1

6. Wave in space plasma and Turbulence

2

Outline:

Background: wave in medium; Electrostatic Wave in plasma; Langmuir wave

ion-acoustic wave ion-cyclotron wave

Electromagnetic wave in plasma MHD wave

Type III Radio burst

Turbulence; Summary;

3

Wave

4

Wave in solid state physics

Phonon determine the property of the materials;

conductor or semi-conductorElectron-hole pairs dominate the energy transportation

5

Why do we have wave problem in plasma?

Waves transfer energy in medium; Waves dissipate the energy to cause heating; Waves scatter the ions; etc;

6

Waves

Plane wave assumption

)exp(),(, tiit xkkAxA

Phase and group velocities:

kV

kV

gr

ph kˆ Wave propagation

Velocity of energy flow

7

Dispersion relation

Light in prism

8

Dispersion relation in solid state materials

9

Dispersion relation in space plasma

10

Earth whistler wave

11

Type III Solar radio burst (Electron burst)

12

Waves in the plasma

Electrostatic waves Langmuir waves or ion cyclotron waves

Electromagnetic waves light waves, MHD waves

13

Wave frequency range in plasma fluid

Ultra-low frequency Less than 1Hz

Extremely-low frequency

1Hz to 1kHz

Very-low frequency 1kHz to 10kHz

High frequency case

Assume ions are stationary.

14

15

Two condition for an existing plasma waves

Must be a solution of appropriate equations;

Amplitude of wave is great than the background thermal fluctuations in the plasma.

Quiz

简要文字说明或者用数学表达式分别阐述波动中群速度和相速度。

16

17

x0

0

xen

E

+

+

+

+

+

-

-

-

-

-

Possible electron plasma oscillation

x

18

Langmuir oscillation

One of the electrostatic waves

The waves are generated by the electric charge separation, which is caused by thermal oscillation.

19

Irving Langmuir (31 January 1881 – 16 August 1957)

He was awarded the 1932 Nobel Prize in Chemistry for his work in surface chemistry.

20

Langmuir oscillation (cont.)

0

22

e

epe m

en

If only consider a separation of charges, we have plasma electron frequency

21

Langmuir wave

Adding electron thermal pressure

eeBee nTkp

2222thepel Vk

Langmuir dispersion relation

22

Dispersion relation of Langmuir Wave

23

Ion-Acoustic waves

Now consider relative low frequency, while the ions’ contribution must be included.

21

0

22

i

ipi m

eZn

Ion-Acoustic waves (cont.)

24

22

22

)1(k

km

Tkk

m

Tk

Dei

eBe

i

iBiia

25

Ion-Acoustic waves (cont.)

Also adding electron thermal pressure contribution

2222s

i

iBieBeia ckk

m

TkTk

Dispersion of ion-Acoustic waves at small k limit

26

Dispersion relation of Ion-Acoustic waves

27

Cyclotron Frequency

有磁场存在的等离子体

m

qBg

28

Cyclotron wave generated by pickup ions

29

Electrostatic waves

Only consider the oscillation dominated by the electric field which is caused by the separation of charges.

30

Electromagnetic waves

Also include the currents caused by charges oscillation.

31

Alfvén waves (MHD waves)

The waves is named after Dr. Hannes Olof Gösta Alfvén

Nobel Prize in Physics 1970

Alfvén wrote in a letter to the journal Nature in 1942:

"If a conducting liquid is placed in a constant magnetic field, every motion of the liquid gives rise to an E.M.F. which produces electric currents. Owing to the magnetic field, these currents give mechanical forces which change the state of motion of the liquid. Thus a kind of combined electromagnetic-hydrodynamic wave is produced."

Alfvén waves initiated the field of magnetohydrodynamics which subsequently earned Alfvén a Nobel Prize.

32

色散关系在电离层电磁波反射上的应用

Reflection of waves

2222 kcpeom

A cut-off occurred at the plasma frequency

0

22

e

epe m

enAlso note:

Two-stream instability

High speed cold electron stream moves fast relative to the ions, and plasma waves are generated;

33

34

35

Solar flare is the typical case of two-stream instability;

Solar radio burst (MHz) can be observed on ground.

36

Whistler mode

Why we see a whistler?

37

222 pegew ck

High phase and group velocities correspond high frequency, vica verse.

38

Solar radio emission

In addition to the strong thermal radiation of the quiet Sun there is intense radio emission from bursts that are associated with phenomena of solar activity like flares and coronal mass ejections (CMEs).

Radio bursts cause “snow storm” on CCD

39

Solar radio bursts

Type I (Short, narrow band events that usually occur in great numbers together with a broader band continuum.)

Type II (shock front burst) Type III (electron burst) Type IV (Flare-related broad-band continua) Type V (Langmuir burst)

40

Type II radio burst

41

Coronal shock

42

Type III solar radio burst

These bursts are generated when suprathermal electrons (velocity ~ 0.05 to 0.3 c, where c is the speed of light) are ejected from solar active regions and then travel outward along open magnetic field lines through the corona and interplanetary medium.

43

Scenario of Type III burst and Type U burst

44

45

46

Green Bank Solar Radio Burst Spectrometer

The Green Bank Solar Radio Burst Spectrometer (GBSRBS) provides dynamic spectra of solar radio bursts during daylight hours in the western hemisphere.

47

Solar Radio Bursts Could Cripple GPS空间天气预报的重点之一

All satellites broadcast at the same two frequencies, 1.57542 GHz (L1 signal) and 1.2276 GHz (L2 signal).

48

Importance of solar radio observations

Observations of the flare related processes can help to improve the understanding of solar activity. Today, many of them are far from understood.

Monitoring the solar activity can help to minimize damage of strong CMEs on technical equipment on Earth. A better understanding of the observations can eventually lead to predictions of the effects on Earth and allow for fast provision.

49

One application: electromagnetic waves can be used to measure density of ionoshpere

50

Wave particle interaction

How do ions response the waves?

Resonant absorption or resonant amplification

飞船与地面的通讯深空网全球深空探测站

51

NASA专用的 2300 和 8450兆赫与深空飞船通讯。

Quiz

简要说明 type III solar radio burst产生的过程。

52

53

Turbulence

54

Turbulence

由一些随机过程产生；湍流还是悬而未决的问题； flows with high Reynolds numbers (>3000)

usually become turbulent, while those with low Reynolds numbers usually remain laminar.

55

Laminar flow （ streamline flow）

56

湍流的特性

不规则性

57

湍流的特性（ cont.） Diffusivity

Quasi-Perpendicular

Quasi-Parallel

Diffuse ions

FAB

Ion

Fore

shoc

k B

ound

ary

B

GyrophaseBunched

I

Electrons

Earth

Diffuse distribution

58

湍流的特性（ cont.） Rotationality

Turbulent flows have non-zero vorticity and are characterized by a strong three dimensional vortex generation mechanism known as vortex stretching

tornado turbulencehttp://en.wikipedia.org/wiki/Tornado

59

湍流的特性（ cont.）

Dissipation

The kinetic energy is converted into internal energy (heat)

60

湍流的特性（ cont.）

Energy cascade:

The energy "cascades" from these large scale structures to smaller scale structures.

http://www.nasa.gov/topics/solarsystem/features/solar_mystery.html

Cascade (串级 )

61

from these large scale structures to smaller scale structures.

62

湍流的特性（ cont.）

Kolmogorov length scale (1941)

In his 1941 theory, A. N. Kolmogorov introduced the idea that the smallest scales of turbulence are universal (similar for every turbulent flow) and that they depend only on ε and ν.

63

Kolmogorov scaling (1941) –K41 theory base on fluid theory dissipation rate ~ vl

3/l, k -5/3 in energy spectrum

Kraichnan scaling (1965) – IK theory add magnetic field into eddy transportation in incompressible MHD turbulence dissipation rate ~ vl

4/l, k -3/2 in energy spectrum

W H MatthaeusPresentation to the Solar and Heliospheric Survey Panel, 2001

65

Turbulence in space physics

Solar wind is heated by some energy sources, and one possible source is turbulence;

The turbulent cascade of solar wind may be caused by the fast solar wind stream from some holes;

Two scaling laws are predicted in the cascade of solar wind, however the MHD turbulence theory (IK theory) seems not to agree the observation

66

Solar Wind

67

Turbulence in solar wind

Belcher and Davis [1971] first demonstrated that the solar wind contains MHD turbulence: Figure 12.1 shows coupled variations in the three component's of the magnetic field and fluid velocity of the solar wind.

68

Turbulence in solar wind

http://solarprobe.gsfc.nasa.gov/solarprobe_science.htm

69

K41 scaling law in space plasma

Kraichnan (-1.5) scaling law seems not be shown?

70

Summary

Wave in plasma Electrostatic waves Electromagnetic waves Whistler mode & radio burst

Turbulence Turbulence in solar wind

Energy Cascade K41 scaling law