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This book explores several key issues in beam phase space dynamics in plasma-based wakefield accelerators. It reveals the phase space dynamics of ionization-based injection methods by identifying two key phase mixing processes. Subsequently, the book proposes a two-color laser ionization injection scheme for generating high-quality beams, and assesses it using particle-in-cell (PIC) simulations. To eliminate emittance growth when the beam propagates between plasma accelerators and traditional accelerator components, a method using longitudinally tailored plasma structures as phase space matching components is proposed. Based on the aspects above, a preliminary design study on X-ray free-electron lasers driven by plasma accelerators is presented. Lastly, an important type of numerical noise-the numerical Cherenkov instabilities in particle-in-cell codes-is systematically studied.
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