Transcript 2.空间等离子体
6. Wave in space plasma and Turbulence 1 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; 2 Wave 3 Wave in solid state physics Phonon determine the property of the materials; conductor or semi-conductor Electron-hole pairs dominate the energy transportation 4 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; 5 Waves Plane wave assumption Ax, t A(k, ) exp( ik x it ) Phase and group velocities: V ph Vgr ˆ k k k Wave propagation Velocity of energy flow 6 Dispersion relation Light in prism 7 Dispersion relation in solid state materials 8 Dispersion relation in space plasma 9 Earth whistler wave 10 Type III Solar radio burst (Electron burst) 11 Waves in the plasma Electrostatic waves Langmuir waves or ion cyclotron waves Electromagnetic waves light waves, MHD waves 12 Wave frequency range in plasma fluid Ultra-low frequency Less than 1Hz Extremely-low frequency 1Hz to 1kHz Very-low frequency 1kHz to 10kHz 13 High frequency case Assume ions are stationary. 14 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. 15 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 x + - + - + x + - + - E n0 ex 0 Possible electron plasma oscillation 17 Langmuir oscillation One of the electrostatic waves The waves are generated by the electric charge separation, which is caused by thermal oscillation. 18 Irving Langmuir (31 January 1881 – 16 August 1957) He was awarded the 1932 Nobel Prize in Chemistry for his work in surface chemistry. 19 Langmuir oscillation (cont.) 2 ne e me 0 2 pe If only consider a separation of charges, we have plasma electron frequency 20 Langmuir wave Adding electron thermal pressure pe e k BTe ne Langmuir dispersion relation 2 l2 pe k 2 eVth2 21 Dispersion relation of Langmuir Wave 22 Ion-Acoustic waves Now consider relative low frequency, while the ions’ contribution must be included. ni Z e pi mi 0 2 2 1 2 23 Ion-Acoustic waves (cont.) 2 ia i k BTi mi e k BTe 2 k k 2 mi (1 e k D ) 2 24 Ion-Acoustic waves (cont.) Also adding electron thermal pressure contribution Dispersion of ion-Acoustic waves at small k limit 2 ia e k BTe i k BTi mi k 2 k 2 cs2 25 Dispersion relation of Ion-Acoustic waves 26 Cyclotron Frequency 有磁场存在的等离子体 qB g m 27 Cyclotron wave generated by pickup ions 28 Electrostatic waves Only consider the oscillation dominated by the electric field which is caused by the separation of charges. 29 Electromagnetic waves Also include the currents caused by charges oscillation. 30 Alfvén waves (MHD waves) The waves is named after Dr. Hannes Olof Gösta Alfvén 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. Nobel Prize in Physics 1970 31 色散关系在电离层电磁波反射上的应用 Reflection of waves c k 2 om 2 pe 2 2 A cut-off occurred at the plasma frequency 2 Also note: ne e me 0 2 pe 32 Two-stream instability High speed cold electron stream moves fast relative to the ions, and plasma waves are generated; 33 34 Solar flare is the typical case of twostream instability; Solar radio burst (MHz) can be observed on ground. 35 Whistler mode Why we see a whistler? 36 w k c ge 2 2 2 pe High phase and group velocities correspond high frequency, vica verse. 37 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 38 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) 39 Type II radio burst 40 Coronal shock 41 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. 42 Scenario of Type III burst and Type U burst 43 44 45 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. 46 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). 47 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. 48 One application: electromagnetic waves can be used to measure density of ionoshpere 49 Wave particle interaction How do ions response the waves? Resonant absorption or resonant amplification 50 飞船与地面的通讯 深空网全球深空探测站 NASA专用的2300和8450兆赫与深空飞船通讯。 51 Quiz 简要说明type III solar radio burst产生的过 程。 52 Turbulence 53 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. 54 Laminar flow （streamline flow） 55 湍流的特性 不规则性 56 湍流的特性（cont.） Diffusivity Quasi-Parallel Diffuse ions Gyrophase Bunched I FAB B Earth Quasi-Perpendicular Diffuse distribution 57 湍流的特性（cont.） Rotationality Turbulent flows have nonzero vorticity and are characterized by a strong three dimensional vortex generation mechanism known as vortex stretching tornado turbulence http://en.wikipedia.org/wiki/Tornado 58 湍流的特性（cont.） Dissipation The kinetic energy is converted into internal energy (heat) 59 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 60 Cascade (串级) from these large scale structures to smaller scale structures. 61 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. 62 Kolmogorov scaling (1941) –K41 theory base on fluid theory dissipation rate ~ vl3/l, k -5/3 in energy spectrum Kraichnan scaling (1965) – IK theory add magnetic field into eddy transportation in incompressible MHD turbulence dissipation rate ~ vl4/l, k -3/2 in energy spectrum 63 W H Matthaeus Presentation to the Solar and Heliospheric Survey Panel, 2001 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 65 Solar Wind 66 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. 67 Turbulence in solar wind http://solarprobe.gsfc.nasa.gov/solarprobe_science.htm 68 K41 scaling law in space plasma Kraichnan (-1.5) scaling law seems not be shown? 69 Summary Wave in plasma Electrostatic waves Electromagnetic waves Whistler mode & radio burst Turbulence Turbulence in solar wind Energy Cascade K41 scaling law 70