1. Analysis Methods for Magnetopause & Boundary Layer Studies Hiroshi Hasegawa ISAS/JAXA In collaboration with B. U. Ö. Sonnerup & W.-L. Teh

2. Outline Wavelet analysis (cascade in KH vortices) Reconstruction of 2D structures in a plasma fluid 1. Grad-Shafranov (magneto-hydrostatic) reconstruction of magnetic field lines 2. Grad-Shafranov-like reconstruction of streamlines 3. MHD reconstruction (ideal & resistive) 4. Hall-MHD reconstruction

3. Wavelet analysis can be used to reveal to what extent the KH instability grows Roles of Kelvin-Helmholtz instability Momentum and/or mass transport (Miura, 1984; Fujimoto & Terasawa, 1994) Generation of ULF waves that may accelerate radiation belt electrons (e.g., Elkington, 2006) Generation of vortical auroral forms via M-I coupling (e.g., Lui et al., 1989)

4. Nakamura et al., 2004 Matsumoto & Hoshino, 2004 (Inverse-) cascade Miura, PoP, 1997

5. C1 electron C1 ion density Cluster event on 20 Nov 2001 (19 LT) (Hasegawa et al., 2004; Chaston et al., 2007; Foullon et al., 2008) temperature velocity magnetic field

6. streamline Force balance Total-P perturbation in the vortex Dominant-mode period ~200 s: Wavelength ~6 Re. Power also at ~400 s: Beginning of vortex pairing?

7. Wavelet analysis (cascade in vortices) Reconstruction of 2D structures in a plasma fluid 1. Grad-Shafranov (magneto-hydrostatic) reconstruction of magnetic field lines 2. Grad-Shafranov-like reconstruction of streamlines 3. MHD reconstruction (ideal & resistive) 4. Hall-MHD reconstruction Outline

8. Flux Transfer Event 2D map of an FTE Time series data to 2D image

9. X A 2D structure X Y Z (invariant axis) Reconstruction frame Y Reconstruction plane Lx = V ST_X * T (analyzed interval) X axis: SC trajectory in the x-y plane V ST_X V ST (V HT ) (in the x-z plane) Integration as a spatial initial value problem

10. Assumptions: magneto-hydrostatic (time-independent) structures ×× 2-D (no spatial gradient in z direction) Grad-Shafranov (GS) equation (e.g., Sturrock, 1994) 1. Grad-Shafranov (GS) reconstruction Hasegawa et al., 2006 B & p recovered (Hau & Sonnerup, 1999)

11. V, n, & T recovered (Sonnerup et al., 2006) Assumptions: MHD, 2D, time-independent, & B along z axis GS-like equation for the stream function  2. GS-like reconstruction of streamlines Hasegawa et al., 2007

12. Dominant-mode wavelength ~6 Re Vortex structure from GS-like reconstruction of streamlines C1 C3 Two vortices within one dominant-mode wavelength. Breakup of a parent MHD-scale vortex (cascade)?

13. All MHD parameters recovered, e.g., in the X-line rest frame (Sonnerup & Teh, 2008) Assumptions: MHD, 2D, time-independent 3. MHD reconstruction (ideal) isentropic flow perp. to invariant axis

14. Eriksson et al., 2009 MHD reconstruction of an FTE Seen by THEMIS-A on the MP surface wave sheath side LLBL side Streamline Field line

15. All MHD parameters, E, & electron velocity recovered Sonnerup & Teh, 2009 Assumptions: Hall-MHD, 2D, time-independent 4. Hall-MHD reconstruction (ideal) isentropic flow perp. to invariant axis

16. Benchmarking (Sonnerup & Teh, in press, 2009)

17. What could be analyzed? Behavior of coalescence/breakup (inverse- cascade/cascade) of KH vortices Structural properties (shape, size/width/amplitude, & orientation) of FTEs, KH waves/vortices, magnetic islands in/around the vortices, reconnection jets, & ion diffusion regions. Reconnection rate/electric field. Drawback… The reality may rarely be 2D & d/dt~0.