur via an avalanche process, as free electrons in the plasma are accelerated to high energies in the field of the incident light. 12 Chapter 2. Theory 13 Direct photo-ionization is generally much less probable, as for most lasing wavelengths it requires a multiphoton process. As an example, 43 CO2 photons must be absorbed before the excited states decay to singly ionize a lithium atom. Some models to explain why such processes happen at all propose distortions of the atomic energy levels in the presence of the very intense electric fields of a laser focus. If local thermodynamic equilibrium can be assumed, the populations of the ionization stages are governed by the Saha equation [19] = NeN* _ 2Z2(T) (mkT\ Nz-i ~ z*-i(T) \2<K%2) 3/2 exp E^1 - AE^ kT (2.1) where, iVe is the density of free electrons, Nz is the density of ions in the z stage of ionization, ZZ(T) is the partition function of stage z, at temperature T, E^1 is the ionization energy of stage z for isolated systems, and AEgo is the correction for interactions in the plasma. 2.3 Plasma Expansion 2.3.1 Fluid Equations The bulk motion of the plasma expanding from the solid interface is usually modelled using the fluid approximation. The plasma species are regarded as interpenetrating conducting fluids, moving in the presence of macroscopic electric (JS) and magnetic (J3) fields. One of the equations that form the basis of fluid theory is the continuity equation: dtn.(x,t) + V-(n 8V s) = 0 (2.2) Chapter 2. Theory 14 where, n„ is the fluid density of species s, and Vg is the velocity of a fluid element. This equation implies that the fluid is not being created or destroyed, and as a conse-quence application of fluid theory requires LTE as a necessary condition. The remainder of the equations governing the evolution of the plasma in fluid theory are the momentum equation, dtV8 + V, • V V , = _ 1 -VP, + -^-E + —Va X B ngms m. m. an equation of state, and Maxwell's equations: — = constant nsf V • E = 4.irp V • B = 0 V X E = --dtB _ 47T , 1 . „ V X B = — J + -dtE c c (2.3) (2.4) (2.5) (2-6) (2.7) (2.8) where, Ps is the pressure of species s, 7 is one for an isothermal system, while for an adiabatic system, 7 = (24-N)/N, and N is the number of degrees of freedom, p = Yls asns is the total charge density, and J = Y^,s q.8nsVs is the total current density Chapter 2. Theory 15 These equations form a complete, though approximate, description of plasma dynam-ics. In practice, however, these equations are impractical to use to describe a general plasma. They involve coupled nonlinear differential equations in three dimensions and four parameters (x and t). Such equations may be solved analytically only in a few very simple systems, and computationally very quickly entail the evaluation of unfeasible numbers of operations to model a plasma with any degree of precision as it develops in time. Consequently, further approximations and assumptions are usually made when calculating the dynamics of a given plasma system. One approach entails linearizing the equations, by assuming equilibrium values for the system variables, to which first order perturbations are added to the quantities of interest. Another method of reducing the complexity of the calculations is by assuming symmetry in a given dimension, to produce a set of equations in two or even one dimension. Assumptions may be made regarding the equation of state, to provide expressions relating the fluid density and pressure, often expressing them as functions of the mean kinetic energy or temperature of a species. The most cumbersome of the equations to manipulate, the momentum equation, may be simplified by regarding one of the fields as being negligible relative to the other, or by setting bounds on the gradients in velocity or pressure. All of these methods must be approached with some caution when one is attempting to model an experimental plasma. In the absence of information about the system, few approximations may be made about the variables, and a generalized description of the plasma must be employed, with limited precision. Results from experimentation provide a feedback mechanism which allows refinement of the assumptions, and thus improvements in the precision of the model. An alternative approach entails attempting to design an experimental system which restricts variations to a few variables, and testing the validity of a given model. Such results are sometimes difficult to compare to the dynamics of a highly coupled system. The system studied in this work attempts to balance these two Chapter 2. Theory 16 approaches. In terms of filamentation, observations can be made with well characterized parameters in a configuration that unambiguously exhibits large scale filamentation. As a representation of x-ray lasing schemes, the system is not idealized, and should provide an accurate description of plasma dynamics in closed geometry x-ray laser applications, although no attempt was made to measure x-ray amplification. 2.3.2 Thermal Expansion At early times in the plasma expansion, the bulk motion of the plasma is dominated by the pressure term in the momentum equation. The relative importance of the pressure and electromagnetic forces in the motion may be estimated by comparing the thermal speed, (2.9) to the jitter speed, v = qsEQ (2.10) mau) where, Ta is the mean temperature of species s (in energy units), ma is the mass of a particle of species s, qs is the charge of a particle of species s, EQ is the amplitude of the electric field of the laser, and u is the angular frequency of the laser radiation. Bulk motion due to oscillatory magnetic fields in a laser beam are typically related to those due to the electric fields by the ratio Va/c, and thus are generally neglected in non-relativistic plasmas. Chapter 2. Theory 17 The thin, hot plasma formed by high-powered laser ablation from a solid surface is known to stream away from the surface supersonically, and be nearly isothermal [20]. Analytical solutions published for such systems typically describe ablation from a plane surface, or divergent expansion from a sphere or cylinder in an attempt to model com-pression of ICF pellets. One such analysis by Schmalz provides generalized self-similar solutions for one-dimensional unsteady outflow of a gas into a vacuum for plane, cylin-drical, and spherical symmetry [21]. The closest description of expansion in a cylindrical cavity is likely given by the plane symmetry case, as the flow is convergent when the cylinder forms the outer boundary of the system. Fortunately, the behaviour is similar for all the geometries examined, and consequently a general form is described regardless of the geometry of the boundary. The fluid equations for the system are: where, a is 1, 2 or 3 for plane, cylindrical or spherical symmetry, respectively, n is normalized by n0, the number density at the boundary, V is normalized by cs, the isothermal plasma sound speed, c8 = (Tg/m,)1/2 r is normalized by R, an arbitrary normalization factor, and t is normalized by Rjcs. The solution for the unsteady early phase of the expansion is given by: (2.11) (2.12) V = a1<2 + t (2.13) n (2.14) Chapter 2. Theory 18 where, £ is the similarity coordinate, £ = (r — r\)/(t — ti), and ri,<i are constants that may be freely chosen. The steady-state solutions that arise later in time are unlikely to be applicable, as at such times plane symmetry can no longer be assumed. Furthermore, the assumption that the number density vanishes at infinity does not have a counterpart at the symmetry axis of the cylinder. As well, at later times the fields can no longer be negected, as is described below. Both Cunningham et al. [15] and Daido et al. [11] have published fluid model computer simulation results for the expansion of of plasma produced by ablation from the inner wall of a cylindrical cavity. Cunningham et al started with the same eulerian equations for the conservation of momentum and mass used in the analytic model of Schmalz described above. The temperature was varied by assuming a constant fraction of the laser energy was absorbed by the plasma. The results were shown in terms of the critical density surface for frequency doubled radiation from the driver laser. This surface moved approximately linearly in time, and for early times resembled an exponential decay with distance from the cylinder wall as described by Schmalz. At later times, the density contours developed a peak at the symmetry axis, and by ~300 ps the plasma is everywhere opaque to the radiation. Daido et al use a one-dimensional Lagrangian hydrodynamic simulation code to model the expansion. In this system, the laser penetrated the cavity for ~60 ns. Comparing the parameters, the system of Daido et al had lower intensities, and a longer wavelength driver laser than the system studied by Cunningham et al. As well, the target had a greater diameter, and was made of a lower Z material. Chapter 2. Theory 19 2.3.3 Ponderomotive Force Up to this point the effects of the laser radiation fields have been neglected. In the case of short wavelength driver lasers, such as Nd-glass, where the quiver velocity is low (v oc A), and high Z targets, where the temperatures required to produce ionization are high and consequently the thermal speeds are high (v oc T), such effects can likely be neglected throughout the plasma development. If v >• v does not hold true, however, pressures on the plasma due to the fields must be considered. If there exist gradients in the electric field, these give rise to a ponderomotive force on the plasma, Fp = --^—VE2 (2.15) 4m,w2 If the laser beam is incident along the symmetry axis of the cavity, with a Gaussian pro-file peaked at the centre, this force acts radially, and opposes the thermal pressure of the plasma expanding from the wall. As the beam is confined to a progressively smaller region about the symmetry axis as the plasma fills the cavity, the field gradients increase, and thus the ponderomotive force grows as well. Plasma density profile steepening due to ra-diation pressure has been observed experimentally for long wavelength (CO2 at 10.6//m) radiation [22]. As a consequence, the plasma will take considerably longer to close off the cavity than simple consideration of thermal expansion would indicate. 2.4 Beam Propagation in a Plasma 2.4.1 Dielectric Properties of a Plasma Consider an electromagnetic wave oscillating with frequency u incident on a plasma with electron density no. Assume that the system is non-relativistic, and that there are no externally imposed magnetic fields, so that the response of the plasma to magnetic fields may be regarded as negligible. Further, assume that u> > u)^ where u>pe = 4.7ce2no/me Chapter 2. Theory 20 is the electron plasma frequency, the frequency at which plasma oscillations are driven resonantly. This last assumption implies that the ions may be regarded as stationary. Applying these assumptions to the fluid equations produces wave equations for the field variables [23]: V2JS7 - V(V • E) + ^ eE = 0, and (2.16) V 2 B -I- ^ r t B + -Ve x (V x B ) = 0 (2.17) where, 2 e is the dielectric function of the plasma, e = 1 — ^ If the wave is incident on a uniform plasma, with the further assumption of a spatial dependence of e'^  ' x , then the dispersion relation for the wave once it enters the plasma is given by: w 2 = u; 2 e+ k2c2 (2.18) For u < cjpe, k becomes imaginary, and the wave is reflected. Thus u>pe = u) defines the maximum plasma density to which the electromagnetic wave can penetrate. This density, termed the critical density, is given by: ,2 If the plasma is inhomogenous, then an obliquely incident electromagnetic wave reflects at a density of ne = ncrcos29 (2.20) where, 6 is the angle between the propagation vector fe Chapter 2. Theory 21 and the direction of the density gradient 2.4.2 Diffraction and the Geometrical Optics Limit Numerical simulation of the propagation of an laser beam through an inhomogeneous plasma usually follows one of two basic approaches, the paraxial approximation, and ray tracing [24]. In the paraxial approximation the wave equation described in the previous section for the electric field of the laser beam is solved, but the direction of propagation k is assumed to be mainly along one axis, usually designated as z. This method includes the effects of diffraction, and provides a simple determination of energy deposition from a calculation of the field amplitude. Drawbacks include reflections from artificial grid boundaries, and the restriction to small deviations from the symmetry axis. The second technique traces the propagation of a representative set of beam rays through the plasma, using the techniques of geometric optics. Geometric optics provides a good model of wave behaviour when the relevant length scale, which in this case is the beam width, is much longer than the wavelength of the radiation. As well as allowing the application to cases where the beam is not confined to a narrow region about the symmetry axis, ray tracing can naturally account for reflections from critical surfaces, and scattering from random density fluctuations. It does not, however, model diffraction effects, and typically requires large numbers of rays to be traced in order to accurately model intensity and absorption profiles. Consequently, geometric optics may be applied to laser beam propagation through the cylindrical cavity studied in this work for early times in the laser pulse. At such times the beam reflects in the vicinity of a critical density layer near the cylinder wall. Chapter 2. Theory 22 The geometric optics limit is satisfied, as the cylinder radius is more than an order of magnitude larger than the laser wavelength. The equation of motion for the position x of a ray is determined in this approximation by [24]: d2:r r2 At sufficiently early times the distance from the wall to the turning point of the beam is much smaller than the cylinder radius, and the ray path can be modelled as a simple mirror-like reflection. At later times, a profile for the plasma density must be assumed, such as that provided by the analytical model analyzed by Schmalz described previously [21]. The zeroth-order approximation to the profile assumes a constant refractive index within each grid element of the simulation, and straight ray paths within each element. Problems arise due to the discontinuities at the grid boundaries, and the fact that the rays do not experience gradients within the grid elements. Simple analytic solutions exist for quadratic density profiles [24], and thus it is often better to model the profile by fitting it with quadratic sections for each element. This allows continuity to be maintained at the grid boundaries, within gradients approximated within the element, without markedly increasing the computational requirements for each element. At later times, when the inward movement of the plasma has restricted the beam propagation to a narrow region about the symmetry axis, the effects of diffraction must be included. An accurate evaluation of the wave equation would require a detailed knowledge of the development of the plasma density profile with time. Such a profile for the geometry studied in this work would require a two-dimensional hydrocode (fluid approximation) model of the plasma. Some aspects of the effects of diffraction, however, be realized from rather simple considerations. For a gaussian beam, the angular beam spread f?{,eam introduced by diffraction is given by [25]: Obeam = tan'1 I-—] —^ — (2.22) Chapter 2. Theory 23 where, Qbeam is the half-apex angle of the beam cone in the far field, A is the wavelength of the beam, UIQ is the beam waist, or minimum radius, and n is the refractive index of the medium, n = (ck/u) This equation may be inverted to determine the minimum beam radius, given the beam angle in the far field where geometric optics may be applied. 2.4.3 Absorption and Emission Up to this point, absorption of the beam by the plasma has not been considered. At very early times, much of the beam energy is absorbed by sublimation and ionization of the wall material. Once the plasma is formed, however, most of the beam propagates through the underdense plasma with very little attenuation. Two forms of absorption, however, are significant, and will be considered. For an electromagnetic wave obliquely incident on an inhomogenous plasma, the elec-tric field may be divided into two components. The s-polarized component points out of the plane of incidence spanned by the propagation vector k, and the direction of the density gradient, defined as z, while the p-polarized component lies in the plane of in-cidence. Part of the p-polarized component penetrates to the critical density surface as an exponentially decaying evanescent wave. This portion resonantly excites electron plasma waves at the critical density boundary, and thus energy is transferred from the electromagnetic wave in a phenomena termed resonant absorption. Assuming a linear density profile (ne = nCTz/L), the fractional absorption fa of the beam is approximately Chapter 2. Theory 24 [23]: fA ~ 2.6r2e"4r3/3 (2.23) where, L is the scale length from the critical layer to the plasma boundary, r is given by r = (u>L/'c)xlzsin6, and theta is the angle between k and z The fractional absorption is a maximum at 0, max sm~1[0.8(c/wX)1/'3], while it becomes negligible for normal and grazing incidence. Collisions between particles in a plasma leads to modification of the dielectric function e, and results in damping of the laser beam, a process known as inverse bremmstrahlung. If the the ions are treated as fixed, providing a neutralizing background, then the modified dielectric function becomes [23], vei is the collision frequency which describes electron scattering by ions The fractional absorption is then given by e= 1 (2.24) U>(w + ivei) where (2.25) for a linear density profile (ne = ncrz /L), and (2.26) Chapter 2. Theory 25 for an exponential profile (ne = ncrexp(—z/L)). For a Maxwellian distribution of elec-trons, the collision frequency is given approximately by: uei ~ 3 x 10"6/nA (±^J (2.27) where, A is the ratio of maximum to minimum impact parameters, ne is measured in cm - 3 , and Te is measured in eV The maximum impact parameter is given by v/u>, where v is the thermal speed of the electrons, while the minimum parameter is given by the larger of either the classical distance of closest approach (6m,„ ~ Ze2/mv2), or the DeBroglie wavelength of the electron (6m,n « h/mv). In the ponderomotive regime the electron-electron collisions can not equilibriate the distribution as fast as the electron ion collisions cause it to heat, and the distribution becomes super-Gaussian. This reduces the damping rate by a factor of about 2. For moderately high temperatures in regions away from the critical density boundary, this absorption becomes negligible. Emission from the plasma is primarily due to continuum or bremmstrahlung radiation, with narrow emission bands due to energy level transitions in the ion species of the plasma superimposed. With temperatures in the vicinity of 100 eV typical for the plasma studied in this work, the most intense emission is in the VUV region of the electromagnetic spectrum. Thus, emission in the visible region is at the tail end of the emitted radiation spectrum, and is primarily due to bremmstrahlung radiation. Additional emission can occur in the vicinity of the incident laser frequency if the intensities are sufficient to drive harmonic generation, or parametric processes. Chapter 2. Theory 26 This concludes the consideration of the theoretical background of the laser-plasma interaction processes. The next two chapters examine the development of a physical infrastructure with which to conduct experiments on the interactions in a cylindrical cavity, ae Chapter 3 The C 0 2 Laser System 3.1 Introduction One of the most important elements of this thesis project was the development of a laser system capable of achieving the high intensities and short pulse lengths required to simulate x-ray lasing conditions, and the steep electric field gradients and long laser wave-lengths necessary to produce filament-like ponderomotive effects. The avenue that was pursued was a synthesis of the best components of two laser systems that had previously been employed for plasma studies in this laboratory. As desired, the new system proved to be more reliable than the previous configurations, and provided a better contrast ra-tio for the beam pulse, an important factor in reducing pre-pulse, and hence the early formation of plasma. A further improvement was the elimination of tri-n-propylamine, a carcinogenic arc suppressant, which had been used as an additive to the lasing gas mix of the old system. This alleviated the problems of handling of the tri-n-propylamine, the dangers of gas leaks, and the concerns about exhaust gases that had to be addressed previously. 3.2 Details of the Components 3.2.1 The Hybrid Oscillator The 2 ns laser pulse that propagates through the system is initiated in the hybrid os-cillator (Figure 3.1). The lasing cavities are the same ones described in the thesis of 27 Chapter 3. The CO2 Laser System 28 M.Laberge [27]. The low pressure section both provides a CW beam that facilitates alignment of the system, and allows only a single longitudinal mode of the laser transition to oscillate, as described in the thesis of J. Bernard [26]. The lasing medium for the low pressure section is a flowing mixture of gas containing 15% CO2, 15% N2, and 70% He, maintained at 18 torrs of pressure. As in all of the gas mixes, the N2 is added as its first excited vibrational state is very close in energy to the upper level of the CO2 lasing transition (the first asymmetric stretching mode of the CO2 molecule), and serves to pump this level via molecular collisions and direct electron impact. The He is added to aid in the depopulation of the lower level of the transition (the first symmetric stretching mode of the C0 2 molecule), as well as to minimize arcing in the discharge. An 11 kV potential maintained between two brass ring electrodes at either end of the glass tube through which the gas mix flows produces an 8 mA current which forms an 80 cm glow discharge column. The tube is water cooled, and the water is temperature regulated, to minimize thermal expansion of the tube, which results in misalignment of the end mirrors. At one end of the tube is a fully reflecting concave mirror, with a focal length of 3.0 meters. At the opposite end is a KC1 salt flat, oriented such that its normal is in the horzontal plane, at 57° relative to the laser axis, which is the Brewster's angle for KC1 for 10.6 fim radiation. Since in addition the salt flats at either end of the high pressure section are similarly aligned, this serves to polarize the laser beam in the horizontal plane. Part of the vertical polarization component of the beam is reflected out of the beam axis at each KC1 interface, and thus over the many round trips through the cavity that a photon makes before exiting this component is essentially eliminated from the beam. An adjustable iris was positioned between the low and high pressure sections, with its center aligned with the center of the laser axis. This iris aided in alignment of the oscillator, as well as providing a simple means of inhibiting lasing. A second adjustable Chapter 3. The C02 Laser System 29 Spectrum Analyzer Low Pressure Section High Pressure Section Figure 3.1: Schematic diagram of the hybrid oscillator Chapter 3. The C 0 2 Laser System 30 iris on the other side of the high pressure section served as a further aid to alignment. The high pressure section, in combination with the low pressure section, produces a temporally smooth, 150 mJ, 60 ns gain switched pulse. This section operates with a gas mixture containing 8% CO2, 8% N2 and 84% He at a pressure of 25 psi above atmospheric pressure. The cavity is UV preionized by sparks between Chang profile electrodes on either side of the cavity. The main discharge occurs transversely to the laser axis, between Rogowski profile electrodes running the length of the cavity. The preionizer and main electrode potentials are generated by an LC inversion circuit, charged to 24 kV, and both discharges are triggered by a single spark gap [28]. In the old system one of the salt flats was somewhat mechanically distorted, and exhibited lens-like effects. This was replaced, considerably improving the beam quality. The gas pressure was also reduced from 210 kPa to 170 kPa above atmospheric to minimize distortions and damage. An aluminum Faraday cage was built to surround the high pressure section to isolate the spark gap and LC circuit from the EM noise of the rest of the system. A temperature controlled Ge etalon served as the partially reflecting mirror for the laser cavity. The etalon was placed in thermal contact with a copper block, the tem-perature of which was regulated and monitored by an electronic circuit, with a precision of <0.1° C. This allowed precise control of the optical length of the etalon, as both the refractive index and the length of the etalon are temperature dependent. By maximizing the Q of the laser cavity for a particular wavelength, a desired lasing transition may be selected by adjusting the temperature of the etalon. The transition used throughout these experiments was the P(20) transition at 10.6 pm, as it has the greatest gain at room temperature. A new mount for the etalon was constructed which provided im-proved mechanical rigidity, while still allowing the freedom to adjust the orientation of the mirror as required. Chapter 3. The CO2 Laser System 31 3.2.2 2 ns Pulse Generation Amplification of the 60 ns gain switched pulse to the intensities required for the exper-iments would have demanded a large expenditure of energy, and would have put undo strain on the optical components. Furthermore, if the pulse is sufficiently short, the laser pulse energy is deposited in the plasma before significant hydrodynamic motion of the plasma can occur. Consequently, a dual Pockels' cell electro-optic switch configuration was used to extract a 2 ns pulse from the peak of the gain switched output (see Fig. 3.1). As described above, the beam output from the hybrid oscillator is polarized in the horizontal plane. Thus, when it encounters the Ge polarizer Pi, oriented with its normal in the horizontal plane at 76.0° relative to the beam axis (the Brewster's angle for Ge at 10.6 ^m), the beam is transmitted with virtually no reflection. The transmitted beam is directed into an Optical Engineering CO2 Spectrum Analyzer, which is used to monitor the lasing transition. When an electric field is applied to the Pockels' cell Ci, however, a birefringence effect is produced, resulting in a rotation of the beam polarization after passage through the GaAs crystal of the cell. To produce the maximum reflection of the laser beam pulse from the Brewster's angle Ge mirror the voltage applied across the cell must produce a 90° rotation of the polarization. A pulse peaked at such a voltage is produced by charging a 20 cm length of cable to 29 kV, and using a UV triggered spark gap to discharge this cable into a 50 fl cable which is impedance matched with the 50 ft characteristics of the travelling wave Pockels' cell. The temporally smooth 2 ns FWHM voltage pulse peaked at 14.5 kV which results first rotates the polarization of the laser beam as it passes through the cell Ci, resulting in a vertically polarized, 2 ns FWHM portion of the laser pulse which is reflected by the polarizer Pi. The voltage pulse then continues to propagate along a 50 Cl cable to the cell C2, while the laser beam pulse is directed by mirrors along a path that is configured such that the voltage and laser beam Chapter 3. The CO2 Laser System 32 pulses arrive at the cell C 2 simultaneously. The cell C 2 again rotates the beam polar-ization by 90°, and a 2 ns FWHM, horizontally polarized laser beam pulse is reflected from the polarizer P 2 , with an improved contrast ratio. A small portion of the beam is transmitted through the polarizer P 2, and this is directed to a Labimex P005 HgCdTe detector in the eletromagnetically shielded screened room, for use as a pulse monitor. 3.2.3 Backscatter Protection Between the hybrid oscillator and the amplifier chain, a tight-focused telescopic system was introduced into the beam path to prevent backscattered radiation from the amplifiers from propagating back through the amplifiers, and damaging the Ge etalons, or the GaAs crystals of the Pockels' cells. The pulse from the hybrid oscillator passes through the tight focus unimpeded. An intense backscattered beam, however, produces an air spark at the focus, refracting the beam into all directions, and leaving the system's components unharmed. 3.2.4 The Preamplifier The output from the hybrid oscillator is passed five times through a transversely pumped, UV preionized preamplifier which operates as a closed system with a gas mix containing 15% C0 2 , 15% N 2 and 70% He at an absolute pressure of 1.5 atmospheres (See Fig. 3.2). A detailed description of this amplifier is given in a report by W. Liese [29]. Because it operates as a closed system, the preamplifier makes efficient use of the lasing medium as the gas only needs to be replaced once over the course of a day of experimenting. However, this also means that the repetition rate is very low, as it takes about five minutes for the gas to return to room temperature and maximum gain. The gas chamber forms a closed rectangular loop, of which the lasing cavity forms the lower arm. A fan in the upper arm of the loop allows the gas to be circulated intermittently to remove Chapter 3. The CO2 Laser System 33 reactant products from the laser cavity, and to aid in cooling of the gas. The beam from the oscillator enters the preamplifier through a small (24 mm diameter) salt flat above a 80 mm diameter mirror with a focal length of +3.0 m. At the end of the first pass, the beam exits the amplifier through a 76 mm diameter salt flat, and reflects off the corner of a flat rectangular mirror. The second pass is reflected off the f.l.=+3.0 m mirror to a 21 mm diameter mirror with a focal length of -65 cm. Following the second reflection from the f.l.=+3.0 mirror at the end of the fourth pass through the amplifier, the beam is collimated, with a diameter of about 30 mm, and consequently draws energy from a significant volume of the amplifier cavity. After the fifth pass through the amplifier, the beam is directed by turning mirrors to the next stage of the amplifier system, the 3-stage amplifier. Unlike earlier schemes, the beam is not focused through a spatial filter between these two stages, as the 200 mJ pulse exiting the preamplifier was sufficently strong to produce an air spark at the focus, even when focused over several meters with an f/# of > 100. The voltage for the preamplifier's preionizer electrodes is provided by a two stage Marx bank charged to 18 kV. As the Marx bank capacitors are charged in parallel, but discharged in series, this produces a voltage of 36 kV across the Chang profile electrodes. The main discharge is produced by a six stage Marx bank charged to 23 kV, which produces a voltage across the main Rogowski profile electrodes of almost 140 kV. The main discharge requires an auxilliary trigger unit to fire the six spark gaps for the Marx bank. The adjustment of the timing between the preionizer discharge and the main discharge is critical to minimize arcing. The preionizer fires 1.0 ps before the main discharge. A set of relays was constructed to dump the voltage from the main and preionizer circuits, as it was found that allowing the capacitors to discharge through the power supplies was damaging the charging resistors of the power supplies. When the relays were turned on, they connected the capacitor banks to the power supplies, and Chapter 3. The C02 Laser System 34 3-Stage Amplifier T IK c "1 H I J ji 9^ 1 \ Preamplifier I* Hybrid Oscillator - 7 ^ Lumonics TEA-600 Amplifier Figure 3.2: Overview of the amplifier chain. Chapter 3. The CO2 Laser System 35 when they were turned off, the banks were shorted through 1 kfi high current capacity ring resistors to ground potential. 3.2.5 The 3-Stage Amplifier The 3-stage amplifier has evolved over the years at this laboratory as it has been used by successive groups for laser-plasma studies (See Fig. 3.2). An early version of the amplifier is described in detail in a report by H. Houtman and C.J. Walsh [30], and a somewhat more recent version is described in the thesis of J. Bernard [26]. Improvements that have been made since the thesis of J. Bernard include modifications to the triggering system, rebuilding of the second stage preionizers, and elimination of tri-n-propylamine from the system. The 3-stage amplifier, as its name suggests, consists of three pairs of Rogowski shaped electrodes discharging transversely across the lasing cavity, each set UV preionized by a series of sparks between curved washers at the top and bottom of the cavity. The active volume of the cavity for each stage is 60 cm long, with an 8 cm width of the flat section of the electrodes, and a separation of 5 cm between the electrodes. The lasing medium is a mix of 19% CO2, 16% N 2 , and 65% He at a pressure of one atmosphere that continuously flows through both the 3-stage amplifier and the final stage of the amplifier chain, a Lumonics TEA-600A which is described in the next section. The preionizer discharge is produced by a two stage Marx bank charged to 30 kV, producing a discharge pulse of 60 kV. The main discharge is supplied by a three stage Marx bank charged to 27.5 kV, resulting in a voltage across the electrodes of more than 80 kV. Again the relative timing of the preionizer and main discharges is critical for minimizing arcing in the main discharge. For this amplifier the trigger pulses for the two discharges are separated by 4.0 ps. The beam pulse passes twice through the 3-stage amplifier, reflecting from a 50 mm diameter flat mirror at the back of the amplifier. The pulse exiting the amplifier has a FWHM of 2 ns, and an energy of 1 to 2 joules. This Chapter 3. The C02 Laser System 36 pulse provided sufficient intensity for most of the studies carried out. 3.2.6 The Lumonics Amplifier The final stage of the amplifier chain is a commercially manufactured Lumonics TEA-600A (See Fig. 3.2). A three stage Marx bank is charged in parallel to 49 kV, and then discharged in series through spark gaps to provide a voltage pulse of 147 kV across the main electrodes. The preionizer circuit is charged to 30 kV by a separate power supply. The relative timing of the preionizer and main discharges is maintained by the Lumonics laser control unit. The active volume of the amplifier's lasing cavity is 50 cm in length by 8.9 cm in width by 8.9 cm in height. The laser beam pulse is reflected off a diverging mirror which is located below the lasing cavity axis of the Lumonics amplifier, so the beam is expanding and rising as it enters the amplifier through the lower half of a 127 mm diameter NaCl flat. After passing once through the cavity, it reflects off a converging mirror at the back of the amplifier, and exits through the NaCl flat as a collimated beam with a diameter of 76 mm. Four percent of the beam is then reflected off a 127 mm NaCl flat in front of the target chamber, which is slightly tilted relative to the beam axis, and is focused onto a Rofin #7415 photon drag detector which is used to monitor the output of the amplifier chain. The signal from the photon drag detector is calibrated by simultaneously measuring the beam energy by placing the detector head of an Apollo Lasers Model ALC Calorimeter directly in the main beam path behind the salt flat. Typical beam energies produced when all stages of the amplifier chain were fired were 9 to 12 J. 3.2.7 Triggering and Timing Control A single push-button is used to trigger an eight channel electronic adjustable delay unit located in the screened room. The delay unit allows the time between the initial trigger Chapter 3. The CO2 Laser System 37 and the output of a 40 V pulse for each channel to be varied in steps of 100 ns to 100 ps. Each channel is electrically isolated from the cables exiting the screened room by an opto-isolator. The cables leaving the screened room run through aluminum tubes to connector boxes located throughout the laboratory. Shielded coaxial cables are then used to complete the connection to krytron triggering units in the vicinity of the component to be triggered. Thus, when the screened room door is closed, this system provides reliable triggering of the laser system, unaffected by the electromagnetic noise produced by the firing of the amplifiers. The krytron units contain fast vacuum tube switches that amplify the 40 V trigger pulse to a pulse of typically 10 kV which is then passed through a 1:4 step up transformer to fire the spark gaps for the capacitor banks. In some units the krytron unit triggers the spark gap of an auxiliary trigger unit which discharges its capacitors through the step up transformer to discharge the main capacitor bank. 3.2.8 Minimization of Parasitic Oscillations and Pre-Pulse Parasitic oscillations or "self-lasing" occurs when random noise signals within the ampli-fiers pass through a sufficient length of gain medium to grow to an amplitude comparable to, or greater than the main pulse. To combat this problem the salt flats at the ends of the amplifiers are tilted relative to the beam axis so that they do not act as partially reflecting mirrors. In addition, saturable absorber cells are located between the third and fourth passes through the preamplifier, between the preamplifier and the 3-stage amplifier, and in front of the mirror at the back of the 3-stage amplifier (see Fig. 3.2). The saturable absorber used is SF6, which strongly attenuates small amplitude signals in the region of 10.6 pm, but is bleached by large amplitude signals. Consequently, these cells inhibit the growth of parasitic oscillations in the amplifiers, as well as reducing the small amplitude pre-pulse of the main beam pulse as only large amplitude signals are transmitted through them. The first two cells are filled with 3 torr of SF6, and enough Chapter 3. The C0 2 Laser System 38 He to bring the cell pressure to one atmosphere. The third cell at the back of the 3-stage amplifier contains in addition to 3 torr of SF6 and the He, 35 torr of ethanol and 100 torr of freon-502 which absorb strongly in the 9 to 10.3 fim region, but only weakly at 10.6 fim. It is thus used absorb radiation in the vicinity of 9.6 fim, which is a lasing transition in the C0 2 molecule from the first asymmetric stretching mode to the second bending mode, and hence the cell serves to eliminate self-lasing of the amplifier on this transition. Thus, a laser system has been developed combining reliability with the short pulse, high intensity, and long wavelength requirements of studying a highly ionized, non-LTE plasma in a cylindrical cavity, coupled with strong ponderomotive effects. Before the experiments carried out with this system are described, however, the parameters influ-encing the design of the target, and the means by which the design goals for the target were met must first be described.ae Chapter 4 The Target 4.1 Parameters Influencing Target Design In view of the desire to simulate the conditions of the lasing medium of a recombination pumped x-ray laser, the target material was chosen to have a low enough Z to allow complete ionization in the 10 u — 1012 W/cm 2 intensities on the wall of the cavity typical of the CO2 driver laser. The material chosen was lucite, a polyacrylate plastic, and hence a hydrocarbon polymer [CH 2=C(CH3)C02(CH 2)„CH 3]. Thus the ions were chiefly hydrogen (Z=l) and carbon (Z=6). The material was also chosen because soft x-ray lasing had previously been observed in the C VI Balmer-a transition at 182 A. Another factor influencing the choice was ease of machining, to allow boring of the cavity and appropriate dimensioning of the target. Further benefits were derived from the fact that the plastic is transparent to visible light, allowing flexibility in diagnostic design, and permitting visual inspection of the bounding surface of the cavity. The diameter of the cavity had to be large enough to allow most of the laser beam, with a measured waist diameter at focus of 100 /tm [26], to be injected into the cavity. Furthermore, a maximum limit was imposed on the diameter so that intensities on the wall were sufficient to completely ionize the carbon ions. The length was chosen to be much larger than the radius, to minimize the influence of end effects during the time scale of interest (a few nanoseconds). The upper limit was set by the requirements 39 Chapter 4. The Target 40 of fabrication. The outer surfaces of the cavity were chosen such that a large flat side running parallel to the cavity axis was exposed to facilitate optical imaging of the plasma dynamics along the cylinder axis. This side was as close to the cylinder boundary as the requirement of mechanical integrity from shot to shot would allow. 4.2 Target Fabrication The targets were fashioned from rectangular sections of lucite plate, 12 mm in height, 10 mm in length, and 3 mm in width (See Fig. 4.1). The 12 mm x 10 mm faces were the smooth sides of the plate, while the other sides were machined to the required dimensions. A single hole was drilled through the length of each target with either a #80 or a #76 size drill bit. The bits are 343 fim and 508 fim in diameter, respectively. Drilling was performed with a variable speed precision bench drill. A special mount was constructed to allow the targets to be held upright and rigid on the movable drilling table. Considerable patience and care had to be maintained while drilling the holes. Once the holes were deeper than a few millimeters, it was difficult to remove material from the drilling front. Further, heat generated from the drilling process could no longer be adequately dissipated, resulting in melting of the lucite, and jamming of the drill. Consequently the hole was continuously cooled with water, and the depth could only be increased in intervals of a few hundred micrometers before raising the drill bit to remove material and allow the drilling surface to cool. In spite of such precautions, drill bits were frequently broken, and only about one in three targets was not discarded upon visual inspection. Of the targets that passed inspection, microscopic examination revealed hole diameters of 400±50 fim for the holes drilled with #80 drill bits, and 550±50 for the holes drilled with #76 drill bits. The holes typically were widest where the drill entered the target, and tapered to the exit hole, likely as a result of abrasion due to Chapter 4. The Target 41 ^Translational Stage ^-Target Holder ^•Rotational Stage |^ Target j Figure 4.1: The target and its positioning system loose material, and possibly wobble of the drill bit. Unused targets exhibited spiraling scraping patterns from the drilling process that were typically < 10 pm thick, and some evidence of fusing. Targets which had been fired upon had glassy fused cavity surfaces with frost-like fractures superimposed. 4.3 The Target Chamber The intensities of 1012- 1013 W/cm2 produced by the laser beam near focus are sufficient to ionize air and produce an air spark which refracts the beam in all directions. In order to avoid this, the target was located in an evacuated chamber. The target chamber was Chapter 4. The Target 42 an aluminum cylinder, with outer dimensions of 48 cm in height by 32 cm in radius, and a wall thickness of 3 cm. The symmetry axis of the chamber was oriented vertically (See Fig. 4.2). Four 10 cm diameter ports were located around the circumference of the chamber, two along the laser beam axis, and two at right angles to it. The port through which the beam entered had a 20 cm extension attached to it. A 12 cm diameter, 50 cm focal length KC1 lens mounted in this extension could be adjusted along the beam axis to focus the beam in the middle of the chamber. Four additional 6 cm diameter ports were evenly spaced between each pair of 10 cm ports to provide access for optics, mechanical manipulators and electrical feedthroughs. An aluminum plate, mounted 3 cm above the floor of the chamber was perforated with a 5 cm spacing grid of 1/4-20 tapped holes to facilitate the mounting of apparatus within the chamber. The lid of the chamber was attached to a pulley and counterweight system which allowed it to be raised and lowered with little effort. A roughing pump, mounted below the chamber, was capable of reducing the pressure in the chamber to < 1 torr in less than ten minutes. 4.4 Positioning of the Target An essential requirement of the experiments conducted in the cylindrical cavity was the ability to position the target such that the laser focus was in the plane of the entrance to the cavity (within a tolerance of about 500 u m), and aligned with the symmetry axis of the cavity (within a tolerance of about 10 u m). Furthermore, the axis of the cavity and the axis of the beam had to remain parallel throughout the length of the target. This alignment could not be permitted to vary from shot to shot. Thus, considerable effort was put into the mounting of the target in the chamber. A Newport Corporation Model 471 rotational stage was attached to an aluminum plate, and mounted on the floor of the target chamber (See Fig. 4.1). This stage provided Chapter 4. The Target 43 10cm dia. port 50cm f.l. Lens Figure 4.2: The target chamber Chapter 4. The Target 44 0.3 arc-seconds of resolution over a range of 16° about a vertical axis, and when disengaged could be rotated to any angle. A rigid aluminum right angle was mounted on this stage, to which was affixed a Newport Corporation Model 400 dual-axis translational stage. The translational stage provided 12 mm of travel, with one micrometer of resolution along the vertical axis, and along the symmetry axis of the cavity. A Newport Corporation Model 384 fine-positioning post mount was attached to the translational stage to provide adjustment along the horizontal axis perpendicular to the cavity symmetry axis. A 7 cm long, 2.5 cm inner diameter lucite tubing sleeve was attached to the end of the post mount. A 7 cm long, 2.5 cm diameter lucite rod slid smoothly within this sleeve allowing rotation about a horizontal axis, and could be held firmly in place by tightening a nylon bolt mounted in a tapped hole through the sleeve. This rod had a 10 mm thick rectangular section machined at one end, through which a 12.5 mm hole was drilled. The end of the rod was removed by muling until a 90° section of the hole was exposed. The target was mounted in this hole, with the symmetry axis of the cavity aligned with the hole axis, held in place by a nylon bolt mounted at the top of the hole and pressing against one of the small faces of the target. Thus, the positioning system provided precise alignment, with full translational and rotational freedom, while allowing access for diagnostics to the front and back of the cavity, as well as one large smooth face on the side of the target. Accurate determination of the focal plane was required to position the target. Align-ment lasers could not be used, as the 0.633 pm wavelength of a HeNe laser has a signif-icantly different index of refraction from the 10.6 pm wavelength of the CO2 laser, and thus focuses at a different length. Even the characteristics of the CW CO2 alignment beam could not be assumed to follow exactly the path of the pulse through the ampli-fiers when they are discharged. Thus, the position of focus was determined by firing the amplifier chain, with the Lumonics stage turned off, through a pattern in a mask in front of the focusing lens. Thus pattern was recorded on thermal paper attached to a 12 Chapter 4. The Target 45 mm diameter lucite rod mounted in the target holder. The rod was graduated in 1.00 cm intervals, and the change in separation of the pattern elements on the thermal paper as the rod was moved along the laser axis was plotted (See Fig. 4.3). This provided a determination of the focal position when the system was fired with an accuracy of better than 1 mm. An aluminum right angle was mounted on the floor of the chamber, and extended vertically to just below the target, with with one face aligned with the focal plane to provide a reference for positioning. Alignment of the cavity along the beam axis was accomplished with the aid of two HeNe lasers. A piece of aluminum foil was mounted on the target holder such that it lay in the focal plane. The target chamber was evacuated, and the laser system was fired, with the Lumonics stage turned off. This produced a small hole in the foil. One HeNe was located behind the target chamber, and was aligned such that it passed though the 10 cm ports at the front and back of the chamber, and retraced the path of the CO2 beam back through the Lumonics amplifier, and as far as the last turning mirror from the 3-stage amplifier. Fine adjustments were made to pass the HeNe beam through the hole in the foil. The chamber was then opened, and the second HeNe beam was directed along the beam path of the CO2 beam by placing an adjustable mirror in a mount in front of the last turning mirror from the 3-stage amplifier. This beam was also aligned with the hole in the foil. Final adjustment was made by placing a paper screen in front of the foil, and adjusting the second HeNe beam until there was no visible change in the spot when the HeNe beam from the back of the chamber was intermittently blocked. The foil was then removed, and the HeNe laser behind the chamber was turned off. The target was placed in the target holder, and the positioning system was adjusted until the HeNe beam passed through the center of the cavity entrance, and formed a bright, symmetric spot on a paper screen positioned at the back of the chamber. The position along the cavity axis was adjusted until the front of the target was aligned with the face Chapter 4. The Target 46 Mean Separation (cm) Figure 4.3: A plot used to determine the focal plane Chapter 4. The Target 47 of the aluminum right angle marking the focal plane. Chapter 5 Experimental Diagnostics and Results 5.1 Introduction In order to investigate the energy balance of the plasma, to aid in characterizing the pa-rameters of a laser produced plasma within a cylindrical cavity, a series of measurements were conducted to determine the energy transmitted through the cavity. A phenomenon that was at first greeted with annoyance, as it caused damage to the detection appa-ratus, but then with considerable interest as its implications were understood was the small divergence of the transmitted beam. The other principal approach to providing diagnostics for this closed geometry was the observation, with the use of a streak camera, of the visible light emission along the symmetry axis of the cavity. This interior region of the closed geometry had received limited previous experimental investigation. Previous diagnostic investigations of sim-ilar cylindrical cavities had only observed end effects, or emission through openings in the cavity wall, through which the plasma freely streamed. The streak camera observa-tions were made to obtain some diagnostic guidance for modelling what is clearly a two dimensional system, but they too displayed anomalous results. The results presented in this chapter are divided into these two major categories of beam transmission, and optical emission. 48 Chapter 5. Experimental Diagnostics and Results 49 5.2 Transmitted Beam Results Measurements of the transmitted beam energy were made using a GenTec Model ED-200 Fast-Response Joulemeter. This detector provides a response that is uniform over the visible and infrared spectrum out to A = 30 urn, with an accuracy of better than 10% for pulses of less than 1 ms. The detector is limited to a maximum recommended incident energy of 0.5 J/cm2. Because of this, the beam to be measured often had to be attenuated, requiring that the attenuators in turn be calibrated. The particular detector used had a response calibrated as 6.85 V/J. The GenTec was mounted directly behind the target in the target chamber. The base of the mount was made of lucite to electrically isolate the detector from the chamber to minimize random noise signals. A shielded coaxial cable connected the detector to an electrical feedthrough in one of the 6 cm diameter ports near the back of the cham-ber, which was also electically isolated from the chamber wall. A second shielded cable connected the outside of the feedthrough to a Tektronix Model 466 storage oscilloscope. The 5 ms response time of the detector meant that the EM noise in the room had sig-nificantly diminished before the signal appeared on the oscilloscope. No synchronization was required, as the peak of the pulse^  which determines the amount of energy measured by the detector, occurs so long after the start of the pulse that the oscilloscope can easily be triggered on the rising slope of the signal. The transmitted energy measurements through 400±50 um cavities, with no attenu-ation and with 4 layers of Mylar in front of the detector are displayed in Figure 5.1. Also included in the figure is a plot of the detector response with no target present, but with 4 layers of Mylar in front of it. The transmitted energy values were determined using the calibration of 6.85 V/J. The beam energy values were determined from a calibration of the photon drag detector beam monitor with the Apollo energy meter as described Chapter 5. Experimental Diagnostics and Results 50 Figure 5.1: Measurements of transmitted beam energies through 400±50 ^m cavities. in Chapter 3. Figure 5.2 displays the results of similar measurements for transmission through 550±50 pm cavities, including the results when two layers of Mylar were intro-duced in front of the detector. Table 5.1 gives the average fractional transmission for each configuration. For the measurements made with no attenuation, this was simply an average ratio of the transmitted to the incident beam energies. For the values ob-tained with four layers of Mylar providing attenuation, the ratio was a comparison of the energies recorded with and without a target present. A more interesting result arose from an incidental observation made while recording the energy values. The Mylar attenuators were consistently suffering damage in small Chapter 5. Experimental Diagnostics and Results 51 Figure 5.2: Measurements of transmitted beam energies through 550±50 pm cavities. Cavity Number of Fractional Diameter Mylar Sheets Transmission (pm.) 550±50 - 0.3 550±50 4 0.8 400±50 - 0.2 400±50 4 0.2 Table 5.1: Fractional energy transmission through cylindrical cavities. Chapter 5. Experimental Diagnostics and Results 52 regions, typically ~2 mm in diameter, even when they were located 8 cm behind the target. Similar damage was occuring on the surface of the GenTec detector. Such damage was indicative of intesities much greater than the incident beam could produce so far from the focus, as was shown conclusively when such damage was not observed on the attenuators when the measurements were made with the target removed. A germanium flat was placed in front of the detector, and 6 cm behind the target, to see if the tightly collimated beam was CO2 radiation. Unfortuately, it too was damaged with a spot ~2 mm in diameter. Such damage on a high Z, metallic substance such as Ge indicated that the intensities must approach those of the driver beam near focus. A piece of B-10, 10 thick aluminum foil on plastic substrate, was placed 7 cm behind the target only to have a small section of the foil removed from the substrate by the beam (See Figure 5.3). Only a KC1 flat of the materials tested was undamaged by the beam, and transmitted the energy to the GenTec. Thermal paper placed approximately 7 cm behind the target exhibited burn patterns about 2 mm in diameter when the alignment through the cavity was mediocre (as judged by simultaneous observation of streak camera images), and about 4 mm in diameter when the alignment was good. The light regions in the middle of the burn patterns in figure 5.3 are produced by the removal of the surface of the thermal paper by the intensity of the beam. 5.3 Optical Emission from the Plasma The emission from the plasma in the visible range of the spectrum was observed with a Hamamatsu Temporal Disperser System, or streak camera. A telescopic system was contructed to transfer the image of the symmetry axis of the cavity into the input optics of the Model C979 Temporal Disperser camera (See Figure 5.4). A 7 cm diameter, 40 cm focal length lens was positioned just outside one of 10 cm diameter ports of the target Chapter 5. Experimental Diagnostics and Results 53 Figure 5.3: Images of damage patterns formed on (A) : Mylar, (B,C): thermal paper, and (D) B-10 foil located 6-8 cm behind the target. Chapter 5. Experimental Diagnostics and Results 54 chamber perpendicular to the cavity axis. This lens was adjusted such that its focal plane coincided with the symmetry axis of the cavity. Thus, light emitted from the cavity was collected by the lens, and transferred as a collimated beam, via a turning mirror, to a 7 cm diameter, 23 cm focal length lens which focused the reduced image through the entrance slit to the streak camera. This telescopic system produced an image reduced in size by a magnification factor of M = 23/40. Care had to be taken to keep the optic axis of the system in a plane, as the image of the cavity was only about 250 fim in width, while the entrance slit width of the camera was typically 100-200 fim in width during the experiments. Thus any tilt to the image would have resulted in only part of the image passing through the slit. The spectral transmission range of the input optical system of the camera was 400-800 nm, thus setting a limit on the wavelengths observed. The input optics of the camera focused an image onto a photocathode. The electrons emitted by this photocathode were accelerated through a region between two deflection plates and onto a channel plate. A sweep voltage generator connected to the deflection plates caused the electron image of the light passing through the entrance slit to scan rapidly from the top of the channel plate to the bottom. This produced a record of the light intensity along one axis as a function of time. The channel plate then amplified the electron image, and produced a visible image on a phosphor screen behind it. The accelerating voltages between the photocathode and the channel plate, and the voltages across these to elements were reduced before the flyback sweep of the sweep voltage generator superimposed a second image on the first. The visible image on the phosphor screen was then recorded by a Model C1000 Video Camera Unit, which then transferred the digitized signal to the Model C1440 Frame Memory Image Analysis System. This system stored the image in memory as a 256x256 array of 16 bit intensity values. A CRT display provided a representation of the data to the user. Although the Image Analysis System provided commands for manipulating the data, the raw image data Chapter 5. Experimental Diagnostics and Results 55 Figure 5.4: Optical system for streak camera observation of visible light emission along the cavity axis. Chapter 5. Experimental Diagnostics and Results 56 were usually immediately transferred via a serial connector cable to a microcomputer. The microcomputer provided much more flexibility for manipulation and analysis of the data. The Temporal Disperser System provided a focus mode, which allowed a constant, or slowly varying input signal to be observed on the display screen. This mode was used to align the collection optics. A collimated HeNe laser beam was shone through the cavity from the back of the target chamber. Light scattered from the walls of the cavity was sufficient to provide an image on the display. The optics could then be adjusted to improve the focus, or provide the desired positioning of the image. Such an image was recorded with each set of data to provide a reference for the limits of the cavity. An example of a focus mode image is given in Figure 5.5. This image also provides an idea of the resolution along the vertical axis for a 200 pm wide entrance slit, as well as the reduction in the resolution when the signal intensity is near saturation. A balance was always being made in the amount of attenuation of the signal between minimizing the amount of saturation, while still allowing the sensitivity to distinguish low intensity signals. Synchronization of the streak camera was provided by connecting a high voltage 50 fi cable from the output of the second Pockels' cell through a voltage attenuator to a Hamamatsu Model C1097 Delay Unit, and from there to the trigger port of the streak camera. The trigger signal, once attenuated, had an amplitude of 20 V, and a FWHM of 2 ns. The length of the beam path from the second Pockels' cell to the target, and the light path from the target to the streak camera were measured to determine the length of cable required for synchronization. The transit time of the electrical pulse through the cable, plus a fixed delay in the streak camera which varied with the streak speed, were required to coincide with the arrival of the plasma image to within a bound that could be spanned with the delay unit. The delay unit could then be adjusted to observe the Chapter 5. Experimental Diagnostics and Results 57 Figure 5.5: Streak camera image of the cavity in focus mode. Chapter 5. Experimental Diagnostics and Results 58 desired period of the plasma development. The remainder of this chapter displays a representative set of streak camera images of the visible light emission along the axis of the cavity. A description of the relevant system and diagnostic parameters accompanies each figure. Analysis of the principles influencing the observed dynamics will be presented in the next chapter. Figure 5.6 is an example of an intentionally misaligned shot. The laser beam is incident on the target from the left, and the time axis starts at the top of the figure and extends to the bottom, as is the case for all of the streak camera images. As is evident from the figure, most of the emission, and thus the absorption of the laser beam occurs at the entrance surface of the target. The incident beam energy was 1.4 J, and the GenTec measuring the energy transmitted through the cavity did not even trigger. This image was recorded on the slowest streak speed, with a range of 5.42 ns from the top of the image to the bottom. Figure 5.7 displays a typical streak camera image of the visible light emission from a 550±50 pm diameter cavity. The time axis once again spanned 5.42 ns, and the streak camera entance slit width was 200 pm. The measured incident laser beam energy was 1.6±0.1 J. The error quoted is the standard deviation of the energy calibration values. Figure 5.8 demonstrates the typical shot-to-shot variations of the visible light emission from the cavity. The cavity diameter for these and all of the following images is 400±50 pm. Both images have a time axis spanning 5.42 ns, and were taken with a slit width of 200 jam. The incident laser beam energy for Figure 5.8A was 1.8±0.1 J, while the energy for Figure 5.8B was reduced to 1.2±0.1 J. Images were generally quite similar for consecutive shots, but could drift over a sequence of observations, and were often significantly different between different sets of measurements. An interesting reversal of the region of maximum emission, from the back of the cavity to the front, is evident in the images taken from consecutive shots displayed in Figure Chapter 5. Experimental Diagnostics and Results 59 Figure 5.6: Streak camera image of an intensionally misaligned shot. Chapter 5. Experimental Diagnostics and Results 60 Figure 5.7: Streak camera image of the visible light emission from a 550±50 pm diameter cavity. Chapter 5. Experimental Diagnostics and Results 61 A B Figure 5.8: Typica l shot-to-shot variations of the visible light emission from the cavity. Chapter 5. Experimental Diagnostics and Results 62 SBHHB A B Figure 5.9: Reversal of the maximum emission peak from the back of the cavity to the front in successive shots. 5.9 The time axis and slit width are the same as for Figure 5.8. An incident laser beam energy of 1.3±0.1 J was measured for Figure 5.9A, and an energy of 1.5±0.1 J for Figure 5.9B. Figure 5.10 presents a counterintuitive demonstration of two intense emission peaks at the back of the cavity, with very little emission near the front of the cavity. The time axis and slit width values remain unchanged from the previous three figures. The incident laser energy was measured as 1.6±0.1 J, while the GenTec detector recorded the transmitted energy as 440±10 mJ. Chapter 5. Experimental Diagnostics and Results 63 Figure 5.10: Streak camera image of visible light emission dominated by peaks at the back of the cavity. Chapter 5. Experimental Diagnostics and Results 64 Figure 5.11 shows the emission from the cavity when the final stage of the amplifier chain, the Lumonics amplifier, was fired. The incident beam energy for this shot was 7.0±0.3 J, and the time scale and slit width were unchanged from the previous figures. Few shots of this type were made, as the target often did not remain intact when subjected to such energy densities. The particular shot depicted resulted in extensive fracture damage to the back of the target. The streak speed was increased, and the resolution was improved for the shot recorded in Figure 5.12. The time scale spans only 3.26 ns, and the slit width was reduced to 100 fim. The input laser energy was 1.2±0.1 J. An image on the fastest streak speed recorded is presented in Figure 5.13. The range along the time axis is only 1.26 ns. The input laser energy was measured to be 1.5±0.1 J. This chapter has presented a description of the experimental diagnostics used to probe this system, and displayed the data in raw form. In the next chapter, the results will be analyzed, and interpretations of the underlying principles will be presented. Figure 5.11: Streak camera image of emission with the lumonics fired. Chapter 5. Experimental Diagnostics and Results Figure 5.12: Fast, high resolution image of visible plasma emission dynamics. Chapter 5. Experimental Diagnostics and Results 67 Figure 5.13: High speed streak camera image of plasma emission dynamics. Chapter 6 Discussion and Analysis of the Experimental Results 6.1 Introduction This chapter provides interpretation of the results presented in the last chapter, and analyzes the principles underlying the processes observed. The transmitted energy values are examined by calculating estimated bounds on the absorption processes in the plasma. The exit beam divergence is considered in terms of plasma density profiles, and diffraction limits. The implications of the observations of visible light emission along the cavity are viewed in connection with the dynamics of the plasma, and the propagation of the laser beam through the plasma. 6.2 Transmitted Beam Energy The fraction of the beam energy transmitted through the cavities varied widely, from roughly 20% for the 400±50 fim cavities, measured with no attentuation, to the vicinity of 80% for the 550±50 /xm cavities with 4 layers of Mylar used as attenuators. The fluctuations are not surprising, considering how sensitive the transmission is to alignment of the beam in the cavity. Indeed, the data collected for the 400±50 fim cavities, measured without attentuation, shows much more scatter than the other plots as a result of the fact that it was collected over the course of several sets of measurements. The other plots were each collected during a single set of measurements while the alignment remained essentially fixed. Only a single measurement was taken a 550±50 [im cavity, with no 68 Chapter 6. Discussion and Analysis of tie Experimental Results 69 attentuation present, but the value of fractional transmission is similar to the values obtained for the 400±50 um cavities, measured without attentuation. If this value can be considered typical, then the discrepancy between this ratio and the fraction of the beam transmitted measured for the same diameter cavity with attenuators present must be considered. The most likely answer, unfortunately, is simply that the detector was saturated without attenuation. The experimental configurations were originally designed assuming that the transmitted beam energy would be less than, but of the same order as the incident energy. It was also assumed, however, that the beam exiting the cavity would have an f-number no greater than the incident beam. This was clearly not the displayed by the damage patterns shown in Figure 5.3. Assuming a transmitted energy of at least 400 mJ, and a transmitted beam area of less than 0.1 cm2, as estimated from the damage patterns, the recommended maximum energy density of 0.5 J/cm2 for the GenTec detector is greatly exceeded. The low transmission values for the 400±50 //m cavity with attenuation may simply be the result of poor alignment for that set of measurements. Can a fractional transmission of 80% be considered reasonable if the expected amounts of absorption are evaluated? The two principal means of absorption in such a plasma, as described the Chapter 2, are resonant absorption, and inverse bremmstrahlung. For resonant absorption, the density profile will be assumed to be linear, with a scale length equal to the cavity radius, which will be taken to be 200 fim. Substituting for (UJ/C) = (27r/A), with a wavelength of 10.6/nn, and assuming 6 to be the complement of the maximum angle admitted by the focusing optics, an evaluation of equation 2.23 obtains a value of r « 5. A plot given by Kruer [23] shows that the fractional absorption becomes negligible for r > 2, and with the above assumptions, /A « 10~66. The resonant absorption assumes a maximum for r ~ 1, and thus for A = 10.6 ^m, implies a scale length of L ~ 2/im, becoming negligible for L > 10 ^m. The -^dependence of T is Chapter 6. Discussion and Analysis of the Experimental Results 70 only likely to produce significant absorption in the vicinity of modulations in the plasma density plofile along the symmetry axis of the cavity, and when expansion of the plasma has essentially closed the cavity off to the laser beam. To evaluate the absorption due to inverse Bremmstrahlung, an estimate of the elec-tron temperature is required. Baldis et al. [31] measured an electron temperature of 170±40 eV in a plasma produced by irradiating solid carbon disks with a pulsed CO2 laser producing peak power densities of ~5xl0 1 2 W/cm2. As a conservative estimate, considering the power densities of roughly one tenth of this value produced at grazing incidence on the wall of the cavity, and applying the scaling law of Caruso and Gratton [32], a value of 100 eV is obtained as an estimate for the electron temperature. The electron density will be taken to be one half of its critical value, n^ ~ 1019 cm - 3. As-suming Z=6, its value for the carbon ions, and applying the assumptions made above for resonant absorption, the approximate for the collision frequency given by Equation 2.27 becomes vei ~ 3xl0 1 2s _ 1. The fractional absorption is then 1.6 xlO - 5 for a linear density profile as given by Equation 2.25, and is 10 -3 for an exponential profile as given by Equation 2.26. Thus, even assuming several reflections through the plasma gradient, a transmission value of 80% is reasonable if the time while L < 10 //m is short, and the plasma expansion does not block the cavity early in the pulse. 6.3 Transmitted Beam Divergence The narrow divergence of the transmitted beam suggests some interesting characteristics about the dynamics of the plasma within the cavity. From simple considerations of gaussian beam optics, the damage radius of 1 mm at a distance of 7 cm indicates, making use of Equation 2.22, that diffraction limits the minimum radius of the cavity through Chapter 6. Discussion and Analysis of the Experimental Results 71 which the laser beam propagates to ~200 pm for much of the duration of the pulse. Even the 2 mm damage radius on the thermal paper for some of the better aligned shots suggests a minimum radius of more than 100 pm. This is especially surprising considering that according to Equation 2.20, the beam reflects at n e = nCTcos2Q, which may be considerably inside the bounds of the critical density surface for grazing incidence rays, unless the density gradient is very steep. Such self-steepening of the density profile in a CO2 laser produced plasma was observed by Fedosejevs et al. [22], and attributed to ponderomotive effects. Consideration must thus be given to the magnitude of the ponderomotive forces in this system. According to Equation 2.20, the beam is confined to an ever tightening region about the symmetry axis as the critical density boundary propagates inward. Assuming that the beam power is not significantly attenuated by absorption or deflection, the magnitude of the electric field of the beam must correspondingly increase. The energy density of the field is given by: **=2*-*L (6.1) 2 V ACT K ' where, U is the beam energy, A is the area through which the beam passes, and r is the length of the pulse. Thus, the electric field is inversely proportional to the radius of the critical boundary. For the system studied in this work, the values are approximately U = 2 J, and r = 2 ns. Using this estimate of the field strength, and the previously derived estimate of Chapter 6. Discussion and Analysis of the Experimental Results 72 the electron temperature, the quiver velocity of the electrons is equal to their thermal velocity when the beam is confined to a radius of ~ 100 fim.. This is an interesting value for the equality, as it corresponds to the beam width suggested by the beam divergence. As well, this region corresponds to the area of low absorption discussed in the previous section, thus allowing a large fraction of the beam to be transmitted. Thus the diagnostics appear to suggest that the ponderomotive force plays an important role in the development of the plasma once the beam is compressed to a diameter of about 100 fim. This force slows the expansion of the plasma, and steepens the density profile. The focusing properties of a medium with a convex refractive index such as this system exhibits are well known, as is discussed in the paper by McMullin et al. [24]. Such properties, however, assume that the profile remains constant along the length of the system. That such properties exist in a system that exhibits considerable variation along the axis, as is evident from the streak camera images is encouraging for the prospects of wave-guiding, and the focusing of x-ray beams produced by such a configuration. 6.4 Visible Light Emission along the Axis The relationship between the intensity distribution of the incident beam in the cavity, the absorption of that radiation, and subsequent radiation of light is by no means clear. Nevertheless, a first attempt at modeling the propagation of the beam through the plasma was made by assuming simple reflecting boundary conditions at the walls of the cavity, and performing a ray tracing simulation to determine the intensity of the beam on the walls as a function of length along the axis. The results of such a simulation are presented in Figure 6.1 for a 400±50 fim diameter cavity, along with a corresponding plot from a streak camera image of the intensity contours of experimentally measured visible light Chapter 6. Discussion and Analysis of the Experimental Results 73 1.10 ) H r-1 1 1 1 1 1 1 1 1 1 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 Distance along cavity (mm) A B Figure 6.14: Ray tracing simulation of incident beam intensity (A), and corresponding streak image of visible emission (B), for a 400±50 pvo. diameter cavity. emission as a function of distance along the cavity symmetry axis, as viewed along the time axis. A similar comparison is made for a 550±50 pm diameter cavity in Figure 6.2. Thus, at least to first order, this simulation provides some guidance to the dynamics involved. The parameters of this simulation are valid only for early times, once the plasma has formed, but before it has propagated radially significantly. The reason that these structures remain as the plasma expands is likely due to the fact that the plasma in these regions expands faster than in the surrounding regions at early times, producing axial Figure 6.15: Ray tracing simulation of incident beam intensity (A), and corresponding streak image of visible emission (B), for a 550±50 fim diameter cavity. Chapter 6. Discussion and Analysis of the Experimental Results 75 density gradients. These gradients reduce the angle between the propagation vector of the beam and the plasma density gradient, which enhances resonant absorption and in-verse bremmstrahlung, as discussed previously. Thus a growth mechanism is established, as this enhanced absorption will further increase the local plasma temperature, and is expansion rate. The peaks will continue to grow as long as the beam pulse propagates through the cavity. This simple model does not explain the emission peaks toward the back of the cavity in some shots, as shown in Figure 5.10, although the peak separation is similar. Such effects can not be explained simply as the result of tapering of the cavity, since peak intensity reversals are observed, as shown in Figure 5.9. One possible explanation suggests that the reduced ponderomotive forces at the back of the cavity, perhaps coupled with variations in the wall radius, can result in the plasma at the rear of the cavity expanding to the axis faster than the plasma at the front of the cavity, and thus stongly absorbing the laser beam. Such effects would require a two dimensional hydrocode calculation to simulate. The movement of the peaks at the ends of the cavity, as can be seen clearly in Figures 5.12 and 5.13 may be attributed to cooling effects through the ends, followed by hydrodynamic expansion. The next chapter, although brief, attempts to draw together the findings of this work, as well as to examine what remains to be studied.ae Chapter 7 Conclusions A CO2 laser system has been developed, which is able to produce pulses of up to 12 J with a FWHM of 2 ns at a wavelength of 10.6 / i m . This system was able to achieve intensities of « 1013 W/cm2 at the focus, using F/7 optics. The principal advantages of this system over previous systems were achieved in terms of reliability, and an improved contrast ratio for the pulse produced by a synchronized dual Pockels' cell configuration. A means of achieving a higher repetition rate, which does not seriously effect the efficiency, could be examined in the future. Both the amount of transmitted radiation, and the divergence of the transmitted beam suggest that ponderomotive forces, balancing the thermal expansion, play an important role in the development of the plasma. These forces need consideration in any schemes to use long wavelength drivers for x-ray lasers. It is possible that these effects, combined with the focusing effects of the resulting density profile, may be used to improve the beam characteristics of such a laser. Additional studies of the reflected radiation, as well as spectral resolution of the transmitted beam should be conducted. A growth mechanism was proposed for the development of regular peaks in the in-tensity of the emitted visible light. Anomalous maxima at the rear of the cavity were attributed in part to ponderomotive effects. Streak camera observations of the radial development, as well as extensions of the observations to the UV and x-ray regions are further suggestions. A two dimensional hydrocode simulation complementing the exper-imental results would help to examine the processes involved. 76 Chapter 7. Conclusions 77 Finally, as with magnetic confinement, it would appear that this technique is pushing its limits of non-destructive confinement of an x-ray lasing medium, as was shown by the damage to the target produced when the entire amplifier chain was fired. Bibliography [1] Gordon,J.P., Zeiger,H.J., and Townes,C.H., Phys. Rev. 99, 1264 (1955). [2] Gudzenko,L.L, Shelepin,L.A., Sov. Phys. Dokl. 10, 147 (1965). [3] Dewhurst,R.J., Jacoby,D., Pert,G.J. and Ramsden,S.A., Phys. Rev. Lett. 37, 1265 (1976). [4] Irons,F., and Peacock,N.J., J.Phys.B 7, 1109 (1974). [5] Jacoby,D., Pert, G.J., Ramsden,S.A., Shorrock,L.D., and Tallents,G.J., Opt. Com-mun. 37, 193 (1981). [6] Matthews,D.L., et al., Phys. Rev. Lett. 54 110 (1985). [7] Suckewer,S., et al., Phys. Rev. Lett. 55, 1753 (1985). [8] Lin,Z., et al., Opt. Commun. 65, 445 (1988). [9] Lin,Z., et al., Opt. Commun. 68, 418 (1988). [10] Muira,E., et al., Appl. Phys. Lett. 55, 223 (1989). [11] Daido,H., et al., J. Opt. Soc. Am. B 7, 266 (1990). [12] Vinogradov,A.V., Sobelman,I.L, and Yukov,E.A., Sov. J. Quant. Elect. 7, 32 (1977). [13] Rankin,R., et al., Phys. Rev. Lett. 63, 1597 (1989). [14] Kruer,W.L., in Laser Plasma. Interactions 4, ed. by Dr. M.B.Hooper (Scottish Uni-versities Summer School in Physics, 1989), p. 96. 78 Bibliography 79 [15] Cunningham,P.F., et al., Opt. Commun., 68, 412 (1988). [16] Weber,R., et al., Appl. Phys Lett., 53, 2596 (1988). [17] Stockl, O, "Erzeugung weicher Rontgenstrahlung in lasergeheizten Hohlzylindern" (in German), Max-Plank-Institute fur Quantenoptik, Report MPQ-139 (1989). [18] Duderstadt,J.J. and Moses,G.A., Inertial Confinement Fusion (John Wiley and Sons, Toronto, 1982), ch. 5. [19] Griem,H.R., Plasma Spectroscopy (McGraw-Hill Book Company, New York, 1964). [20] Schmalz,R.F. and Eidmann,K., Phys. Fluids, 29, 3483 (1986). [21] Schmalz,R.F., Phys. Fluids, 29, 1389 (1986). [22] Fesosejevs,R. et al., Phys. Rev Lett., 39, 932 (1977). [23] Kruer,W.L., Tie Physics of Laser-Plasma Interactions (Addison-Wesley Publishing Company, Don Mills, Ontario, 1988). [24] McMullin,J. et al., Comput. Phys. Commun. 47, 47 (1987). [25] Yariv,A., Quantum Electronics: 2nd Edition (John Wiley and Sons, Toronto, 1975). [26] Barnard,J.E., Ph.D. Thesis, University of British Columbia (1985). [27] Laberge,M., Ph.D. Thesis, University of British Columbia (1990). [28] Houtman,H., and Meyer,J., Opt. Lett., 12 87 (1987). [29] Liese,W., U.B.C. Plasma Physics Report #101 (unpublished), (1984). [30] Houtman,H., and Walsh,C.J., U.B.C. Plasma Physics Report #79 (unpublished) (1982). Bibliography [31] Baldis,H.A., Samson,J.C. and Corkum,P.B., Phys.Rev.Lett., 41, 1719 (1978). [32] Caruso,A. and Gratton,R., Plasma Physics, 10, 867 (1968). 

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