Université Paris-Saclay
Master: Mention Physique
First year: General Physics / Physique et Applications
«!Plasma Physics and Applications!»
Part II
Sébastien Galtier
Laboratoire de Physique des Plasmas
Ecole Polytechnique
4 Lectures + 4 tutorials
“Magneto-hydrodynamics (MHD)”
(7 Oct., 14 Oct., 21 Oct., 4 Nov.)
• Applications: space plasma physics
• What is magneto-hydrodynamics ?
• Conservation laws (Alfvén’s theorem, magnetic helicity)
• MHD waves (magnetic tension, Alfvén waves)
• Static equilibrium (z-pinch, tokamaks)
Application:
space plasma physics
Space plasmas
• What is a plasma ?
• What do we mean by space plasmas ?
• A word about turbulence
• Some open problems in space plasma physics
- solar coronal heating
- solar wind dynamics
• Conclusion
What is a plasma ?
• Plasma = (partially) ionized gas => Lorentz force is important
• The fourth state of matter
• Universe = more that 99.9% of the visible matter
Sun (SDO/NASA)
30.4 nm
ITER
30.4 nm
Most famous equation: the Vlasov equation
What happens when a distribution is disturbed ?
Some mathematical answers given by C. Villani (Field medal 2010)
Landau damping !
The Sun
A short CV of the Sun
Age: 4,6 109 years
Diameter: d=1,4 106 km =100*dEarth
Mass: M=1030 kg =200 000*MEarth
(109 kg / s of plasma is lost)
Position: 150 106 km from Earth
Medium star among 200 109 other starsin the Milky Way
Structure of the Sun
Thermonuclear core = 1/4 RS
Radiative zone = 1/2 RS
Convective zone= 1/4 RS
600 million tonnes of hydrogen converted per second
Chemistry of the Sun
Composition at the surface of the Sun (photosphere):
- Hydrogene: 73,5%
- Helium: 25%
- Oxygene: 0,77%
- Carbone: 0,29%
- Fer: 0,15% ! Useful as a tracer !
- Neon: 0,12%
98,5% of the matter
SoHO (17.1nm)
Fe IX 106 K
Galileo Galilei (1613) Télescope-Sol DOT-Tenerife (1999)
Magnetic field up to 1000 Gauss (104 times BEarth)
Sunspots and the dynamo (MHD) problem
Sunspots from space
!"#$%&'($)*(+,+#-./0'1$23454-67889:
Sun spot surface in latitude
Évolution des taches solaires
Total surface of Sun spots
Solar spots and the dynamo problem
11 years cycle (Schwabe, 1825)
*;+##-/&$-+<$
Dynamo: production of magnetic field / MHD
!"#$%&!&'
o 4=4>-?@-/;+<$%-'A-BC$-*D0
o E0,F$-*D0G-+##-BC$-,;$
o =;+<$%-$H$FI-J8-%
o K-J-!L-2-1+I-M
Solar Dynamics Observatory(Cap Canaveral, 11/02/2010)
07/06/2011 (30,4nm, He+ line; 50 000 K)
Linear (MHD) stability analysis
Same event seen with a coronograph
STEREO
MHD wavestemperature
Solar Optical Telescope / Hinode / JAXA
Solar coronal heating problem
SOHO/ESA
TRACE/NASASDO/NASA
103 K
104 K
106 K
Anomalous temperaturein the solar corona
7N
N(E) ~ E-1.
8
Universality
1024 erg 1032 ergTime
Intensity
0 104 min Log E
Log N(E)
- Propose physical heating mecanisms ! Turbulence
- Develop models ! Numerical MHD simulations
- Generate observables ! Comparison with observations
Statistical model of solar flares
How can we tackle this problem ?
Example: 2D MHD model
(!J2)
Pseudo-spectral codes
Solar wind plasma
Sun-Earth interaction
Solar wind origin
SoHO (17.1nm)
Resolution: 1850 kmSept. 1997
Active region
Coronal hole
Bright points
Solar wind (E. Parker, 1958)
- Wind blows by the Sun = heliosphere (~ 100AU)
- Magnetized plasma (collisionless)
- Fluctuations ~ 10-7 Hz to 102 Hz
- Hot plasma > 105 K
- Low density: n ~ 107 m-3 (1 AU)
- Fast and slow winds (> 20RSUN)
- Reynolds number > 109
We can measure particule distributions !
T!" T//
Typical scales
Spatial scales
• Heliocentric distance : L ~ 108 km
• Inertial length scale (1AU) : di = VA/#ci ~ 100 km
• m.f.p. : lc ~ 107 km
Time scales
• Solar rotation: $SUN ~ 5 10-7 Hz
• Alfvén (MHD) waves: 1/%A < 0.1 Hz
• Cyclotronic frequency (1AU): #ci ~ 0.5 Hz
• Whistler waves : 1/%W ~ 1-103 Hz
MH
DK
INE
TIC
S
Fluctuations measurements
Ulysses
&v and &b are correlated : &v ! &b
Solar wind fluctuations
[Kiyani et al., Phil. Trans. R. Soc. A, 2015]