短脈衝的 X-ray 在科學和生物醫學中應用廣泛，而雷射電漿尾場加速（LWFA）產 生的 Betatron 輻射是一種產生超短脈衝 X-ray 的方法。LWFA 利用短脈衝雷射與電漿 交互作用加速電子，具有比傳統射頻加速器高約 1000 倍的加速梯度，因此無需大型實 驗設施。在 LWFA 中，強橫向聚焦力使電子束在加速過程中震盪，類似波盪器的運動 產生超短脈衝 X-ray。 我們通過破壞衝擊波前沿的對稱性來增加電子束震盪強度，並用粒子模擬（PIC） 驗證其可行性。利用 OSIRIS 模擬程式，我們成功再現了先前研究中的二維模擬 [1]， 通過 15◦ 傾角破壞衝擊波前沿的對稱性，實現了單邊注入的電子束。進一步研究發現， 只需降低雷射參數中的 𝑎0 並升高雷射束腰，即可在 15◦ 傾角傾角下達成完全單邊注 √入。然而，二維模擬與三維模擬的雷射演化條件不同，需要將二維模擬中的 𝑊0 除以 2 才能達到相似的雷射強度演化，但這會導致雷射束腰的演化差異，表明二維模擬無 法討論更複雜的雷射演化現象。 因此，我們使用三維 PIC 模擬探討傾角衝擊波前沿的條件。發現橫向注入電子束 在 15◦ 傾角下無法完全單邊注入，且注入總電量與 0◦ 傾角相差不大。為達成單邊注 入，我們將傾角增加到 65◦，成功產生單邊注入電子束。縱向注入電子束也是如此，只 有在 65◦ 傾角下才達到 85 % 的單邊注入率，說明無論是橫向還是縱向注入電子束，三 維模擬需更大角度才能實現高單邊注入率。 為驗證單邊注入電子束的群體運動效應，我們追蹤電子束並分析其行為。結果顯 示，橫向和縱向注入電子束在較大角度下平均震盪強度較強，且縱向注入角度越大， 群體運動行為越強，但在另一方向的標準差差異也越大，意味輻射強度更強，導致降 低了偏震度。光通量分析表明，縱向注入電子束的偏震度不隨角度增加而變化，與橫 向注入的行為相反，後者隨傾角增加而偏震度增加，在 65 度傾角下達到 62% 的偏震 度，因此橫向注入產生 X-ray 之偏震效果也越好。我們分析了橫向注入電子束的亮度， 發現其在 65◦ 傾角下可產生阿秒等級、光通量高達 1020 之 X-ray。

Short-pulse X-rays find universal applications in science and biomedicine. Betatron radiation generated from laser wakefield acceleration (LWFA) offers a method for pro- ducing ultrashort-pulse X-rays. LWFA utilizes the interaction between short-pulse lasers and plasmas to accelerate electrons, achieving acceleration gradients approximately 1000 times higher than conventional radio frequency accelerators, thus decreasing the need for large-scale experimental facilities. In LWFA, strong transverse focusing forces cause the electron beam to oscillate during acceleration, similar to the motion of an Wiggler, producing ultrashort-pulse X-rays. We enhanced the electron beam oscillation by breaking the symmetry of the shock front and verified its feasibility using particle-in-cell (PIC) simulations. By tilting the shock front by 15◦, we successfully reproduced the 2D simulation results in [1] and achieved single-sided electron injection. Further studies show that by reducing 𝑎0 and increasing the laser waist at a 15◦, complete one-side injection can be achieved. However, the laser evolution conditions in 2D and 3D simulations differ. To achieve similar laser intensity evolution in 2D simulations, 𝑊0 needs to be divided by √2, leading to differences in laser waist evolution. This indicates that 2D simulations cannot fully capture more complex laser evolution phenomena. Therefore, we employed 3D PIC simulations to investigate the conditions of the tilted shock front. It was found that transverse injected electrons could not be completely one- side injected at a 15◦, and the total injected charge was not significantly different from that at a 0◦. To achieve one-side injection, we increased the tilt angle to 65◦, successfully generating a one-side electron beam. Similarly, for longitudinal injected electrons, only at a 65◦ did we achieve an 85 % one-side injection rate, indicating that both transverse and longitudinal injected electrons require a larger angle in 3D simulations to achieve a high one-side injection rate. To verify the collective motion of single-sided injected electron beams, we tracked and analyzed their behavior. Results show that both transverse and longitudinal injections exhibit stronger average oscillations at larger angles, but longitudinal injections lead to larger deviations in the other direction, reducing polarization. Flux analysis indicates that transverse injections yield higher polarization, reaching 62 % at 65◦, while longitudinal injections show no angular dependence. We found that transverse injections at 65◦ can produce attosecond-level X-rays with a brilliance of 1020.

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