Analysis Methods for Magnetopause & Boundary Layer Studies

Hiroshi Hasegawa

ISAS/JAXA

In collaboration with B. U. Ö. Sonnerup & W.-L. Teh

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

Wavelet analysis can be used to revealto 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)

Nakamura et al., 2004

Matsumoto & Hoshino, 2004

(Inverse-) cascade

Miura, PoP, 1997

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

TotalPvv

)(

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?

• 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

Flux Transfer Event

2D map of an FTE

Time series data to 2D image

X

A 2D structure

X

Y

Z (invariant axis)

Reconstruction frame

YReconstruction plane

Lx = VST_X* T (analyzed interval)

X axis: SC trajectory in the x-y plane

VST_X

VST (VHT)(in the x-z plane)

Integration as a spatial initial value problem

pBj

Assumptions: magneto-hydrostatic (time-independent) structures

PBJVVt

V

)(× ×

)(002

2

2

2

AjAd

Pd

y

A

x

Az

t

)2( 02 zt BpP

zAA

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)

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

TotalPvv

)(

Dominant-mode wavelength ~6 Re

Vortex structurefrom GS-like reconstruction of streamlines

C1

C3

• Two vortices within one dominant-mode wavelength.

Breakup of a parent MHD-scale vortex (cascade)?

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

Eriksson et al., 2009

MHD reconstruction of an FTESeen by THEMIS-A on the MP surface wave

sheath side

LLBL side

Streamline

Field line

All MHD parameters, E, & electron velocity recoveredSonnerup & Teh, 2009

Assumptions: Hall-MHD, 2D, time-independent

4. Hall-MHD reconstruction (ideal)

isentropic flow

perp. to invariant axis0 v

BjPPvv ei

)(

),(0 eisSv ss

0 B

)(nePBjBvE e

Benchmarking (Sonnerup & Teh, in press, 2009)

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.