Post on 05-Jan-2016
description
MHD Shocks and Collisionless Shocks
Manfred Scholer
Max-Planck-Institut für extraterrestrische PhysikGarching, Germany
The Solar/Space MHD International Summer School 2011 USTC, Hefei, China, 2011
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
12. The Bow Shock
Electrons at the Foreshock Edge
Field-Aligned Beams
Diffuse Ions
Brief Excursion on Diffusiv Acceleration
Large-Amplitude Pulsations
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
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 flowabout presence of object
A shock is launched which stands in upstream flow and effetcs a super- to sub-sonictransition
The sub-sonic flow behind the shock is then capable of being deflected around the object
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
Ernst Mach
Examples of a Gasdynamic Shock
‘Schlieren‘ photography
Shock attached to a bullet Shock around a blunt object:detached from the object (blunt = rounded, not sharp))
More Examples
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 balancedby viscous dissiplation.
Characteristics cross at one point at a certain time
Results in 3-valued solution
Add some physics:
Introduce viscosity in Burgers‘ equation
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/secAlfven speed about 40 km/sec:
There have to be shocks
Coronal Mass Ejection(SOHO-LASCO) in forbidden Fe line
Large CME observedwith SOHO coronograph
Interplanetary traveling shocks
Quasi-parallel shock
Quasi-perpendicularshock
Belcher and Davis 1971
Vsw
N
B
Corotating interaction regions and forward and reverse shock
CIR observed by Ulysses at 5 AU
70 keV
12 MeV
Decker et al. 1999
F
R
Earth‘s bow shock
Perpendicular Shock
Quasi-Parallel Shock
The Earth‘s Bow Shock
solar wind300-600 km/s
Magnetic field during various bow shock crossings
Heliospheric termination shock
Schematic of the heliosphere showing theheliospheric termination shock (at about 80 –90 AU) and the bow shock in front of the heliosphere.
Voyager 2 at the termination shock(84 AU)
Friedrichs-diagram
Rankine – Hugoniot Relations
William John Macquorn Rankine 1820 - 1872
Pierre-Henri Hugoniot 1851 - 1887
h h
F
1 2
n
t
Oblique MHD Shocks
Fast Slow
Intermediate Switch-on
Switch-off Rotational
de Hoffmann-Teller Frame (H-T frame) and Normal Incidence Frame (NIF frame)
Unit vectors
Incoming velocity
Subtract a velocity vHT perpto normal so that incomingvelocity is parallel to B
This is widely used in order to determine the shock normal from magnetic field observations
Adiabatic reflection (conservation of the magnetic moment)
Note: only predicts energy of reflected ions, not whether an ion will be reflected