This textbook provides a comprehensive introduction to the physics of laser-plasma interactions (LPI), based on a graduate course taught by the author. The emphasis is on high-energy-density physics (HEDP) and inertial confinement fusion (ICF), with a comprehensive description of the propagation, absorption, nonlinear effects and parametric instabilities of high energy lasers in plasmas.
The recent demonstration of a burning plasma on the verge of nuclear fusion ignition at the National Ignition Facility in Livermore, California, has marked the beginning of a new era of ICF and fusion research. These new developments make LPI more relevant than ever, and the resulting influx of new scientists necessitates new pedagogical material on the subject. In contrast to the classical textbooks on LPI, this book provides a complete description of all wave-coupling instabilities in unmagnetized plasmas in the kinetic as well as fluid pictures, and includes a comprehensive description of the optical smoothing techniques used on high-power lasers and their impact on laser-plasma instabilities. It summarizes all the key developments from the 1970s to the present day in view of the current state of LPI and ICF research; it provides a derivation of the key LPI metrics and formulas from first principles, and connects the theory to experimental observables.
With exercises and plenty of illustrations, this book is ideal as a textbook for a course on laser-plasma interactions or as a supplementary text for graduate introductory plasma physics course. Students and researchers will also find it to be an invaluable reference and self-study resource.
Author(s): Pierre Michel
Series: Graduate Texts in Physics
Publisher: Springer
Year: 2023
Language: English
Pages: 422
City: Cham
Preface
Contents
1 Fundamentals of Optics and Plasma Physics
1.1 Basic Principles of Optics and Description of Light Waves
1.1.1 Vacuum Propagation of Light; The Paraxial Wave Equation
1.1.2 Fourier Optics
1.2 Basic Principles of Plasma Physics
1.2.1 The Plasma State; Debye Length and Screening
1.2.2 The Plasma Frequency
1.2.3 Equilibrium (Maxwellian) Velocity Distributions in Plasmas
1.2.4 Kinetic (Vlasov) and Fluid Descriptions of Plasmas
1.2.4.1 The Vlasov Equation
1.2.4.2 The Fluid Equations
1.3 Waves in Plasmas
1.3.1 Fluid Description: Dielectric Framework
1.3.1.1 Plasma as a Dielectric Medium
1.3.1.2 Transverse (Electromagnetic) Waves
1.3.1.3 Longitudinal (Plasma) Waves: General Description
1.3.1.4 Electron Plasma Waves (EPWs)
1.3.1.5 Ion Acoustic Waves (IAWs)
1.3.2 Rapid Derivation of the Wave Equations; Acoustic Waves in the Presence of Background Flow
1.3.3 Kinetic Description of Plasma Waves
1.3.4 Landau Damping
1.3.5 Wave Energy and Action
1.3.6 Ion Acoustic Waves in Multi-Species Plasma
1.4 Electron-Ion Collisions
1.4.1 Single Electron-Ion Coulomb Collision
1.4.2 Momentum Loss for a Single Electron Interacting with a Background of Ions
1.4.3 Momentum Loss for a Drifting Maxwellian Distribution of Electrons Interacting with Ions
1.5 Isothermal Expansion of Plasma in Vacuum (and Ion Acceleration) in 1D
Problems
References
2 Single Particle Dynamics in Light Waves and Plasma Waves
2.1 Particle Dynamics in a Uniform Light Wave
2.2 Particle Dynamics in a Uniform Plasma Wave
2.2.1 Phase-Space Analysis: Analogy with the Simple Pendulum
2.2.2 Transit Time and Bounce Period of Passing and Trapped Particles
2.2.3 Wave–Particle Energy Conservation: Connection with Landau Damping
2.3 Particle Dynamics in a Non-uniform Light or Plasma Wave: The Ponderomotive Force
2.3.1 Ponderomotive Force from Plasma Waves
2.3.2 Ponderomotive Force from Light Waves
2.3.3 Beat Pattern Between Two Overlapped Waves
2.3.4 Connection Between the Ponderomotive Force and the Single Particle Motion in Uniform Light or Plasma Waves
Problems
References
3 Linear Propagation of Light Waves in Plasmas
3.1 The WKB Method
3.2 Airy Description at the Turning Point
3.2.1 Connection Between WKB and the Airy Description Up to the Turning Point
3.2.2 Field Evanescence Past the Turning Point
3.2.3 Regions of Validity
3.3 Oblique Incidence (s-Polarization)
3.4 Ray-Tracing
3.5 Frequency Shift of a Light Wave Reflecting Off an Expanding Density Profile
Problems
References
4 Absorption of Light Waves (and EPWs) in Plasmas
4.1 Ballistic Model of Collisional (or Inverse Bremsstrahlung) Absorption
4.1.1 Physical Picture
4.1.2 Low-Field Limit (vos vTe)
4.1.3 High-Field Limit (vos vTe)
4.2 Collisional Absorption from a Fluid Model: Dielectric Constant with Absorption
4.3 Collisional Heating Rate
4.4 Coulomb Logarithm
4.5 Collisional Damping of EPWs
4.6 Non-Maxwellian Electron Distributions from Collisional Heating: The Langdon Effect
4.7 Estimating Collisional Laser Absorption in Idealized Plasma Profiles
4.7.1 Laser Absorption at a Turning Point
4.7.2 Absorption in Isothermal 1D Density Profiles
4.8 Resonance Absorption of p-Polarized Light Waves
4.8.1 Physical Picture
4.8.2 Qualitative Analysis
Problems
References
5 Nonlinear Self-action Effects in Light Propagation in Plasmas
5.1 The Ponderomotive Force: Fluid Approach
5.2 Linear Plasma Response to a Laser's Ponderomotive Force: Transient Stage
5.3 Nonlinear Plasma Response to a Laser Ponderomotive Force in Steady-State
5.4 Plasma Response to a Ponderomotive Driver: Linear Kinetic Model
5.5 The Nonlinear Refractive Index of Plasmas
5.6 Self-Focusing
5.6.1 Geometric Optics Description
5.6.2 Wave Optics Description
5.6.2.1 Envelope Equations and Soliton Solution
5.6.2.2 Behavior at P>Pc
5.7 Laser Beam Deflection in Flowing Plasmas
5.7.1 Physical Picture
5.7.2 Nonlinear Density Perturbation Displacement by Plasma Flow
5.7.3 Expression for the Beam Bending Rate
Problems
References
6 Introduction to Three-Wave Instabilities
6.1 Physical Picture
6.2 List of Possible Three-Wave Coupling in Plasma
6.3 Derivation of the Second-Order Coupled Mode Equations
6.3.1 Driven Light Wave Equation
6.3.2 Driven EPW Equation
6.3.3 Driven IAW Equation
6.4 General Concepts and Methods for Three Wave Coupling
6.4.1 The Slowly Varying Envelope Approximation
6.4.2 Coupled Equations with Wave Damping
6.4.3 Temporal Growth Rate
6.4.4 Spatial Amplification Rate and Definition of the Strongly Damped Regime of Instability
6.4.5 Instability Dispersion Relation
6.4.6 Conservation Laws in Three-Wave Coupling; The Manley–Rowe Relations
6.5 Spatial Amplification in a Non-Uniform Plasma: The Rosenbluth Gain Formula
6.5.1 Coupled Mode Equations in a Non-Uniform Plasma
6.5.2 Weakly Damped Waves
6.5.3 Strongly Damped Plasma Wave
6.6 Absolute vs. Convective Instabilities
6.6.1 Physical Picture
6.6.2 Green's Function of the Three-Wave System
6.6.3 Convective and Absolute Growth Rates and Thresholds
6.6.4 Final Remarks
Problems
References
7 Wave Coupling Instabilities via Ion Acoustic Waves
7.1 Stimulated Brillouin Scattering (SBS)
7.1.1 Phase-Matched Coupled Mode Equations and Temporal Growth Rate
7.1.2 Spatial Amplification in Uniform and Non-uniform Plasmas
7.1.3 Dispersion Relation: Strongly vs. Weakly Coupled Regimes
7.1.4 Mitigation of SBS Using Mixed-Species Plasmas
7.2 Crossed-Beam Energy Transfer (CBET)
7.2.1 Introduction
7.2.2 Fluid Analysis
7.2.3 Kinetic Analysis
7.2.4 Electric Field Dephasing and Variation of the Refractive Index in Off-resonance CBET
7.2.5 Polarization Effects
7.3 The Filamentation Instability
7.3.1 Introduction
7.3.2 Dispersion Relation and Growth Rate
7.3.3 Weakly vs. Strongly Coupled Regimes of Filamentation
7.3.4 Transition from Forward SBS to Filamentation
7.3.5 Physical Interpretation of the Filamentation Instability in Terms of Four-Wave-Mixing Phase-Matching Condition
7.3.6 Connection Between Self-focusing and Filamentation
7.3.7 Thermal Filamentation
Problems
References
8 Wave Coupling Instabilities via Electron Plasma Waves
8.1 Stimulated Raman Scattering (SRS)
8.1.1 Generalities: Spectrum of Raman Scattered Light vs. Plasma Conditions
8.1.2 Coupled Mode Equations: Temporal Growth Rate
8.1.3 Spatial Amplification in Uniform and Non-uniform Plasma
8.1.4 Scattering Geometry: Forward- vs. Side- vs. Back-Scatter
8.1.4.1 Back- vs. Forward-Scatter
8.1.4.2 Side-Scatter
8.2 Two Plasmon Decay (TPD)
8.2.1 Coupled Mode Equations and Temporal Growth Rate
8.2.2 Spatial Amplification in a Density Gradient
8.2.3 Multi-beam Process
8.2.4 Experimental Signatures of TPD from Half-Harmonic (ω0/2 and 3ω0/2) Emission
8.3 Ion Acoustic Decay (IAD) Instability
8.4 Suprathermal Electrons from Driven EPWs
8.4.1 General Considerations
8.4.2 Measurement of Suprathermal Electrons via Bremsstrahlung Emission
Problems
References
9 Optical Smoothing of High-Power Lasers and Implications for Laser–Plasma Instabilities
9.1 Random (or Continuous) Phase Plates (RPP/CPP)
9.1.1 General Concept and Expression of the Resulting Electric Field
9.1.2 Speckle Size
9.1.3 Statistics of the Intensity Distribution
9.1.4 Statistics of Speckles as Local Maxima of Intensity
9.1.5 Impact of Refraction on the Speckle Pattern
9.2 Polarization Smoothing (PS)
9.2.1 General Concept
9.2.2 Intensity Statistics and Reduction of the Speckle Contrast Using PS
9.3 Smoothing by Spectral Dispersion (SSD)
9.3.1 General Concept, Expression of the Electric Field at the Lens
9.3.2 Electric Field at Best Focus with an RPP and SSD
9.3.3 Speckle Lifetime
9.4 Induced Spatial Incoherence (ISI)
9.5 Laser–Plasma Instabilities from Optically Smoothed Laser Beams
9.5.1 Filamentation of Optically Smoothed Laser Beams
9.5.1.1 RPP Beams
9.5.1.2 Mitigation of Filamentation Using PS, SSD, and ISI
9.5.2 Backscatter from Smoothed Beams
9.5.2.1 Backscatter from RPP Beams: Onset of Nonlinear Behavior due to Speckles
9.5.2.2 A Simple Model for Reflectivity Saturation of an RPP Beam
9.5.2.3 Mitigation of Backscatter Using PS
9.5.2.4 Backscatter Mitigation via SSD or ISI
Problems
References
10 Saturation of Laser–Plasma Instabilities and Other Nonlinear Effects
10.1 Saturation by Pump Depletion in Uniform Plasma
10.1.1 Pump Depletion for 1D Backscatter: The ``Tang formula''
10.1.2 Pump Depletion for 1D Forward Scatter and Co-Propagating Geometry
10.1.3 Pump Depletion in 2D for CBET
10.2 Fluid Nonlinearities: Secondary Instabilities and Harmonics Generation
10.2.1 Langmuir Decay Instability (LDI)
10.2.2 Two-Ion Decay (TID)
10.2.3 Electromagnetic Decay Instability (EDI)
10.2.4 Harmonics Generation
10.3 Kinetic Effects
10.3.1 Reduction of Landau Damping and ``kinetic inflation''; Threshold from De-Trapping Processes
10.3.1.1 Kinetic Inflation Process
10.3.1.2 Inflation Threshold from Convective De-Trapping
10.3.1.3 Inflation Threshold from Collisional De-Trapping
10.3.2 Saturation of Inflation by Nonlinear Frequency Shifts
10.3.3 Plasma Heating
Problems
References
A Formulary
A.1 Plasma Parameters
A.2 Waves in Plasmas
A.2.1 EMWs
A.2.2 EPWs
A.2.3 IAWs
A.3 Plasma Dispersion Function
A.4 Landau Damping
Index
