雷射電漿加速器（Laser Wakefield Accelerators， LWFA）具備利用極小的空間便能產生高亮度相對論性電子束的潛力，適合驅動小型自由電子雷射(FEL)，輸出真空紫外及X光輻射波段。然而，目前利用LWFA所產生之電子還具有高能散的缺點，為解決此問題，常見作法是加入一個電子束能量壓縮器（4-dipole energy compressor）拉長電子束，以有效降低電子束的片段能散，這會導致另一個問題出現，即電流大小會因為拉長而被削弱，並且在電子縱向能量分布上會有能量梯度出現，從而導致FEL的輸出能量降低，本研究針對LWFA所產生之電子束進行完整的三維模擬分析，並分析具有能量梯度的電子束在聚頻磁鐵內的動力學，結果顯示帶有能量梯度的電子束會由於能量差異在聚頻磁鐵內的色散關係而使得FEL交互作用所產生的微群聚間距逐漸拉長，進而影響整體的FEL效應，隨後我們提出利用具有梯度磁場強度的聚頻磁鐵抵銷經過能量壓縮器之能量梯度所帶來的影響，利用梯度磁場所改變的共振條件使得輻射波長能夠跟上拉長的微群聚間距，讓FEL交互作用能夠延續，模擬結果與使用沒有梯度的聚頻磁鐵相比，此方法能夠有效的增強約兩個數量級的能量輸出，除此之外，我們還測試了初始能散以及中心能量偏移對於整體FEL表現的敏感度測試，本研究對於小型FEL光源提供具有可行性的方案，將有助於發展更有效的能量梯度補償策略，以及優化以雷射電漿加速器驅動之自由電子雷射的設計。;Laser wakefield accelerators (LWFAs) can generate high-brightness relativistic electron beams within an extremely compact footprint， making them promising drivers for compact free-electron lasers (FELs) operating in the vacuum-ultraviolet and X-ray regions. However， the relatively large energy spread of LWFA electron beams remains a major challenge for FEL applications. A commonly used method to reduce the slice energy spread is to employ a four-dipole energy compressor to longitudinally stretch the electron bunch. Nevertheless， this process reduces the peak current and introduces a longitudinal energy chirp， which significantly degrades FEL performance. In this thesis， comprehensive three-dimensional simulations are performed to investigate the dynamics of energy-chirped electron beams in an undulator. The results show that the energy chirp causes the microbunch spacing to gradually increase due to longitudinal dispersion in the undulator， thereby weakening the FEL interaction. To compensate for this effect， a tapered undulator with a longitudinally varying magnetic-field strength is proposed. By continuously adjusting the resonant condition， the radiation wavelength can follow the evolving microbunch spacing， allowing sustained FEL amplification. Simulation results show that the proposed method enhances the FEL output power by approximately two orders of magnitude compared with the untapered case. In addition， sensitivity studies on the initial energy spread and central beam-energy variation are carried out to evaluate the robustness of the scheme. This work provides a feasible approach for the development of compact LWFA-driven FEL light sources.
