利用二維粒子式模擬來研究雷射電漿波電子加速器中被加速電子的物理特性。首先，利用改變雷射與電漿之參數來研究可形成單能電子束之最大電子能量，並深入探討其中關於電子能量飽和之物理機制，及研究在特定條件下電漿波加速結構隨時間不穩定振盪而影響電子最大能量的情形，以及找到不穩定加速結構的存在區間。另外，藉由模擬結果的分析可推導出形成電漿bubble的電子運動軌跡之曲率半徑，進而推估電子之能量scaling law，即加速電子之最大能量隨電漿密度及雷射強度組成之複合參數的影響，且藉由我們的模擬數據及先前實驗結果驗證了此電子能量scaling law之準確性，故此趨勢可用來估計電子可獲得的最大能量。
為了研究雷射電漿波電子加速器之注入電荷量的空間電荷效應，建立了一個等效於第一個電漿bubble之模擬模型來研究，其模型考慮了電磁場的效應、相對論效應及拋物線電位分布。用此模型所計算出來的空間電荷極限之電流可用來與雷射電漿波電子加速器之注入電荷量來做比較。

In a laser wakefield accelerator (LWFA), two dimensional particle-in-cell simulations were performed to demonstrate the fluctuation of the maximum beam energy while varying the plasma density under the transition from mildly relativistic regime to relativistic regime. The fluctuation of the beam energy is induced by the unstable accelerating structure, which length is dynamically oscillating between the plasma wavelength and the relativistic plasma wavelength. The simulation results also reveal the existence of the parameter space for the stable operation of a LWFA.
An empirical formulation was derived by the calculated radius of curvature of the returning electrons along the boundary of the plasma bubble in a stably operated LWFA. The comparisons between the energy scaling law derived from the empirical formulation, the two-dimensional and three-dimensional PIC simulation and previous experimental results with self-guided laser pulses show good agreement. The scaling law derived in the study can provide a correct estimation of the maximum beam energy for a newly designed LWFA experiment with an optimal configuration of the laser pulse.
In addition, in order to study the space charge effect of the charge number for the injected electrons in LWFA, the simplified simulation model equivalent to first plasma bubble in LWFA considering full electromagnetic field, relativistic field, and parabolic potential profile was constructed. The space-charge-limited current was studied by the equivalent model and compared with the electron charge in the 2D LWFA simulation.

Acknowledgements

Abstract

1 Introduction 1
1.1 Development of the Laser Wakefield Accelerator (LWFA) 2
1.2 Physical Picture of LWFA 3
1.3 Current Research Works and Challenge 8
1.4 Organization of the Thesis 11
2 Parametric Study of LWFA 13
2.1 Simulation Model and Parameters 13
2.2 Saturation of Monoenergetic Electron Beams 14
2.3 Discussion of Unstable Acceleration Structure 19
3 Empirical Formulation and Energy Scaling Law for a Stably Operated LWFA 23
3.1 Review of the Previous Energy Scaling Law 23
3.2 Empirical Formulation 25
3.3 Validation and Application of the Energy Scaling Law 32
4 Verification by 3D PIC Simulation 39
4.1 Verification of Radius of the Ion Sphere 39
4.2 Verification of Energy Scaling Law 41
5 Space Charge Effects of the Injected Electrons in LWFA 45
5.1 Review of 1D Electrostatic (ES) Theory for a Short-Pulse in a Diode 47
5.2 Verification of the ES Theory by 2D PIC Simulation 50
5.3 Electromagnetic (EM) Simulation in a Diode 53
5.4 Comparison of the Current Limit with the Self-Guided LWFA 57
6 Conclusions 61

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