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WAVES AND INSTABILITIES IN SPACE PLASMAS

WAVES AND INSTABILITIES IN SPACE PLASMAS. TUTORIAL PRESENTED AT THE SUMMER SCHOOL ON BASIC PROCESSES OF TURBULENT PLASMAS SEPTEMBER 23, 2003 HALKIDIKI GREECE. Dennis Papadopoulos University of Maryland USA. ACKNOWLEDGMENT. USED DATA FROM THE FOLLOWING SOURCES

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WAVES AND INSTABILITIES IN SPACE PLASMAS

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  1. WAVES AND INSTABILITIES IN SPACE PLASMAS TUTORIAL PRESENTED AT THE SUMMER SCHOOL ON BASIC PROCESSES OF TURBULENT PLASMAS SEPTEMBER 23, 2003 HALKIDIKI GREECE Dennis Papadopoulos University of Maryland USA

  2. ACKNOWLEDGMENT • USED DATA FROM THE FOLLOWING SOURCES • UCLA, R. STENZEL : LABORATORY WHISTLER EXPERIMENTS • UNIVERSITY OF IOWA, D. GARNETT : SATELLITE VLF MEASUREMENTS • STANFORD UNIVERSITY, R. HELLIWELL AND U. INAN: TRIGGERED EMISSIONS AND HAARP-CLUSTER EXPERIMENTS • ADVANCED POWER TECHNOLOGIES INC. : HAARP ELF/VLF EXPERIMENTS

  3. Waves in Space Plasmas Physics or Botany?

  4. WAVES ARE A UBIQUITOUS FEATURE OF SPACE PLASMAS

  5. BASICS- THEEARTH’s MAGNETIC FIELD

  6. Internal Response Functions Field Equations Plasma Model Maxwell’s Equations with r and J Particle dynamics with em fields r,J J(E,B) r (E,B) self-consistent link E,B E,B Linearized E-dynamics of Homogeneous Plasmas Fluid, Particle,.. E-static, quasi-static,..

  7. we2=ne2/eom Cold Electron Plasma dJ/dt =eowe2E m(dv/dt)=-eE, J=-nev Es Field Equs for d2E/dt2 +we2E=0 Harmonic Oscillator Equivalent to LC circuits or pendulum Non propagating mode Electron Plasma Oscillations

  8. OBSERVATIONSFrequency-Time Spectrogram Voice print or Sonogram (use transducer to convert el energy to sound energy) of crossing the bow shock of Jupiter

  9. Epo’s becomes waves E,c Generalized Ohm’s law neglecting ions Standard Wave Eqs Y,V P, cs ES WAVES – DISPERSION RELATION Add thermal motion of electrons (pressure), a=3/2

  10. Velocity of Energy or Info transfer-wavepacket w2=k2c2 -> Vp=Vg=c, non-dispersive propagation Wave equs Plane Waves – Phase and Group Velocity Assume E~ Exp(-iwt+ikx)~Exp[if(x,t)]; f(x,t)=constant ; df(x,t)=0 Phase velocity Vp=dx/dt=w/k, not a real velocity can be >c Epo’s -> w2=we2 , Vp= anything, Vp=0 Plasma waves -> w2=we2+(3/2)k2Ve2 and Vg=(3/2)(Ve/Vp)Ve<Ve Vp2=(3/2)Ve2+ we2/k2> Ve2 Cold plasma approximation: lD=Ve/21/2we if k lD<<1 or Ve so low that particles move less than one wavelength in we-1

  11. h->0, w=we cut-off , reflection Vp-> infinity, Vg->0 pile up w<we wave evanescent, skin depth c/ we Em Waves in Isotropic Plasmas

  12. Ionospheric Reflection

  13. TYPE II AND III SOLAR RADIOBURSTS

  14. w Vg we Vp k Dispersion Diagrams

  15. Dielectric constant for drifting plasmas Wave Energy-Poynting Flux Negative Energy waves Fast and slow wave. For slow wave <W><0, negative. Meaning? Beam+wave less average energy than beam Quiver reduces Vb

  16. Radiation Patterns from Antenae

  17. Introduction of AnisotropyB Finite

  18. Modulated Beams as Antenae

  19. Kinetic Effects - Cerenkov Emission q=arccos(VP/v) Cerenkov condition w-kv=0 Es but no em emission for B=0 Spontaneous emission

  20. w-kv Doppler shifted frequency Landau DampingStimulated Emission and For w>>kv Dv=(eE/mw)cos(wt); for w<<kv Dv=eE/mkv … For w-kv=0 Dv=(eE/m)t secular behavior, replace with 1/ (w-kv)+ie Landau perscription

  21. Mechanical Examples of Landau Damping Cyclotron damping

  22. Cyclotron Resonance

  23. Landau Damping - Growth Absorption Stimulated Emission-Instability

  24. >>1 definition of plasma. Low level broadband noise Sources of Plasma Waves Thermal Equilibrium expect ½ kT/ per mode Balance Cer. Emission to Landau damping to find Wk=(1/2 kT) [1/1+(klD)2] Strongly damped modes weakly excited.

  25. Super-thermal tails f=fo(v)+bfh(v), b<<1 Wk~fh(Vp)/f’(Vp) Beam-plasma or Bump-on-tail instability e.g beam created by electrons Streaming away from shock+ velocity dispersion Sources of Plasma Waves (cont) Effective TVh2. Large enhancement. Broadband , isotropic ? Depends.

  26. What is a Plasma Instability? Positive energy wave coupled to negative dissipation unstable Resistive or kinetic instability

  27. Reactive Instability – Beam Plasma Look at we2/w(w+in) . For w>>in plasma reactive, like inductance. For w<<in plasma behaves like a resistor or conductor. Dielectric constant imaginary -iwe2/wn. Reactive plasma with drift supports negative energy waves

  28. Phase Space B-P Interaction Run Movie-Event simulation concept – Karimabadi (UCSD)

  29. Phase Space Bunching Reactive instabilities are driven by bunching of particles by the growing wave. The bunches drive the field that amplifies the wave. Bunching can be due to the es force or due to the Lorentz force (gyrotron and Weibel)

  30. Bump-in-tail Instability Negative damping interacts with positive energy wave

  31. Quasi-linear Theory Physics analogy with other instability systems- ion beam, LH, etc

  32. How to generate em waves in an isotropic plasma and why at multiples of the plasma frequency

  33. Else Conventional Conversion Processes Weak Turbulence or Else? w3=w1+w2 k3=k1+k2 How to drive current vorticity at we and harmonics

  34. x x t t Ponderomotive Force Requires a spatially varying high frequency E-field, e.g electron plasma wave. strong weak Low frequency force transmitted to ions through quasi-neutrality

  35. Zakharov Equations Envelope equation – multi-time scale analysis

  36. Soliton Caviton Pairs

  37. Structures Generate Current Vorticity

  38. Plasma Non-Thermal Heating

  39. Ion Acoustic Waves Epos 6 kHz Ion sound 1-2 kHz ?

  40. Quasi-Neutrality Supermassive black hole emission – 57 octaves below middle C

  41. Anisotropic Plasmas • phase velocity angle • group velocity angle a different than zero Ray Velocity Phase velocity in the direction of the group velocity

  42. Refractive Index and Associated Surfaces Polar diagrams Ray vel Surface vs q Phase velocity surface Vp/c vs f Group velocity surface Vg/c vs q Refractive index surface h vs q Wave normal k makes an angle a to the normal to the refractive index tana=-dh/df

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