雷射尾流場電子加速(laser wakefield acceleration, LWFA)可藉由聚焦具數兆瓦(terra watt, TW)尖峰功率之雷射脈衝至高密度薄氣體靶材達成。當雷射脈衝於密度高於1019 cm-3的電漿中傳播下，其強度即可因自聚焦(self-focusing)與自調變(self-modulation)等非線性效應而大幅增加而有效激發電漿波並加速電子至10 MeV等級之能量。除持續提升兆瓦級、高重複頻率雷射之技術，發展具適當空間分布、密度與成分之氣體靶材也有助於提升LWFA所產出電子數之特性，並得以應用於新型電子治療中或用以產生X光進行射線照相。因此本研究之重點即參考使用1 TW、40 fs的雷射脈衝進入次毫米長的高密度氮氣氣靶所產生之LWFA實驗結果，透過計算流體力學(computational fluid dynamic, CFD)模擬取得氣靶中氮原子的空間分佈，並將CFD模擬所得之氮原子密度分佈帶入電漿粒子體模擬(particle-in-cell simulation, PIC)以分析LWFA中雷射與電漿交互作用的物理機制以及所加速出的電子束特性。
本研究建立450 μm長之氣腔的三維CFD模擬， 通入20 psi與25 psi之氮氣背壓，可分別得到具尖峰原子密度為7.6\times1018cm-3與9.5\times1018cm-3之分布，並透過PIC模擬可驗證在使用25 psi背壓時可相比於使用20 psi背壓下增加約1.5倍的電子束電荷，然而雷射脈衝在氣體密度較高時會因感受到較強的游離誘導折射(ionization-induced refraction)而具有一定程度散焦現象，進而導致電子束往橫向發散程度較高。本研究另於CFD模擬中對孔徑為178 μm的噴嘴建立二維軸對稱流體模型，並用以研究在馬赫數(Mach number)M\approx2.4之超音速噴流暫態模擬中，為滿足Courant-Friedrichs-Lewy條件(Courant-Friedrichs-Lewy condition, CFL condition)C_r\le1所需要的網格大小與時間步驟(time step)，以及精進網格劃分與求解器設定使模擬數值收斂性提升。研究另建立二維x-y平面模型並於178 μm噴嘴上方引入刀片以調變氣體噴流密度分佈，在通入400 psi之氮氣背壓的條件下，以平面模型討論不同刀片對噴嘴的遮蓋率以及刀片幾何形狀對產生之氣體噴流密度下降梯度所造成的影響。由模擬結果可知改變刀片遮蓋率可調變密度下降坡長度L與密度下降梯度\frac{
artial n}{
artial x}。而模擬也顯示氣靶前端會因氣體經由刀片與噴嘴側的反彈而出現額外的次密度尖峰，此時改變刀片幾何形狀即有助於避免氣體反彈而造成的影響，使噴流分佈呈現單一密度尖峰並具有可調變的密度下降緩坡區間。

Laser wakefield acceleration (LWFA) can be achieved by focusing a few-terawatt (TW) laser pulse into a thin gas target. When propagating in a plasma with an electron density >1019 cm-3,
the pump pulse experiences nonlinear effects such as the self-focusing and the self-modulation that can result in a greatly increased laser intensity to excite plasma waves and generate 10-MeV-scale electrons from LWFA. In addition to inventing high-average-power, high-repetition-rate, TW-level lasers, developing gas target with a modified density profile, an increased density, or an appropriate gas component also opens up opportunities to enhance further the properties of output electron beams from LWFA and facilitate their downstream application in electron therapy and X-ray radiography. Therefore, based on the experimental results acquired by introducing 1-TW, 40-fs pulses into a sub-mm, dense nitrogen gas target, this work focuses on developing computational fluid dynamics (CFD) simulations to investigate the density distributions of nitrogen atoms in the target, which can be subsequently applied into particle-in-cell (PIC) simulations for resolving the process of LWFA and the characteristics of the accelerated electrons.
Three-dimensional CFD model was first developed to study the distribution of nitrogen atom density inside a 450-μm-long gas cell, which showed that the peak atom density reached 7.6\times1018cm-3 and 9.5\times1018cm-3, respectively, when backing pressures of 20 and 25 psi were applied. The associated PIC simulations then indicated that the 25% increase in nitrogen atom density inside the cell could lead to a 1.5-fold increase of charge for the output electron beam but with a trade-off in a beam divergence.
This study also developed two-dimensional CFD model in axisymmetric geometry for simulating gas jets produced from a 178-μm-diameter. This model was applied for optimizing the mesh size and the time step set in the simulation to satisfy the Courant-Friedrichs-Lewy (CFL) condition C_r<1 under the supersonic flow regime with a Mach number M\approx2.4, along with the modifications for the mesh refinement and the solver to substantially improve the convergence of the numerical results.
With a two-dimensional planar geometry (in x and y coordinates), the CFD simulations were extended to study gas jets with a modulated density profile achieved by placing a blade above a nozzle; whereby length L of the density down-ramp region of the gas jet and the density gradient \frac{
artial n}{
artial x} across this region can be varied by tuning the blade coverage with respect to the nozzle. The results also showed that the multiple reflections of gas flows between the blade and the nozzle lip could result in the appearance of an extra density peak located prior to the main peak of the gas jet, which can be avoided by changing the geometry of the blade.

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