多種類帶電粒子普遍存在於太空、天文及實驗室電漿環境中，本研究主要為發展非線性靜電孤立波的廣義模型，模型中各帶電粒子的電性可任意調整，因此可應用在各類型多成份電漿上，如dust-ion-electron及electron-positron-ion等系統，其中假設較冷的帶電粒子(如離子或灰塵粒子)為流體，並以kinetic Vlasov方程式來描述較熱的粒子(如電子)狀態，所使用的速度分佈可為kappa或highly nonthermal函數。模型中之粒子分佈函數為決定波結構的重要因素，並可將結果應用在two-component系統中，如electron-ion plasmas，其中之電子可以有兩種不同的溫度狀態。本文將推導廣義靜電波的頻散關係， Korteweg-de Vries方程式及Sagdeev potential，分析其特性，並應用於滿足不同速度分佈下的粒子組合，分析各類型孤立波的存在條件，並解釋非線性解之特徵。研究顯示，在highly nonthermal的條件下，可得到異常電位解，此結果可用於解釋人造衛星所觀測到之靜電波結構。 Plasma systems consisting of multi-species of charged particles are quite common in space and astrophysical environments as well as in the laboratory. A generalized formulation is developed for nonlinear electrostatic acoustic solitons in multi-component such as dust-ion-electron and electron-positron-ion plasmas with the charge of each species being unspecified. The cold charged particles (e.g., ions or dust particles) are treated as a fluid while the hot components (e.g., electrons) are described by the kinetic Vlasov equation with separate velocity distributions which can be of kappa function or highly nonthermal distributions. The model is applicable for two-component such as electron-ion plasmas with two different temperatures for electrons. The generalized dispersion relation for acoustic waves and the Korteweg-de Vries (KdV) equations as well as the Sagdeev potential are derived for various models with different combinations of velocity distributions. The parameter regimes for the existence of acoustic solitons are analyzed and examples of nonlinear solutions are illustrated. The polarity of electric potential is found to exhibit anomaly for highly nonthermal cases which may explain some of the electrostatic structures observed by the spacecraft in space environments.
