數值粒子追蹤技術 (Numerical particle tracking technique) 在模擬加速器中之射束動力學是一個非常有用的工具。此方法之基礎在於建立粒子的基本運動方程式，並在給定機器相關的參數之後，便能進行各種動力學參數的計算。本論文目的在於發展此粒子追蹤模擬程式，並利用其探討同步加速器中增能環之電子束縱向動力學。我們以台灣光子源 (Taiwan Photon Source, TPS) 之增能環的參數為基準來進行探討研究。討論的議題包含：粒子加速過程中，射束動力學參數隨時間的演變以及各種雜訊對電子束團之影響。另外，我們同時利用此模擬程式考慮一個較實際的狀況，即電子束團從上游之直線加速器注入增能環時，入射條件偏差對粒子加速過程期間之射束動力學的影響。

在此論文中，我們首先以解析的方式分析幾個對單一粒子可能造成的各種效應的影響。接著，以發展出來的多粒子模擬程式考慮一些更接近實際的狀況，並將其結果與解析公式作對照。我們嘗試對粒子加速過程時的射束動力學予以分段探討，並分析各階段中主要之作用機制。另外，我們也利用此模擬程式作了一系列關於系統雜訊、隨機雜訊與偏差效應的計算。

根據計算的結果顯示，若是電子注入增能環之能量偏差可以控制在0.25 %之內，或是，相位(或時間)偏差在0.3 rad (或100 psec) 之內，則電子束在加速過程中的捕獲效率 (capture efficiency) 可以維持在99.9 %以上。另外，考慮由於速調管之漣波效應 (klystron ripple effect) 引起的高頻加速腔之相位調制影響時，若調制強度可以維持在-50 dBc以下 (調制頻率相對於操作頻率為180 Hz)，則此效應對電子束團的動力學影響是不明顯的。接著，對於高頻加速腔之振幅與相位雜訊的影響也在此論文中探討。其結果顯示，在振幅與相位誤差分別小於 ± 1 %與 ± 0.1 deg時，電子束的運動是幾乎不受影響的。

The purpose of this thesis is to develop a particle tracking code for the booster synchrotron of Taiwan Photon Source (TPS). Issues of longitudinal beam dynamics during energy ramping were discussed, including noise effects and injection errors of beam from linear accelerator (linac).

In the thesis, analytical approaches to various effects on beam dynamics were presented first. Then, the numerical approach employing multi particle tracking was used to simulate realistic situations and the results were compared with analytical ones in order to validate the simulation codes. In addition, beam dynamics has been characterized and discussed during energy ramping cycle from three bunches merging into one. Moreover, based on the developed simulation program, there have been a series of numerical experiments conducted to investigate the evolution of beam dynamical parameters involving those effects such as injection offsets, RF output phase modulations, and various noises.

The results indicated that capture efficiency can be preserved (99.9 %) with an individually allowed fractional energy offset of 0.4 % and phase or time offsets of 0.63 rad or 200 psec from injection. Both interleaving effects are expected to further degrade the performance and their estimates are presented. The phase modulation strength less than 50 dBc (0.3 deg) at 180 Hz has been shown less effective on beam dynamical properties. Radio frequency (RF) amplitude and phase errors are also examined via particle tracking simulation. It is noted that the amplitude error within ± 1 % and phase error within ± 0.1 deg are tolerable for beam evolution during ramping process.

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