基礎太空電漿物理學

【本書由國立中央大學出版中心與Airiti Press共同出版】

隨著太空電漿物理現象的不同，其所涵蓋的特徵尺度範圍可小至電子的慣性尺度，也可大至磁流體力學（MHD）的尺度。雖然利用磁流體電漿模型，已經可用來描述許多的太空物理現象，但是就像大氣物理中的地轉風模式一樣，我們應該要謹慎考慮它們的適用範圍。本書的重點之一，就是要教導學生，科學家是如何得到那些特定電漿模型的控制方程式，並讓讀者了解，要獲得這套控制方程式，需要做哪些基本的假設。我們相信，除非學生能徹底了解各種電漿模式的控制方程式以及它們的線性色散關係是如何推導出來的，否則是很難真正了解不同電漿模型的適用條件，也自然很難對症下藥，選用正確的電漿模式，來解釋分析觀測到的物理現象。

本書一開始先介紹電漿微觀動力模式、電子－正離子雙流體模式、與單流體電漿模式的基本方程式。接著介紹電子－正離子雙流體電漿與磁流體電漿中的線性波色散關係式。並於本書後段介紹電漿微觀動力模式中的線性波色散關係式。因為認識帶電粒子在相空間中的運動軌跡，將有助於了解電漿微觀動力模式中，波與粒子的交互作用，因此在介紹電漿微觀動力模式的線性波色散關係前，本書將先介紹如何分析帶電粒子在不同電磁場環境中，所可能出現的多重時間尺度的運動情形。

本書是針對兩學期研究所課程所設計的教科書。內容只涵蓋電漿物理的基本課題，因此授課老師可在一學年的時間裡，輕鬆的教完本書全部的課程。本書中第二、三章所推導的各種基本方程式，可為太空觀測資料的分析工作以及不同尺度電漿模擬碼的設計工作，提供非常實用的理論基礎。包括了太空物理、天文物理、與實驗室電漿物理等領域的學生與研究人員將發現本書的內容實用，且對相關研究工作有所幫助。

本書封面圖片為沿著日地連線方向所作的磁鞘觀測結果。這項觀測結果顯示
 ，或 式(3.62)，是一個比著名的CGL雙絕熱狀態方程式，還更具普遍性的絕熱方程式。（感謝趙寄昆教授提供這份珍貴的太空觀測資料分析結果。）

The characteristic scale lengths of various space plasma phenomena range from the electron inertial length to the magnetohydrodynamic (MHD) scale length. The MHD plasma model in the space physics is like the geostrophic-wind approximation in the atmospheric physics. Both of them have the limitation in their applications. One of the important goals of this book is to show the students how scientists obtain the governing equations of a given plasma model and what assumptions have been made to obtain the set of governing equations shown in the literatures. We believe that, unless the students know how to derive the governing equations and how to obtain the wave mode from a simplified linear dispersion relation, it will be difficult for the students to fully understand the limitations of a given plasma model and to apply the right model for the observed phenomena.

The basic equations of the kinetic plasma, the ion-electron two-fluid plasma, and the one-fluid plasma are derived at the beginning of this book. They are followed by the examinations of linear-wave dispersion relations in the ion-electron two-fluid plasma and in the one-fluid MHD plasma. The linear-wave dispersion relations in the kinetic plasma are presented at the end of this book. Because understanding the particle trajectories in the phase space are essential to the study of the wave-particle interactions in the kinetic plasma, the multiple-time-scale particle motions are examined before studying the linear-wave dispersion relations in the kinetic plasma.

This book is written for a two-semester graduate course. It contains only the fundamental subjects in the plasma physics. Thus, an instructor can easily cover the entire book in two semesters. The basic equations derive in Chapters 2 and 3 are particularly useful in analyzing the space plasma data and in designing simulation codes for different plasma models. This book is of interest to students and researches in space physics, astrophysics, and laboratory plasma physics.

Front cover shows magnetosheath observations along the Sun-Earth line. These results indicate that or Eq. (3.62) is a more general adiabatic condition than the CGL double adiabatic equation of states. (Courtesy of Professor J. K. Chao)

呂凌霄
國立中央大學太空科學研究所&大氣科學系副教授
美國阿拉斯加大學費班克分校太空物理博士
研究專長：太空物理、電漿物理、數值模擬

Ling-Hsiao Lyu
Associate professor, Institute of Space Science ﹠Department of Atmospheric Science National Central University.
Ph.D., University of Alaska Fairbanks, USA, 1991.
Physics, Plasma Physics, Numerical Simulation

Preface

Chapter 1 Introduction
1.1. Definition of Plasma
1.2. The SI Units and The Gaussian Units
1.3. Temperature in Units of oK and eV
1.4. Boltzmann Relation
1.5. Debye Shielding and Debye Length
1.6. Plasma Parameter
1.7. Plasma Frequency
1.8. Gyro Frequency and Gyro Radius (or Larmor Radius)
1.9. Collisions

Chapter 2 Deriving the Vlasov Equation From the Klimontovich Equation
2.1. Klimontovich Equation
2.2. Vlasov Equation

Chapter 3 Deriving the Fluid Equations From the Vlasov Equation
3.1. The Vlasov-Maxwell System
3.2. The Fluid Variables
3.3. The Fluid Equations

Chapter 4 Deriving the Vlasov Equation From the Liouville Equation
4.1. Liouville Equation
4.2. BBGKY Hierarchy

Chapter 5 Linear Waves in the Electron-Ion Two-Fluid Plasma
5.1. How to Linearize the Nonlinear Plasma Equations
5.2. Linear Plane Waves in Uniform Two-Fluid Plasma
5.3. Dispersion Relations of High-Frequency Waves in a Uniform Two-Fluid Plasma
5.4. Dispersion Relations of Cross-Ion-Electron-Time-Scale Linear Wave Modes in Uniform Two-Fluid Plasma

Chapter 6 Linear Waves in the MHD Plasma
6.1. Linearized Wave Equations in a Uniform Isotropic MHD Plasma
6.2. Linear Wave Modes in the MHD Plasma

Chapter 7 Particle Motions With Multiple Time Scales
7.1. Periodic Motions and Drift Motions of a Charged Particle
7.2. Fluid Drift 103
7.3. Drift Motion in Time-Dependent Fields 106

Chapter 8 Equilibrium Solutions of the Vlasov Equation
8.1. Characteristic Curves of a Partial Differential Equation
8.2. Equilibrium Solutions of Time-Independent Vlasov-Maxwell Equations
Chapter 9 Electrostatic Linear Waves in the Vlasov Plasma
9.1. Landau Contour
9.2. Linear Dispersion Relations of Electrostatic Waves
9.3. Landau Damping
9.4. Nyquist Method

Chapter 10 Two-Stream Instability

Chapter 11 Linear Waves in the Vlasov Plasma
11.1. Linear Waves in Field-Free Plasma (E00, B00)
11.2. Linear Waves in Magnetized Plasma With Uniform Background B0

Appendix A Static Electric Field and Magnetic Field
A.1. General Solutions
A.2. Solutions of Special Cases

Appendix B Ohm’s Law in One-Fluid Plasma

Appendix C Frozen-in Flux
C.1. Proof of Frozen-in Flux (Method 1)
C.2. Proof of Frozen-in Flux (Method 2)
C.3. Conservation of Circulation vs. Frozen-in Flux in MHD Plasma
C.4 Equipotential Surface in MHD Plasma

Appendix D Curvature Drift

Appendix E Gradient B Drift

Appendix F Deriving the Relativistic Vlasov Equation From the Relativistic Klimontovich Equation
F.1. Relativistic Klimontovich Equation
F.2. Relativistic Vlasov Equation

Appendix G Functions of Complex Variable
G.1. Analytic Function & Residue Theorem
G.2. Branch Point and Riemann Surface

Appendix H Special Functions for Studying Linear Waves in Kinetic Plasmas
H.1. Bessel Function
H.2. Error Function
H.3. Plasma Dispersion Function

Index