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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
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 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
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 2a, where sin a =c / v
Surface a disturbance can reach is called Mach‘s surface
Ernst Mach
Examples of a Gasdynamic Shock
‘Schlieren‘ photography
More Examples
Shock attached to a bullet
Shock around a blunt object:
detached from the object
(blunt = rounded, not sharp))
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.
Characteristics cross at one point at a certain time
Results in 3-valued solution
Add some physics:
Introduce viscosity in Burgers‘ equation
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
Interplanetary traveling shocks
Coronal Mass Ejection
(SOHO-LASCO) in
forbidden Fe line
Large CME observed
with SOHO coronograph
Quasi-parallel shock
Quasi-perpendicular
shock
Vsw
N
B
Belcher and Davis 1971
Corotating interaction regions and
forward and reverse shock
CIR observed by Ulysses at 5 AU
70 keV
12 MeV
R
F
Decker et al. 1999
Earth‘s bow shock
The Earth‘s Bow Shock
Quasi-Parallel Shock
solar wind
300-600 km/s
Perpendicular Shock
Magnetic field during various
bow shock crossings
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.
Voyager 2 at the
termination shock
(84 AU)
Friedrichs-diagram
Rankine – Hugoniot Relations
William John Macquorn Rankine
1820 - 1872
Pierre-Henri Hugoniot
1851 - 1887
2
1
F
h
h
t
n
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 perp
to normal so that incoming
velocity 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