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

空间物理学（ I ）

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

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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。

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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.

http://en.wikipedia.org/wiki/Plasma_%28physics%29

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See http://en.wikipedia.org/wiki/Plasma_%28physics%29

Plasma lamp

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？

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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

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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 。

20

0

en

kTeD

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Debye Length 由温度和带电粒子的密度共同决定

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Debye and Coulomb potential

r

Q

04

1

)exp(4

1

0 D

r

r

Q

库仑势

德拜势

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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：

e

e

e

e

kT

qVm

kT

mn

2212

3

0e exp2

(v)f

* 相空间指（ vx, vy, vz, rx, ry, rz ）组成的坐标空间

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解 Poisson 方程

e

q

kT

eenexp1

0

0

0

2

)exp(4

1

0 D

r

r

Q

20

02

en

kTeD

12

09.6 nTe

D

德拜长度的快速估算

Debye Length in cmTe in kn0 in cm-3

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研究对象尺寸要求

DL 保持等离子体电中性

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典型的德拜长度Plasma

Densitne(m

-3)

Electron temperature

T(K)

MagneticFieldB(T)

DebyeLengthλD(m)

Solar core 1032 107 -- 10−11

Tokamak 1020 108 10 10−4

Gas discharge 1016 104 -- 10−4

Ionosphere 1012 103 10−5 10−3

Magnetosphere 107 107 10−8 102

Solar wind 106 105 10−9 10

Interstellar medium 105 104 10−10 10

Intergalactic medium

1 106 -- 105

http://en.wikipedia.org/wiki/Debye_length#Debye_length_in_silicon

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Debye length vs spacecraft

Spacecraft potential

光电子效应产生的电荷

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Debye sphere

13 DeD nN

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”

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21

23

nTND

13 DeD nN

20

en

kT

e

eD

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如何联系自由带电粒子和 ND ？

1

ekT

e库仑势能远小于粒子热运动的动能

考虑极限条件下：31

1min

enr

于是：

min04

1

r

e

32

31 1

4

1

4

1 2

0 D

eee Nn

kT

e

kT

e

1

ekT

e 13 DeD nN

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Plasma frequency

x0

0

xen

E

+

+

+

+

+

-

-

-

-

-

Possible electron plasma oscillation

x

20

xen

Eedt

xdme

0

20

2

2

)(

单个电子的运动方程

整理后： 00

20

2

2

xm

en

dt

xd

eHarmonic oscillator equation

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21

0

2

e

epe m

en

谐振子方程的特征频率

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等离子体对碰撞的限制

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sDsps C

Relationship between Plasma Frequency, Debye length, and thermal speed

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散射问题（碰撞） 和电中性粒子的碰撞

和带电粒子的碰撞

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碰撞频率 Cnvf

41 vC 31 vf Hot Plasma is collisionless