2.空间等离子体和单粒子的运动、Kinetic Theory 和 MHD 简介

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1 2.空间等离子体和单粒子的运动、Kinetic Theory 和 MHD 简介

2 Outline: 等离子体的定义 Debye长度和等离子体的特性 空间等离子体 单个带电粒子的运动 回旋波
Guiding center motion 磁矩守恒量 磁镜效应 Trapped particles 辐射带 电离层 极光的产生 磁冻结效应 Kinetic theory简介 MHD简介

3 等离子体 等离子体的定义: 由自由电子和自由离子组成的集合体（气体），其正负电荷数目相同。在平均作用的意义上，等离子体对外呈现电中性。
等离子体的直接特性： 自由离子和自由电子占主导地位（即带电粒子所受到的势能远小于粒子热运动的动能），随机的热运动克服库仑势。

4 http://en.wikipedia.org/wiki/Plasma_%28physics%29 Property Gas Plasma
Electrical Conductivity Very low Air is an excellent insulator until it breaks down into plasma at electric field strengths above 30 kilovolts per centimeter. Usually very high For many purposes, the conductivity of a plasma may be treated as infinite. Independently acting species One All gas particles behave in a similar way, influenced by gravity and by collisions with one another. Two or three Electrons, ions, protons and neutrons can be distinguished by the sign and value of their charge so that they behave independently in many circumstances, with different bulk velocities and temperatures, allowing phenomena such as new types of waves and instabilities. Velocity distribution Maxwellian Collisions usually lead to a Maxwellian velocity distribution of all gas particles, with very few relatively fast particles. Often non-Maxwellian Collisional interactions are often weak in hot plasmas and external forcing can drive the plasma far from local equilibrium and lead to a significant population of unusually fast particles. Interactions Binary Two-particle collisions are the rule, three-body collisions extremely rare. Collective Waves, or organized motion of plasma, are very important because the particles can interact at long ranges through the electric and magnetic forces.

5 分离的正离子和电子是否会在电场力的库仑相互作用下结合成电中性原子或者分子？频繁的带电粒子碰撞对等离子体的影响是什么？
Plasma lamp See

6 什么样的条件使得等离子体稳定存在？ 1.保持电中性 2.自由粒子的存在 3.发生碰撞的几率低

7 德拜屏蔽(Debye Shielding)
等离子体存在一个特征长度，在此特征长度以外，带电粒子间库仑势场因为屏蔽效应迅速减弱。这个特征长度定义为Debye length。

8 Debye Length由温度和带电粒子的密度共同决定

9 Debye and Coulomb potential
库仑势 德拜势

10 德拜屏蔽(Debye Shielding)
统计物理指出自由粒子在相空间*的分布大致如下： *相空间指（vx, vy, vz, rx, ry, rz）组成的坐标空间

11 解Poisson方程

12 德拜长度的快速估算 Debye Length in cm Te in k n0 in cm-3

13 研究对象尺寸要求 保持等离子体电中性

14 Electron temperature T(K)
典型的德拜长度 Plasma Densit ne(m-3) Electron temperature T(K) Magnetic Field B(T) Debye Length λD(m) Solar core 1032 107 -- 10−11 Tokamak 1020 108 10 10−4 Gas discharge 1016 104 Ionosphere 1012 103 10−5 10−3 Magnetosphere 10−8 102 Solar wind 106 105 10−9 Interstellar medium 10−10 Intergalactic medium 1

15 Debye length vs spacecraft
Spacecraft potential 光电子效应产生的电荷

16 Debye sphere 德拜球的定义如下： ND讨论了自由带电粒子的中的“自由问题”

17

18 如何联系自由带电粒子和ND？ 库仑势能远小于粒子热运动的动能 考虑极限条件下： 于是：

19 Plasma frequency + - - + - + - + - +
Possible electron plasma oscillation

20 单个电子的运动方程 整理后： Harmonic oscillator equation

21 谐振子方程的特征频率 等离子体对碰撞的限制

22 Relationship between Plasma Frequency, Debye length, and thermal speed

23 散射问题（碰撞） 和电中性粒子的碰撞 和带电粒子的碰撞

24 碰撞频率 Hot Plasma is collisionless