臺灣博碩士論文加值系統

在粒子模擬法中數值熱化的現象(即速度分佈變成馬克士威爾)已經被廣泛的進行，在早期階段，其發展[1]已被認為很好地解釋。然而，最近在模擬弱游離氣體的模擬碰撞研究[2](這個碰撞模型描述電子與背景粒子(如原子和分子)的碰撞，當電子與中性背景氣體碰撞，電子將會被反彈。)發現當存在是一個額外的隨機力作用於粒子，對於之前對熱化時間的描述可能需要改變。在我們的工作中，我們感興趣的問題是，電子-離子在完全游離電漿中所發生的碰撞。我們研究在一維羅倫茲電漿(Lorentz plasma)[3]中粒子模擬法的熱化過程。所用到的小角度碰撞(small-angle collition)模型是使用蒙地卡羅演算法讓電子對固定的離子背景發生碰撞。我們的計算結果表明，熱化時間與 (每個德拜長度包含粒子的數目)成正比，而不是一般標準粒子模擬所認同的 。另一方面，我們的研究結果還指出，碰撞率對自我加熱機制(self-heating)的影響並不大，即使在發生強烈碰撞的環境也一樣。我們的研究結果可以補充那些先前被發現的研究[2]。

The phenomenon of numerical thermalization (i.e., relaxation of the velocity distribution toward a Maxwellian) in the standard particle-in-cell (PIC) simulation of Vlasov plasmas has been extensively studied at the early stage of its development[1] and was considered well understood. However, it was recently reported[2] that the well-established scaling law for the thermalization time could be compromised by the presence of an additional stochastic force acting on the particles, which has been used to simulate collisional processes in a weakly ionized gas. The collision model is described that the electrons collide with background particles, i.e., atoms and molecules. When electron collide with neutral background gas, the electron will be rebounded. In the our work, we are interested in the problem of electron-ion collisions in a fully ionized plasma. We examined the thermal relaxation processes in the PIC simulation of a Lorentz plasma in one dimension[3]. The small-angle collision of the electrons by the stationary ion background is modeled by a Monte-Carlo algorithm. Our numerical results show that the thermal relaxation time is proportional to ND (the number of particles per Debye length), but not ND2 as shown in the standard PIC simulations. On the other hand, our results also point out that the collision rate affects self-heating slightly even in a strong collision environment. Our results appear to complement those found by the previous study[2].

中文摘要 i
英文摘要 ii
致謝 iii
目錄 iv
圖目錄 vi

第一章 序論 1
第二章 羅倫茲電漿之數值模擬與分析方法 4
2.1羅倫茲電漿模型 4
2.2粒子模擬法PIC (particle-in-cell) 5
2.3小角度碰撞模型(small-angle collision model) 7
2.4計算結果的方法─電漿熱化時間之分析 10
第三章 數值模擬之結果 12
3.1模擬參數 12
3.2熱化時間之分析 16
3.3數值自我加熱的影響 18
3.4粒子數ND與熱化時間 的關係 22
3.5數值格點 與 對模擬結果的影響 23
3.6不同初始分布對熱化時間 的影響 26
3.7碰撞對電漿波的影響 28
第四章 模擬法之比較與討論 31
第五章 結論 34
參考文獻 35
附錄A
1、電漿(Plasma) 36
2、德拜長度(Debye Length) 37
3、電漿頻率(Plasma frequency) 38
4、電漿參數(plasma parameter)和群集作用(collective behavior) 39
5、PIC (particle-in-cell) 的優點 40
附錄B
1. PIC input file 43
2. Source code 44

[1] C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulation (McGraw-Hill, New York, 1985).
[2] M. M. Turner, Phys. of Plasmas 13, 033506 (2006).
[3] R. Shanny, J. M. Dawson, and J. M. Greene, Phys. of Fluids 10, 1281 (1967).
[4] C. K. Birdsall and A. b. Langdon, Plasma Physics via Computer Simulation, IOP Publishing Ltd, London, 1991.
[5] R. W. Hockney and J. W. Eastwood, Computer Simulation Using Particles, IOP Publishing Ltd, Bristol, 1988.
[6] C. K. Birdsall, IEEE Trans. Plasma Science, vol. 19, p. 65, 1991.
[7] J. M. Dawson, Rev. Mod. Phys. Vol. 55, p. 403, 1983.
[8] C. K. Birdsall and N. Maron, J. Comp. Phys. Vol. 36, p. 1, 1980.
[9]J. M. Dawson, Phys. Fluids 7, 419 1964.
[10]J. Virtamo and H. Tuomisto, Phys. Fluids 22, 172 1979.
[12] F. F. Chen, Plasma Physics and Controlled Fusion (Plenum, New York, 1984).
[11]A. H. Boozer and G. Kuo-Petravic, Phys. Fluids 24, 851 (1981).
[13] Eldridge, O.C., Feix, M.R. (1963): Numerical Experiments with a Plasma Model. Phys.Fluids 6, 398-406.
[14] 等離子體粒子模擬－邵福球編著－北京：科學出版社，2002