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

25 研究对象是否是等离子体的判据总结 Debye shielding Free charged particle
Less collision with neutral

26 等离子体中的量子效应？ Heisenberg’s uncertainty principle LHS:
LHS: The boundary of classical and quantum regime

27 空间中的等离子体 太阳风 磁层 辐射带 电离层

28 空间等离子体的典型参数 太阳风：ne=5 cm-3, Te = 105k, B=5nT

29 Quiz 3 何为“等离子体”？ 为什么太阳风等离子体能够保持电离状态而不会发生离子和电子的复合？ 1AU处太阳风质子热速度为35km/s，试推算太阳风质子温度。

30 研究等离子体的方法 单粒子运动 流体力学的方法（Magnetohydrodynamics） Kinetic theory

31 单个带电粒子的运动 库仑力和洛仑兹力

32 回旋运动 受洛仑兹力影响的带电离子的运动方程 假设在均匀磁场中

33 Cyclotron Frequency 有磁场存在的等离子体

34 带电粒子回旋运动的轨迹 Cyclotron Frequency (gyrofrequency) gyroradius Note:

35 Guiding center and pitch angle(俯仰角)

36 Drift motion – Electric Drift

37 其它几种漂移运动 Polarization Drift Magnetic Gradient Drift
General Force Drift Curvature Drift

38 Guiding Center motion

39 磁矩守恒 Magnetic moment

40 磁镜效应

41 磁镜效应推导

42 Loss cone

43 Van Allen 辐射带 Trapped charged particles

44 The outer belt The outer belt consists mainly of high energy (0.1–10 MeV) electrons The large outer radiation belt extends from an altitude of about three to ten Earth radii (RE) or 13,000 to 19,000 kilometres above the Earth's surface. Its greatest intensity is usually around 4–5 RE.

45 Inner belt The inner Van Allen Belt extends from an altitude of 100–10,000 km (0.01 to 1.5 Earth radii) Ions energy exceeding 100 MeV and electrons in the range of hundreds of keV, trapped by the strong (relative to the outer belts) magnetic fields in the region It is believed that protons of energies exceeding 50 MeV in the lower belts at lower altitudes are the result of the beta decay of neutrons created by cosmic ray collisions with nuclei of the upper atmosphere. The source of lower energy protons is believed to be proton diffusion due to changes in the magnetic field during geomagnetic storms

46 地面实验室模拟的辐射带

47 木星的辐射带

48 Aurora

49 Kinetic theory Distribution function

50 Kinetic theory Note:

51 等离子体中的Vlasov方程

52 类似Maxwellian分布曲线

53 卫星位于地球bow shock以外 卫星位于磁尾

54 离子束流的速度、压强和温度 The 1st order moment The 2nd order moment T

55 典型Flux的范围

56 Non-Maxwellian distribution function
Kappa distribution---power law distribution

57 MHD简介 流体力学的理论在于寻求宏观参量的演化方程；（宏观参量指：n(r,t), v(r,t), p(r,t), T(r,t) etc.）； 当单粒子理论中的粒子所带电荷、质量无限变化时（如：e’=e/M, m’=m/M），等离子体的德拜长度、回旋半径和回旋频率等保持不变（可作为流体处理）。

58 连续性方程

59 磁冻结（frozen-in condition）
Faraday’s law

60 magnetopause

61 磁压 等离子体beta常数

62 磁声速（Alfven velocity） Note: sound speed

63 MHD使用范围

64 地球舷激波周围离子加速的情况 Earth B Intermediate distribution Diffuse
Quasi-Perpendicular Quasi-Parallel Diffuse ions FAB Ion Foreshock Boundary B Earth Field-aligned beams Specularly reflected ions Intermediate distribution Diffuse

65 Dynamic of the Earth’s Bow Shock
The dynamic of the Earth’s bow shock creates variations of the local ΘBn, which can lead to particle release in turn.

66 磁矩守恒失效的情况

67 总结： 简单介绍了等离子体的概念； 单粒子运动 Kinetic theory MHD