1. 1 K. Stasiewicz, Plasma Space Science Center, NCKU Swedish Institute of Space Physics, Uppsala Multi-spacecraft studies of nonlinear waves

2. 2 Turbulence in the foreshock

3. 3 Shocklets in the foreshock

4. 4 Fast solitons in the foreshock

5. 5 mirror structures (shifted timeseries)

6. 6 Propagating mirror modes (holes)

7. 7 Multi-point measurements by Cluster: velocity determination R 21 V sn

8. 8 Magnetosonic solitons: observations and model Stasiewicz, Shukla, …et al, Phys. Rev. Lett. 90, 085002 (2003)

9. 9 Convergent E structure negative potential Divergent E structure positive potential Auroral acceleration structures (alfvenons) as solutions of two-fluid equations

10. 10 How particles are accelerated?.... by electric fields only, but

11. 11 Auroral acceleration structures: negative or positive potentials 10-20 keV

12. 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. 13 Two fluid equations for ions j=i and electrons j=e Can be reduced to ion momentum equation And the generalized Ohm’s law Two-fluid equations

14. 14 Soliton solutions

15. 15 Dispersion diagram for slow alfvenons

16. 16 THE END www.cluster.irfu/ks/