The latest generation of high-power pulsed lasers has renewed interest in the ultra-relativistic effects produced by the interaction between laser beams and electrons. Synthesising previous research, this book presents a unitary treatment of the main effects that occur in the ultra-relativistic interactions between laser beams and electrons. It uses exact solutions of relativistic and classical quantum equations, including a new solution of the Dirac equation, to fully describe the field and model the main ultra-relativistic effects created within it. Aimed at scientists, graduate students and professionals working in high-power laser facilities and labs, as well as those studying relativistic optics, the book presents a comprehensive survey of the field, intended to facilitate high-level engagement.
Key Features:
- Models the ultra-relativistic effects of laser beam and electron interactions
- Presents a comprehensive, unitary treatment of the main effects occurring in ultra-relativistic interactions between laser beams and electrons.
- Based on exact solutions of relativistic quantum and classical equations.
- Includes instructions for designing new experiments
- Contains Mathematica(R) for further understanding
Author(s): Alexandru Popa
Series: IOP Series in Coherent Sources, Quantum Fundamentals, and Applications
Publisher: IOP Publishing
Year: 2022
Language: English
Pages: 183
City: Bristol
Preface
Author biography
Alexandru Popa
Symbols
About the pagination of this eBook
Chapter 1 Introduction
References
Chapter 2 Exact solutions of the basic equations
2.1 Initial hypotheses
2.2 Solution of the classical equation of electron motion
2.2.1 Equation of the electron motion
2.2.2 Calculation of velocities and accelerations
2.2.3 Calculation of the electron coordinates
2.3 Solution of the Klein–Gordon equation
2.3.1 Relation necessary for our analysis
2.3.2 Solving the Klein–Gordon equation
2.4 Solution of the Dirac equation
2.4.1 Dirac equation
2.4.2 Solution of the system equivalent to the Dirac equation
2.4.3 Verification of the solution of the Dirac equation
2.4.4 Determination of the conditions of validity of the classical models
References
Chapter 3 Modelling ultra-relativistic interactions in electron plasmas
3.1 Initial hypotheses
3.2 Phase effect
3.2.1 Bijective dependence between phase η and time t
3.2.2 The decreasing of Δη when IL increases
3.3 Effect of strong electron acceleration in the ultra-relativistic regime
3.3.1 Variation of electron velocity with phase η
3.3.2 Physical interpretation of the effect of variation of Δη with IL
3.4 Electromagnetic field generated by the electron motion
3.4.1 Calculation of the components of the electromagnetic field
3.4.2 Periodic and aperiodic domains
3.4.3 Modelling the electromagnetic field in the periodic domain
3.4.4 Modelling the electromagnetic field in the aperiodic domain
3.5 Very intense pulses having very large frequency spectra
3.5.1 Algorithm of our calculations
3.5.2 Generation of extremely bright pulses
3.5.3 Calculation of the frequency spectrum and comparison with the experimental data
References
Chapter 4 Modelling interactions between laser beams and ultra-relativistic electron beams
4.1 Initial hypotheses
4.2 Solution of the equation of electron motion in the S′ system
4.3 Solution of the Klein–Gordon equation in the system S′
4.4 Solution of the Dirac equation in the S′ system
4.5 Relations for the linearly polarized laser field
4.6 Comparison with experimental results from the literature
4.6.1 Preliminary observations
4.6.2 Results from SLAC experiments
4.6.3 Results from CERN experiments
4.6.4 Concordance between our solution and the experimental data from the literature
4.7 General conditions for the validity of classical equations in the S′ system
References
Chapter 5 Modelling the radiation damping effect in ultra-relativistic interactions
5.1 Initial hypotheses
5.2 Expressions for damping force and damping energy
5.2.1 Conventions for writing the four-vectors and the electromagnetic field tensor
5.2.2 Components of the radiation damping force and the damping energy
5.3 Radiation damping parameters calculated in the S′ system
5.3.1 Components of the external force and kinetic energy of the electron in the S′ system
5.3.2 Relations for damping force and damping energy
5.3.3 Phase effect in the S′ system
5.3.4 Ratios between damping energy and average kinetic energy and between damping force and external force
5.4 Comparison between theory and data from the literature
References
Chapter 6 Modelling interactions in the vicinity of the ultra-relativistic regime
6.1 Initial hypotheses
6.2 Interactions between a laser beam and electron plasmas
6.2.1 Preliminary presentation
6.2.2 Electromagnetic field generated by interactions between laser beams and electron plasmas
6.2.3 Algorithm of the calculations
6.3 Head-on interaction between a laser beam and an electron beam
6.3.1 Preliminary presentation
6.3.2 Components of the electromagnetic field in the S′ system
6.3.3 Intensity of the electromagnetic field generated by electron motion in the S′ system
6.3.4 Intensity of the electromagnetic field generated by electron motion in the S system
6.3.5 Components of the four-dimensional wave vector in the S system
6.3.6 Angular relations
6.3.7 Energetic relations
6.3.8 Comparison between theoretical and experimental data
6.4 Interactions in 180◦ and 90◦ configurations
6.4.1 Preliminary presentation
6.4.2 Relations between the field parameters in the S and S′ systems
6.4.3 The motion of the electron in the S′ system
6.4.4 The electromagnetic field generated by Thomson scattering in the S′ system
6.4.5 Properties of the hard x-rays in the laboratory system
6.4.6 Comparison between theoretical and experimental data
6.5 Comparison with similar models from the literature
6.6 Interaction between laser beams and atoms
6.6.1 Preliminary presentation
6.6.2 Accurate relations for atom ionization and for the generation rate of radiation
6.6.3 Parameters of the electron motion in the ionization domain
6.6.4 Calculation of the harmonic spectrum
6.6.5 Typical shapes of harmonic spectrum, for medium intensities of laser beam
6.6.6 Typical shapes of harmonic spectrum in the vicinity of the ultra-relativistic domain
6.6.7 Technical limits of applications of very powerful impulse lasers
References
Chapter 7 Condition of applicability of classical models
7.1 Initial hypotheses
7.2 Schrödinger equation, wave equation and characteristic equation
7.3 The characteristic Σ surface and its normal C curves
7.4 Properties of the characteristic curves and surfaces
7.5 The periodicity of the system
7.5.1 Stationary Σ surfaces and C curves
7.5.2 General relation of the Σ surfaces
7.5.3 The reduced action function
7.5.4 Relations between vw and v and between τw and τ
7.5.5 Relation necessary for our analysis
7.6 The integral relation of the Schrödinger equation
7.6.1 Solution of the integral relation of the Schrödinger equation
7.6.2 Quantization relations
7.7 De Broglie relations for multidimensional systems
References
Chapter 8 Conclusions
Chapter
A.1 Calculation of Δη and variation of time as a function of η
A.2 Variation of the electron velocity with η
A.3 Variation of averaged value of E as a function of θ
A.4 Variation of E as a function of η
A.5 Variation of I_av as a function of θ
A.6 Variation of I as a function of η
A.7 Calculation of the harmonic spectrum in the ultra-relativistic regime
