1. Anomalous resistivity due to lower-hybrid drift waves. Results of Vlasov-code simulations and Cluster observations. Ilya Silin Department of Physics University of Alberta isilin@phys.ualberta.ca

2. Cluster results are courtesy of A. Vaivads and Yu. Khotyaintsev IRFU,Uppsala, Sweden K.-H. Glaßmeier TU Braunschweig and E. Panov MPI für Sonnensystemforschung

3. Outline Thin current sheets and reconnection Instabilities of current sheets General perturbation theory Vlasov-code simulations Cluster measurements at magnetopause Sheared magnetopause models

4. Thin current sheets: dynamical regions Magnetotail Magnetopause Solar corona Current sheets - regions of plasma accumulation in magnetic “traps”.

5. Magnetic reconnection E. Priest, A&A, 2001 C. T. Russell, Adv. Sp. Res., 2002

6. Thin current sheets: separation of regions of oppositely directed magnetic field Biot-Savart law: or

7. Instabilities of thin current sheets P. Yoon et al., Phys. Plasmas, 2002

8. General perturbation theory Vlasov equation Wave-like perturbations Perturbations of density and current

9. After ensemble averaging General perturbation theory Collision term integrated over velocities Effective anomalous collision frequency

10. Normalized to LH frequency Anomalous collision rates Quasi-linear estimate (Davidson and Gladd, Phys. Fluids, 1975) Anomalous resistivity

11. Vlasov-code simulations initial equilibrium - Harris current sheet (Harris, Nuovo Cim., 1962) normalization distribution function moments

12. Vlasov-code simulations equations for potentials Coulomb gauge equations for electromagnetic fields Vlasov equation

13. Vlasov-code simulations

14. Simulation results: lower-hybrid drift (LHD) waves LHD waves grow at the edges of the current sheet and gradually penetrate towards the central plane.

15. Simulation results: kink and sausage modes The interaction of LHD waves from the edges can trigger either global kink or sausage eigen-mode.

16. Simulation results: effective collision rates ions electrons 2D simulations with m i /m e =100 electrostatic part electromagnetic part

17. Simulation results: effective collision rates 3D simulations with m i /m e =16 Bale et al., GRL (2002): Our Vlasov-simulations:

18. Cluster magnetopause encounter March 30 th 2002, 13:11:46 X Z Z Y

19. Cluster measurements at magnetopause tangential magnetic fields electric fields normal magnetic field LHD electric fields plasma density

20. tangential magnetic fields electric fields average momentum density fluctuations electric field fluctuations product of density and electric field fluctuations Cluster: ν eff due to e/s fluctuations

21. Cluster: ν eff due to e/m fluctuations magnetic field fluctuations current fluctuations product of current and magnetic field fluctuations

22. Observations of the magnetopause magnetic field component hodographs in local magnetopause frame: B L and B M – tangential components, B N – normal component (from Cluster s/c1 06.16.02, 00:54-00:58 and 01.15.03 00:30-01:30, courtesy of K.-H. Glaßmeier and E. Panov)

23. Magnetopause current sheet model magnetic field hodograph ion drift velocity hodograph

24. LHD waves at the sheared magnetopause

25. Conclusions The effective collision frequency calculated from results of numerical simulations and Cluster measurements is of the order of ν eff ~ Ω LH Anomalous collisions become significant only when LHD waves reach a non-linear phase Contributions to ν eff from e/s and e/m fluctuations are comparable The dissipation due to microscopic kinetic effects becomes significant for large-scale processes, e.g., reconnection at Earth magnetopause However, for more realistic magnetopause configuration, the situation is still not quite clear