Classical and Quantum Description of Plasma and Radiation in Strong Fields

Description

This thesis presents several important aspects of the plasma dynamics in extremely high intensity electromagnetic fields when quantum electrodynamics effects have to be taken into account. This work is of utmost importance for the forthcoming generation of multipetawatt laser facilities where this physics will be tested. The first part consists of an introduction that extends from classical and quantum electrodynamics in strong fields to the kinetic description of plasmas in the interaction with such fields. This can be considered as an advanced tutorial which would be extremely useful to researchers and students new to the field. The second part describes original contributions on the analysis of the signatures of classical and quantum radiation reaction on the distribution function of the charged particles and of the photon spectrum, and leads to significant advances on this topic. These results are then extended to the analysis of the so-called QED cascades which are of central importance for a better understanding of some astrophysical phenomena and basic physics problems. Finally, the book discusses future directions for the high intensity laser–plasma interaction community. The results presented in this thesis are expected to become more and more relevant as the new multipetawatt facilities become operative. Supervisor’s Foreword Acknowledgements Contents List of Symbols Conventions and Units 1 Introduction 1.1 Strong-Field Regime of Quantum Electrodynamics 1.2 Schwinger-Sauter Mechanism 1.3 Strong-Field QED Processes 1.4 Sources of Strong Fields and High-Energy Particles in Nature and in the Laboratory 1.5 Laser-Plasma Interaction at Ultra-High Intensity 1.6 Presentation of This Work References Theoretical Background 2 Classical Electrodynamics 2.1 Outline 2.2 Classical Field Theory 2.2.1 Euler-Lagrange Equations 2.2.2 Noether's Theorem 2.2.3 Poincaré Invariance 2.2.4 Energy-Momentum Tensor 2.3 Classical Electrodynamics 2.3.1 Lagrangian 2.3.2 Equations of Motion 2.3.3 Energy-Momentum 2.4 Radiation by Moving Charges 2.4.1 Physical Picture 2.4.2 Retarded and Advanced Propagators 2.4.3 Liénard-Wiechert Potentials 2.4.4 Radiated Electromagnetic Field 2.4.5 Larmor Formula 2.4.6 Radiated Spectrum 2.4.7 Charged Particle in a Plane-Wave Field 2.4.8 Linear and Nonlinear Thomson Scattering 2.4.9 Radiation by an Ultra-Relativistic Particle in Arbitrary Motion 2.5 Classical Radiation-Reaction 2.5.1 The Lorentz-Abraham-Dirac Equation 2.5.2 The Landau-Lifshitz Equation 2.5.3 Charged Particle in a Constant-Uniform Magnetic Field with RR 2.5.4 Charged Particle in a Plane-Wave Field with RR 2.5.5 Limit of Applicability of CED and Classical Radiation Dominated Regime (CRDR) References 3 Quantum Electrodynamics 3.1 Outline 3.2 Quantum Field Theory 3.2.1 Canonical Quantization of Classical Fields 3.2.2 Fock Space 3.2.3 The S-Matrix 3.3 Quantum Electrodynamics 3.3.1 Lagrangian 3.3.2 Equations of Motion 3.4 Strong Field QED 3.4.1 Coherent States 3.4.2 Furry Picture 3.4.3 Volkov States 3.4.4 Position Space SFQED Feynman Rules 3.5 Non-linear Compton Scattering 3.6 Non-linear Breit-Wheeler Pair Production 3.7 Quantum Radiation-Reaction References 4 Kinetic Description 4.1 Outline 4.2 Kinetic Description 4.2.1 The Klimontovich Equation 4.2.2 The Vlasov Equation 4.3 Kinetic Description of Radiation-Reaction 4.3.1 Motivation 4.3.2 Vlasov Equation with Classical RR 4.3.3 Vlasov Equation with Quantum RR 4.3.4 Vlasov Equation with Pair-Production 4.4 Extended PIC Method for SFQED 4.4.1 Classical RR Pusher 4.4.2 Monte-Carlo Module References From Quantum to Classical Radiation Reaction 5 Effect of RR on the Electron Distribution Function 5.1 Outline 5.2 Dynamics of a Radiating Electron in Classical and Quantum Electrodynamics 5.2.1 Dynamics of a Classical Radiating Electron 5.2.2 Radiation Friction Force Acting on an Ultra-Relativistic Electron 5.2.3 Dynamics of a Quantum Radiating Electron 5.3 From Quantum to Classical Radiation Reaction for Ultra-relativistic Electrons 5.3.1 Kinetic Point of View: The Linear Boltzmann Equation 5.3.2 Toward the Classical Limit: The Fokker-Planck Approach 5.3.3 Domain of Validity of the Fokker-Planck and Quantum-Corrected Landau-Lifshitz Descriptions 5.4 Local Temporal Evolution of Integrated Quantities 5.4.1 Local Energy Moments of the Collision Operators 5.4.2 Equations of Continuity for the Electrons and Photons 5.4.3 Equation of Evolution of the Mean Momentum 5.5 Global Temporal Evolution of Average Quantities 5.5.1 Conservation of the Number of Electrons and Total Energy, and Photon Production Rate 5.5.2 Equations of Evolution 5.5.3 The Perturbative Expansion 5.5.4 Electron Mean Energy 5.5.5 Variance in Energy: Radiative Cooling vs. Energy Spreading 5.5.6 Third Order Moment and Link to the Quenching of Radiation Losses 5.6 Conclusion References 6 Domain of Validity of the Different Descriptions and Numerical Simulations 6.1 Outline 6.2 Domain of Validity of the Three Descriptions 6.2.1 Case of an Initially Symmetric Energy Distribution 6.2.2 Case of an Initially Non-symmetric Energy Distribution 6.2.3 Physical Implications 6.3 Stochastic (Fokker-Planck) Pusher 6.4 Numerical Results 6.4.1 Constant-Uniform Magnetic Field 6.4.2 Linearly Polarized Plane-Wave 6.4.3 Electron Population with a Broad Energy Dispersion 6.5 Interpretation of the ``Vlasov Terms'' 6.6 Conclusion References 7 Photon Distribution Function 7.1 Outline 7.2 High-Energy Photon Emission and Its Back Reaction 7.2.1 Photon Emission Rate and Energy Spectrum 7.2.2 Radiation Reaction 7.2.3 High Energy Photon Spectrum Accounting for Radiation Reaction 7.3 Numerical Simulations 7.3.1 Method 7.3.2 Results 7.3.3 Electron Beam Head-On Collision with an UHI Plane-Wave 7.3.4 Hot (Maxwell-Jüttner) Electron Population Radiating in a Constant Magnetic Field 7.4 Conclusions References 8 QED Cascades in Counterpropagating Plane-Waves 8.1 Outline 8.2 Motion of a Single Electron in Two Counter-Propagating Plane-Waves 8.2.1 Without RR 8.2.2 With RR 8.3 Evolution of the Electron Distribution Function … 8.3.1 Equations of Evolution of the Energy Moments of the Electron and Photon Distribution Functions in the Presence of a Source 8.3.2 Asymptotic Energy Spread 8.3.3 Asymptotic Third Order Moment 8.3.4 Average Energy 8.3.5 Evolution of an Initial Cold Electron Distribution Function 8.3.6 Interaction of a Hot Maxwell-Jüttner Distribution Function with a Uniformly Rotating Electric Field 8.4 Evolution of the Electron Distribution Function … 8.4.1 Equations of Evolution of the Energy Moments of the Electron and Photon Distribution Functions in the Presence of a Source and with Pair Production 8.4.2 Number of Particles 8.4.3 Average Energy 8.4.4 Asymptotic Energy Spread 8.5 Conclusion References Nonlinear Breit-Wheeler Pair Production with Laguerre-Gauss Beams 9 Orbital Angular Momentum of Light: A State of the Art 9.1 Introduction 9.2 Paraxial Optics 9.2.1 The Helmholtz Equation 9.2.2 The Paraxial Wave Equation 9.3 Linear and Angular Momentum of Light 9.3.1 Linear Momentum of Light 9.3.2 Angular Momentum of Light 9.4 Gaussian Beam 9.5 Higher-Order Beams 9.5.1 Laguerre-Gaussian Beams 9.6 Angular Momentum of LG Beams References 10 Soft Pair Showers in the Collision of Gamma Rays with Laguerre-Gauss Beams 10.1 Outline 10.2 The Nonlinear Breit-Wheeler Process 10.3 Characteristics of the LG Beams 10.4 Nonlinear Breit-Wheeler Pair Production in an External LG Beam 10.5 Conclusion References 11 Conclusion and Perspectives Appendix A Classical Electrodynamics A.1 Bessel Functions A.1.1. Bessel Functions of the First Kind A.1.2 Modified Bessel Functions of the Second Kind A.2 Airy Functions A.3 Tensor Identities A.3.1 Levi-Civita Symbols A.3.2 Constant Field Tensor Identities A.4 Light-Cone Coordinates A.5 Solution of the Equation of Motion of a Charged Particle in a Plane-Wave Electromagnetic Field Without RR A.6 Non-linear Thomson Scattering A.6.1 Circularly Polarized Plane-Wave A.6.2 Linearly Polarized Plane-Wave A.7 Regularized Self-field A.8 Solution of the Equation of Motion of a Charged Particle in a Plane-Wave Electromagnetic Field with RR Appendix B Quantum Electrodynamics B.1 Gamma Matrix Algebra Product of Gamma Matrices Trace of Gamma Matrices B.2 Useful Identities for QED Trace Identities Slashed Quantities Identities B.3 The Dirac Spinors B.4 The Dirac-Volkov States B.5 Nonlinear Compton Scattering Appendix C Electron Distribution Function C.1 Derivation of the Master Equation (5.31摥映數爠eflinkeq:Master55.315) C.2 Exact and Approximate Expressions of an(χ) Functions C.3 Exact and Approximate Expressions of bn(χ) Functions