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MHD Shocks and Collisionless Shocks

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  1. MHD Shocks andCollisionless Shocks Manfred Scholer Max-Planck-Institut für extraterrestrische Physik Garching, Germany The Solar/Space MHD International Summer School 2011 USTC, Hefei, China, 2011

  2. Overview • Information, Nonlinearity, Dissipation • Shocks in the Solar System • MHD Rankine – Hugoniot Relations • de Hoffmann-Teller Frame, Coplanarity, and Shock Normal Determination • Resistive, 2-Fluid MHD – First Critical Mach Number • Specular Reflection of Ions: Quasi-Perpendicular vs Quasi-Parallel Shocks • Upstream Whistlers and the Whistler Critical Mach Number • Brief Excursion on Shock Simulation Methods • Quasi-Perp. Shock: Specular Reflection, Size of the Foot, Excitation of • Alfven Ion Cyclotron Waves • 10. Cross- Shock Potential and Electron Heating • 11. Quasi-Parallel Shock: Upstream Ions, Ion-Ion Beam Instabilities, and • Interface Instability

  3. The Bow Shock • Electrons at the Foreshock Edge • Field-Aligned Beams • Diffuse Ions • Brief Excursion on Diffusiv Acceleration • Large-Amplitude Pulsations

  4. Literature D. Burgess: Collisionless Shocks, in Introduction to Space Physics, Edt. M. G. Kivelson & C. T. Russell, Cambridge University Press, 1995 W. Baumjohann & R. A. Treumann: Basic Space Plasma Physics, Imperial College Press, 1996

  5. Object in supersonic flow – Why a shock is needed If flow sub-sonic information about object can transmitted via sound waves against flow Flow can respond to the information and is deflected around obstacle in a laminar fashion If flow super-sonic signals get swept downstream and cannot inform upstream flow about presence of object A shock is launched which stands in upstream flow and effetcs a super- to sub-sonic transition The sub-sonic flow behind the shock is then capable of being deflected around the object

  6. Fluid moveswithvelocityv; a disturbanceoccursat 0 andpropagateswithvelocityofsound c • relative tothe fluid • The velocityofthedisturbance relative to 0 isv + c n, wherenisunitvector in anydirection • v<c : a disturbancefromanypoint in a sub-sonicfloweventuallyreachesanypoint • v>c: a disturbancefromposition 0 canreachonlytheareawithin a conegivenbyopening • angle 2a, where sin a =c / v Surface a disturbance can reach is called Mach‘s surface

  7. Ernst Mach

  8. Examples of a Gasdynamic Shock ‘Schlieren‘ photography

  9. More Examples Shock attached to a bullet Shock around a blunt object: detached from the object (blunt = rounded, not sharp))

  10. Schematic of how a compressional wave steepens to form a shock wave (shown is the pressure profile as a function of time) The sound speed is greater at the peak of the compressional wave where the density is higher than in front or behind of the peak. The peak will catch up with the part of the peak ahead of it, and the wave steepens. The wave steepens until the flow becomes nonadiabatic. Viscous effects become important and a shock wave forms where steepening is balanced by viscous dissiplation.

  11. Characteristics cross at one point at a certain time Results in 3-valued solution

  12. Add some physics: Introduce viscosity in Burgers‘ equation

  13. MHD In MHD (in addition to sound wave) a number of new wave modes (Alfven, fast, slow) Background magnetic field, v x B electric field We expect considerable changes Solar System Solar wind speed 400 – 600 km/sec Alfven speed about 40 km/sec: There have to be shocks

  14. Interplanetarytravelingshocks CoronalMassEjection (SOHO-LASCO) in forbiddenFeline Large CME observed with SOHO coronograph

  15. Quasi-parallel shock Quasi-perpendicular shock

  16. Vsw N B Belcher and Davis 1971

  17. Corotating interaction regions and forward and reverse shock

  18. CIR observed by Ulysses at 5 AU 70 keV 12 MeV R F Decker et al. 1999

  19. Earth‘sbowshock

  20. The Earth‘s Bow Shock Quasi-Parallel Shock solar wind 300-600 km/s Perpendicular Shock

  21. Magnetic field during various bow shock crossings

  22. Heliosphericterminationshock Schematicoftheheliosphereshowingthe heliosphericterminationshock (atabout 80 – 90 AU) andthebowshock in front ofthe heliosphere.

  23. Voyager 2 at the termination shock (84 AU)

  24. Friedrichs-diagram

  25. Rankine – Hugoniot Relations Pierre-Henri Hugoniot 1851 - 1887 William John Macquorn Rankine 1820 - 1872

  26. 2 1 F h h t n

  27. Oblique MHD Shocks