本研究旨在探討相對論性電子雲在結構光場—拉蓋爾-高斯(Laguerre-Gaussian, LG)光束驅動下的微觀動力學行為。本研究採用粒子網格有限時域差分法(PIC-FDTD)，透過VSim模擬軟體建立二維模型，並結合MATLAB進行數據處理、頻譜分析與軌跡繪製。本研究系統性地探討了單一及雙 LG 光束在多種空間極化態(圓極化、方位角極化以及徑向極化)下的物理響應，並深入分析電場強度(E)、光束腰半徑(ω0)、波長(λ)以及光束角動量(SAM 與 OAM)等關鍵參數對電子運動軌跡、迴旋頻率及電子保留率的調控機制。
研究結果顯示，電子在 LG 光束下的操控主要由橫向有質動力(Transverse Ponderomotive Force)與方位角波向量(Azimuthal wave-vector)共同驅動。有質動力主要負責對電子產生徑向約束，而LG光束攜帶的方位角波向量則在波前傳播中產生切向力矩，誘導電子進行顯著的角向旋轉運動，也決定了光束攜帶的軌道角動量(OAM)。模擬結果證實，電子旋轉頻率與電場強度呈現線性正相關，而與光束腰半徑及波長呈現反比關係；當光束參數變動時，方位角波向量引起的角向動力學變化，與有質動力產生的徑向偏移共同演化，造就了電子在強場中獨特的花瓣狀軌跡。研究也發現經傅立葉轉換(FFT)繪製出的頻譜圖，通過不同頻率結構進行分類，可以分為三大類，共六種頻率組合。在角動量特徵方面，當軌道角動量(OAM)與自旋角動量(SAM)互相抵消(ℓ =m+s=0)時，方位角波向量對電子的驅動效應消失，此時電子雲能達到最穩定的束縛狀態。此外，於雙LG光束疊加場中，電子展現出豐富的跨場遷移與八字形共振軌跡的渾沌現象(Chaotic phenomena)，證明了電子在跨場運動時，其軌道受方位角波向量的耦合調變，進而形成穩定且具高度週期性的動力學系統。

This research investigates the micro-dynamics of relativistic electron clouds driven by Laguerre-Gaussian (LG) laser beams. Employing the Particle-in-Cell Finite-Difference Time-Domain (PIC-FDTD) method, a two-dimensional model is constructed in VSim, with MATLAB utilized for data processing, spectral analysis, and trajectory simulation. The study systematically explores the physical responses of electrons under single and dual LG beams with varying polarizations—circular, azimuthal, and radial. Key parameters, including electric field intensity, beam waist radius, wavelength, and angular momentum (SAM and OAM), are analyzed to determine their impact on electron trajectories, gyro-frequency, and retention mechanisms.
Results demonstrate that electron manipulation under LG beams is primarily driven by the transverse ponderomotive force and the azimuthal wave-vector. The ponderomotive force facilitates radial confinement, while the azimuthal wave-vector induces torque, driving significant rotational motion and defining the OAM. Simulation results confirm that electron rotation frequency is positively correlated with electric field intensity, while exhibiting an inverse relationship with beam waist and wavelength. The synergy between these forces produces unique petal-like trajectories in strong fields. Spectral analysis via Fast Fourier Transform identifies three main frequency categories comprising six combinations. Notably, when the total angular momentum vanishes (ℓ=m+s=0), the driving effect disappears, allowing electron clouds to reach optimal stability. Furthermore, in dual LG beam configurations, electrons exhibit complex cross-field migration and chaotic figure-eight resonance, demonstrating that coupling between orbital trajectories and the azimuthal wave vector leads to the formation of stable, highly periodic dynamic systems.

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