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]