空间等离子体和单粒子的运动、KineticTheory和MHD简介
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medium
Densit ne(m-3)
1032 1020 1016 1012 107 106 105
1
Electron temperature
T(K) 107 108 104 103 107 105 104
106
Magnetic Field B(T) -10 -10−5 10−8 10−9 10−10
7
Debye Length由温度和带电粒子的密度共同决定
8
Debye and Coulomb potential
库仑势
1 Q
4 0 r
德拜势
1 Q exp( r )
4 0 r
D
9
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：
37
Guiding Center motion
38
磁矩守恒
Magnetic moment
mv
2
W
2B B
39
磁镜效应
40
磁镜效应推导
mv
2
mv 2 sin2
2B
2B
Bm a x
sin2 2 sin2 1
B2 B1
90
sin
B Bm a x
41
Plasma
Usually very high
For many purposes, the conductivity of a plasma may be treated as infinite.
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.
空间等离子体和单粒 子的运动、Kinetic Theory 和 MHD 简介
1
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
/wiki/Plasma_%28physics%29 4
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 /wiki/Plasma_%28physics%29
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.
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.
Independently acting species
Velocity distribution
Interactions
Gas Very low
Air is an excellent insulator until it breaks down into plasma at electric field strengths above 30 kilovolts per centimeter. One All gas particles behave in a similar way, influenced by gravity and by collisions with one another.
1 Q exp( r )
4 0 r
D
2D
0kTe
n0e2
11
德拜长度的快速估算
D 6.9
Te n0
Debye Length in cm
Te in k n0 in cm-3
12
研究对象尺寸要求
保持等离子体电中性 L D
13
典型的德拜长度
Plasma
Solar core Tokamak Gas discharge Ionosphere Magnetosphere Solar wind Interstellar medium Intergalactic
Loss cone
sin min
Bm in Bm a x
42
Van Allen 辐射带
Trapped charged particles
43
The outer belt
The outer belt consists mainly of high energy (0.1–10 MeV) electrons
2
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。
3
Property Electrical Conductivity
24
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
25
等离子体中的量子效应？
Heisenberg’s uncertainty principle
LHS:
The boundary of classical and quantum regime
15
Debye sphere
德拜球的定义如下：
N D ne3D 1
ND讨论了自由带电粒子的中的“自由问 题”
16
N D ne3D 1
D
0 k Te
nee2
3
ND
T
2
1
n2
17
如何联系自由带电粒子和ND？
e
1
库仑势能远小于粒子热运动的动能
k Te
考虑极限条件下：
rmin
1
1
ne3
于是：
1 e
4 0 rmin
e kTe
1 4 0
e2 kTe
n1 3 e
1 4
1
N2 3 D
e 1 k Te
ND ne3D 1
18
Plasma frequency
x
+ + +
x
+
+
-
-
E n0ex
-
0
-
Possible electron plasma oscillation
Maxwellian Collisions usually lead to a Maxwellian velocity distribution of all gas particles, with very few relatively fast particles.
Binary Two-particle collisions are the rule, three-body collisions extremely rare.
rg
v
g
mv qB
gyroradius
Note:
v
vx2
v
2 y
34
Guiding center and pitch angle(俯仰角)
tan1
v v//
35
Drift motion – Electric Drift
36
其它几种漂移运动
Polarization Drift Magnetic Gradient Drift General Force Drift Curvature Drift
19
单个电子的运动方程
me
d 2x dt 2
(e)E
n0e2
0
x
整理后：
d 2x dt 2
n0e2
me 0
x
0
Harmonic oscillator equation
20
谐振子方程的特征频率
1
pe
nee2
me 0
2
等离子体对碰撞的限制 2
5
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
6
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。
பைடு நூலகம்D
0 k Te
n0e2
21
Relationship between Plasma Frequency, Debye length, and thermal speed
psDs Cs
22
散射问题（碰撞）
和电中性粒子的碰撞 和带电粒子的碰撞
23
碰撞频率
f nv C
C 1 v4
f 1 v3
Hot Plasma is collisionless
磁层—磁尾： ne=10-2 cm-3, Te = 105k, B=30nT 电离层： ne=105 cm-3, Te = 103k, B=104nT
28
Quiz 3 1. 何为“等离子体”？ 2. 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？ 3. 1AU处太阳风质子热速度为35km/s，试推算太阳 风质子温度。
3
fe
(v)
n0
me
2kTe
2
exp
1 2
meV 2 k Te
q
*相空间指（vx, vy, vz, rx, ry, rz）组成的坐标空间
10
解Poisson方程
2
q 0
n0e
0
1
exp
e k Te
B Beˆ z
mvx qBvy
mvy qBvx
mvz 0
vx
qB m
vx
vy
qB m
v
y
32
Cyclotron Frequency
有磁场存在的等离子体
g
qB m
33
带电粒子回旋运动的轨迹
qB
g m
Cyclotron Frequency (gyrofrequency)
Te3 2 ne
/ 23 3mek 3 2
26
空间中的等离子体
太阳风 磁层 辐射带 电离层
27
空间等离子体的典型参数
太阳风：ne=5 cm-3, Te = 105k, B=5nT 磁层--辐射带： ne=1 cm-3, Te = 107k, B=100-
1000nT
29
研究等离子体的方法
单粒子运动 流体力学的方法（Magnetohydrodynamics） Kinetic theory
30
单个带电粒子的运动
库仑力和洛仑兹力
F qE qV B
31
回旋运动
受洛仑兹力影响的带电离子的运动方程
F qV B m dv dt
假设在均匀磁场中
--
Debye Length λD(m)
10−11 10−4 10−4 10−3 102 10 10
105
/wiki/Debye_length#Debye_length_in_silicon
14
Debye length vs spacecraft
Spacecraft potential 光电子效应产生的电荷
Collective
Waves, or organized motion of plasma, are very important because the particles can interact at long ranges through the electric and magnetic forces.
Densit ne(m-3)
1032 1020 1016 1012 107 106 105
1
Electron temperature
T(K) 107 108 104 103 107 105 104
106
Magnetic Field B(T) -10 -10−5 10−8 10−9 10−10
7
Debye Length由温度和带电粒子的密度共同决定
8
Debye and Coulomb potential
库仑势
1 Q
4 0 r
德拜势
1 Q exp( r )
4 0 r
D
9
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：
37
Guiding Center motion
38
磁矩守恒
Magnetic moment
mv
2
W
2B B
39
磁镜效应
40
磁镜效应推导
mv
2
mv 2 sin2
2B
2B
Bm a x
sin2 2 sin2 1
B2 B1
90
sin
B Bm a x
41
Plasma
Usually very high
For many purposes, the conductivity of a plasma may be treated as infinite.
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.
空间等离子体和单粒 子的运动、Kinetic Theory 和 MHD 简介
1
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
/wiki/Plasma_%28physics%29 4
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 /wiki/Plasma_%28physics%29
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.
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.
Independently acting species
Velocity distribution
Interactions
Gas Very low
Air is an excellent insulator until it breaks down into plasma at electric field strengths above 30 kilovolts per centimeter. One All gas particles behave in a similar way, influenced by gravity and by collisions with one another.
1 Q exp( r )
4 0 r
D
2D
0kTe
n0e2
11
德拜长度的快速估算
D 6.9
Te n0
Debye Length in cm
Te in k n0 in cm-3
12
研究对象尺寸要求
保持等离子体电中性 L D
13
典型的德拜长度
Plasma
Solar core Tokamak Gas discharge Ionosphere Magnetosphere Solar wind Interstellar medium Intergalactic
Loss cone
sin min
Bm in Bm a x
42
Van Allen 辐射带
Trapped charged particles
43
The outer belt
The outer belt consists mainly of high energy (0.1–10 MeV) electrons
2
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。
3
Property Electrical Conductivity
24
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
25
等离子体中的量子效应？
Heisenberg’s uncertainty principle
LHS:
The boundary of classical and quantum regime
15
Debye sphere
德拜球的定义如下：
N D ne3D 1
ND讨论了自由带电粒子的中的“自由问 题”
16
N D ne3D 1
D
0 k Te
nee2
3
ND
T
2
1
n2
17
如何联系自由带电粒子和ND？
e
1
库仑势能远小于粒子热运动的动能
k Te
考虑极限条件下：
rmin
1
1
ne3
于是：
1 e
4 0 rmin
e kTe
1 4 0
e2 kTe
n1 3 e
1 4
1
N2 3 D
e 1 k Te
ND ne3D 1
18
Plasma frequency
x
+ + +
x
+
+
-
-
E n0ex
-
0
-
Possible electron plasma oscillation
Maxwellian Collisions usually lead to a Maxwellian velocity distribution of all gas particles, with very few relatively fast particles.
Binary Two-particle collisions are the rule, three-body collisions extremely rare.
rg
v
g
mv qB
gyroradius
Note:
v
vx2
v
2 y
34
Guiding center and pitch angle(俯仰角)
tan1
v v//
35
Drift motion – Electric Drift
36
其它几种漂移运动
Polarization Drift Magnetic Gradient Drift General Force Drift Curvature Drift
19
单个电子的运动方程
me
d 2x dt 2
(e)E
n0e2
0
x
整理后：
d 2x dt 2
n0e2
me 0
x
0
Harmonic oscillator equation
20
谐振子方程的特征频率
1
pe
nee2
me 0
2
等离子体对碰撞的限制 2
5
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
6
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。
பைடு நூலகம்D
0 k Te
n0e2
21
Relationship between Plasma Frequency, Debye length, and thermal speed
psDs Cs
22
散射问题（碰撞）
和电中性粒子的碰撞 和带电粒子的碰撞
23
碰撞频率
f nv C
C 1 v4
f 1 v3
Hot Plasma is collisionless
磁层—磁尾： ne=10-2 cm-3, Te = 105k, B=30nT 电离层： ne=105 cm-3, Te = 103k, B=104nT
28
Quiz 3 1. 何为“等离子体”？ 2. 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？ 3. 1AU处太阳风质子热速度为35km/s，试推算太阳 风质子温度。
3
fe
(v)
n0
me
2kTe
2
exp
1 2
meV 2 k Te
q
*相空间指（vx, vy, vz, rx, ry, rz）组成的坐标空间
10
解Poisson方程
2
q 0
n0e
0
1
exp
e k Te
B Beˆ z
mvx qBvy
mvy qBvx
mvz 0
vx
qB m
vx
vy
qB m
v
y
32
Cyclotron Frequency
有磁场存在的等离子体
g
qB m
33
带电粒子回旋运动的轨迹
qB
g m
Cyclotron Frequency (gyrofrequency)
Te3 2 ne
/ 23 3mek 3 2
26
空间中的等离子体
太阳风 磁层 辐射带 电离层
27
空间等离子体的典型参数
太阳风：ne=5 cm-3, Te = 105k, B=5nT 磁层--辐射带： ne=1 cm-3, Te = 107k, B=100-
1000nT
29
研究等离子体的方法
单粒子运动 流体力学的方法（Magnetohydrodynamics） Kinetic theory
30
单个带电粒子的运动
库仑力和洛仑兹力
F qE qV B
31
回旋运动
受洛仑兹力影响的带电离子的运动方程
F qV B m dv dt
假设在均匀磁场中
--
Debye Length λD(m)
10−11 10−4 10−4 10−3 102 10 10
105
/wiki/Debye_length#Debye_length_in_silicon
14
Debye length vs spacecraft
Spacecraft potential 光电子效应产生的电荷
Collective
Waves, or organized motion of plasma, are very important because the particles can interact at long ranges through the electric and magnetic forces.