粒子網格法(Particle-in-Cell)模擬至今已發展到能透過電漿波回聲去觀察電漿波與粒子間的交互作用可逆與否。 透過PIC模擬能觀察到給予電漿兩個外加的電場脈衝所產生的電漿波回聲, 但電漿波在考慮庫倫碰撞的情況下形成不可逆現象, 除了影響電漿波回聲的發生時間外也會降低電漿波回聲的振幅。 為了將二元碰撞納入粒子網格法(PIC)模擬去觀察庫倫碰撞對電漿波回聲造成之影響, 我們參考了一種用於解質心問題的演算法名叫 Barnes and Hut 演算法並將其簡化來預估多體的庫倫力。

An electrostatic Particle-in-Cell (PIC) simulation is developed to investigate the origin of irreversibility in the electron plasma wave. By giving two external pulse electric field to the plasma, the temporal plasma echo is observed in the PIC simulation. If Coulomb collisional effects are considered, the plasma wave echo will become irreversible phenomena. The Coulomb collisional effect is manifested as the time-shift of the echo peak and the damping of the echo peak amplitude. Binary collisions into the PIC simulation is incorporated to demonstrate collisional effects on the plasma wave echo. A simplified algorithm which can approximate the N-body force calculation is employed learning from the Barnes and Hut algorithm by the gravitational problems.

摘要 III
Abstract IV
List of Figures V
Chapter 1 Introduction 1
Chapter 2 Theoretical and Computation Model 6
2-1. Vlasov Kinetic theory from a discrete particle system (Klimotovich equation) 6
2-2. Wave-particle interaction (Landau damping) 12
2-3.Temporal plasma wave echo 17
2-4. Coulomb collisional effects on plasma echo 19
Chapter 3 Numerical Simulation by Particle-In-Cell Simulation 30
3-1. Normalization of Vlasov-Poissson system 32
3-2. Time advance particles’ motion 34
3-3. Loading of the initial distribution 35
3-4. Interpolation scheme for density gathering 38
3-5. Poisson solver 39
3-6. Barnes and Hut algorithm for Coulomb collisions 43
Chapter 4 Simulation Results 48
4-1. Landau damping of Langmuir waves 48
4-2. Collisionless plasma wave echo 52
4-3. Plasma wave echo with Coulumb collisions 55
Chapter 5 Summary and Discussions 68
Appendix 70
Appendix 1 70
Appendix 2 70
References 71

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