近年來，碰撞效應對於電漿粒子群體運動的影響再度成為一項重要的議題。這篇論文主要探討碰撞對於粒子束-電漿不穩定 (beam-plasma instability) 的影響。我們主要的工作是理論數值計算不同程度的碰撞率對於粒子束-電漿系統中不穩定波之線性成長率 (linear growth rate) 的影響。我們利用 Lenard-Bernstein (LB) 碰撞算子來描述粒子的碰撞行為並且將一階微擾的Boltzmann-Poisson系統以Hermite多項式展開並解出其數值解。此理論計算本質上是一個特徵值問題，找出令此系統自洽 (self-consistent) 的特徵模 (eigenmode) 後，即可得到系統的線性成長率。除了理論計算之外，我們也會提供粒子格點法 (Particle-in-Cell) 的模擬來支持理論數值計算的結果。根據我們的結果，無論是理論數值計算或者是數值模擬，均顯示粒子束-電漿系統中不穩定波的線性成長率會隨著粒子碰撞率的提高而有下降的趨勢。 There is renewed interest in the effects of Coulomb collisions on the collective behavior of plasmas in recent years. This thesis investigates the effects on beam-plasma instability. We focus on the linear regime of the instability and consider that how collisions affect the linear growth rate in the beam-plasma system. The linearized Boltzmann-Poisson equations including the Lenard-Bernstein (LB) collision operator, which is used to describe Coulomb collisions among the plasma particles, are solved by expanding the perturbed distribution function in terms of Hermite polynomials. This problem is treated as an eigenvalue problem and which yields the eigenmodes of this system, hence the growth rate of the instability. We also perform the simulation results by means of Particle-in-Cell (PIC) simulation to support the theoretical calculation. Both theoretical calculation and simulation show a decreasing linear growth rate as the collision rate increases.
