SHORT-SCALELENGTH PLASMA SPECTROSCOPY By Andrew Forsman B.Sc.fl, Acadia University, 1988 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 November 1992 © Andrew Forsman, 1992 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 of Physics The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: 1 4c /° /7r2. Abstract Traditional x-ray plasma spectroscopy techniques employ long scalelength laser-produced plasmas in an attempt to moderate the density and temperature gradients present in the ablation plasma. These approaches have the disadvantages that the large plasma may lead to significant opacity effects, lasers having substantial power must be used and numerical simulations of the laser-produced plasma frequently must be used to interpret the data. As an alternative technique the use of short-scalelength plasmas as sources for x-ray spectroscopy have been investigated. High-resolution silicon K-shell spectra from a short-scalelength, laser-produced plasma have been obtained in temporally and spatially integrated measurements. Density-sensitive line-intensity ratios of the helium like satellites and that of the lithium-like satellites are employed simultaneously with temperature-sensitive line-intensity ratios between the helium and lithium-like satellites to assess their diagnostic value. A constant, uniform plasma model is used to interpret the data. It appears that the emission of dielectronic satellite lines is dominated by a region with a relatively well-defined density and temperature in the ablation zone. II Table of Contents Abstract II List of Tables V List of Figures Vi Acknowledgement ix 1 2 Introduction 1 1.1 Laser-produced plasmas 1 1.2 X-ray spectroscopy 3 1.3 Present work 8 1.4 Thesis organization Background Theory for K—Shell Spectroscopy 2.1 General approach 2.2 RATION 2.3 3 10 2.2.1 Rate equations and opacity 2.2.2 Atomic levels 2.2.3 Rate coefficients 11 Results of RATION Experiment 52 3.1 52 The laser facility in 3.2 Irradiation parameters 54 3.3 x-ray spectrometers 63 3.4 Processing of data 65 3.5 Dynamic range of the spectroscopic measurement 75 4 Results and Discussions 5 77 4.1 Experimental results 77 4.2 Discussion 98 Conclusions 107 5.1 Summary of present work 107 5.2 New Contributions 108 5.3 Future work 108 Bibliography 110 iv List of Tables 2.1 Useful notation 3.1 Plasma size estimates and laser intensities 62 3.2 Calibration lines 67 4.1 Measured line-intensity ratios 90 . V 22 List of Figures 1.1 Qualitative picture of a laser-heated solid 1.2 Spatial profiles of temperature and density 5 1.3 Micro-dot technique 7 2.1 First level diagram for lithium—like satellites 2.2 Second level diagram for lithium—like satellites 2.3 Third level diagram for lithium—like satellites 2.4 First level diagram for helium—like satellites 2.5 Second level diagram for helium—like satellites 2.6 Third level diagram for helium—like satellites 2.7 Fourth level diagram for helium—like satellites 2.8 abcd/jkl line ratio assuming a plasma length of 10 pm 2.9 qr/jkl line ratio assuming a plasma length of 10 tm 2.10 #1 — 2 . 21 . 36 . 37 9/#l2 line ratio assuming a plasma length of 10 um 38 2.11 1O/jkl line ratio assuming a plasma length of 10 tm 2.12 12/jkl line ratio assuming a plasma length of 10 pm 39 . 40 . 2.13 Opacity for the abed lines assuming a plasma length of 10 1 um 2.14 Opacity for the qr lines assuming a plasma length of 10 tim. 2.15 Opacity for the jkl lines assuming a plasma length of 10 m 2.16 Opacity for the #1 2.17 Opacity for the #4 — — 3 lines assuming a plasma length of 10 tm 44 9 lines assuming a plasma length of 10 1 um 45 2.18 Opacity for the #10 line assuming a plasma length of 10 m vi . 46 2.19 Opacity for the #12 line assuming a plasma length of 10 pm 47 2.20 Opacity for the Lya line assuming a plasma length of 10 pm 48 2.21 Opacity for the Ly line assuming a plasma length of 10 pm 49 2.22 Opacity for the Hea line assuming a plasma length of 10 pm 50 2.23 Opacity for the He, 3 line assuming a plasma length of 10 pm 51 3.1 Laser facility 53 3.2 Typical laser pulse 55 3.3 Lens focussing arrangement 3.4 Pictures of best focus 58 3.5 Pinhole photograph arrangement 59 3.6 X-ray pinhole photograph 60 3.7 Microdensitometer scan of a pinhole photograph 61 3.8 Spectrometer arrangement 64 3.9 Film cassette 66 . . 56 . 3.10 Microdensitometer performance test 69 3.11 Spectrometer geometry 71 3.12 Film calibration 73 3.13 Dispersion 74 3.14 Background 76 4.1 Some prints of raw data 78 4.2 2 Lya and Hea satellite spectrum, 1.1 x iO’ W/cm 4.3 High order resonance line spectrum, 1.1 x 1015 W/cm 2 4.4 2 Lyc and Hecy satellite spectrum, 4.4 x iO’ W/cm 4.5 High order resonance line spectrum, 4.4 x 1014 W/cm 2 4.6 Lithium—like satellites, 1.1 x l0’ W/cm 2 vii . . . 79 . 80 . . 81 82 84 4.7 Helium—like satellites, 1.1 x 1015 W/cm 2 85 4.8 Lithium—like satellites, 4.4 x iO’ W/cm 2 86 4.9 Helium—like satellites, 4.4 x iO’ W/cm 2 87 4.10 High order lithium—like satellites, 1.1 x 1015 W/cm 2 88 4.11 Density—temperature plot, 1 1 um plasma, 1.1 x 1015 W/cm 2 91 4.12 Density—temperature plot, 10 um plasma, 1.1 x 1015 W/cm 2 92 4.13 Density—temperature plot, 50 m plasma, 1.1 x 1015 W/cm 2 93 4.14 Density—temperature plot, 1 tm plasma, 4.4 x 1014 W/cm 2 94 4.15 Density—temperature plot, 10 im plasma 4.4 x 1014 W/cm 2 95 4.16 Density—temperature plot, 50 1 um plasma, 4.4 x 1014 W/cm 2 96 4.17 Density and temperature results 97 4.18 Opacity and data for a 1 m plasma, 1.1 x 1015 W/cm 2 101 4.19 Opacity and data for a 10 m plasma, 1.1 x 1015 W/cm 2 102 4.20 Opacity and data for a 50 tm plasma, 1.1 x iO’ W/cm 2 103 4.21 Opacity and data for a 1 im plasma, 4.4 x 1014 W/cm 2 104 4.22 Opacity and data for a 10 ,um plasma, 4.4 x i0’ W/cm 2 105 4.23 Opacity and data for a 50 m plasma, 4.4 x iO’ W/cm 2 106 Viii Acknowledgement I would like to thank my research supervisor, Dr. A. Ng, for providing an excellent laser facility and for the many discussions relating to lasers, plasmas, and x-ray spectroscopy. Also, I thank R. W. Lee for his contribution to our calculations involving laser-produced plasmas. Alan Cheuck performed great services in ensuring that equipment worked and that supplies were available. I also thank Guang Xu for his help in operating the experiment and Peter Celliers for his assistance in operating the laser. I thank my family for their moral support and my friends for their company. The financial assistance of the Natural Sciences and Engineering Research Council is appre ciated. ix Chapter 1 Introduction 1.1 Laser-produced plasmas The use of lasers as a tool to study matter under extreme coilditions of temperature and pressure began very shortly after the invention of the laser in 1960. Laser-produced plasmas offer a wide range of temerature and pressure conditions and have been found to be useful for laboratory research of exotic states of matter not readily accessable in the laboratory. In addition to providing fundamental understanding in plasma physics, research involving laser-produced plasmas has found applications in many fields, including atomic physics, astrophysics and astronomy, ultrahigh pressure shock waves, inertial confinement fusion, x-ray lasers and x-ray lithography. A more detailed description of the use of laser-produced plasmas has been given by Hora . Although plasmas can be 1 produced using gas targets , we will focus our discussion on plasmas produced by the 2 interaction of intense laser light with a solid only. Figure 1.1 shows a qualitative picture of a laser-heated solid. Such experiments are done in vacuum since the laser light is intense enough to ionize and form a plasma from any background gas in front of the target, blocking the laser beam. A target chamber pressure of less than 100 mTorr is generally sufficient to allow the entire laser beam to reach the target. The laser light is initially absorbed within a skin depth on the surface of the target. The surface material is rapidly evaporated and ionized. The resulting free electrons gain energy from the laser field and transfer it to the ions through collisions , 3 1 Chapter 1. Introduction Figure 1.1: Qualitative picture of a laser-heated solid. 2 Chapter 1. Introduction 3 thus forming a high temperature, low density plasma called the coronal plasma. The laser light will penetrate through the coronal plasma until it encounters the critical den sity layer. Here, the electron density yields a plasma frequency equal to that of the laser frequency and the laser light is reflected. Electron thermal conduction and radiation transport carry the absorbed laser energy from the underdense plasma inward, effecting ablation of the target material up to the ablation front beyond which the heat flux is no longer sufficient to cause ablation. The ablated material flows outwards from the ablation front as a hot dense plasma, becoming more rarefied as it expands through the coronal plasma into the vacuum. The expansion velocity of this plasma readily exceeds iO cm/s. The momentum of the outflow drives a strong shock wave into the target, producing a highly compressed material. Accordingly, the states of matter attainable in the interac tion of intense laser light with solid ranges from the extremely dense (greatly exceeding normal solid densities) but relatively cold shock-compressed material to a highly ionized coronal plasma no denser than a candle flame but having temperatures of millions of degrees. 1.2 X-ray spectroscopy The foregoing description presents a simplified view of the physical processes involved in the interaction of intense laser light with a solid. Some of these processes are not well understood on a quantitative level, for example, ionization balance and radiative opacities in the dense ablation plasma and thermal transport across the very steep temperature gradient in the ablation zone. In order to test the many physics models describing such processes, the first requirement would be to characterize the plasma conditions with regard to electron density and temperature. For such hot, dense plasmas, x-ray spectroscopy appears to be the only viable means. Generally, temperature and density Chapter 1. Introduction 4 diagnostics using x-rays employ the measurements of emission or absorption spectra, or continuum emission. A comprehensive review of the subject has been given by Michelis and Mattioli 4 and D. J. Nagel . Of specific interest is the use of line-intensity ratios as plasma diagilostics. 5 The basis of using line-intensity ratios to infer the temperature and density of a plasma is that line intensities reflect the population of atomic levels. This in turn reflects the rates of various atomic processes which depend on the temperature and density of the plasma. Generally, temperature diagnostics are obtained from line-intensity ratios governed by the population of different ionizatioll stages, which are much less sensitive to density. On the other hand, density diagnostics are obtained from line-intensity ratios which are determined by collisional population and depletion of atomic levels of the same ionization stage, which are only weakly dependent on temperature. Although x-ray spectroscopy represents a very powerfull diagnostic technique and is widely applied, there is an inherent difficulty in its use in the study of laser-produced plasmas. This is the line of sight integration from a non-uniform source. Figure 1.2 shows a typical snap-shot of the spatial profiles of temperature and density of a laser-produced plasma. The measured intensity of any x-ray spectral line would include emissions from plasma regions with different temperatures and densities. Even if the lille emission were localized to a dominant plasma region, its observation through an inhomogeneous plasma will be influenced by the convolution of plasma opacities at various temperatures and densities. In general, the interpretation of line-intensity ratios cannot rely simply on calculations assuming a uniform plasma which is either optically thick or optically thin . 7 It would require detailed information of the plasma hydrodynamics as well as radiative properties such as emissivity and opacity. This renders x-ray spectroscopy dependent not only on atomic physics models but also on models governing laser-plasma coupling as well as thermal and radiative energy transport. For high-irradiance experiments, the 5 Chapter 1. Introduction A —D--— ne Te 24 I p 23 1 22 10 1 io21 i o2 400 1000 2000 PLASMA COORDINATE (nm) Figure 1.2: Spatial profiles of temperature and density in numerical simulation of a laser-produced plasma, with the laser incident from the right. The simulation was per code to model the plasma produced formed by using a one-dimensional hydrodynamic 6 by illuminating a silicon target with a laser pulse having a peak intensity of 1.1 x 1O’ W/crn and having a Gaussian time-dependence with a 2.5 ns full-width half-maximum 2 duration. The density and temperature profiles shown occur at the peak of the laser pulse. Chapter 1. Introduction 6 accuracy of hydrodynamic simulations may be limited by the ability to model non-local thermal conduction across the steep temperature and density gradients 8 existing in the ablation zone, parametric instabilities , hot-electron transport’° and radiation transport processes”. To mitigate this problem, several techniques have been developed. The buried layer technique was first demonstrated by Ilyukhin 12 and co-workers in 1981. Using a com posite target with a thin layer of the sample material embedded in a substrate, the axial expansion of the plasma produced from the sample layer was inertially tamped by the plasma produced from the substrate material. This yielded a localized and nearly uni form plasma source in the direction of the laser axis. The opacity effect of the substrate material was kept to a minimum by using a low-Z material. Such an inertial confinement of the buried layer plasma has also led to plasmas with higher densities’ . On the other 3 hand, the micro-dot technique’ 4 was used to reduce lateral gradients in the plasma. This is illustrated in Figure 1.3. A small dot of the sample material is deposited on top of a planar substrate. This composite target is irradiated with a laser spot much larger than the dot. By using a sufficiently large area for the laser illumination, the expansion of the laser-produced plasma can be kept approximately 1-dimensional along the laser axis during the laser pulse. The inertial confinement of the plasma produced from the micro-dot material by the plasma produced from the substrate material then significantly reduces its lateral gradients so that a nearly uniform plasma can be observed in a direc tion perpendicular to that of the axial plasma flow. The target substrate is usually a low-Z material such as a hydrocarbon plastic to limit the x-ray opacity of the resulting plasma. The extension of these two techniques to the use of a buried tracer 5 dot’ has then led to the localization of a nearly uniform plasma source in both the axial and the lateral directions of the plasma flow. Coupled with temporally and spatially resolved measurements, this yields the most well-defined x-ray spectroscopic diagnostic. 7 Chapter 1. Introduction LASER PLASMA FLOW I I I I I I I I I I I I I I I ‘ ‘ I I I I I I ‘ I I I I I I SAMPLE SUBSTRATE a Figure 1.3: Illustration of the micro-dot technique, with indications of the outward plasm flow from the sample and from the substrate. Chapter 1. Introduction 8 The preceeding techniques developed to overcome the difficulties caused by temper ature and density gradients in laser-produced plasmas have also led to some stringent experimental requirements. The application of the buried-layer technique requires both uniform illuminatioll of the target and a uniform target surface. Any non-uniformities may seed the Rayleigh-Taylor instability’ 6 growth of perturbations at the interface be tween the sample and substrate materials, which can lead to mixing of the two layers. Alternatively, one may use very short-pulse laser irradiation to limit the growth of the hydrodynamic instability. Micro-dot targets and buried tracer dot targets are difficult to fabricate. The relatively large area of illumination needed also requires the use of lasers with substantial power to obtain sufficiently high irradiances (above iO’ W/cm ) for pro 2 ducing a hot plasma. This requirement of a high power laser becomes even more stringent in temporally and spatially resolved measurements, especially for the study of relatively weak spectral lines such as inner-shell dielectronic satellites which have been widely used for electron density and temperature measurements in laser-produced plasmas 1.3 13,17—23 Present work The primary objective of the present work is to demonstrate the viability of a novel, alternative concept of using a plasma with extremely short gradient scalelengths as a source for x-ray spectroscopy, in particular, for the study of the K-shell dielectronic spectra in spatially and temporally integrated measurements. This is the direct opposite of using a uniform plasma source. If proven successfull, this concept offers a much simpler means of accessing a well-defined plasma source which can be used to test atomic physics and x-ray spectroscopic models for hot, dense plasmas. A short-scalelength, laser-produced plasma is formed when a laser beam is tightly focussed onto a solid target such that the diameter of the laser focal spot is much less Chapter 1. Introduction than the product CSTI 9 where c 5 is the sound speed of the resulting plasma and Tj is the laser pulse duration. The expansion of such a plasma becomes strongly spherical and the scalelength of the laser-heated, underdense corona will be limited to the order of the laser spot diameter at all times. Evidently, lateral thermal energy transport dominates in such a plasma, which sets the ultimate scalelength. This yields a very short-scalelength underdense plasma region, thereby allowing the observation of K-shell spectral lines from a higher density region by substantially reducing the emissivity and opacity of the intervening plasma. In the higher density ablation zone, the plasma density gradient is governed by radiative and thermal energy transport processes as well as the hydrodynamics of plasma expansion. In this ablating plasma, the emissivity of K-shell dielectronic satellites would increase along the density gradient because of the increased populations of the upper levels with increased density. On the other hand, as the plasma density increases its temperature decreases resulting in a decrease of the helium-like and lithium-like ionization states. The overall effect then leads to a localized emitting region for the K-shell dielectronic satellite lines, negating the deleterious effects of a nonuniform plasma. With a sufficiently small laser focal spot, the expansion of the plasma can be made to become strongly diverging near the onset of irradiation. Spatial localization of the emission of the K-shell dielectronic satellites from the ablation zone in the plasma thus persists almost throughout the entire duration of the laser pulse. Undoubtedly, the density and temperature of the localized emitting region will vary with time because of the temporal variation in the laser intensity. However, dominant emission is expected to appear at the time of peak laser intensity when maximum heating of the ablation plasma occurs. This leads to temporal localization of the satellite emissions to within the high intensity portioll of the laser pulse during which a steady-state ablation (and hence a steady-state plasma gradient) is maintained. It is the combined effect of these spatial Chapter 1. Introduction 10 and temporal localizations of the emissioll that may render it possible to perform plasma diagnostics based on spatially and temporally integrated spectroscopic measurements. To demonstrate the viability of this alternative concept, we examine spatially and tem porally integrated K-shell spectra obtained from very short-scalelength, laser-produced silicon plasmas. A new approach is also used in the diagnostic interpretation. On the elec tron density-temperature plane, contours derived from the density-sensitive line-intensity ratios are compared with those derived from temperature-sensitive line-intensity ratios. The derivation assumes a uniform aild constant plasma source. If the emission of the spectral lines is sufficiently localized in space and time for such a short-scalelength plasma, all of these contours will intersect at one point on the density-temperature plane, which then yields the diagnostic result. It should also be iloted that this approach overcomes the usual difficulty that an individual line-intensity ratio cannot provide a unique deter mination of the plasma density and temperature. 1.4 Thesis organization In Chapter 2, a brief description of the RATION 24 code is presented. RATION is a steady state, collisional-radiative 25 atomic physics model used for the calculation of level populations and x-ray emission spectra for a uniform plasma. Details of the experiment are given in Chapter 3. The data together with discussions are presented in Chapter 4. Concluding remarks are givell in the final Chapter. Chapter 2 Background Theory for K—Shell Spectroscopy 2.1 General approach The most important aspects to modelling a laser-produced plasma are the laser-plasma interaction, the hydrodynamic plasma flow, energy transport mechanisms including ra diative energy transport, and the prediction of ionizations and atomic level populations. A complete plasma simulation would incorporate all these aspects. As was mentioned in the first Chapter, one of the goals of the present work is to establish a plasma diag nostic which is independant of hydrodynamic, thermal and radiative energy transport models. This is done by assuming that the region of the plasma which dominates the x-ray emission may be approximated by a constant, uniform plasma and that in the short-scalelength plasma the corona will not be thick enough to significantly affect the x-ray emission from the ablation plasma. Consequently, we are concerned only with cal culating the atomic level populations, and their corresponding emissivities and opacities, for a constant plasma of a given size, temperature, density and composition. There are three traditional approaches to predicting atomic level populations in dense, highly ionized plasmas. The first model is known as the coronal-radiative (CR) 26 and is based on the assumption that ionization and excitation of atomic states model are due primarily to collisions with free electrons, and that electronic recombination and depletion of atomic states are due primarily to spontaneous radiative decay. However, for the plasmas of interest to the present work the temperature is approximately five 11 Chapter 2. Background Theory for K—Shell Spectroscopy 12 million degrees and the electron density is approximately 1022 cm . Previous work 3 has 27 shown that electronic recombination and depletioll of atomic states are strongly affected by collisional transitions as well as radiative transitions and hence the CR model cannot be applied to plasmas with such high densities. The second traditional approach is to assume that the plasma is in local thermody . At sufficiently high densities, collisional processes dominate. 26 namic equilibrium(LTE) As a consequence, each process is accompanied by its inverse which occurs at an equal rate by the principle of detailed balance. For a Maxwellian distribution of free electrons the ionization balance may be predicted through application of the Saha-Boltzmann equation and the atomic level populations may be predicted using the Boltzmann equation . The 26 requirement that collisional processes dominate imposes a lower bound on the electron density. Equation 2.1 is a necessary but not sufficient condition that the free electron 28 in order to apply the local thermodynamic equilibrium (LTE) density must satisfy model: e where x(i k) > 3 (j,k) 12 1.8 x 10’ T’ [cm ] 3 , (2.1) in eV is the largest transition energy available in the system being consid ered, and Te in eV is the plasma temperature. In order to satisfy the criterion of equation 2.1 the the electron density must be greater than 1024 cm 3 and hence an LTE model cannot be applied to our plasma. The third approach is the collisional-radiative equilibrium (CRE) model. Unlike the CR and LTE models, which are based on the assumptions that either radiative or col lisional processes are dominant, CRE models do not assume that either collisional or radiative processes may be neglected. Application of a CRE model involves determin ing the transition rates due to all significant radiative and collisional processes and then using them to formulate a set of rate equations. Section 2.2 contains a more detailed Chapter 2. Background Theory for K—Shell Speciroscopy 13 description of the rate equations. As was previously mentioned, interpretation of data in the current work assumes that a uniform, steady-state plasma model may be used to infer temperatures and densities from the data. For a laser-produced plasma the minimum 29 time required for the atomic level populations of the plasma to reach steady-state is estimated to be 1012 [s] where Tie fl (2.2) 3 is the electron density of the plasma. For the ablation plasma which cm we expect to dominate x-ray emission, is approximately 40 ps. Since the plasma is produced by a nanosecond laser pulse, the plasma will evolve on time scales that are far longer than t. Thus, the CRE model which takes into account both collisional and radiative atomic transitions is the most appropriate technique available to predict the atomic level populations in such plasmas. However, the CRE model suffers from a drawback in that extensive data on atomic transition rates is required in the rate equations. Since there are many atomic states, ionization stages and transitions available, a large volume of atomic data is required. Two general assumptions are frequently made in order to facilitate the modelling process. The first assumption is that the free electrons are in LTE with each other and therefore may be described by a Maxwellian velocity distribution. This assumption is a consequence of the large cross-section for electron-electron collisions and is valid when the electron temperature is sufficiently low 28 (Te < 20 KeV) so that Bremsstrahlung is not significant. The second assumption is the principle of detailed balance which states that a process changes the population of an atomic state at the same rate as an inverse process restores the population of the same atomic state. The atomic states must be coupled by a collisional process with, in our case, an electron population with a Maxwellian velocity distribution. In this way it is possible for two or more atomic states of ions in a plasma Chapter 2. Background Theory for K—Shell Spectroscopy 14 to be in LTE with each other while the entire plasma is not in LTE. Ideally, the CRE calcnlation will inclnde all atomic levels and transitions. Unfor tunately, such a set of rate equations wonld be unwieldy, even if all the atomic data necessary to construct the rate equations could be found or calculated. However, the problem is made tractable by including only those transitions that have a significant effect on the plasma of interest and those transitions that have a direct bearing on the x-ray lines to be considered. The x-ray lines which serve as our plasma diagnostics are the satellite lines on the long-wavelength side of the hydrogen-like and the helium-like 2 p — ls resonance lines. The characteristically low opacity of the satellite lines and the sensitivity to density of the populations of the doubly excited levels which give rise to the satellite lines render them attractive as density and temperature diagnostics. The density sensitivity of the doubly excited states arises since the doubly excited states are strongly populated and depleted through collisionally induced transitions. Collisionally induced transitions between singly and doubly excited atomic states and between two doubly excited atomic states have been studied for use as density and temperature diagnostics for many . 21 18 years 3 ’ 7 0 The CRE model used in the present work includes detailed atomic data for the transitions and levels shown in figures 2.12.7. Figures 2.1—2.3 show schematic diagrams for the atomic level system of the lithium—like satellites of the Hec, resonance line with indications of the significant atomic transitions. Figures 2.4—2.7 are a similar set of figures for the helium—like satellites of the Lya resonance line. Table 2.1 lists the x-ray lines and their transition states. In the present work, the computer code used to perform the CRE calculation and to calculate the line-intensity ratios and opacities was written by R.W. Lee et al. and is known as RATION . The RATION code was chosen since it is fast, accurate and has 24 been widely used for the analysis of K-shell spectra from laser-produced plasmas . 3236 15 Chapter 2. Background Theory for K—Shell Spectroscopy S 2 ls2r? 1 s2p2s(3P) i’ sIt’ 2 1 s2p P 22 p ls2p2s(1P) 2 I S 22 1s2s mn q r’ I 1 I I I — — Li T 1 j k 1 a’bcd I I I D 22 1s2p I I I I I — ........ I I I — , 1s22p F 2 2 2s is S 2 Figure 2.1: Atomic level diagram for the lithium—like satellites of the He resonance line, with indications of radiative transitions. 16 Chapter 2. Background Theory for K—Shell Spectroscopy 1 s2p S 2 1 2 1s2p2s(3P) P 22 1s2p D 22 1s2p f 2 1s2p2s(1P) S,” 22 1s2s ____—.c•_—__ I — I I F I I , / I il I 1, 11, Ii I, _ ( I I I I I I I I I I I I I I %% .,‘ S. ‘ I \ I I ‘I ‘I ‘I I S I I I I F 2 1S22p 2 2s is S 2 Figure 2.2: Atomic level diagram for the lithium—like satellites of the HCa resonance line,with indications of collisionally induced transitions between singly and doubly excited states. All upper levels are subject to autoionization. 17 Chapter 2. Background Theory for K—Shell Spectroscopy S 22 is2p , \ I 1 s2p2s(3P) P 2 P 2 is2? 1% 1 1 \‘\1s2p2s(1P)2p I ) I’ \ 0 ‘. ‘ ‘%%__. \ .._.- ‘ ,.. S 22 1s2s ‘‘ •% .. % N ‘ ...‘ / / I I I, j / // / I I —- — ‘ ——-s—— , •.%\•. —. .—--—..-——— % \ -.-. _/ / / / i D 22 1s2p I I I — , — - _// ...—‘ / — , — , _ / / , —, / / —— —.- p 1s 2 2 2 S 2 2 2s is Figure 2.3: Atomic level diagram for the lithium—like satellites of the Hea resonance line, with indications of collisionaly induced transitions between doubly excited states. -t- I-” o Co O I. 0 I- C) —. CD - (I) ci) U) (13 - N) -o (14 -o N) CI3 • •—.t, -D U) (0 cc 0) c_,4 — (J N) - o -o --0 ) 1) (.14 - -D 1’) 0 1%) N) 00 I is 19 Chapter 2. Background Theory for K—Shell Spectroscopy 2 2p 1 ls2p ‘F P 3 ls2p 1 S 3 1s2s ls2s Figure 2.5: Atomic level diagram for the helium—like satellites of the Ly resonance line, with indications of collisionally induced transitions between singly and doubly excited states. All upper levels are subject to autoionization. 20 Chapter 2. Background Theory for K—Shell Spectroscopy So 21 2p 2 D 21 2p I // / / / — _..—— / —— 1 —— P 3 2s2p 2s2p P I I I — I I I I / / / / / / / I, — ——i. / 1 I. I!, I, ———— — — — / 2s21So I —— % — , I I / / I ,,/ 1/ I, j/ I I \ -..—— / / I, — — — 11% A’ I 2p? —— ——————.—— / — — / — .% •%_/ / r Ill / / / / / ‘ / / ‘ ‘S / / / / F 1 1s2p II P 3 ls2p II ‘ ‘ ‘I ‘4 1 S 3 1s2s 0 ls2s ‘S Figure 2.6: Atomic level diagram for the helium—like satellites of the Lya resonance line, with indications of collisionaly induced transitions between singly and doubly excited states. All upper levels are subject to autoionization. 21 Chapter 2. Background Theory for K—Shell Spectroscopy 2 2p 2D2 ‘I If 11 I ‘ / — \ 1 2s2 p P\ ,l S. _ I 1 _/ —— —— / / // S.—. — ?<... —— —— .— S. ———————— — 1 S. S. P 3 2s2p ‘‘ 55- —— S. —— ‘ __._/ — ——— — / / IS. —— —— — ———— ———— — P ls2p 1 P 3 ls2p 1 S 3 1s2s ls2s ‘S 0 Figure 2.7: Atomic level diagram for the helium—like satellites of the Lya resonance line, with indications of collisionaly induced transitions between doubly excited states. Chapter 2. Background Theory for K—Shell Spectroscopy shorthand notation Lya Ly 7 Ly 5 Ly Ly Hec. 3 He He 5 He #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 ii #12 #13 abcd qr jkl spectroscopic notation p 2 is— is—3p is—4p is—Sp is—6p 1s2 ls2p 1s2 ls3p 1s2 ls4p 2 1s lsSp 1s2s 35 22 p3 0 P ls2s S1 2s2p 3 1 P ls2s 3 2 P 1 2s2p 3 S ls2p 3 1 2p P 23 0 P ls2p 3 0 2p P 23 1 P ls2p 3 1 2p P 23 1 P ls2p 3 2 2p P 23 1 P is2p 3 1 2p P 23 2 P ls2p 3 2 2p P 23 2 P Pi 1 ls2s’So—2s2p Pi—2s 1 ls2p So 21 —2p 1 ls2p’P 2 D 21 is2p 1 P 2p 2 ‘So 2 1s P 2 P 22 o—1s2p p 2 1s 5 0 F 2 —ls2p2s(’P) s 2 1s P 2 D 22 o—is2p p — — 22 RATION notation ls—2p ls—3p ls—4p ls—5p ls—6p 1s2 ls2p 2 1s p 3 ls — — — 1s2 — — 1s2 — — — — — — — — — — — he2st 2s2p3p he2st 2s2p3p he2st 2s2p3p he2pt 2p2p3p he2pt 2p2p3p he2pt 2p2p3p he2pt 2p2p3p he2pt 2p2p3p he2pt 2p2p3p he2ss—2s2pip he2ps—2s2sis he2ps—2p2pld he2ps 2p2pis li2p—abcd li2s—qr li2p—jkl — — — — — — — — — — Table 2.1: Notations used in this thesis and in RATION. abcd is actually four lines of a multiplet dominated by a and d, which are not resolved in this experiment. qr and jkl are also muitipiets which are not fully resolved, and hence the detailed spectroscopic information has been omitted. Note that RATION groups the lines #1 3, #4 9, abed, jkl and qr into single lines. The transitions given here are only some of the lines in RATION. — — Chapter 2. Background Theory for K—Shell Spectroscopy 23 RATION is based on a steady-state collisional-radiative equilibrium model which includes all ionization stages from the fully stripped ion to the neutral atom. The following section is a detailed discussion of RATION, which largely follows the the discussion given by R. W. Lee in the users’ manual for RATION. 2.2 RATION 2.2.1 Rate equations aild opacity The rate equations are written as follows: ji—1 m j=1 j=i+1 Rrij, ji where R, is the transition rate from state i to state j, (2.3) n is the number density of the state i, and the available atomic states are numbered 1—rn. For the steady state solution, are all set to zero and the additional constraint of charge conservation is invoked to close the system of rate equations. The rate coefficient R 3 may be subdivided into rate coefficients for collisional processes, rate coefficients for radiative processes, and rate coefficients for autoionization. Opacity effects will change some of the rate coefficients since some line radiation will be re-absorbed inside the plasma. Therefore, the rate coefficients depend on the populations of the atomic levels. The atomic level populations are determined by solving the rate equations. Consequently the rate equations are no longer linear and must be solved iteratively. The rate equations are initially solved in the optically thin limit, that is assuming that opacity will not affect the rate coefficients. The initial solutions of the rate equations for the atomic state populations are then used to modify the rate coefficients to account for opacity and the rate equations are solved again for a new set of atomic state populations. This iterative process continues until the atomic state Chapter 2. Background Theory for K—Shell Spectroscopy 24 populations converge. An atomic state which strongly contributes to the opacity of the plasma could be significantly ionized, but in a highly ionized plasma the ionization of a single ion stage does not significantly raise the number of free electrons. Consequently this iterative process will change the calculated ion populations without substantially changing the electron density and thus the iterations converge rapidly. The effects of opacity are included in the calculation by writing the radiative rate coefficients so that the effects of all processes to depopulate a level are summed into one term known as an escape factor (2.4) where is the total radiative rate for a transition from level i to level j and is the escape factor. More explicitly, X.j where and n(A + B7) (2.5) — are the Einstein spontaneous emission and stimulated absorption coefficients, respectively, 6.67 x iO’ gj —fjj = g:J = where fj 4 e 2 mchv is the oscillator strength and = [s —1 1’ [s’], (2.6) (2.7) is a Planckian field: f J(v)(v) dv. (2.8) qS is a Doppler line profile given as a function of the frequency z and J(v) is J(v) 3 1 2hv = C2 h’ CkT (2.9) Chapter 2. Background Theory for K—Shell Spectroscopy 25 The use of a Planckian radiation field is an approximation and not an assertion that the radiation field obeys local thermodynamic equilibrium. The optical depth of a line is proportional to the plasma size and an arbitrary plasma length L is used in the calculation of the optical depth T, TI, = re 2 n—fjLc(v). mc (2.10) The escape factor defined by equations 2.4 and 2.5 is 38 A A where 0 T 1 = ’../7r 0 T = if 0 lilT 3 7 e_Tl’1. if 0 T 0 r 2.5 <2.5 (2.11) (2.12) is the line center optical depth. Accordingly, the emitted line radiation intensity due to a transition from state i to state j is I where 2.2.2 = njEjA A (2.13) is the energy of the transition. Atomic levels This section lists the atomic levels considered in the calculation. RATION focusses on primarily the calculation of emission from highly ionized atomic states. Therefore, ion stages with more than three bound electrons are not dealt with in detail. Ion stages from beryllium-like to neutral are represented only by their ground states with the ionization potentials determined by Kelly and Palumbo 39 and the statistical weights given by the 46 g relation = 2J + 1. Lithium-like ionization stages are considered in more detail for lower n than for higher n, where n is the principal quantum number. Averaged hydrogenic levels 46 are used to ’ 40 calculate ionization potentials for m between 6 and 10. Screening effects are included . 41 Chapter 2. Background Theory for K—Shell Spectroscopy 26 Energies for the 5s and the 5p levels are taken from a calculation based on perturbation theory which includes relativistic and screening effects . Energy levels for the 5d, 5f 42 and 5g levels are taken from formulae due to Edlen . 40 The lower, singly excited, detailed energy levels are calculated with semi-empirical 43 which are derived from interpolations of various available predicted and ob formulae served data. All the data in the literature, most of it calculated, describes many of the detailed states as doublets. In RATION these doublets are averaged to provide a single energy of an averaged state. There is a group of doubly excited states which are significant because radiative transitions from these states give rise to the satellite lines which are very useful as density and temperature diagnostics due to their low opacity. The opacity of satellite lines tends to be low since the satellite lines have an excited lower state and hence the resonance absorption of the satellite lines is low. The lithium-like autoionizing states included in RATION are 1s2 22 P, ls2p( P)2s 2 3 P, 2 1s2p D S, ls2p(’P)2s 2 2P 2, and 1s2p 2, 1s2p 2 23 The energy levels were calculated through the use of Hartree-Fock theory, with the basis states calculated by LS 19 coupling 4 ’ 4 for the upper and lower levels of the satellite lines and for the helium-like resonance line. The helium-like resonance transition energy would then be scaled to match observed data and the satellite lines would receive a corre sponding shift. Therefore’ , systematic errors due to relativistic effects in the calculation, 9 among other things, would cancel out because the calculation is of differences among a set of closely spaced transitions. In the following discussion of helium-like atomic level energies the notation follows that used in RATION, as given in table 2.1. Energies for the he2pt and the he2ps levels were taken from work by Scofield . The energy level of the he2ss state was calculated 45 by Clark 47 and the energy level of the he2st state was calculated by Vainshtein and . Energies for the helium-like states where n > 2 were derived from Scofield 42 Safronova 45 Chapter 2. Background Theory for K—Shell Spectroscopy 27 by lumping all the states for each n into the n 1 p state. The level energies for n > 7 helium-like states were calculated using Scofield’s 45 ionization potentials for helium-like ions in equation 2.14: E(n, Z) = I(Z) (1 — -k), (2.14) where the energy of the level is E and I is the ionization potential of the helium-like species. R. W. Lee claims that this interpolation is accurate to .02 %, by comparison to rigorous calculation. A series of helium-like autoionizing states which are analagous to the lithium-like autoionizing states and are of similar interest are included in RATION. The energy levels have been calculated by Vainsthein and Safronova using an average atom model 48 and the results are in agreement with those obtained by others ° to within a m4. The 5 ’ 49 six states included are 2s2 15, 2s2p P 3 21 , 2p 2 ‘D, 2p 23 P. P, and 2p 1 S, 2s2p For the hydrogen-like ion species, equation 2.14 is used with ionization potentials provided by Scofield . 45 2.2.3 Rate coefficients Collisional ionization and recombination, radiative recombination, collisional excitation and de-excitation, autoionization and electron capture are considered to be the impor tant atomic transitions. Stimulated absorption and emission are only included in the calculation of the escape factors. (i) electron collisional ionization: Electron collisional ionization rates for all ions are calculated using a semi-empirical formula due to Lotz: = 2.97 x l0_6E,E1(c) [cm / 3 sJ, (2.15) Chapter 2. Background Theory for K—Shell Spectroscopy where is the ionization rate from state i to state j, 28 is the number of electrons in the outer shell of the electron being ionized, E is the ionization potential, and E 1 is an exponential integral 54 of the first kind. E and Te are in electron volts. According to Lotz, the formula agrees to within 40% of experimental results . 51 (ii) collisional recombination: Collisional recombination, or three body recombination, is the inverse process of elec tron collisional ionization and is calculated by applying the principle of detailed balance. These rate coefficients will be determined by the relation: 1_R , +i, , = 1 + 1 R 1 ni+ (2.16) where 1 ,+ is the collisional ionization rate from equation 2.15 and the ratio n/n+i is R determined from the Saha-Boltzmann equation, n = 1.66 X E eTe (2.17) l0 fle. 22 g+i Te’ E and Te are in electron volts and the ion density n. is in cm . Again, E is the ionization 3 energy of the state i and gj is the statistical weight of state i. The application of the Saha-Boltzmann equation incorporates the assumption that the two states i and j are in LTE with each other. The rate coefficient for collisional recombination is given by = 1.66 eE/Te x i+i 3/2 Te R,+i /s], 3 [cm (2.18) where E and Te are again in electron volts. (iii) Gaunt factor: The remaining atomic processes are calculated using methods appropriate to the ion stage concerned. In the following discussions of collisional excitation and de-excitation and radiative recombination mention is made of the Gaunt factor, G. For example, not all electron-ion collisions result in a transition from one atomic state to another. One method Chapter 2. Background Theory for K—Shell Spectroscopy 29 of modifying the rate coefficients to account for the dependancy of the transition rate on the energy of the incident electron is to multiply the rate coefficients by a Gaunt factor. Another method is to evaluate all the collisional excitation rate coefficients and then use the Gaunt factor as an adjustable parameter to fit the rate coefficients to empirical data or to detailed calculations. Loosely speaking, a Gaunt factor is the ratio of the actual atomic reaction cross section to the classical reaction cross section, G = (2.19) --. o-c A Gaunt factor is not the only formalism used to satisfy the quantum mechanical require ments of electron-ion collisions. Other calculations 52 use different methodology but the basic idea is equivalent to that of the Gaunt factor. In practice plasma modelling uses effective Gaunt factors instead of Gaunt factors. An effective Gaunt factor is a number that is either set to a constant value or is determined by an interpolation formula. In each case the criteria used to determine the effective Gaunt factors comes from rigorous calculations or from experimental data. (iv) radiative recombination: The radiative recombination rate involving only one electron for all ion stages ex cluding hydrogenic ions is calculated by applying the principle of detailed balance to photoionization, its own inverse process. In this calculation the Gaunt factors are set to unity, an assumption that is accurate 53 to within 20%. The resulting formula for the recombination rate is thus R = 5.20 x 10_14Z-eEi(ç) [cm / 3 s] (2.20) where Z is the initial ion charge, E is the ionization ellergy, and E 1 is an exponential integral of the first kind . RATION only calculates photoionization in order to calculate 54 opacity, unless the plasma simulation includes an external radiation field. Chapter 2. Background Theory for K—Shell Spectroscopy 30 Radiative recombination rates for hydrogen-like ions are calculated using an interpo lation formula due to Seaton This yields R = 5.2 x 10_14 /s]. 3 [cm (2.21) n(XoU + X U+X 1 U) 2 U = luTe where I is the ground state ionization potential of a hydrogenic ion of charge Z, and Xo, X , 2 1 X are functions of the parameter miTe, where Is,., is the ionization potential of the state n of the same ion. According to Seaton , the uncertainty in the 55 recombination rate predicted by this formula is less than 10% for the plasma conditions of interest in this work. (v) spontaneous emission: RATION calculates line radiation from singly excited lithium- like states using aver ages of the detailed states corresponding to each 13 of the excited state n where n 5, and using a hydrogenic approximation for n > 5, where n is the principal quantum num ber and 1 is the orbital angular momentum. The spontaneous emission rate from state i to state j, for n 5 is given by 3 = R X 1n15 [s —1 ] —fj ij 93 (2.22) where the wavelength \ is in Angstroms. The oscillator strengths were obtained 56 exper imentally for transitions of the type flh.s and 3 n — nup, flhP — , 8 u hP — nd where 2 h 4 7. In all other transitions, the oscillator strengths were obtained through application of the parametric potential method The radiative transition rates for the satellite lines arising from doubly excited lithium like ions are calculated by Gabriel and Bhalla’ . 4 ’ 9 4 Various factors were considered in the calculation performed by Gabriel and Bhalla, most notably the incorporation of autoionization of the upper level of the transition and the corresponding reduction in the radiative transition rate for a given plasma density. The autoionization rates were calculated using an LS coupling scheme. Chapter 2. Background Theory for K—Shell Spectroscopy 31 Radiative transition rates in helium-like ions were calculated using the detailed state specifications when n < 3 and using averaged hydrogenic states for all other cases . 58 The transition rates for the helium-like satellite lines were calculated using hydrogenic oscillator strengths’ . 4 ’ 9 4 The error introduced by this approximation should be less than a factor of two. (vi) collisional excitation and de-excitation: Collisional excitation and de-excitation rates for hydrogenic ions are evaluated using a semi-empirical formula . The calculation of the electron activation cross section in the 59 formula interpolates observed and theoretical data by varying the effective Gaunt factor while maintaining a consistent formulation of the effective Gaunt factor. The collisionally induced excitation rate from state i to state = where j is 2.50 x 10_ E 5 is the transition energy and 3 f /s] 3 [cm (2.23) is the absorption oscillator strength. The tran sition energy and electron temperature are measured in electron volts. The collisionally induced de-excitation rate is calculated using the principle of detailed balance, which yields = 2.50 x lO5Efij /s]. 3 [cm (2.24) Collisionally induced transitions between singly excited states of helium—like atoms are modelled using data due to Vinogradov 6O Collisionally induced transitions between the doubly excited and the singly excited helium-like states are given by Sampson ’ 6 but have been modified to illclude Gaunt factors due to Mewe , yielding the following 62 expression: R and = 1.25 x 104EeT2fjjG /s]. 3 [cm (2.25) f are again the transition energy and absorption oscillator strength, respectively. j 1 Chapter 2. Background Theory for K—Shell Spectroscopy 32 & is the Gaunt factor given by -E C for Sn 0 = Ei(2) 1 0.15 + 0.28e (2.26) 0 dipole allowed transitions. The collisional coupling of doubly excited states was evaluated using a set of rate coefficients due to Sampson . Collisional de-excitation 63 rates are determined using the principle of detailed balance, as was done in the case of the collisional de-exitation rate of hydrogen-like ions. Collisional excitation rates of singly excited lithium-like ions were obtained from two sources. The first is a group of interpolation formulae, due to Cochrane and McWhirter 52 which are applicable to the 2p — 2s, 2s — 3s, 2s — 3p, 2p — 3p and 2p — 3d transitions. These formulae are obtained by interpolating predictions of close-coupling, distorted wave, and Coulomb-Born calculations. Very few experimental data are available. Again, the interpolation is performed by using a semi-empirical formula to evaluate the effective Gaunt factor. Uncertainties in the interpolation formulae arise from the uncertainties in the source data. Although there are not enough experimental data available to enable a comprehensive evaluation of the theoretical data, Cochrane and McWhirter consider the interpolation formulae to be accurate to within 10%. The remaining transition rates where n 5 are calculated using a formula that is identical in form 32 to equation 2.26, involving a calculation of the effective Gaunt factor. The hydrogenic approximation is used for the higher, non-detailed levels. The coupling of doubly excited to singly excited states was done using rate coefficients due to Sampson . The doubly excited lithium-like states are collisionally coupled to 61 each other using electron collision cross sections calculated by Jacobs and 27 Blaha who , applied distorted wave theory to an LS coupling scheme. For our purposes their most interesting result was that angular momentum changing collisions betweell the doubly excited lithium-like states strongly populate the upper levels of the abcd and qr satellite Chapter 2. Background Theory for K—Shell Spectroscopy 33 lines but not the jkl satellite lines, thus making the hue-intensity ratios of abcd and qr to jkl useful as plasma density diagnostics. (vii) autoionization aild dielectronic recombination: The doubly excited helium-like and lithium-like ions are subject to autoionization. Autoionization rates of the doubly excited helium-like atoms are calculated using a hy drogenic atom model . Autoionization rates for the doubly excited lithium-like ions 48 are taken from the work of Gabriel , who derived the rates from configuration-mixing 19 calculations using LS basis states. Dielectronic recombination, or rnverse autoionization, is the process whereby an elec tron interacting with the ground state of a lithium-like or helium-like ion is captured into a doubly excited state, with no radiation being emitted. This rate may be calculated through application of the principle of detailed balance to the autoionization rate. This gives = 1.66 1O_22 e -i Te /s]. 3 (2.27) fleAji [cm 3 T 2 g R is the dielectronic recombination rate from the ground state of the initial ion stage to X the doubly excited state of the next ionization stage, E is the energy difference between the doubly excited state and the first ionization potential of the ion, and is the autoionization rate. 2.3 Results of RATION In order to choose the appropriate line-intensity ratios for use as density and tempera ture diagnostics we used the theoretical model to study the dependences of the various line-intensity ratios on the temperature and the density of the plasma. By repeated ap plications of RATION for a wide range of temperatures, densities, and plasma lengths, one can also determine which spectral lines are affected similarly by opacity. Only a few Chapter 2. Background Theory for K—Shell Spectro.scopy 34 of the line-intensity ratios involving the satellites of the Lyc resonance line and the Hea resonance line hold any promise of being useful to the present work. In Chapter 3, measurements of the plasma size are discussed and an upper limit of 70 tm is established. Since the size of the plasma affects the opacity, a range of possible sizes of the ablation plasma are investigated. These lengths represent the thickness of the plasma through which the x-rays must propagate in order to reach the spectrometer. For the case in which opacity may be negligible, a 1 ,um plasma length is specified. A more reasonable scale length, based on estimates of the diameter of the laser focal spot, um to account for is 10 m. Finally, the calculations are done for a plasma length of 50 1 the possibility of a very large ablation plasma. Although the measurements presented in Chapter 3 indicate that the plasma itself is approximately 70 tm long, the measurement does not distinguish between x-ray emission from the ablation plasma and x-ray emission due to radiative recombination in the coronal plasma. 50 um was used in the analysis to represent an estimate of the largest expected plasma size, as opposed to using the upper limit of 70 ,um. Since a strongly divergent plasma flow is expected, it is not obvious that um. a hot, dense, ablation plasma should even be as large as 50 1 Figures 2.8—2.12 are the results of RATION calculations for x-ray line-intensity ratios, used for both temperature and density diagnostics, for a plasma length of 10 tm. The temperature of the dominant emission region is expected to be close to 600 eV. Suitable line-intensity ratios for use as density diagnostics are relatively insensitive to changes in temperature in the vicinity of 600 eV. The line-intensity ratio should also vary strongly enough with density so that the uncertainties in the measured line-intensity ratios do not result in great uncertainties in the inferred densities. As can be seen from table 4.1 the uncertainties in the measured line-intensity ratios are typically less than 10 abcd/jkl, qr/jkl and #1 — %. The 9/#12 lrne-mtensity ratios will provide density diagnostics. Similarily, the line-intensity ratios used as temperature diagnostics would exhibit weak Chapter 2. Background Theory for K—Shell Spectroscopy density dependance in the near a density of 1022 35 3 and a sufficiently strong tem e/cm perature dependance so as to avoid large uncertainties in the measured temperatures. The #l0/jkl and 12/jkl line-intensity ratios will provide temperature diagnostics. Figures 2.13—2.23 are results of opacity calculations. The opacities for all the lines used in the density and temperature diagnostics for a plasma length of 10 m are presented as well as the opacites for the Hea, He , Ly and Ly 13 13 resonance lines. The opacity as defined by equation 2.12, is plotted as a function of density for several different temperatures for each emission line. r 0.1 would correspond to an absorption of less than 5% over the length of the plasma. The calculation results corresponding to a plasma length of 10 tm are chosen for presentation here since a 10 1 um plasma simulation represents a moderate plasma size rather than an extreme plasma size. It should be noted that the opacities for the satellite lines are small. Also, it should be noted that the resonance lines are far more opaque than the satellite lines and con sequently may not be localized to the same region of the plasma as the K-shell satellite lines. Due to their great opacity, the resonance lines could even be dominated by the recombining plasma and therefore, in addition to inappropriate spatial localization, the resonance lines may not even be emitted at the same time as the satellite lines. 36 Ghapter 2. Background Theory for K—Shell Spectroscopy 1 0.8 0 I— Cl) z 0.6 LU 1- z LU z i 0.4 0.2 10 io22 ) 3 ELECTRON DENSITY (cm Figure 2.8: abcd/jkl line ratio assuming a plasma length of 10 pm. 23 io 37 Chapter 2. Background Theory for K—Shell Spectroscopy 1.2 0 I 0.8 Cl) z LU I— 0.6 z LU z -J 0.4 0 io21 io22 ) 3 ELECTRON DENSITY (cm Figure 2.9: qr/jkl line ratio assuming a plasma length of 10 turn. io23 38 Chapter 2. Background Theory for K—Shell Spectroscopy 1.4 1.2 0 I-. ci: C,) z 1 LU I— z LU z —I C’J 0.8 0.6 0.4 1 o21 22 io23 ELECTRON DENSITY (cm ) 3 Figure 2.10: #1 — 9/#12 line ratio assuming a plasma length of 10 m. 39 Chapter 2. Background Theory for K—Shell Spectroscopy 101 100 0 C,, 10_i z uJ I— z Ui z -J 1 o2 0 1 -4 10 0 0.4 0.8 1.2 1.6 2 ELECTRON TEMPERATURE (KeV) Figure 2.11: lO/jkl line ratio assuming a plasma length of 10 uin. 40 Chapter 2. Background Theory for K—Shell Spectroscopy i 101 0 ct 100 Ci) z w I z w z 1 0_i -J c’J 1 4t: 2 1o 1 0 0.4 1.2 0.8 ELECTRON TEMPERATURE (KeV) 1.6 Figure 2.12: #12/jkl line ratio assuming a plasma length of 10 ,um. 2 41 Chapter 2. Background Theory for K—Shell Spectroscopy 1 101 100 ii w 10_i D -J 0 1 o2 0 1 io6 1 io23 ) 3 ELETR0N DENSITY (cm Figure 2.13: Opacity (r) for the abcd satellite lines assuming a plasma length of 10 tm Chapter 2. Background Theory for K—Shell Spectroscopy 42 10 1 o2 101 100 w 10_i 1 o2 0 1 1 10 -6 1 10 Figure 2.14: Opacity 2 io 2 (cm ) ELECTRON DENSITY 3 (T) io23 for the qr satellite lines assuming a plasma length of 10 m. Chapier 2. Background Theory for Ic—She1] Spectroscopy 43 1 1 o2 101 io0 Lii 10_i -J C) I— 1 o2 a 0 1o io6 1 o21 1o 22 ) 3 ELECTRON DENSITY (cm io23 Figure 2.15: Opacity (r) for the jkl satellite lines assuming a plasma length of 10 m. 44 Chapter 2. Background Theory for K—Shell Spectroscopy 101 1 o0 10_i I— w -J io2 () I— 0 1 1 1021 io22 ) 3 ELECTRON DENSITY (cm Figure 2.16: Opacity (r) for the 1 Inn. — io23 3 satellite lines assuming a plasma length of 10 Chapter 2. Background Theory for K—Shell Spectroscopy 45 101 100 :i: b0 -1 Lii 0 -J 0 0 2 io 1 10 -4 io21 io22 ) 3 ELECTRON DENSITY (cm Figure 2.17: Opacity (r) for the L4 11 — io23 9 satellite lines assuming a plasma length of 1.0 Chapter 2. Background Theory for K—Shell Spectroscopy 46 100 Ui -J C) I— 0 io23 ELECTRON DENSITY (cm ) 3 Figure 2.18: Opacity (r) for the #10 satellite line assuming a plasma length of 10 1 um. Chapter 2. Background Theory for K—Shell Spectroscopy 47 101 100 10_i z 1 o2 w 0 -j 0 1 0 10 -6 21 10 io22 io23 ELECTRON DENSiTY (cm ) 3 Figure 2.19: Opacity (r) for the #12 satellite line assuming a plasma length of 10 pm. ackgro T h for ‘She11 Spectrosco Chapt 2. B 2 0 48 •10 0 LU a I -I i •1 1 (c111 ) ELECTRON DENSITY 3 Figure 2.20: Opacity (T) fo the Ly resonance line assulflhiig a plasma lemlgth of 10 Chapter 2. Background Theory for K—Shell Spectroscopy 49 1 o2 101 100 I Lu -j 10_i C) I— 0 1 o2 1 1 1 o21 io22 io23 ELECTRON DENSITY (cm ) 3 Figure 2.21: Opacity (T) for the Ly resonance line assuming a plasma length of 10 tm. Chapter 2. Background Theory for K—Shell Spectroscopy 50 1 101 z I 0 LU ci -J C) I— a 0 10_i -3 10 o21 io22 ELECTRON DENSI1Y io23 ) 3 (cm Figure 2.22: Opacity (r) for the Hea resonance line assuming a plasma length of 10 tm. grQ Theory for —l ack2 Sh SPectroscop 2. B 2 I0 l 51 10 a 0 1 10 10 ., 2 1 io22 () (ciri ELECTRON DENSIP 3 Figu 2.23: Opacity (r) for the He resonance line g aSS1niU 1 o23 a plasma lengtJ of 10 Chapter 3 Experiment 3.1 The laser facility Figure 3.1 is a schematic diagram of the laser facility. The laser consisists of a Nd YAG oscillator, a Nd-YAG preamplifier, and four Nd-glass amplifiers. The oscillator is passively Q-switched to provide a single laser pulse which is approximately Gaussian with a full-width-half-maximum length of 2.5 ns at a wavelength of 1.06 pm. Following the oscillator, as well as each amplifier, is a vacuum spatial filter whose function is to reduce spatial nonuniformities present in the beam. The polarization of the laser beam is preserved by installing pairs of Brewster—angle polarizers following each of the first two Nd—glass amplifiers. Typical energy of the laser pulse at 1.06 ,um is 24 J. The laser beam then passes through a deuterated potassium dihydrogen phosphate (KD*P) second harmonic conversion crystal where approximately 60% of the laser energy is frequencydoubled. The upconverted beam is subsequently steered by a series of dichroic mirrors to the beam diagnostic apparatus and the target chamber. For every shot the laser energy and pulse shape are measured by monitoring the leak age laser light through a beam splitter reflector. The energy measurement is obtained usrng a Gentek piezoelectric detector . The absolute response of the Gentek detector is checked routinely with a Scientech calorimeter by measuring the energy of the main laser beam before it enters the target chamber and comparing the readings of the calorimeter 52 Chapter 3. Experiment BSR 53 LENS 8S GENTEK PD TARGET CHAIBER BSR 1- IRM t IRM’ IRM p3 IRI oSc Figure 3.1: Schematic of laser facility. OSC is the oscillator, PA is the preamplifier, A1-A4 are amplifiers, IRM is infrared mirror, SF1-SF6 are the vacuum spatial filters, P1-P4 are polarizers, BS is beam-splitter, BSR is beam-splitter reflector, ND is a neu tral-density optical absorber, IF is an interference filter, PD is photodiode, and GENTEK is a piezoelectric cystal beam energy monitor. Chapter 3. Experiment 54 and the piezoelectric detector. The pulse shape is monitored by a Hammamatsu photodi ode. The output is displayed on a Tektronix 7104 oscilloscope. The temporal resolution of the combined photodiode—oscilliscope system is roughly 500 ps. A typical laser pulse is shown ill figure 3.2. The shot—to—shot variations in the peak laser power are generally less than 10%. 3.2 Irradiation parameters The laser is focussed onto the target plane by a diffraction-limited doublet. The targets are boron-doped silicon. Boron-doped targets are used due to their ready availability, and the boron concentration is of the order of 10—8%. The low boron concentration and the long wavelength emission lines characteristic of boron render its presence in the targets inconsequential. The lens is positioned to bring the laser focal spot to best focus. The diameter of the best focus laser spot is typically several times the 2.6 ,um diffraction limit of the lens. To locate the lens for best focus at the target plane, the target plane is imaged onto Polaroid film using a f/l.4 camera lens as shown in figure 3.3. The magnification of the imaging system is measured by placing a grid of known dimensions in the target plane. The grid is illuminated with an incandescent lamp. An interference filter centered at .53 tm and having a bandwidth of 100 A is placed in front of the Polaroid camera to eliminate potential chromatic problems and the image of the grid is photographed. The grid is removed and the image of the laser focal spot at the target plane is recorded. For this measurement, the laser is fired at full power to take account of thermal lensing in the amplifier rods, which will affect the focussed position of the laser beam by several mm. To avoid damaging the imaging system, a high reflectance mirror is used to divert nearly all of the laser beam into a Scientech calorimeter before it enters the target chamber. Chapter 3. Experiment Figure 3.2: A sample laser pulse. The time scale is lns per division. 55 Chapter 3. Experiment 56 IF CAMERA LENS LAS ER TARGET PLANE ATTENUATORS CAMERA Figure 3.3: Experimental arrangement for measuring the laser focal spot size. IF is an interference filter centered at .53 im with a bandwidth of 100 A. Chapter 3. Experiment 57 This also provides a calibration of the Gentek energy meter as described in the preceeding section. The fraction of the laser beam transmitted through the high reflectance mirror is further attenuated in front of the Polaroid camera by a series of neutral density filters which serve to increase the dynamic range of the measurement. The laser focal spot at the target plane is recorded with different attenuations in front of the Polaroid camera to provide an estimate of the spot diameters corresponding to the 10% and 1% intensity levels of the laser beam. This measurement will be referred to as vacuum focus measurement. Figure 3.4 shows results of the measurement with the laser beam at best focus at the target plane. This suggests that the diameter of the focal spot at a 1% intensity level is about 25 m. Pinhole photographs of the x-rays emitted from the target plasma were used to esti mate the plasma size. These are taken using a pinhole camera, as shown in figure 3.5. Samples of the photographs are shown in figure 3.6. The pinhole diameter is 12.4 + 1 urn and a 12 urn aluminum foil is placed in front of the film as an absorption filter. The x-ray emission recorded by the pinhole camera is thus dominated by photons with energies above the aluminum Ka absorption edge at 1.56 KeV. An x-ray pinhole camera photograph is not a measurement of the focal spot size in the plasma, but a measurement of the spatial x-ray emission profile of the plasma. The pinhole photographs suggest that the plasma is nearly spherical. This can be seen in the microdensitometer measurements of a pinhole photograph as shown in figure 3.7, which indicate an axial extent of roughly 60 urn and a lateral extent of roughly 70 urn. The difference in size between the vacuum focus measurement and the x-ray pinhole photograph may be indicative of a strong lateral plasma flow or significant lateral thermal electron conduction. If so, then the laser energy may be being deposited over a larger region than the vacuum focus measurement indicates. The plasma itself will also affect the propagation of the laser beam, possibly altering the focal intensity distribution. Chapter 3. Experiment 58 I I Figure 3.4: Pictures of the laser spot at best focus. Attenuation of the top picture is 100 times greater than the attenuation of the bottom picture and 10 times greater than the attenuation of the center picture. The magnification of these images is 198 times the actual size of the focal spot. The horizontal bar represents a 100 pm distance at the target plane. Chapter 3. Experiment LASER Figure 3.5: Target chamber arrangement for taking x-ray pinhole photographs. 59 60 Chapter 3. Experiment I— I Figure 3.6: X-ray pinhole photograph of a plasma produced by an unattenuated laser pulse.The background is due to x-rays penetrating the steel substrate through which the pinhole is drilled. The image of the plasma is the small, bright spot. The horizontal bar represents 2 mm on the film. The magnification of the pillhole camera itself is 13 times. 61 Chapter 3. Experiment 0.6 0.5 0.2 z 0.1 0 30 0 90 60 AXIAL POSITION (jim) 120 150 0.6 0.5 z I 0.4 0.3 0.2 0.1 0 a 30 60 90 120 150 LATERAL POSITION (pim) Figure 3.7: Microdensitometer scans of a pinhole photograph. The top figure is the scan of the horizontal, or axial aspect of the plasma plume and the bottom figure is the vertical aspect, or the diameter of the plasma plume. Both traces have been corrected using a typical film calibration curve. Chapter 3. Experiment 62 beam irradiance 2 W/cm x-ray pinhole photograph lateral axial aspect aspect 15 1.1x10 69±4tm 83±5tm 7.4 x iO’ 63 + 4 m 84 + 2 um 4.4 x iO’ 69 ± 6 ,um 71 ± 6 m Table 3.1: Plasma size estimates from x-ray pinhole photographs, and laser intensities. Chapter 3. Experiment 63 There is no known technique to directly measure the intensity distribution of the focussed laser beam in a plasma. The plasma size estimates are shown in table 3.1. The estimated focal diameter inferred from the 1% intensity level in the vacuum focus measurement is 25 1 um. It is evident that the size of the laser-heated plasma is much larger. The pinhole photographs are recorded for several different laser irradiances to correspond to the measurements of x-ray spectra. The laser intensity is varied by placing glass absorbers in the path of the laser beam to reduce its power. The irradiances given in table 3.1 are calculated according to the following formula: 1= E (3.1) rirr where E is the energy of the laser beam, r is the full-width half-maximum duration of the laser pulse, and r is the radius of the laser focal spot. The laser focal spot radius corresponds to the 1% laser intensity level of the vacuum focus measurement. 3.3 x-ray spectrometers Figure 3.8 shows the layout of the spectrometers in the target chamber. One Bragg reflection crystal spectrometer views the plasma at an angle 5 degrees away from the target plane and records emissions between 4 A and 6 A. Another Bragg reflection crystal spectrometer views the opposite side of the plasma at an angle of 10 degrees away from the target plane and records emissions between 6 A and 7 A. Both spectrometers are used simultaneously. Plastic shields are used to eliminate spurious film exposure due to secondary flourescence of the x-rays. The spectrometers are tested for spurious exposure by firing the laser onto a silicon target without the PET crystals present in the spectrometer. Spurious exposure may also arise due to imperfections or damage in the PET crystals or from Bragg reflection from atomic planes near the back surface of the crystal. It Chapter 3. Experiment 64 HIGH RESOLUTION SPECTROMETER LASER LOW RESOLUTION SPECTROMETER chamber is Figure 3.8: Target chamber and spectrometers. The diameter of the target approximately 90 cm. Chapter 3. Experiment 65 has been our experience that crystal damage manifests itself as obvious defects in the recorded spectra. Bragg reflection from the back surface of the crystal seems unlikely. Theoretically, distortion in the spectra may arise due to Bragg reflections from deep in the crystal because as x-rays penetrate the crystal they yield a Bragg reflection from every crystal plane they cross. Consequently an x-ray is not reflected as a single x-ray but rather as a set of parallel x-rays. The physical width of this set of parallel rays would have to be greater than the width of the source plasma in order to degrade the resolution of the spectrometer and in this experiment the x-rays would have to penetrate deeper than 0.1 mm into the crystal in order to cause distortions. Since the reflectance of a PET crystal plane is typically on the order 64 of 5 x 10 and the planes are 4.371 A apart, no appreciable x-ray flux will penetrate 0.1 mm into the crystal. The spectra are recorded on Kodak PF469 film. The film consists of Kodak emulsion number 2530 on a acetate base. The film is cut into pieces 7 cm long and 2.5 cm wide and placed inside a portable film cassette, which is then installied in the spectrometer. The film cassettes are machined from brass and each cassette has a 6.5 cm long by 1 cm wide beryllium step-wedge x-ray filter as an entrance window, as shown in figure 3.9. The beryllium step wedge filter is comprised of 3 layers of 12.5 jtm beryllium foil. The resulting attenuation of the x-rays provides a sufficient range of film exposures for an in-situ calibration of the film response. 3.4 Processing of data The exposed film is developed, dried, and mounted between two glass slides. Mounting is necessary to protect the easily damaged film. The spectra are then measured using a microdensitometer. The microdensitometer measures the exposure of a 1 mm tall by 8 m wide section, 66 Chapter 3. Experiment KODAK PF469 FILM / STEP WEDGE FILTER / \ 7 \ - \ L %_ ACCESS CAP Figure 3.9: Film cassette. The dashed line indicates the film plane. Chapter 3. Experiment 67 transition wavelength (A) reference abed 6.726 19 #10 6.2284 48 #12 6.2637 48 ls2p’P 6.647 68 ls3p 1 P 5.6805 68 P 1 ls—2p 6.19 68 P 1 ls—3p 5.218 68 ls—4p’P 4.947 68 1s2 1s2 - - Table 3.2: Common wavelength calibration lines. A detailed list of atomic transitions and their shorthand notation will be found in table 2.1. Chapter 3. Experiment 68 hereafter referred to as the scanning window, of the film using a photomultiplier tube. Thus, the resolution of the measurement is nominally 8 tm. The digitized output of the photomultiplier tube is recorded for every 5 ,um step of scanning the film. The imaging system has some minor shortfalls which allow some light from outside the scanning window to enter the photomultiplier tube. In order to assess the effect of this scattered light, a razor blade was laid flat on the scanning carriage and the knife edge was scanned. Figure 3.10 shows the output of the microdensitometer as the razor blade moved across the scanning window. If the imaging system were perfect, the output would yield 100% transmission (indicating no obstruction) until the knife edge reaches the scanning window, and the output would drop to 0% transmission once the knife edge had completely crossed the scanning window. Obviously, this is not the case with our microdensitometer. Figure 3.10 shows that at least 94% of the light reaching the photomultiplier tube comes from the scanning window, and that nearly all the scattered light comes from a 15 ,um wide by 1 mm tall region adjacent to each side of the scanning window. Since the intensity of the x-ray exposure on the spectra vary over scale lengths which are typically hundreds of m, this scattered light will not noticeably affect the measured spectra. It is also obvious from figure 3.10 that the dynamic range of the microdensitometer is roughly 100. Therefore the dynamic range of the measurement is limited by the dynamic range of the x-ray film, which is typically 30. Consequently, the process of measuring the spectra does not degrade the resolution and dynamic range of the observed spectra. All three exposures corresponding to the different attenuations provided by the step wedge filter are scanned. The fog level of the film, the unobstructed and the fully ob structed trallsmission levels are recorded and used as references. The digitized spectra are analyzed in five steps using a computer. Since the raw data obtained from the mi crodensitometer scan of the exposed film displays the observed spectrum as a functioll 69 Chapter 3. Experiment 100 z 0 Cf) Cl) Cl) z a: I— I— z U] C.) 10 a: U.’ 0 1 0 20 40 60 80 100 POSITION (kim) Figure 3.10: Microdensitometer performance test. The knife edge advances across the 8 m scanning window from left to right. Chapter 3. Experiment 70 of distance along the film, the first step is to convert the space scale to a wavelength scale. This spectral calibration is derived using three reference lines whose wavelengths are accurately known and the Bragg diffraction equation. Preferably, the reference lines span a large portion of the spectrum. Figure 3.11 shows the arrangement of the x-ray spectrometer, which is used to evaluate the spectral dispersion at the film plane. For photons with a wavelength ), the Bragg diffraction angle 0 is given by A=2dsin0 (3.2) where d is the spacing of the crystal planes. Using equation 3.2, the three wavelength reference lines, and the arrangement of the spectrometer one can derive a relation which transforms the space scale into a wavelength scale: = 0 2dsin[0 — arctan( Xsina R X cos a )]. (3.3) — X is the spatial film coordinate and d is the spacing between the PET crystal planes. The three reference lines are necessary to calculate the three parameters 00, a, and R. Of the three reference lines, the one with the longest wavelength is used to define the three parameters of equation 3.3. o 0 is the Bragg angle corresponding to the longest wavelength reference line. R is the path lellgth from the plasma to the film plane for this line and a is the angle of intersection this line makes with the film plane, as shown in figure 3.11. Various spectral lines were tested for use as wavelength references and the best wavelength calibrations were obtained by using the satellite lines and avoiding the resonance lines. The resonance lines have high opacity and a tendency to overlap emission lines from other, more highly excited atomic states . Thus, the resonance lines, 65 although dominant, are superimposed on other lines and it is impossible to accurately locate the resonance lines in the observed spectra. Unfortunately, the He , aild the Ly 0 0, resonance lines have to be used as reference lines when the laser irradiance is 4.4 x 1014 71 Chapter 3. Experiment PLASMA I I 1 IC I I — — FILM PET CRYSTAL — — , — — — xc— R=a+b ‘V x Figure 3.11: The arrangement of the x-ray spectrometer. The path length I-? the longest wavelength reference line is indicated. = a + b of Chapter 3. Experiment 72 2 since the satellite lines become too weak. Also, the higher order resonance lines W/cm are used as reference lines for analyzing spectra from the low-resolution spectrometer since there are no other lines with greater accuracy available. The second step of the analysis is to transform the film exposure into x-ray intensity using an in-situ calibration method . 66 All x-ray intensities obtained in the analysis are relative intensities. No absolute intensity measurement has been made. With the step wedge filter, three different intensites corresponding to any one wavelength may be measured. These intensities are governed by the thickness of the steps in the step wedge filter and the known absorption 67 coefficients of the filter material. Generally all available emission lines on the 4-6A and 6-7A spectra are used to plot a series of 12 to 18 calibration curves. These curves are then shifted along the relative intensity axis to coalesce into one film response curve, as shown in figure 3.12. A best fit polynomial corresponding to the coalesced response curve is then used to transform the film exposures into relative intensities on the film. Both pieces of film from the two spectrometers are developed simultaneously so that the film response curve applies equally to each film. The third step is to take into account the different attenuation due to the steps in the step wedge filter and due to the wavelength dependence of the absorption coefficients. Following completion of this stage the data is now represented by relative intensity of the x-rays reaching the film cassette as a function of wavelength. The fourth stage is to correct the relative intensites for the variations in dispersion across the spectral range covered by each spectrometer and between the two spectrometers. Figure 3.13 shows the dispersion of each spectrometer. Finally, since the plasma is a point source and the film cassettes are at different distances from the plasma the decrease in intensity as a function of distance is corrected using the inverse squares law. Since the horizontal aspect of x ray dispersion is already accounted for by the fourth step, multiplication of the x-ray 73 Chapter 3. Experiment .: 100 ......z..4 ..4... ........ 1_?_.. i-:—-——i-— ...; ........—. I._._..._. ——----h——F— 1 ......- ‘........... .._... — .. . —. .. ....,._.. I : 10 — ... .. .........._.............f_. ....... — — ._..., .. z’E. -.r: Ez: — .... 1 . f ....... ....4. ,.— I a...., i . : 3 ZE -ï 3, 3;P Z I t 1 1 I i.... I 10 I ..._..L......LJ_ : I’!I. 100 FILM EXPOSURE Figure 3.12: Typical film calibration curve. The relative x-ray intensity is plotted as a. function of the film exposure. The single, long, smooth curve is the polynomial function used to transform film exposure into relative x-ray intensity. The triplets of points connected by short, straight lines are the curves of three relative intensities and fihn exposures which are used to provide the data for the construction of the film response curve. 74 Chapter 3. Experiment -10 ‘1TF 1- • • i • —, i r’ s— —11 -12 I, i::z..::zj -13 -14 I -15 6 r I t 6.2 I t I 6.4 I II 6.6 I I L I L 7 6.8 WAVELENGIN -20 -24 I -82 -36 -40 4 4.4 4.8 52 5.6 6 WAVELENGTh Figure 3.13: Dispersion, in mA/mm, as a function of wavelength for the two spectrom eters. The top diagram is for the high resolution spectrometer and the bottom diagram is for the low resolution spectrometer. Chapter 3. Experiment 75 intensites of one cassette by the ratio of the two different plasma to cassette distances fully corrects for the x-ray attenuation due to distance. This final correction need only be made when comparing the results of one spectrometer to the other. 3.5 Dynamic range of the spectroscopic measurement The dynamic range of the film, between the fog level and the strongest exposure, is roughly 30, as can be seen from figure 3.12. Film saturation is not a limitation. The fog level, on the other hand, sets a lower limit on the weakest x-ray signals that can be visible. When film exposure is transformed into relative intensity, the areas of the film that are not exposed above the fog level are assigned the lowest relative intensity available on the film calibration curve. This fog level thus manifests itself as a smooth background continuum in the processed spectra, as visible in figure 3.14, which has been plotted on a logarithmic scale to accentuate this feature. The slope appears when the relative x-ray intensity is adjusted to take into account the wavelength dependent attenuation of the beryllium step wedge filter and for the variation in spectral dispersion along the length of the film. 76 Chapter 3. Experiment 100 z 0.1 6.1 6.2 6.3 6.4 6.5 WAVELENGTH (A) 6.6 6.7 6.8 Figure 3.14: Example of maximum estimated continuum. The slight slope visible on the logarithirnic scale and the smooth background are indications of the data being lost below the fog level of the film. Chapter 4 Results and Discussions 4.1 Experimental results Although the experiment was repeated using three different irradiation intensities, oniy the results corresponding to data obtailled at an irradiance of 1.1 x 1015 W/cm 2 and at an irradiance of 4.4 x io’ W/cm 2 will be discussed. The results obtained at the intermediate irradiance are not included since they are not significantly different from those obtained at the highest irradiance. Figure 4.1 shows prints made from the spectra recorded with the spectrometers. The spectra are free from any detectable spurious exposure due to, for example, x-rays scat tered from the lens mount. The intrinsic resolving power of the high-resolution spectrom eter should be at least 10,000 for a plasma smaller than 50 ,um and the intrinsic resolving power of the low-resolution spectrometer should be at least 3,500. The measured spec tra do not contain emission lines sufficiently close together to demonstrate the expected resolutions. However, the high-resolution spectrometer did resolve the j line from the k and 1 lines, which indicates that it must have a resolving power of at least 6,000. Figures 4.2 to 4.5 show the spectra obtained with the high-resolution and the low resolution spectrometers at different laser irradiances. During the experiment, no abso lute x-ray intensity measurements were made. Consequently, there is no accurate relative intensity scale that is common to spectra obtained from different laser shots. For any given pair of spectra obtained from a single laser shot, the relative intensity scales are 77. Chapter 4. Results and Discussions Ly 78 Hea #12 Ly Ly 8 LyHe L 7 He klj He Figure 4.1: Prints of raw spectra for data obtained at a laser irradiance of 1.1 x 1015 . The wavelength increases from left to right. The top print is from the 2 W/cm high-resolution spectrometer and shows the helium—like and the hydrogen—like satellites. Their respective Lycy and Hea resonance lines are the extremely bright lines. The bottom print is from the low-resolution spectrometer and the bright lines are the higher order resonance lines. The satellites of the He are visible in the extreme left of the bottom print. 79 Chapter 4. Results arid Discussions 20 15 z D I— 10 Cl) z LL1 I 5 0 6.1 6.2 6.3 6.4 6.5 WAVELENGTH (A) 6.6 6.7 6.8 Figure 4.2: Analyzed microdensitometer tracing of the helium—like satellites of the Lya resonance line and the lithium—like satellites of the He resonance line obtained at a . 2 laser irradiance of 1.1 x 1015 W/cm 80 Chapter 4. Results and Discussions 2.5 1f2 2 z D cc 1.5 I— cc 1 (I) z LU I— z 0.5 0 4.3 4.5 4.7 •4.9 5.1 WAVELENGTH 5.3 5.5 5.7 5.9 (A) Figure 4.3: Analyzed microdensitometer tracing of high order helium—like and hydro 2 gen—like resonance lines obtained at a laser irradiance of 1.1. x 1015 W/cm - 81 Chapter 4. Results and Discussions 12 10 F I— z 8 6 Cl) z w 4 I— z 2 0 6.1 6.2 6.3 6.4 6.5 WAVELENGTH (A) 6.6 6.7 6.8 Figure 4.4: Analyzed microdensitometer tracing of the helium—like satellites of the Lya resonance line and the lithium—like satellites of the Hec, resonance line obtained at a . 2 laser irradiance of 4.4 x 1014 WJcm 82 Chapter 4. Results and Discussions 1 .5 z D 1 cc I cc 0.5 0 4.3 4.5 4.7 5.1 4.9 5.3 WAVELENGTH (A) 5.5 5.7 5.9 Figure 4.5: Analyzed microdensitometer tracing of high order helium—like and hydro . 2 gen—like resonance lines obtained at a laser irradiance of 4.4 x 1014 W/cin Chapter 4. Results arid Discussions 83 derived from the same in-situ film response calibratioll curve and hence accurafe intensity comparisons may be made between such pairs of spectra. Although accurate comparisons of intensity cannot be made between data from one laser shot aild data from another laser shot, an adjustment to the relative intensity scales has been made to permit rough comparisons between the data from two different laser shots, which in this case are the high irradiance and the low irradiance laser shots whose data are shown in figures 4.2— 4.5 and 4.6—4.10. This adjustment was performed by scaling the relative intensity of one in-situ film response curve so that it overlays the other in-situ film response curve. As was mentioned in Chapter 3, the low-resolution spectrometer covers a spectral range from 4A to 6A and the high-resolution spectrometer from 6A to 7A. The high- resolution spectrometer monitors the Lyc and the Hea resonance lines and their corre sponding dielectronic satellites, from which all the density and temperature diagnostics were made. The data from the low-resolution spectrometer was used to construct the moderate intensity section of the film response calibration curve, since the high-resolution spectrometer measured x-ray intensities which were either very strong or very weak. In the original design of the experiment, it was envisaged that some of the spectral lines recorded by the low-resolution spectrometer might also be useful as density and tem perature diagnostics but the opacities of these resonance lines were too high. We were also not able to include the satellite lines of the high-order resonance lines in the plasma simulation. Each of the spectra are measured and analyzed according to the procedure described in Chapter 3, and each of the spectra consists of at least 10,000 data points. Figures 4.6—4.9 show the expanded relevant portions of figures 4.2—4.5. Figure 4.10 shows an enlargement of the He satellites recorded by the low-resolution spectrometer. These satellites have been previously used as density and temperature diagnostics, but unfortunately it is out of the scope of RATION to model these emission lines. 84 Chapter 4. Results and Discussions 4 z 3 D >I-. 2 C’) z Iii F z 0668 6.7 6.74 6.72 WAVELENGTH (A) 6.76 6.78 Figure 4.6: Analyzed microdensitometer tracing of the lithium—like satellites of the Hea . 2 resonance line obtained at a laser irradiance of 1.1 x 1O’ W/cm Chapter 4. Results and Discussions 85 4 3 z D >- 2 ci) z w I. z 1 6.19 6.2 6.21 6.22 6.23 WAVELENGTH 6.24 6.25 6.26 6.27 (A) Figure 4.7: Analyzed microdensitometer tracing of the helium—like satellites of the Ly . 2 resonance line obtained at a laser-irradiance of 1.1 x 1015 W/cm Chapter 4. Results and Discussions 86 4 3 z D b2 rz Cl) z zi Lii I 0 6.68 6.7 6.74 6.72 WAVELENGTH (A) 6.76 6.78 Figure 4.8: Analyzed microdensitorneter tracing of the lithium—like satellites of the Hea resonance line obtained at a laser irradiance of 4.4 x 1014 W/cm . 2 87 Chapter 4. Results and Discussions 4 3 z D I— 2 Co z z 1 LU I. 6.19 6.2 6.21 6.22 6.23 WAVELENGTH 6.24 6.25 6.26 6.27 (A) Figure 4.9: Analyzed microd.ensitometer tracing of the helium—like sateflites of the Lya resonance line for a laser irradiance of 4.4 x 1014 W/cm . 2 88 Chapter 4. Results and Discussions 0.5 0.4 z D 0.3 I— 0.2 Cl) 0.1 0 5.6 5.8 5.7 WAVELENGTH 5.9 (A) Figure 4.10: Analyzed niicrodensitometer tracing of the lithium—like satellites of the He . 2 resonance line obtained at a laser irradiance of 1.1 x iO’ W/cin Chapter 4. Results and Discussions 89 Table 4.1 summarizes the measured line-intensity ratios. The temperature and den sity of the plasma are inferred from these line-intensity ratios using the appropriate methodology described in Chapter 2. Figure 4.11 shows the range of temperatures and densities inferred from all the diagnostic line-intensity ratios obtained at a laser irradi ance of 1.1 x lO W/cm 2 and assuming a uniform plasma with a length of 1 m. Since the actual plasma is non-uniform with a gradient scalelength that could be between 1 1 um and 50 m, the analysis has been repeated assuming plasma lengths of 10 um and 50 tm and the results are summarized in figures 4.12 and 4.13. Figures 4.14, 4.15, and 4.16 are results of similar analysis corresponding to data obtained at an irradiance of 4.4 x 1014 . 2 W/cm From figures 4.11 to 4.16, it is evident that the density or temperature of a plasma cannot be uniquely determined by a single line-intensity ratio. A single line-intensity ra tio yields a diagnostic curve on the density-temperature space. Each curve in the figures 4.11—4.16 thus reveals the possible combinations of density and temperature correspond ing to each of the observed line-intensity ratios. Ideally, if all of the observed spectral lines were to come from a localized plasma region with a unique temperature and density, all of the diagnostic curves will intersect at a single point in the density-temperature space, within experimental accuracy. Conversely, the extent to which such diagnostic curves cross would indicate the range of densities and temperatures of the emission source. The results of such an analysis are summarized in figure 4.17. These show that the plasma pa rameters are reasonably well defined, particularly for assumed scalelengths of 10 —50 m as suggested from the x-ray pinhole photographs and the vacuum focus measurements. Chapter 4. Results and Discussions 90 line ratio 1.1 x 1015 cm 4.4 x 1014 cm abcd/jkl .23+.02 .19+.02 qr/jkl .31 + .01 .29 + .02 .72 + .03 .69 + .06 #l0/jkl .18 + .02 .058 + .008 l2/jkl .56 + .02 .18 + .02 #1 — 9/#12 Table 4.1: Measured line-intensity ratios for both laser irradiances reported in the current work. The quoted uncertainties are standard deviations of the mean. 91 Chapter 4. Results and Discussions 23 ia C) E C., 1o 10 21 100 1000 ELECTRON TEMPERATURE (eV) 3000 Figure 4.11: Density—temperature plot for data obtained at a laser irradiance of 1.1 x 1015 , assuming a 1 tm long plasma. 2 W/cm Chapter 4. Results and Discussions 92 1 o23 (0 E C) Cl) 2 Lii I 10 1 o21 100 1000 ELECTRON TEMPERATURE (eV) 3000 Figure 4.12: Density—temperature plot for data obtained at a laser irradiance of 1.1 x i0’ , assuming a 10 pm long plasma. 2 W/cm Chapter 4. Results and Discussions 93 23 io E 0 I io22 10 21 100 1000 3000 ELECTRON TEMPERATURE (eV) Figure 4.13: Density—temperature plot for data obtained at a laser irradiance of 1.1 x iO’ , assuming a 50 urn long plasma. 2 W/cm Chapter 4. Results and Discussions 94 io23 E C) z 1 o21 100 1000 3000 ELECTRON TEMPERATURE (eV) Figure 4.14: Density—temperature plot for data obtained at a laser irradiance of 4.4 x 1 O W/cm assuming a 1 m long plasma. , 2 Chapter 4. Results and Discussions 95 1 E 0 U) z w ci z 1:5LU -J LU 1 o21 100 1000 3000 ELECTRON TEMPERATURE (eV) Figure 4.15: Density—temperature plot for data obtained at a laser irradiance of 4.4 x 1014 , assuming a 10 pm long plasma. 2 W/cm Chapter 4. Results and Discussions 1 o23 96 rz : :Ezzz: .\ : :z:z: :zz.: C’) C.) 1 22 E::::E::::::::::: :::::::::::‘.::: .:::.:::: :::: :: :::::::::::::::::::::::::::::::::::::::::::‘::::::: ZEZZ7/ .J/ J// ! 10 21 :. ( : I 100 z ... • abcd/jkf S qrfjkl #1-91#12 #1O/jkI . ....i 1000 ELECTRON TEMPERATURE 3000 (eV) Figure 4.16: Density—temperature plot for data obtained at a laser irradiance of 4.4 x i0’ , assuming a 50 im long plasma. 2 W/cm Chapter 4. Results and Discussions 97 i CI, C) 22 io I ia 21 300 800: ELECTRON TEMPERATURE (eV) Figure 4.17: Results of the current investigation plotted on the density—temperature plane. The open squares correspond to data obtained at a laser irradiance of 4.4 x 1014 2 and the solid circles correspond to data obtained at a laser irradiance of 1.1 x 1 0 W/cm . The lengths of the plasma assumed in the interpretation are denoted (a) 1 irn, 2 W/crn (b) 10 trn, amid (c) 50 ,um. Chapter 4. Results and Discussions 4.2 98 Discussion The validity of these results depends on the spatial and temporal localization of the plasma which produces the dominant K-shell emission and on sufficient reduction of opacity effects due to the surrounding lower density plasma. The densities and temper atures shown in figure 4.17 represent an average over the region of the ablation plasma which dominates x-ray emission in the 6A to the 7A range. A specific density and temperature cannot be assigned to a specific volume of plasma on the basis of this mea surement. On the other hand, if the x-ray lines used in the line-intensity ratios were not spatially localized, then the measured line-intensity ratios will reflect densities and temperatures corresponding to different regions of the ablation plasma and one would not expect the curves in figures 4.11—4.16 to intersect at a single point. The observed intersection of the diagnostic curves in a reasonably well-defined range of density and temperature may indicate that the dominant emissions are strongly localized in a region of the ablation plasma. It is possible to argue that opacity due to the coronal plasma is not a strong effect in this measurement. Figure 4.18 shows curves of density and temperature which yield an optical depth of T = 1.73, where r is defined by equation 2.12, for the diagnostic lines used and assuming a 1 jm plasma. It can be seen from equation 2.12 that r = 1.73 is the one e-folding optical depth of the plasma. Also plotted in figure 4.18 is the diagnostic summary of the density-temperature data from a laser irradiance of 1.1 x 1015 W/cm . 2 Finally, the plasma densities and their corresponding temperatures from a numerical plasma simulation have been plotted on the density-temperature plane for three different times in the simulation. This is similar to plotting the data from figure 1.2 on the density-temperature plane instead of in real space. The numerical simulation was done by a one-dimensional finite-element hydrodynamic laser target code . A Gaussian laser 6 Chapter 4. Results and Discussions 99 pulse having a full-width-half-maximum duration of 2.5 ns was used in the simulation, and the peak laser intensity was 1.1 x 1015 W/cm 2 at 4 us. The calculated densitytemperature data was also plotted for times of 3 ns and 5 ns. Figures 4.19 and 4.20 are similar, except that the diagnostic results and the opacity curves were plotted for plasma lengths of 10 tm and 50 ,um, respectively. Figures 4.21—4.23 are analagous to figures 4.18—4.20, except that the data and the hydrodynamic simulation correspond to a laser irradiance of 4.4 x 1014 W/cm . 2 Figures 4.18—4.23 show that the temperatures and densities at which the plasma becomes opaque to the diagnostic emission lines are deeper in the plasma than where the data indicate the dominant x-ray emission region to be. Also, the diagnostic lines become opaque almost for the same density and temperature values as the data indicate if a 50 ,um plasma is assumed. The density-temperature contours predicted by the hydrodynamic code are useful in the interpretation of this scenario. A one-dimensional simulation was chosen because it is computationally feasible in the present work. Although they are from a one-dimensional simulation and do not incorporate radiative energy transport mechanisms, the densitytemperature contour may not be completely inaccurate. The absence of radiative energy transport mechanisms in the simulation is a weakness which cannot be accounted for in the present work. The strongly divergent plasma flow will change the physical distance over which the density and temperature profiles, such as those shown in figure 1.2, will vary. However, it is not unreasonable to suppose that the change will manifest itself as a physical compression of the length scale over which the density and temperature gradients occur while leaving similar density-temperature conditions. The data also fall in the proximity of the density-temperature contours predicted by the hydrodynamic code. There are three remaining points that are noteworthy. The densities inferred from the Chapter 4. Results and Discussions 100 abcd/jkl line intensity ratio do not agree with the densities inferred from the qr/jkl and #1 — 9/#12 line intensity ratios, except for the case where the plasma length is assumed to be 50 [tm. This discrepancy could arise from the sweeping assumptions made to apply the uniform, constant plasma model. Also, it could reflect a deficiency in the values chosen for the atomic rate coefficients or merely a fortuitous choice of plasma length. As discussed in Chapter 3, 50 1 um is an estimate representing an upper limit on the size of the ablation plasma, and that it is improbable that the ablation plasma should be so large. The variation of the measured plasma conditions, shown in figure 4.17, is not un expected. The upper and lower boundaries on the densities found in the ablation zone are determined by the density of the cold target material on one side and by the critical density layer on the other side. The density of these two boundaries does not depend on the laser irradiance, but on the target material and the wavelength of the laser light used to irradiate the target. Reducing the irradiance primarily reduces the temperature, and the reduction in the overall temperature of the ablation plasma may shift the dominant emission region of the ablation plasma to a slightly lower temperature. It is beyond the scope of RATION to predict line emission intensities for the lithium— like satellites of the He resonance line shown in figure 4.10. This is unfortunate, for comparison of temperatures and densities predicted by the satellites of a high order excited state with those of the first order excited state may be useful as a test of the spatial localization of the dominant emission plasma. Chapter 4. Results and Discussions 101 24 EE:E:E:EE s- -- - Ct) t fk 2 0 23 4Z t ::: .;:::::::: 2.tzr - U) 2 fl- -r > — — t . u-I 0 2 - T tr J .—- 0 LI-I -J LU :::::::::; sr - • , t —J I v— ‘% -— 22 -to 1 o21 — — —I . 200 1000 ELECTRON TEMPERATURE • #10 a #12 •— #1-3 A #4-9 —0----— ad —D------- q —0---—— jkI x 2000 (eV) t=4ns —0---—— t=5ns m Exp. Res. t=3ns Figure 4.18: Data and hydrodynamic simulation for a laser irradiance of 1.1 1015 W/cm 2 and opacity contours for r 1.73 assuming a plasma length of 1 ,um. The peak of the laser pulse is at t = 4 ns. x Chapter 4. Results and Discussions 102 1 o24 w ar Cr) EEEEEE” EEE E.hE :..:F E C.) 23 :1: U) - z 0 z Lii ts —A w 1 o22 . L c — — ----z I: ::S-::EE: Ed .— —-... . 10 t 21 I .— 1.._._.__ .......:.._.._i........L.... 200 1000 2000 ELECTRON TEMPERATURE (eV) • t • A #10 #12 #1-3 #4-9 —0---—- ad qr JkI —D—-— —0---— x t=3ns I t=4ns —0---— t=5ns $ Exp.Res. Figure 4.19: Data and hydrodynamic simulation for a laser irradiance of 1.1 x 1015 W/cm 2 and opacity contours for r = 1.73 assuming a plasma length of 10 pm. The peak of the laser pulse is at t = 4 ns. Chapter 4. Results and Discussions 103 24 1a .. :::zi:z: :z:zpr ::::aa.-a N Cr, -a. E C) 1 o23 -‘%: :: t::r’— ---‘ .: —- &,s-z:r.::::::: EEE3EE Cl) ‘%. z 0 I Iii 12 o 1 — — :: .42ZrS.: ‘ rrr — —I- —j --- - ?— c’: — -•----A’1--,j’----ci 1 o22 1—.-.---—- ? t ::i -w Lii ft . -- a--a jPC...$ __*1 : ZZJE z* 200 2000 1000 ELECTRON TEMPERATURE (eV) • • • A #10 #12 #1-3 #4-9 —0——ad —D———qr —o---—jkI X t=3ns I m t=4ns Exp.Res. Figure 4.20: Data and hydrodynamic simulation for a laser irradiance of 1.1 x 1015 W/cm 2 and opacity contours for -r = 1.73 assuming a plasma length of 50 pm. The peak of the laser pulse is at t = 4 us. Chapter 4. Results and Discussions 104 1 o24 I CO E C) 1 o23 — r-ccc C/) z Lu -S—-- c: 4 0 z 0 1 o22 EEEEEE c=-_____ Th— £ •1 . 3- —. —, I —3 — z :::::..::.::::..::. EIEEE . I 1o 21 200 t.......... 2000 1000 ELECTRON TEMPERATURE (eV) • • #12 #1-3 A #4-9 —0---- ad —0----— qr —0-—-- —&-—-- jkI ifi :< I t=5ns Exp. Res. t=3ns t=4ns Figure 4.21: Data and hydro dynamic simulation for a laser irradiance of 4.4 x 1014 W/cm 2 and opacity contours for = 1.73 assuming a plasma length of 1 tm. The peak of the laser pulse is at t = 4 ns. r Chapter 4. Results and Discussions 105 io24 ::::::::::::::::::::::: :::::::::::::::: 1 ::::::±::::L::::xb::::::::;::,_.—” EE:E::-E:E::: .±Cr n—zF: j,=v . I — S ..--A I - C,, — C, 23 -to A7 U) w c_u w z 4-!- w a u-I -J 2V 1 o22 D:::::::::::z: — I 4 a— rzTr r - r e c,.mc— ---- - z 0 a: .—--. J , -> Pt6 :Ø2 6 t .. - f E — ‘— — a — — :::;:::::::::::::::::z::::: :::r——....._±-.:::‘—‘-?t—..-..±- u-i 10 21 i___._.t____t_ 200 1000 ELECTRON TEMPERATURE (eV) • I -- — • A. #10 #12 #1-3 #4-9 —0——— ad —ci——--- qr —4—----- jkI X t=3ns 2000 t=4ns —0--— t=5ns Exp. Res. I Figure 4.22: Data and hydrodynamic simulation for a laser irradiance of 4.4 x 1014 W/cm 2 and opacity contours for r = 1.73 assuming a plasma length of 10 1 um. The peak of the laser pulse is at t = 4 ns. Chapter 4. Results and Discussions io24 106 E1EE ::::::::::t:::::::: ::::::: c:::::::::::::::::::: r ::. A6 ‘S a) 6 C) io23 N\ U) z t nTh— - 2 ..fl. Th, w a 2 — — 0 ‘5 I Lii -- n Lii LC fl S4 W — — io22 t 1 — EEEEHHEfE EEEEEEEE:EEEEEEEEZEEZ3__. .:zE:::z:: 1 o2 t — — 200 — 2000 1000 ELECTRON TEMPERATURE (eV) • #10 —0-——— ad • #12 —0--—— qr • #1-3 —Ø-——— 4 #4-9 x jkI I —0-—--- m t=4ns t=5ns Exp. Res. t=3ns Figure 4.23: Data and hydrodynamic simulation for a laser irradiance of 4.4 x 1014 W/cm 2 and opacity contours for ‘r = 1.73 assuming a plasma length of 50 pm. The peak of the laser pulse is at t 4 ns. Chapter 5 Conclusions 5.1 Summary of present work Short-scalelength plasmas have been investigated as an alternative to the other more conventional plasma spectroscopy techniques described in Chapter 1. Short-scalelength plasma spectroscopy has both advantages and disadvantages. Although the present work does not rigorously support it, the most important ad vantage of short-scalelength plasma spectroscopy is that simple plasma models may be used to interpret the data, instead of modelling a laser-produced plasma. The strongly divergent plasma flow reduces the opacity of the corona and may lead to the spatial and temporal localization of the region of the ablation plasma which dominates the emission of the helium-like and the lithium-like satellite lines. Thus, a constant, uniform, plasma model may be used to interpret the data. Short-scalelength plasma spectroscopy enjoys a number of technical advantages as well. The small laser focal spot leads to extremely high (1015 W/cm result in strong x-ray production. A small ( 2) irradiances which 70 /Lm), bright source allows a simple spectrometer like the one used in the present work to achieve high resolution. In fact it is due to the high resolution that the abcd and qr satellite lines are separated well enough to be used independently from each other in the measurement of line-intensity ratios. The targets irradiated by the laser to form the plasma are uncoated planar targets, which is the simplest possible target configuration. The more conventional techniques 107 Chapter 5. Conclusions 108 discussed in Chapter 1 generally employ more complicated targets. Finally, the laser facility needed to conduct this experiment is modest by comparison with the laser facilites required by the conventional techniques described in Chapter 1. This is due to the efficient x-ray conversion resulting from the use of uncoated planar targets and the inherelltly intense laser focus of short-scalelength plasma spectroscopy. The disadvantage of short-scalelength plasma spectroscopy is that it does not probe a regioll with a single density and temperature in the ablation plasma but an average over the dominant emission region of the ablatioll plasma. As such, detailed information about the ablation plasma will not be obtained from these spectroscopic measurements. 5.2 New Contributions The present work has shown that short-scalelength plasma spectroscopy may provide a relatively simple technique to access and interpret the data from a hot, dense and well localized plasma for the purpose of testing atomic physics models and measuring a general characteristic of the ablation plasma, namely an average temperature and density of the dominant x-ray emission plasma. 5.3 Future work The apparent discrepancy between the densities inferred from the abcd/jkl line-intensity ratio diagnostic the qr/jkl and #1 — 9/#12 line-intensity ratio diagnostic, previously discussed in Chapter 4, may indicate deficiencies in the atomic data. The popularity of the abcd/jkl line-intensity ratio as a density diagnostic warrents further investigation of this discrepancy. Chapter 5. Conclusions 109 Modelling laser-produced plasmas can pose great technical difficulty because it in volves numerous approximations or even omissions of physical processes relating to trans port phenomena. However, numerical modelling of the short-scalelength plasma may be useful as a guide to the application of a constant, uniform plasma model. Bibliography [1] H. Ha, Plasmas at High Temperature and Densities Applications and Implications of Laser-Plasma Interaction , Springer-Verlag, Berlin (1991). [2] A. Ng, D. Salzmann, A.A. Offenberger, Phys. Rev. Lett. 43,1502 (1979) [3] P. Mora, Phys. Fluids 25, 1051 (1982) [4] C. deMichelis and M. Mattioli, Nuclear Fusion 21, 677 (1981) [5] D. J. Nagel X-Ray Emission from High Temperature Laboratory Plasmas, U. S. A. Naval Research Laboratory 16, (1974) [6] LTC University of British Columbia (1991) [7] M. H. Key and R. J. Hutcheon, Advances in Atomic and Molecular Physics (D. R. Bates and B. Bederson, eds.) 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Lett. 42, 1606 (1979) [19] A. H. Gabriel, Mon. Not. R. Astr. Soc.160, 99 (1972) [20] J. G. Lunney J. Phys. B. 16 L631 (1983) [21] R. L. Kauffmann, R. W. Lee, K. Estabrook, Phys. Rev. A 35, 4286 (1987) [22] U. Feldman, G. A. Doscheck, D. J. Nagel, R. D. Cowan, R. R. Whitlock, Astrophys. J. 192, 213 (1974) [23] V. A. Boiko, S. A. Pikuz, and A. Ya Fenov, J. Phys. B. 12, 1889 (1979) [24] R. W. Lee, B. L. Whitten, and R. E. Stout, II, J. Quant. Spectrosc. Radiat. Transfer 32, 91(1984) [25] R. W. P. McWhirter and A. G. Hearn, Proc. Phys. Soc., London 82, 641 (1963) [26] H. Griem, Plasma Spectroscopy, Mcgraw-Hill Book Company, New York (1964) [27] V. L. Jacobs and M. Blaha, Phys. Rev. A 21, 525 (1980) [28] R. W. P. McWhirter, Plasma Diagnostic Techniques (R.H. Huddlestone and S.L. Leonard, eds.), Academic Press, New York (1965) [29] R. W. P. McWhirter and H. P. Summers, Applied Atomic Collision Physics, Vol. 2 (R.H. Huddlestone and S.L. 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Short-scalelength plasma spectroscopy Forsman, Andrew 1992
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Title | Short-scalelength plasma spectroscopy |
Creator |
Forsman, Andrew |
Date Issued | 1992 |
Description | Traditional x-ray plasma spectroscopy techniques employ long scalelength laser-produced plasmas in an attempt to moderate the density and temperature gradients present in the ablation plasma. These approaches have the disadvantages that the large plasma may lead to significant opacity effects, lasers having substantial power must be used and numerical simulations of the laser-produced plasma frequently must be used to interpret the data. As an alternative technique the use of short-scalelength plasmas as sources for x-ray spectroscopy have been investigated. High-resolution silicon K-shell spectra from a short-scalelength, laser-produced plasma have been obtained in temporally and spatially integrated measurements. Density-sensitive line-intensity ratios of the helium like satellites and that of the lithium-like satellites are employed simultaneously with temperature-sensitive line-intensity ratios between the helium and lithium-like satellites to assess their diagnostic value. A constant, uniform plasma model is used to interpret the data. It appears that the emission of dielectronic satellite lines is dominated by a region with a relatively well-defined density and temperature in the ablation zone. |
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Thesis/Dissertation |
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Text |
File Format | application/pdf |
Language | eng |
Date Available | 2008-12-15 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0086522 |
URI | http://hdl.handle.net/2429/2918 |
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Master of Science - MSc |
Program |
Physics |
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Science, Faculty of Physics and Astronomy, Department of |
Degree Grantor | University of British Columbia |
Graduation Date | 1992-11 |
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UBCV |
Scholarly Level | Graduate |
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