Phase Space Dynamics in Plasma Based Wakefield Acceleration (Springer Theses)

Supervisor’s Foreword
Preface
Acknowledgements
Contents
1 Introduction
	1.1 Plasma Based Acceleration
	1.2 Particle-in-Cell Simulations
	1.3 Motivation and Outline
	References
2 Phase Space Dynamics of Injected Electron Beams in Ionization Injection
	2.1 Introduction
	2.2 The Photoionization Process
	2.3 The Residual Momentum
		2.3.1 Initial Momentum from the Tunneling Ionization
		2.3.2 The Momentum from the Lasers: Longitudinal Injection
		2.3.3 The Momentum from the Lasers: Transverse Injection
		2.3.4 The Thermal Emittance
	2.4 Single Particle Motion in the Nonlinear Wake
	2.5 Transverse Phase Mixing
		2.5.1 Emittance Evolution: Growth and Oscillation in the Injection Stage
		2.5.2 Emittance Evolution: Decrease and Regrowth in the Acceleration Stage
		2.5.3 A Phenomenological Model
		2.5.4 Comparisons with PIC Simulations
	2.6 Longitudinal Phase Mixing
		2.6.1 The Trapping Condition
		2.6.2 Longitudinal Phase Mixing
	2.7 Space Charge Effects
	2.8 The Two-Color Ionization Injection
		2.8.1 The Emittance in a Single Laser Case
		2.8.2 The Two-Color Ionization Injection: Longitudinal Injection
		2.8.3 The Two-Color Ionization Injection: Transverse Injection
	2.9 Intrinsic Phase Space Discretization in Laser Triggered Ionization Injection
		2.9.1 Single Laser Pulse Case
		2.9.2 Beam Driver with a Laser Injector
	2.10 Summary
	References
3 Coherent Phase Space Matching Using Longitudinally Tailored Plasma Structure
	3.1 Introduction
	3.2 The Emittance Growth Between Stages
		3.2.1 Emittance Growth in Free Space Drifting
		3.2.2 Emittance Growth in a Uniform Focusing Field
	3.3 Theoretical Analysis of a Matching Plasma
		3.3.1 How to Design the Matching Plasma?
		3.3.2 The Effect of the Energy Spread
	3.4 Verification by PIC Simulations
		3.4.1 Matching Between Two-Stage LWFAs
		3.4.2 Matching in External Injection
		3.4.3 Matching Between LWFAs and the Quadrupoles
	3.5 Summary
	References
4 X-FELs Driven by Plasma Based Accelerators
	4.1 Introduction
		4.1.1 The Basic Principles of FELs
		4.1.2 The Challenges and Opportunities of X-FELs Driven by Plasma Based Accelerators
	4.2 X-FEL Driven by a Two-Stage LWFA
		4.2.1 Simulation of the Injector Stage
		4.2.2 Simulation of the Accelerator Stage
		4.2.3 Simulation of the Undulator Stage
	4.3 Conclusions
	References
5 Numerical Instability Due to Relativistic Plasma Drift in EM-PIC Simulations
	5.1 Introduction
		5.1.1 The Boosted Frame Simulations of LWFA
		5.1.2 Numerical Noise Induced by Relativistic Plasma Drift in PIC Codes
	5.2 Numerical Dispersion Relation for Cold Plasma Drift
		5.2.1 Derivation of Dispersion Relation
		5.2.2 Elements of Dispersion Relation Tensor
		5.2.3 EM Modes, and Wave-Particle Resonance
	5.3 Numerical Instability Induced by Relativistic Plasma Drift for the Yee Solver
		5.3.1 Theoretical Analysis of the 2D Dispersion Relation
		5.3.2 Simulation Study of the Instability
	5.4 Asymptotic Expression for Instability Growth Rate
		5.4.1 Derivation of Asymptotic Expression
		5.4.2 Parameter Scans for Minimal Instability Growth Rate
	5.5 Elimination of the Numerical Cerenkov Instability for Spectral EM-PIC Codes
		5.5.1 The NCI Modes for the Spectral Solver
		5.5.2 The Positions and the Growth Rates of the NCI Modes for the Spectral Solver
		5.5.3 LWFA Simulation in the Lorentz Boosted Frame with Spectral Solver
	5.6 Conclusions
	References
6 Summary
	6.1 Concluding Remarks
	6.2 Future Work
Appendix A Derivation of the Emittance Evolution  in the Acceleration Stage
Appendix B Interpolation Tensor and Finite Difference Operator