Alfvén wave interaction with inhomogeneous plasmas :

acceleration and turbulence.

F. Mottez, V. Génot, P. Louarn

What ?Electron accélération toward the Earth (10 000 km)

How ?An Alfvén wave +A density gradient

How incoming energy from distant regions of the magnetosphere (for example, in the form of the Poynting flux of Alfven waves) can be converted into the kinetic energy of accelerated particles

•up to KeV energies •Efficiency larger than some 10 %

The auroral particle acceleration: a complex chain of processes still not fully described.

Large scale structures bringing energy from other regions of the magnetosphere

Alfvén Waves

SKAW, Freja [Louarn et al., 1994]

Alfvén E/B~VA

Compressional n/n0~0.2

Amplitude B ~60 nTB/B0z~0.01

Strong Poynting flux

Transverse size ~ c/pe~i

Accélérer avec le E// d’une onde d’Alfvén

Une onde MHD (Alfvén ou magnétosonique) ne porte pas de E//

Mais si on s’écarte un peu de la MHD :Onde d’Alfvén inertielle …

L’ onde d’Alfvén inertielle• Théorie bi-fluide, centres guides (dérive de polarisation des ions) • << me/mi, on néglige la pression

Il existe un champ électrique parallèle à B

222//

2

pex

zx

x

z

ckckk

EE

EE

2

222

)/(1 pex

Az

ckVk

L’ onde d’Alfvén inertielleMais il faut du kx. (une vitesse de phase oblique).La vitesse de groupe est assez parallèle. Origine de kx loin de la zone d’accélération ?

Mais alors, pourquoi accélération localisée ?

Quelle est l’origine du kx ?

222//

2

pex

zx

x

z

ckckk

EE

EE

Deep auroral density depletions

Viking, [Hilgers et al., 1992]

Deep cavities: nmin ~ 0.1 n0

Size of the gradients ~2 kmi.e. a few ion Larmor radius, i.e. a few c/pe.

=> Strong density gradients

The basic principle :Alfvén waves + perpendicular density gradients

parallel propagation at VA (E//=0)

+ VA = B/(n1/2) higher in low density region

B0z

high density

low density

high density

Oblique wave frontPlanar wave front

Oblique wave front => E// => energy from wave to plasma => acceleration and turbulence

small VA

small VA

large VA

grad n

grad n

In the auroral zone, VA > Vte

• This is not a resonnant process. The wave goes (initially) much faster than most of the particles.

• Because of the long wavelength of the wave, the particles see an electric field for a few milliseconds. This is enough for acceleration.

Case 1 : cavity alone

Bx

Ne

Ez=E//

Ex

La cavité est stablePas de champ électrique associé

B/B0z=0.1B0z

12

.8

204.8

Cavité n=1/3

Haute densité n=1

z

x axes

Case 2 : Alfvén wave alone

Bx

Ne

Ez=E//

Ex

L’onde se propage le long du champ magnétique ambiantpolarisation circulaire (ici gauche, pourrait être droite ou lin.)Pas de champ électrique parallèle

Alfvén wave on a plasma cavity

Space Earth

Ez=E//

Ex

z

x12.8

204.8axesNe

Bx B0z VA

E//(t) upon a density gradient

Large scale fields

Beam-plasma instability

Buneman instability

Large scale fields of the inertial Alfvén wave

Z (along B)

tim

e

<Ez>(z) over the lower channel

Ez(z,x)

Fe(z,vz) over thelower channel

Lower gradient

Particles

z

Vz

Weak (oblique Alfvén ) E// over large distances

Electron parallel heating : « halo » i.e. tail in the distribution function

Large scale electric field and

electron halo

Assymetry : propagationof the Alfvén wave / electron velocities

Runaway electron

E// over large distances

halo

runaway

Faster electrons from the halo espace first and create an electron beam.

Beam dynamics

Finite beam in an inhomogeneous plasma.

Backward slow vortices(Buneman)

Fast vortices (beam-plasma)

Buneman

electron-beam

Electron holes

Spread velocity distribution

Electron holes in both directions

Remaining localized beams

backward

forwardbeam

Wave and electron energies over 4 Alfvén periods

The energy exchange between the Alfvén wave and the electrons occurs when there are no coherent structures : before their formation (growth of the beam) or after their destruction.

ConclusionAlfvén wave along a density gradient : a cascade of events leading to acceleration and turbulenceParallel electric fields: large scale, then small scale, then large scale, etc.Acceleration: halos, runaway electrons, beamsTurbulence: structuration of beams as series of (z,Vz) vorticesTurbulence: various kind of coherent structures, electron holesPrefered direction of acceleration: direction of Alfvén wave .The plasma cavity is not destroyed : ready for the next Alfvén wave train.

Role of the coherent structures : they contribute to reorganize the plasma under the influence of a large scale parallel electric field; they saturate the electron acceleration process.

Geophysical relevance of this process :Could explain the small scale structuration of the discrete auroras (100 m) and the high level of turbulence observed around the auroral plasma cavities.

publicationsAlfvén wave interaction with inhomogeneous plasmas : acceleration and energy cascade toward small scalesV. Genot, P. Louarn, F. Mottez, Annales Geophysicae, 2004.

Electron acceleration by Alfvén waves in density cavities, Génot et al., J. Geophys. Res. 105, 2000.

Fast evolving spatial structure of auroral parallel electric fields, Génot et al., J. Geophys. Res. 106, 2001.

A study of the propagation of Alfvén waves in the auroral density cavities, Génot et al., J. Geophys. Res. 104, 1999.