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 R 21 V sn

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

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

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

11 Auroral acceleration structures: negative or positive potentials keV

12 Acceleration/heating in the solar corona Flares acceleration potentials ~ kV Solar wind: 600 km/s escape velocity km/s  equivalent: 2-5 kV Heating: (millions K) 5 MK  equivalent: 0.5 kV

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 Soliton solutions

15 Dispersion diagram for slow alfvenons

16 THE END