本篇論文修正並研究了在核融合電漿中, 由百萬電子伏特離子所驅動的相對論性電磁離子迴旋不穩定性的解析理論; 此不穩定性主要是由色散關係中, 慢速離子的一次共振與快速離子的二次共振耦合所導致, 且是在考慮相對論效應的情況下才有此結果; 另外我們也發現由於波磁場, 這樣的不穩定中有Alfvenic行為及不穩定性轉變; 為了要產生三次不穩定性及耦合的二次不穩定性, 快慢離子間的迴旋諧頻必須小於且趨近零.
由於在本論文中主要研究D-He碰撞的核融合反應, 快離子的動能相較以前的D-D反應大很多, 因此在解析理論裡面, 我們需要做更精確的近似, 所以我們在Alfvenic條件裡面加入了修正項, 以期能更準確的預測此不穩定性的慢離子臨界溫度或臨界密度, 以及產生不穩定性的最大外加磁場; 而由研究簡化後的三次色散關係中的二次項係數P, 我們發現當快離子的能量越高, 則主導此不穩定性的波數模也會增高.
我們以在數值計算中以 14.7 MeV 質子為快離子, 氘為慢離子, 並與以前所做的以 3.02 MeV 質子為快離子, 氘為慢離子的結果, 以及修正後的解析理論做比較; 諸如慢離子的臨界溫度臨界密度, 最大外加磁場, 不穩定性轉變等現象, 均有發現, 並與修正後的解析理論有不錯的吻合; 另外在Alfvenic臨界點附近, 主導不穩定性的波數模高低與快離子能量呈正相關, 也從數值計算中得到證實

The analytical theory of relativistic electromagnetic ion cyclotron instabilities driven by MeV ions in fusion plasma is revised and investigated. The instabilities come from the coupling of slow ions’ 1st order pole and fast ions’ 2nd order pole of the dielectric function and this mechanism is due to relativistic effect. The Alfvenic behavior and the instability transition are discovered due to the wave magnetic field. A negative harmonic cyclotron frequency mismatch between the fast and slow ions is required for driving both cubic and coupled quadratic instabilities.
Because of the higher fast proton energy produced by D−He fusion reaction studied in this thesis, the approximation condition in the analytical theory is required to be more accurate than in the case of D-D fusion reaction studied before. Thus we add a correction term in the Alfvenic condition to predict the instability threshold on the slow ion temperature and density (or ceiling on the external magnetic field) accurately. Through the analysis of the dispersion relation’s coefficient P, we know that there is a positive correlation between the wave number of the cubic instability near the Alfvenic threshold and the fast ion energy. That is, the instability of higher k mode will dominate near the Alfvenic threshold if the fast ion energy is higher.
We study the case of fast 14.7 MeV protons in thermal deuterons numerically and compare with the analytical results. Some phenomena discovered before still occur without surprise, such as the threshold on slow ion temperature and density, the ceiling on the external magnetic field and instability transition from cubic to quadratic. We also compare the numerical result of the coefficient P of the fast
3.02 MeV proton case with the current case. And as fast ion energy increased, the instability of high k mode dominates near the Alfvenic threshold which agrees with our analytical theory.

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