1. Plasma Transport and Entropy Considerations at the Magnetospheric Flanks Antonius Otto Outline: Basic Issues Basic processes Properties of the cold dense plasma sheet Lobe/cusp reconnection Diffusion Kelvin-Helmholtz modes Summary

2. What physical processes provide the plasma of the plasma sheet? Specific questions: What are the processes that transport the plasma from the magnetosheath into the magnetosphere on closed field lines? How is this plasma processed and transported deeper into the magnetotail? Focus: Northward IMF Conditions

3. Basic Processes at the Magnetopause Magnetic reconnection (Dungey,1961) Viscous interaction (Axford and Hines, 1961) Diffusion (Micro-instabilities, turbulence) Kelvin-Helmholtz instability (Impulsive penetration (Lemaire and Roth, 1978))

4. Observations I – Strong Correlation of Plasma Sheet and Solar Wind Properties Borovsky et al. (1998): Plasma sheet density correlates with solar wind density. Fujimoto et al. (1998): Neutral sheet temperature and density versus solar wind conditions.  Cold dense plasma sheet for Northward IMF! 4

5. Observations II – DMSP plasma sheet flanks for northward IMF Wing et al. (2006): Flank plasma sheet density and temperature evolution for Feb 4-5, 1998 4

6. Observations III – DMSP average plasma sheet properties for northward IMF Wing et al. (2006): Average plasma sheet density and occurrence for two-component Maxwellian for extended northward IMF periods. 4

7. Observations IV – DMSP median plasma sheet evolution for northward IMF Wing et al. (2006 4 dawn dusk Properties: Rapid decrease of temperature at flank boundaries Increase of density first at flanks Timescale of density and temperature changes in the midnight meridian ~10 hr Asymmetries of the dawn-dusk flanks (distribution, density, temperature) => Plasma entry from magnetosheath along the flank boundaries

8. Cusp Reconnection (Crooker, '79; Song and Russell, '92;..) Dorelli et al, 2007

9. Cusp Reconnection Observations (Fuselier, Phan, Trattner, Wang, Lavraud,..) Ground based (lobe reconnection cells, particle signatures) In-situ spacecraft observations Remote particle signatures Trattner et al, 2004

10. Cusp Reconnection – Global simulation Li et al., '05

11. Cusp Reconnection – Comparison with Cluster Data Oieroset et al., '05 Good agreement for density temperature and magnetic field at cluster location

12. Cusp Reconnection Dayside Hybrid Simulations (Lin and Wang, ’06)

13. Cusp Reconnection - mass transfer potential: Potential to generate closed magnetic flux: Change of the total number of particles due to the added flux: Potential required to cause an average plasma density increase of Typical parameters: =>

14. Diffusion/Viscosity at the LLBL Processes: Kelvin-Helmholtz modes Microinstabilities (LHD turbulence, ion acoustic, ion cyclotron,..) Kinetic Alfven waves (KAW) Microinstabilities: Many observations of wave turbulence at the magnetopause and LLBL Estimated maximum diffusion coefficient (LHD) D = 10 9 m 2 s -1 But: Instabilities require high current densities or gradients to be excited –> Widening of the LLBL switches off instability and diffusion is limited to very narrow layers! Required Diffusion coefficient: D = 10 9 m 2 s -1 (Sonnerup, 1980?)

15. Diffusion at the LLBL - 2 Kinetic Alfven Waves (Hasegawa 1976; Lee et al.,1994; Johnson and Cheng, 1997;..) Courtesy: J. Johnson Lin and Wang, 2005

16.  Kelvin-Helmholtz and Reconnection - 2D  Three-Dimensional Dynamics  Entropy Considerations  Conclusions 2 Kelvin-Helmholtz Modes: Observations (Scopke, Fairfield, Fujimoto, Hasegawa, Nykyri, etc.) Simulation (Miura, Belmont, Wu, Wei,..) Miura: Viscous diffusion (momentum transport) coefficient: D=10 9 m 2 s -1 Mass transport (Otto, Nykyri, Fujimoto)

17. Magnetic Reconnection vs. Kelvin-Helmholtz Modes KH modes unstable for  v > v A along k vector of the KH mode. Magnetic reconnection can operate for v <  v A based on the antiparallel magnetic field components. Stability: Two-Dimensional Dynamics 3

18. Observations – Large Perturbations at the Magnetospheric Flanks for Northward IMF Fairfield et al. (2000) Bx By Bz B T

19. Approach: Kelvin-Helmholtz with a k vector not exactly perpendicular to B => Small magnetic field component in the plane of the KH wave ● Strong amplification of the magnetic field in the KH plane. ● Intense current layers in the KH vortex. Current does not neet to be present in the initial conditions! Two-Dimensional Dynamics - A 5

20. Agreement between 2D Simulation and Observation Bx By Bz T Fairfield et al. (2000) Otto and Fairfield (2000)

21. Magnetic Reconnection in 2D KH Vortices Plasma density, velocity and magnetic field lines (Nykyri and Otto, 2001, 2003) Plasma velocity, density, and magnetic field projected into KH plane for 3 different times. Yellow line and asteriks (fluid tracers) mark original plasma boundary. Plasma filaments are reconnected and become detached from the high density region! 6

22. Two Basic Mechanisms for Reconnection in KH Vortices - Mass transport rate consistent with observed plasma transport for northward IMF. - Mass transport occurs always from the high density into the low density region! Mass transport rate: - Nonlinear KH modes stretch the surface of the plasma boundary ~n (number of rotations) => Pre-existing current layer density intensified ~n! - If initial conditions contains B 0 || k => Vortex motion generates anti-parallel magnetic field. Current density ~ n, B 0. This does not require a pre- existing current layer (magnetic shear)! 7

23. Two-dimensional dynamics - B ● Reconnection of the anti-parallel magnetic field in the KH plane. ● Plasma mixing in the tearing island ● But: Unclear whether plasma is transported onto closed geomagnetic flux Anti-parallel magnetic field along the KH k vector Nakamura et al., 2006 8

24. Three-Dimensional Dynamics: Open Questions Possible Differences of 2D and 3D Kelvin-Helmholtz Modes Stabilization Coupling along magnetic field lines + line tying Reconnection in 3D Mass transport? Signatures In general k vectors of tearing (reconnection) and KH modes are not aligned except for singular cases! => Dynamics in general 3D? 9

25. Three-Dimensional Simulation: Basic Approach Simulation with application to the flank magnetospheric boundaries (close to equatorial plane) - Small magnetic shear - `Sub-Alfvenic' shearflow Current dependent resistivity Initial velocity perturbation to seed Kelvin- Helmholtz modes System size: - Perpendicular to boundary (here x): 4 R E - North/South: 8 R E - Tailward: 3 R E (= KH wavelength) Density asymmetry n msh = 3n msp Magnetosphere (line tying) Magnetosheath 10

26. Numerical Method: KH waves with a finite size along the north/south direction: Magnetosphere: Field-line curvature + line-tying => limited interaction region Simulation: Line-tying by frictional drag increasing toward the min and max boundaries in z (north and southward from equatorial plane): - maintains initial shearflow - absorbs velocity perturbations (wave damping) Normalization: Typical properties at the magnetopause: B 0 = 25nT, n 0 = 4cm −3, L 0 = 600km, v A = 250km/s, and  A = 22s. 11 3D MHD (Hall) Simulation Leapfrog/Dufort-Frankel + FCT, 2nd order accuracy, low dissipation

27. Local Properties 16  Properties similar to 2D Kelvin Helmholtz modes; vortex plasma has either high (MSH) or low (MSP) density.  Stabilization for wavelength larger than the width of the interaction region Example: Magnetic shear 10 o

28. Three-Dimensional Dynamics - Localization Cuts at x = 0 = original boundary; In- and outward plasma motion due to KH Perturbation of the magnetic field normal to the initial boundary 13

29. Issue: Entropy of cold dense plasma sheet 17 Borovsky, GEM’06 Entropy density of plasma sheet populations Cold dense plasma sheet: Only of magnetosheath origin? or Mixture of magnetosheath and magnetospheric plasma

30. Entropy: The great Alaska Earthquake from Nov 4, 2002 T = T 0 + 1hr

31. Entropy - 1

32. Entropy - 2 u

33. Entropy - 3 is conserved except for losses into the ionosphere and nonadiabatic processes (in MHD)! Particle drifts and/or perpendicular heatflux can also alter entropy (important in inner magnetosphere) is conserved only in MHD except for nonadiabatic processes!

34. Entropy change for switch-off shocks: 18 Entropy changes associated with magnetic reconnection/slow switch-off shocks: Compression: Pressure increase: Entropy increase: => Local entropy can increase significantly only for very low plasma 

35. Magnetic Field Lines: => MSP Interchange motion moves MSP flux into MSH and vice versa. However, finite size of interaction region => at large distances field line move unperturbed, i.e., magnetosheath field moves large distance along the boundary  Interaction region must decouple or KH must be stabilized  Decoupling (magnetic reconnection, E || ) must occur at boundaries of interaction region in a systematic manner. 14

36. Parallel Current and Electric Field 16  Filamentary current layers  Well ordered parallel electric field distribution Integrated: Velocity Parallel Electric Field Parallel Current Density

37. Parallel Current and Electric Field 16  Reconnection within the KH vortices

38. Mass Transport: Parallel `Potential’: Specific Flux Tube Mass: 16

39. Mass and Entropy Transport - 45 sec later 16 Positive PotentialNegative Potential Flux Tube MassEntropy Rapid change of the topological boundary Location of boundary agrees excellent with location of the potential

40. Flux Tube Mass and Entropy Mapped to Southern Boundary 16 Time=175 s Time=220 s - Average mass transport velocity 2 to 5 km/s => Diffusion coefficient of 2 to 4 x10 9 m 2 /s - (Average) entropy of newly captured plasma average between MSP and MSH values.

41. Parallel Potential and Magnetic Foot Print Displacement 15 Parallel Potential FT Footprint coordinate at northern boundary Potential + reconnection are present along flux tubes strongly distorted by the KH vortex motion

42. Transport within the plasma sheet Time scale for transport to the noon-midnight meridian: 10 hrs Convection: 3 km/s Diffusion coefficient: D=3x10 11 m 2 s -1 Plasma sheet turbulence (Borovsky and Funsten, 2003) Diffusion coefficient: D=2.6x10 11 m 2 s -1

43. Summary Mass diffusion rate for entry consistent for lobe reconnection 3D KH mass transport mechanism: consistent with required rate very different from 2D qualitatively consistent with mixed plasma entropy observed for cdps Issues: Asymmetries Transport mechanism and path for transport within the plasma sheet 22

44. Summary - KH 2D Dynamics:  KH modes unstable for  v>v A,typ along the k vector of the mode.  Nonlinear modes twist boundary, generate thin current layers, and can cause reconnection in the KH vortices either of type A or B  Mass transport rate for northward IMF is consistent with observations. 3D Dynamics:  The KH mode radiates energy and momentum out of the unstable region along magnetic field lines.  Stabilization for wavelength larger than the width of the interaction region.  Nonlinear KH vortices require reconnection at interaction region boundaries: The required parallel electric fields are generated mainly close to the boundary of the interaction region. Northern and southern potentials are similar but not identical => generation of open and re-closed magnetic flux (different from 2D)  Material transport across a boundary onto ‘closed’ field lines requires reconnection of the ‘same’ field line at different locations (but not necessarily at the same time)  Entropy of cold dense plasma sheet better consistent with 3D KH/reconnection.  Mass transport corresponding to average velocity of 2 to 5 km/s or a diffusion rate of 2 to 4x10 9 m 2 /s 22