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University of California Los Angeles Amplification of Short Laser Pulses via Resonant Energy Transfer in Underdense Thermal Plasmas A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Electrical Engineering by Tyan-Lin Wang 2010 c Copyright by Tyan-Lin Wang 2010 The dissertation of Tyan-Lin Wang is approved. Troy Carter Christoph Niemann Warren Mori Chandrasekhar Joshi, Committee Chair University of California, Los Angeles 2010 ii This thesis is dedicated to the scientists in the field of laser-plasma interactions who had the patience, interest, and most importantly, time to assist and support me throughout the research process. iii Table of Contents 1 Introduction :::::::::::::::::::::::::::::::: 1 1.1 Using plasma for amplification of laser pulses . .1 1.2 Selected previous work on BRA . .4 1.2.1 PIC Simulations . .5 1.2.2 Experiments . .9 1.3 Purpose of this dissertation and outline . 13 2 Stimulated Raman Scattering and Backward Raman Amplifica- tion (BRA) Physical Concepts :::::::::::::::::::::: 18 2.1 Derivation of the Three Wave Equations Describing Raman Scat- tering and Light Wave Coupling . 18 2.2 Theory behind the BRA process . 23 2.3 Plasma wave dynamics and their impact on laser beams in BRA . 26 2.4 Multi-dimensional aspects of BRA . 30 2.5 Motivation for choosing 1054 nm as the pump wavelength . 31 3 1D OSIRIS Simulations of Ultrashort Pulse Backward Raman Amplification (BRA) :::::::::::::::::::::::::::: 35 3.1 Case studies of ultrashort pulse amplification . 35 3.1.1 Case I . 37 3.1.2 Case II . 42 3.1.3 Case III . 47 iv 3.1.4 Case IV . 51 3.2 Optimal plasma conditions for amplification . 54 4 Creating Seed Laser Pulses :::::::::::::::::::::: 60 4.1 Description of the experiment . 60 4.2 Experimental layout and procedure . 66 4.3 Experimental results . 70 5 Amplifying Seed Laser Pulses ::::::::::::::::::::: 78 5.1 Introduction . 78 5.2 Experimental layout and procedure . 84 5.3 Experimental results . 90 6 Experimental Results Compared to Simulations ::::::::: 106 6.1 Description of phase plates . 106 6.2 1D OSIRIS and 2D pF3d simulations using experimental parameters110 6.3 Additional BRA studies comparing 1D OSIRIS to 2D pF3d . 124 7 Summary and Ideas for Future Work :::::::::::::::: 142 7.1 Summary . 142 7.2 Ideas for Future Work . 145 A Extended Three Wave Model ::::::::::::::::::::: 149 References ::::::::::::::::::::::::::::::::::: 159 v List of Figures 1.1 Depiction of the SRS cycle (left) and of BRA (right). .4 2.1 Mathematical plots of a π-pulse solution (left) and a normalized seed intensity waveform (right). 25 2.2 Multi-dimensional representation of a π-pulse solution from a pre- focused seed. 31 2.3 Cartoon drawing showing re-amplified SRS from a LEH (left) and the Janus experiment (right) which has pump and seed lasers in- teracting in a plasma made from a gas jet. 33 3.1 Case I - Snapshots of the seed at various times during amplification (left panels) and k spectrum of the pump, seed, and electrostatic waves (right panels). Reprinted with permission from T.-L. Wang, D. S. Clark, D. J. Strozzi, S. C. Wilks, S. F. Martins, and R. K. Kirkwood, Phys. Plasmas 17, 023109 (2010). Copyright 2010, American Institute of Physics. 39 3.2 Wigner transform of the seed pulse undergoing amplification for Case I. 40 3.3 Case I - Color scheme representation of the seed waveform. The bottom row shows zoomed-out snapshots of the seed waveform in the entire box. 41 vi 3.4 Case I - Phase space features at different locations inside the seed pulse. The center image shows the plasma wave with amplitude a2 = eE2/m!0c = 0:01. Non-resonant wave vector components have been filtered out and shown with the initial unfiltered plasma wave. Reprinted with permission from T.-L. Wang, D. S. Clark, D. J. Strozzi, S. C. Wilks, S. F. Martins, and R. K. Kirkwood, Phys. Plasmas 17, 023109 (2010). Copyright 2010, American Institute of Physics. 43 3.5 Case II - Snapshots of the seed at various times during amplifica- tion (left panels) and k spectrum of the pump, seed, and electro- static waves (right panels). Reprinted with permission from T.-L. Wang, D. S. Clark, D. J. Strozzi, S. C. Wilks, S. F. Martins, and R. K. Kirkwood, Phys. Plasmas 17, 023109 (2010). Copyright 2010, American Institute of Physics. 44 3.6 Wigner transform of the seed pulse undergoing amplification for Case II. 45 3.7 Case II - Color scheme representation of the seed waveform. The bottom row shows zoomed-out snapshots of the seed waveform in the entire box. 46 vii 3.8 Case II - Phase space features at different locations inside the seed pulse. The center image shows the plasma wave with amplitude a2 = eE2/m!0c = 0:007. Non-resonant wave vector components have been filtered out and shown with the initial unfiltered plasma wave. Reprinted with permission from T.-L. Wang, D. S. Clark, D. J. Strozzi, S. C. Wilks, S. F. Martins, and R. K. Kirkwood, Phys. Plasmas 17, 023109 (2010). Copyright 2010, American Institute of Physics. 48 3.9 Case III - Snapshots of the seed at various times during amplifica- tion (left panels) and k spectrum of the pump, seed, and electro- static waves (right panels). Reprinted with permission from T.-L. Wang, D. S. Clark, D. J. Strozzi, S. C. Wilks, S. F. Martins, and R. K. Kirkwood, Phys. Plasmas 17, 023109 (2010). Copyright 2010, American Institute of Physics. 49 3.10 Wigner transform of the seed pulse undergoing amplification for Case III. 50 3.11 Case III - Phase space features at different locations inside the seed pulse. The center image shows the plasma wave with amplitude a2 = eE2/m!0c = 0:0017. Non-resonant wave vector components have been filtered out and shown with the initial unfiltered plasma wave. Reprinted with permission from T.-L. Wang, D. S. Clark, D. J. Strozzi, S. C. Wilks, S. F. Martins, and R. K. Kirkwood, Phys. Plasmas 17, 023109 (2010). Copyright 2010, American Institute of Physics. 51 viii 3.12 Case IV - Snapshots of the seed at various times during amplifica- tion (left panels) and k spectrum of the pump, seed, and electro- static waves (right panels). Reprinted with permission from T.-L. Wang, D. S. Clark, D. J. Strozzi, S. C. Wilks, S. F. Martins, and R. K. Kirkwood, Phys. Plasmas 17, 023109 (2010). Copyright 2010, American Institute of Physics. 53 3.13 Wigner transform of the seed pulse undergoing amplification for Case IV. 54 3.14 Case IV - Phase space features at different locations inside the seed pulse. The center image shows the plasma wave with amplitude a2 = eE2/m!0c = 0:003. Non-resonant wave vector components have been filtered out and shown with the initial unfiltered plasma wave. Reprinted with permission from T.-L. Wang, D. S. Clark, D. J. Strozzi, S. C. Wilks, S. F. Martins, and R. K. Kirkwood, Phys. Plasmas 17, 023109 (2010). Copyright 2010, American Institute of Physics. 55 3.15 Density vs temperature plot showing parameter regime for optimal seed amplification. The four cases presented earlier are indicated by the circles. Optimal amplification of the seed is shown to be possible for plasma densities between 0:01 ncr and 0:015 ncr and temperatures up to 200 eV. Reprinted with permission from T.-L. Wang, D. S. Clark, D. J. Strozzi, S. C. Wilks, S. F. Martins, and R. K. Kirkwood, Phys. Plasmas 17, 023109 (2010). Copyright 2010, American Institute of Physics. 57 4.1 Potential energy curves showing the electronic, vibrational, and rotational levels of a molecule. 62 ix 4.2 Simple energy level diagram showing Stokes and anti-Stokes tran- sitions. 63 4.3 Schematic of the 2 meter long Raman gas cell. The inset shows the arrangement of the internal telescope optics. 65 4.4 Schematic of the Raman cell. 68 4.5 Pictures of the experimental setup. 69 4.6 Results of Raman lines produced with H2, N2O, and C3H8 gases. The red vertical line is a reference marker for 1200 nm, showing where it falls in the seed spectrum. All vertical axes are in raw counts. 73 4.7 COMET laser energy scan for N2O gas at 150 psi. 74 4.8 Typical autocorrelation trace giving a pulsewidth measurement of 3.7 ps for the laser pulse converted by N2O gas. 76 4.9 Comparison of normalized spectra for 0.67 ps and 3.7 ps pulses for N2O gas. 76 5.1 Overall schematic of the seed amplification experiment. 85 5.2 View of the various laser beam paths in Target Area 1. 86 5.3 Pictures of the experimental setup. 87 5.4 Typical plasma density interferogram. 91 5.5 Post-processed plasma density profiles. 92 5.6 Experimental results of short pulse seed amplification with vertical axis in raw counts. The initial seed energies are: 5.88 µJ (top left), 54.4 µJ (top right), 160 µJ (bottom left), 228 µJ (bottom right) . 93 x 5.7 Overlaid raw seed spectra for shots 64 −− 126, 67 −− 132, and 65 −− 129 along with SRS noise spectrum before (top) and after (bottom) amplification. 99 5.8 SRS noise spectrum in terms of peak spectral energy. 100 5.9 Short pulse seed amplification results. Peak spectral energy is shown in shaded green diamonds and integrated energy is shown in blue outlined diamonds. 101 5.10 Long pulse seed amplification results. Peak spectral energy is shown in shaded orange diamonds. 102 5.11 Plot of output peak intensity (top) and intensity gain (bottom) versus input peak intensity. Short pulse data are shown in shaded green diamonds and long pulse data in shaded orange diamonds.
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