利用短脈衝雷射與固態靶材交互作用產生高能質子束是近年來質子加速器發展的一個重要趨勢。由雷射與電漿作用所驅動的高能質子束，可用於癌症的治療，這種加速器的體積比傳統質子加速器要大幅縮小，且價格也比較低，所以發展高效率的雷射電漿質子加速器是極具應用價值的研究工作。 顏學慶等人在2008年提出相位穩定質子機制(PSA, phase-stable acceleration)，藉由雷射光壓形成穩定的加速電場來加速質子束，不僅在能量上有突破性的發展，質子束的單一性也有非常好的呈現，是目前最具潛力的雷射電漿質子加速機制。 我們的研究是利用粒子模擬法(particle-in-cell)檢驗相位穩定質子加速機制的條件，發現電漿密度在低於某一特定值時此加速機制就無法產生穩定的質子加速，此密度值我們稱為門檻密度(density threshold)。接著從模擬中所觀察到的現象，我們找出相位穩定質子加速機制在低於門檻密度區域內失敗的物理原因。另一方面我們也從能量守恆的觀點推導出解析理論，計算出在不同雷射振幅下的門檻密度，並與模擬結果比較，結果相當吻合。另外我們分別改變雷射振幅、電漿密度與靶材厚度進行數值模擬，標示出質子加速器最佳參數範圍，結果也與理論分析相當吻合。 利用理論分析及數值模擬進行參數化分析，我們可以得到在不同雷射振幅下的質子加速器最佳操作範圍，此結果可以劃分出不同醫療應用上的操作區間，因此這研究結果可做為未來質子加速器實驗設計的參考。 The laser-accelerated proton beam has attracted particular interest due to its compactness and low cost as compared to the traditional proton beam accelerators. X. Q. Yan et al. proposed the phase-stable acceleration (PSA) mechanism for producing the mono-energetic proton beam with excellent energy scalability by varying the laser intensity and pulse duration. The stable electrostatic field formed by the light pressure accelerates the proton beam with high collimation. The phase-stable acceleration has become the most promising mechanism for the development of the new generation proton accelerator. In the study, we applied the particle-in-cell (PIC) code on the examination of operational criteria for the phase-stable acceleration proposed by Yan et al. We found that the phase-stable acceleration fails when the plasma density is lower than a certain value, no matter how thick the target is. The density threshold is an essential criterion for the phase stable acceleration. The physical reason for failure of the phase-stable acceleration is the continuous erosion of the surface electrons by the laser pulse at the plasma density lower than the critical value. According to the energy conservation law, we derived the theory to predict the density threshold for different laser parameters. The theoretical results and the simulation result agree very well. In corporation with parametric studies by varying the laser intensity, plasma density, and target thickness, we explore the marginal conditions for the production of mono-energetic proton beams. The optimal operational range for the phase stable proton accelerators obtained by the theoretical criterion and the parametric studies provide a good reference for the design of a novel proton accelerator.
