本研究深入探討了雷射驅動輻射光壓加速（hole-boring RPA）機制及其加速機制的理論基礎，結合數值模擬驗證hole-boring RPA加速機制理論在氣態靶材應用中的適用性。針對現有理論多針對固態靶材的限制，本研究提出以氣態靶材取代固態靶材，並詳細探討了靶材密度與厚度的影響機制。通過動量的通量守恆推導了hole-boring RPA加速機制的速度與離子能量，並且討論了相對論效應的影響，描述了hole-boring RPA加速機制中雙層結構的形成與穩定性條件，並進一步分析了雷射參數（如強度、頻率與偏振形式）對質子加速效果的影響。
為了驗證理論與進一步揭示加速機制的細節，本研究採用基於 Particle-in-cell (PIC) 方法的數值模擬技術。模擬結果顯示，電子與質子之間的雙層結構是影響質子加速品質的關鍵因素。調節雷射橢圓偏振率可以有效抑制雙層結構的振盪，從而提升質子束的能量集中性。然而，模擬結果與現有理論模型存在顯著差異：隨著雷射強度增加，實際允許的橢圓率範圍不僅未下降，反而上升。此外，模擬還揭示了電子溫度的動態演化行為：成功形成雙層結構時，電子溫度隨時間趨於穩定並呈對數增長；而結構失效時，電子溫度則指數性上升，顯示出加熱時間尺度在雙層結構穩定性中的重要性，這是現有理論中尚未考慮的因素。
模擬還發現，不同密度靶材在橢圓偏振率允許範圍上的顯著差異，表明現有理論在描述低密度靶材行為時可能存在不足。希望我們的研究成果能修正理論，找到更完善的橢圓率條件。

This study dives into the basics of laser-driven radiation pressure acceleration (hole-boring RPA) and its acceleration mechanism, using simulations to see how well the theory works with gaseous targets. Most existing theories focus on solid targets, but we switched things up by looking at gaseous ones, exploring how factors like target density and thickness play a role. We worked out the velocity and ion energy of the hole-boring RPA mechanism using momentum conservation, dug into the effects of relativity, and explained how the double-layer structure forms and stays stable. We also looked at how laser settings—like intensity, frequency, and polarization—impact proton acceleration.
To test these ideas and uncover more details, we used numerical simulations with the Particle-in-Cell (PIC) method. The results show that the double-layer structure between electrons and protons is crucial for producing high-quality proton beams. By tweaking the laser’s elliptical polarization, we could suppress oscillations in the double-layer structure and boost the energy concentration of the proton beam. But here's where it gets interesting: as the laser intensity increased, the allowable range for elliptical polarization didn’t shrink like the theory said—it actually got bigger.
We also found some surprising patterns with electron temperature. When the double-layer structure worked well, the temperature leveled off over time and followed a logarithmic trend. But when it broke down, the temperature shot up exponentially. This shows that heating timescales are a big deal for stability—something the current theories don’t fully cover.
On top of that, we saw big differences in how different target densities handled elliptical polarization. This suggests the current theories might not work as well for low-density targets. We hope our work helps refine these theories and pin down better conditions for elliptical polarization.
 

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