1. Numerical simulations of wave/particle interactions in inhomogeneous auroral plasmas Vincent Génot (IRAP/UPS/CNRS, Toulouse) F. Mottez (LUTH/CNRS, Meudon) P. Louarn (IRAP/UPS/CNRS, Toulouse) C. Chaston (SSL, Berkeley)

2. Hilgers et al., 1992 Depth of the cavities: n min ~ 0.1 n 0 Size of the gradients : ~a few km i.e. a few c/  pe. => Strong density gradients Density cavity related physics have initially been investigated in connection with AKR generation (Louarn et al., 1990) Observations of deep cavities by Viking

3. Observations of deep cavities by FAST the cold plasma has been completely expelled plasma instrument Langmuir probe Factor 10 FAST crossed many deep cavities (n/n 0 ~0.1-0.05) in the altitude range 1500-4000 km Factor 20

4. Upflowing ions S/C potential ~ density Cluster observations Electric field For more Cluster observations of density cavities, see Marklund et al.

5. Density cavity Electric turbulence Transverse ion acceleration Ion outflow Fiel-aligned electron acceleration } } } FAST Data Chaston et al., 2007

6. Wave identification in the density cavity inertial range dissipation range Chaston et al., 2007 Alfvén waveSmall perpendicular scales

7. What is the mechanism for the formation of small perpendicular scales ? What is the effect of the associated parallel electric field ? Can it be maintained on sufficiently long time ?

8. The basic principle : Alfvén wave + perpendicular density gradient Initial parallel propagation at V A (E // =0) + V A = B/(n 1/2 ) higher in low density region B0B0 high density low density high density Oblique wave front  k  ≠0  E // small V A large V A grad n

9. Analytic study

10. Génot et al., 1999 Wave front torsion due to differential V A EE Time Propagation of Alfvén waves in a density cavity : analytic model 1/2 ionospheremagnetosphere Alvénic pulse propagation density cavity field line convergence Alfvén velocity profile cavity

11. Génot et al., 1999 Strong E // are formed on density gradients (about 1% of the incoming field) Propagation of Alfvén waves in a density cavity : analytic model 2/2 EE EE E // This 2D model assumes : -electroneutrality -perpendicular ion motion (polarization drift) -parallel electron motion magnetosphereionosphere

12. Self consistent PIC simulations

13. Particle In Cell simulations Full ion dynamics Electron guiding centre dynamics Mottez et al. 1998 Electromagnetic 2D in space, 3D in velocities and electromagnetic fields Periodic boundary conditions Simulation box : 204.8 X 12.8 (c/  pe ) 2 (or multiple) Reduced mass ratio: m i /m e =100, 200, 400 Strong ambient magnetic field:  ce /  pe = 4 (auroral zone) Ordering: c/  pe ~  i for the auroral zone (~1 km) Génot et al., 2000, 2001, 2004

14. A simple situation : infinite cavity and wave VAVA Density map nene k  =0 n e /4  to B // to B

15. Stack plot of E // (z,t) integrated on a density gradient Large scale fields Beam-plasma instability Buneman instability Large scale inertial Alfvén wave Formation of small transverse scales Z (along B) time Génot et al., 2004

16. FAST observations show that 1/ the wave power maximises in the centre of the cavity 2/ large field aligned Poynting flux on the wall of the cavity (directed mostly Earthward) 3/ the wave focuses to the centre of the cavity (converging transverse Poynting flux) The inward focused Poynting flux indicates that the wave group velocity is convergent on the cavity. These observations suggest that wave refraction on the cavity walls leads to the focusing of Alfvén wave energy within the cavity, therefore increasing the wave turbulence inside the cavity. Chaston et al., 2006 FAST observations

17. Chaston et al., 2006 Converging transverse Poynting flux directed inside the cavity Simulation results

18. A more realistic situation : infinite cavity and pulse VAVA Density map nene k  =0 n e /4  to B // to B

19. Mottez & Génot, 2011 Direction along B Time Simulation Simulation: Alfvén pulse in a cavity 4096 X 128 m i /m e =400 ΔN/N=0.8 Δ B/B=0.032 E //

20. 4096 X 128 m i /m e =400 ΔN/N=0.8 Δ B/B=0.032 Simulation Simulation: Alfvén pulse in a cavity Mottez & Génot, 2011 V // (along B) v the_beam =0.04 v drift_beam =0.69 n e_beam =0.026 n e =1.21 Beam/plasma instability V the_beam /V drift_beam << (n e_beam /n e ) 1/3

21. Mottez & Génot, 2011 electronsprotons ↓ ↓ ↑ ↑ ↓ ↓ ↑ ↑ Acceleration in the same direction as the wave propagation is favored Simulation Simulation: Alfvén pulse in a cavity Energy flux

22. E //max m i /m e =400 Identification of the acceleration process Inertial effect: ion polarization drift (~m i /m e ) and electron inertia (~1/m e ) m i /m e =100 m i /m e =200 Mottez & Génot, 2011

23. An even more realistic situation : localized cavity and pulse VAVA Density map n e /4nene k  =0  to B // to B Unpublished work

24. EE n e =0.75 n e =0.5 n e =1.15 E  max Time 1D cut on the density gradient : Perpendicular electric field // to B VAVA Density cavity contours The AW enters the plasma cavity

25. n e =0.75 E  max E // V //e +10% Time // to B 1D cut on the density gradient : Parallel electric field Density cavity contours E// formation Electron acceleration

26. Pre-existing depletion Cavitation/filamentation mechanism Density cavitation Wave focusing Plasma outflow/acceleration in the cavity Wave amplitude enhancement and filamentation E // Wave focusing Converging Poynting flux

27. Perspectives Real mass ratio and quantification of the acceleration process Use multi-spacecraft observations by Cluster to constrain the parallel extension of the cavity w.r.t the size of the Alfvén pulse 3D aspects: use of a Landau fluid code with electron inertia (Borgogno et al. 2009)