1

K. Stasiewicz,

Plasma Space Science Center, NCKU

Swedish Institute of Space Physics, Uppsala

Multi-spacecraft studies of nonlinear waves

2

Turbulence in the foreshock

3

Shocklets in the foreshock

4

Fast solitons in the foreshock

5

mirror structures (shifted timeseries)

6

Propagating mirror modes (holes)

7

Multi-point measurements by Cluster: velocity determination

R21

Vsn

(R j −R1) •Vsn

Vsn2 =tj −t1

8

Magnetosonic solitons: observations and model

Stasiewicz, Shukla, …et al, Phys. Rev. Lett. 90, 085002 (2003)

9

Convergent E structurenegative potential

Divergent E structurepositive potential

Auroral acceleration structures (alfvenons)

as solutions of two-fluid equations

10

How particles are accelerated?

d( )

dm qt= + ×

vE v B

2d

d 2

mvqE v q

t ⊥ ⊥

⎛ ⎞= + ⋅⎜ ⎟

⎝ ⎠E vP P

.... by electric fields only, but

t

∂− =∇×∂B

E

|⋅v

11

Auroral acceleration structures: negative or positive potentials

10-20 keV

12

Acceleration/heating in the solar corona

Flares acceleration potentials ~10-1000 kV

Solar wind: 600 km/s escape velocity

+ 300-800 km/s equivalent: 2-5 kV

Heating: (millions K)5 MK equivalent: 0.5 kV

13

d( )

dj

j j j j j jN m N qt

= + × −∇⋅V

E V B P

Two fluid equations for ions j=i and electrons j=e

Can be reduced to ion momentum equation

[ ( ) ] )iNmt

∂+ ⋅∇ = × −∇⋅

∂V

V V J B P

And the generalized Ohm’s law

2

1([ ( )] )e

em

NeNe tη+ +

×

−

∇⋅

∂+∇

⋅

= ×

+

+∂J

VJ J V B P

E

J

V

J

B

Two-fluid equations

14

Soliton solutions

15

Dispersion diagram for slow alfvenons

16

THE END

www.cluster.irfu/ks/