Post on 03-Jan-2016
description
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6. Wave in space plasma and Turbulence
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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;
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Wave
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Wave in solid state physics
Phonon determine the property of the materials;
conductor or semi-conductorElectron-hole pairs dominate the energy transportation
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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;
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Waves
Plane wave assumption
)exp(),(, tiit xkkAxA
Phase and group velocities:
kV
kV
gr
ph kˆ Wave propagation
Velocity of energy flow
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Dispersion relation
Light in prism
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Dispersion relation in solid state materials
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Dispersion relation in space plasma
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Earth whistler wave
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Type III Solar radio burst (Electron burst)
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Waves in the plasma
Electrostatic waves Langmuir waves or ion cyclotron waves
Electromagnetic waves light waves, MHD waves
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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.
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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。
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x0
0
xen
E
+
+
+
+
+
-
-
-
-
-
Possible electron plasma oscillation
x
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Langmuir oscillation
One of the electrostatic waves
The waves are generated by the electric charge separation, which is caused by thermal oscillation.
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Irving Langmuir (31 January 1881 – 16 August 1957)
He was awarded the 1932 Nobel Prize in Chemistry for his work in surface chemistry.
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Langmuir oscillation (cont.)
0
22
e
epe m
en
If only consider a separation of charges, we have plasma electron frequency
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Langmuir wave
Adding electron thermal pressure
eeBee nTkp
2222thepel Vk
Langmuir dispersion relation
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Dispersion relation of Langmuir Wave
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Ion-Acoustic waves
Now consider relative low frequency, while the ions’ contribution must be included.
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0
22
i
ipi m
eZn
Ion-Acoustic waves (cont.)
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22
22
)1(k
km
Tkk
m
Tk
Dei
eBe
i
iBiia
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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
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Dispersion relation of Ion-Acoustic waves
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Cyclotron Frequency
有磁场存在的等离子体
m
qBg
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Cyclotron wave generated by pickup ions
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Electrostatic waves
Only consider the oscillation dominated by the electric field which is caused by the separation of charges.
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Electromagnetic waves
Also include the currents caused by charges oscillation.
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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.
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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
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e
epe m
enAlso note:
Two-stream instability
High speed cold electron stream moves fast relative to the ions, and plasma waves are generated;
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Solar flare is the typical case of two-stream instability;
Solar radio burst (MHz) can be observed on ground.
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Whistler mode
Why we see a whistler?
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222 pegew ck
High phase and group velocities correspond high frequency, vica verse.
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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
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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)
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Type II radio burst
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Coronal shock
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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.
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Scenario of Type III burst and Type U burst
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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.
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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).
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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.
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One application: electromagnetic waves can be used to measure density of ionoshpere
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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
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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。
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Turbulence
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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.
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Laminar flow ( streamline flow)
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湍流的特性
不规则性
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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
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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
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湍流的特性( cont.)
Dissipation
The kinetic energy is converted into internal energy (heat)
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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 )
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from these large scale structures to smaller scale structures.
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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.
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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
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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
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Solar Wind
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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.
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Turbulence in solar wind
http://solarprobe.gsfc.nasa.gov/solarprobe_science.htm
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K41 scaling law in space plasma
Kraichnan (-1.5) scaling law seems not be shown?
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Summary
Wave in plasma Electrostatic waves Electromagnetic waves Whistler mode & radio burst
Turbulence Turbulence in solar wind
Energy Cascade K41 scaling law