1. MHD Shocks and Collisionless 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 1.Information, Nonlinearity, Dissipation 2.Shocks in the Solar System 3.MHD Rankine – Hugoniot Relations 4.de Hoffmann-Teller Frame, Coplanarity, and Shock Normal Determination 5.Resistive, 2-Fluid MHD – First Critical Mach Number 6.Specular Reflection of Ions: Quasi-Perpendicular vs Quasi-Parallel Shocks 7.Upstream Whistlers and the Whistler Critical Mach Number 8.Brief Excursion on Shock Simulation Methods 9.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. 12.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

7. Fluid moves with velocity v; a disturbance occurs at 0 and propagates with velocity of sound c relative to the fluid The velocity of the disturbance relative to 0 is v + c n, where n is unit vector in any direction (a)v<c : a disturbance from any point in a sub-sonic flow eventually reaches any point (b)v>c: a disturbance from position 0 can reach only the area within a cone given by opening angle  where sin  =c / v Surface a disturbance can reach is called Mach‘s surface

8. Ernst Mach

9. Examples of a Gasdynamic Shock ‘Schlieren‘ photography

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

11. 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.

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

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

15. 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 MHD Solar System Solar wind speed 400 – 600 km/sec Alfven speed about 40 km/sec: There have to be shocks

17. Coronal Mass Ejection (SOHO-LASCO) in forbidden Fe line Large CME observed with SOHO coronograph Interplanetary traveling shocks

19. Quasi-parallel shock Quasi-perpendicular shock

20. Belcher and Davis 1971 Vsw N B

21. Corotating interaction regions and forward and reverse shock

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

23. Earth‘s bow shock

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

25. Magnetic field during various bow shock crossings

26. Heliospheric termination shock Schematic of the heliosphere showing the heliospheric termination shock (at about 80 – 90 AU) and the bow shock in front of the heliosphere.

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

29. Friedrichs-diagram

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

35. hh F 1 2 n t

47. Oblique MHD Shocks

51. FastSlow IntermediateSwitch-on Switch-offRotational

53. de Hoffmann-Teller Frame (H-T frame) and Normal Incidence Frame (NIF frame) Unit vectors Incoming velocity Subtract a velocity v HT perp to normal so that incoming velocity is parallel to B

59. This is widely used in order to determine the shock normal from magnetic field observations

60. Adiabatic reflection (conservation of the magnetic moment) Note: only predicts energy of reflected ions, not whether an ion will be reflected