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1.3 Parametric Instabilities 7 1.4 Layout of the Dissertation 14 UCRL-LR-123744 Distribution Category UC-910 Saturation of Langmuir Waves in Laser-Produced Plasmas Kevin Louis Baker (Ph.D. Thesis) Manuscript date: April 1996 LAWRENCE LIVERMORE NATIONAL LABORATORY HI University of California • Livermore, California • 94551 ^5^ MASTER DISTRIBUTION OF IMS DOCUMENT IS UNLIMITED DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document Saturation of Langmuir Waves in Laser-Produced Plasmas By Kevin Louis Baker B.S. (Mississippi State University) 1989 M.S. (University of California, Davis) 1991 DISSERTATION Submitted in partial satisfaction of the requirements for the degree of DOCTOR OF PHILOSOPHY in Applied Science in the GRADUATE DIVISION of the UNIVERSITY OF CALIFORNIA DAVIS Approved: '~4> •ft 4=*$]. Committee in Charge 1996 -i- Contents Acknowledgments vi List of Figures viii Abstract xv 1 Introduction 1 1.1 Introduction 1 1.2 Plasma Basics 4 1.3 Parametric Instabilities 7 1.4 Layout of the Dissertation 14 2 Saturation Mechanisms 17 2.1 Introduction 17 2.2 Saturation from Damping Effects 17 2.3 Saturation due to Plasma Inhomogeneiiies 19 2.4 Pump Depletion 29 2.5 Secondary Decay Processes 32 2.6 Modulational Instability and Collapse of the Langmuir Waves 37 2.7 Ponderomotive Detuning 43 2.8 Mode Coupling(Unstimulated Processes) 48 -ii- a. Self-interaction Between Different Decay Triangles 48 b. Interaction Between Different Instabilities 58 2.9 Relativistic Detuning 61 2.10 Particle Trapping and Wave Breaking 65 Electromagnetic Decay Instability 73 3.1 Introduction 73 3.2 Electromagnetic Decay Instability from Two Plasmon Decay 77 3.3 Seeding of Simulated Brillouin Scattering and Saturation of the Ion Acoustic Decay Instability 87 3.4 Electromagnetic Decay Instability from Stimulated Raman Scattering 91 3.5 Summary 96 3.6 Future Work 98 Thomson Scattering 101 4.1 Introduction 101 4.2 Thomson Scattering in Homogeneous Plasmas 103 4.3 Thomson Scattering in Inhomogeneous Plasmas 114 Initial Thomson Scattering Experiments; Verification of Raman Scattering Models 121 5.1 Introduction 121 iii- 5.2 Experimental Description 124 5.3 Collective Thomson Scattering 129 5.4 Plasma Characterization 131 5.5 Experimental Observations 136 5.6 Discussion 140 5.7 Summary 143 6 Thomson Scattering Measurements of the Langmuir Wave Spectra Resulting from Stimulated Raman Scattering 146 6.1 Introduction 146 6.2 Experimental Layout 148 6.3 Plasma Characterization 154 6.4 Experimental Results 165 6.5 Discussion 170 6.6 Summary 174 7 Summary 175 Appendix 2.1 Derivation of Equations Describing Stimulated Raman Scattering 183 Appendix 2.2 Rosenbluth Model for Parametric Instabilities in Inhomogeneous Plasmas 187 Appendix 2.3 K-space Resonance Width for Steady State 192 Appendix 2.4 Numerical Solution of Rosenbluth Equations 197 -IV- Appendix 2.5 Saturation of Forward Raman Scattering Due to Ponderomotive Detuning 206 Appendix 2.6 Saturation of Forward Raman Scattering Due to Relativistic Detuning 212 Appendix 3.1 Numerical calculation of the scattering version of EDI from an inhomogeneous plasma 216 Appendix 4.1 Derivation of the Thomson Scattered Signal Using the Fluid Equations 221 Appendix 4.2 Derivation of the Thomson Scattering Form Factor in a Homogeneous Plasma 227 Appendix 4.3 Numerical Calculation of Thomson Scattering from an Inhomogeneous Plasma 232 Appendix 4.4 Graphical Solution of the Roots of the Dispersion Relation Corresponding to Ion Acoustic Waves 239 Appendix 4.5 Contour Integrations for Thomson Scattering 244 Bibliography 250 -v Acknowledgments I would first like to thank my dissertation advisor Paul Drake for suggesting the saturation of Langmuir waves as my dissertation topic. His support and guidance during my time as a graduate student is very much appreciated. I would like to thank my academic advisor John De Groot for first instilling in me an interest in plasma physics which set the foundation for my graduate work. I would like to thank Kent Estabrook for his contributions, which included all of the LASNEX simulations of the experiments conducted for this dissertation. In addition, I had numerous discussions with him regarding the material presented in this dissertation. I would like to thank him most, however, for his support and encouragement throughout the course of this dissertation. I would also like to thank David Villeneuve for the time he spent teaching me a number of the experimental skills that I would use throughout the work presented in this dissertation. I would also like to thank him for providing me with experimental time on the LP2 laser system, as well as for a number of subsequent discussions. I thank Russ Evans for his help with the LabView programming used with one of the diagnostics. I would also like to thank Christine Labaune and Hector Baldis for the time they allowed me on the LULI laser system. Over the course of my dissertation, I have had the opportunity to work with and learn from a number of people collaborating on experiments. These collaborators include: David Villeneuve, and Bruno Lafontaine from the -vi- National Research Council; Paul Drake, Keith Bradley, Bruno Bauer, Katsu Mizuno, Steven Batha, and Brad Sleaford from the Plasma Physics Research Institute; Sophie Baton, Nathalie Renard, Christine Labaune, Elisa Schifano, and Hector Baldis from Ecole Polytechnique; Wolf Seka and Ray Bahr from the Laboratory for laser Energetics; and Bob Watt from the Los Alamos National Laboratory. During my graduate studies, I have profited from a number of discussions on topics related to my dissertation. In particular, I would like to thank Bedros Afeyan for countless discussions on parametric instabilities. I also had a great many discussions with Sasha Rubenchik which primarily focused on strong turbulence issues. My discussions with Linda Powers regarding numerical simulations were very beneficial in the development of most of the FORTRAN codes listed in the appendices. I had a number of conversations with Ed Williams on a wide range of topics, the most notable of which guided the development of the code used to solve for the roots of the plasma dispersion relation in multi-ion plasmas. I would also like to thank Denise Hinkel for her discussions concerning resonance absorption. I also profited from discussions with Martin Goldman, Tudor Johnston, Wojtek Rozmus, and Don DuBois. I would like to express my appreciation to my parents and sisters for their moral support throughout my graduate experience, as well as the many preceding years. I would like to thank Christine Coverdale, my closest friend in graduate school, for her support and encouragement. I would also like to thank a number of my closest friends, Tony Correa, Russ Evans, and Christine Shannon, who provided an outlet for me over the years. -vii- List of Figures 1.3.1 Physical description of parametric instabilities illustrating how the wave interactions lead to instability. 9 1.3.2 Graph showing the corona region of a laser produced plasma. 11 1.3.3 Contour plots of the dispersion relation for stimulated Raman scattering. 13 2.2.1 Homogeneous damping stabilization of convective parametric instabilities. 19 2.3.1 Convective versus absolute parametric instabilities in laser- produced plasmas. 21 2.3.2 Numerical solution of the Rosenbluth equations for a linear phase mismatch between the interacting waves. 26 2.3.3 Measured amplification of the scattered electromagnetic wave associated with stimulated Raman forward scattering 28 2.5.1 Figure showing the amplitude of the Langmuir wave at the threshold for convective instability. 35 -viii- 2,6.1 Range of unstable ion wavenumbers, kia, driven by the modulational instability. 39 2.7.1 Comparison of the Langmuir wave amplitude at saturation predicted by the ponderomotive detuning model(dashed .... 46 2.8.1 Wavenumber resolved Thomson scatter spectrum from Langmuir waves and ion waves participating in 53 2.10.1 Approximate Langmuir wave amplitude for which two plasmon decay goes below the convective damping 67 2.10.2 Plot showing the amplitude at which wave breaking becomes important for Langmuir waves. 68 2.10.3 Flux of stimulated Raman scattering driven from a gold solid target. 70 3.2.1 Plot of the coo/2 emission observed from a solid target experiment. 78 3.2.2 Plot of the absolute magnitude of 3a>o/2 emission and coo/2 emission as a function of incident laser intensity. 81 -ix- 3.2.3 Schematic representation of inverse resonance absorption in an inhomogeneous plasma. 83 3.3.1 Wavevector diagram showing the coupling process which leads to electromagnetic emission near the plasma frequency. 89 3.4.1 Finite spatial pump effects on the absolute and convective nature of parametric instabilities. 93 3.4.2 Schematic representation of absolute electromagnetic decay driven by stimulated Raman scattering. 95 4.2.1 Thomson scattering form factor for a 50:50 CH plasma at various values of Ti/Te. 105 4.2.2 Dependence of the shape factor on the ratio of ion to electron temperature for a CH plasma. 107 4.2.3 Attributes of the Thomson scattering shape factor, SCk,©), for a CH plasma. 108 4.2.4 Thomson scatter spectra in a CH plasma as a function of k^oe with Ti/Te fixed at 0.5. 110 -x- 4.2.5 Thomson shape factor for a Carbon plasma in which there exists a finite drift between the electrons and ions. Ill 4.3.1 Numerical evaluation of the Thomson scattered vector potential for the case of a linear phase mismatch between .... 117 5.1.1 Model distribution of the electrons in a plasma containing a hot electron distribution. 123 5.2.1 Experimental layout showing the interaction and probe beams, along with the interaction chamber. 126 5.2.2 Schematic of the detector circuit used for the Au:Ge detector.
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