1. Particle acceleration in plasma By Prof. C. S. Liu Department of Physics, University of Maryland in collaboration with V. K. Tripathi, S. H. Chen, Y. Kuramitsu, L. C. Tai, S. Y. Chen, J. Wang, N. Kumar, and B. Eliasson

2. Cosmic ray acceleration

4. Magnetosphere of the Earth

5. The Earth’s magnetic field and magnetosphere

6. Cavity flow with reentrant jet

7. “Mono-energetic” electrons on the Earth

8. Acceleration gradient of plasma wave can be large Maximum acceleration gradient limited by the wave breaking or giving,, for Non-relativistic wave- breaking amplitude Relativistic wave-breaking amplitude is the Lorentz factor for plasma wave SLAC on a slab !!! Electron can be accelerated by plasma wave:

9. How to generate plasma wave ?? 1.Mode conversion 2.Beat wave excitation with two laser pulses 3.Raman scattering 4.Relativistic wake plasma wave excitation by electron beam or short pulse laser

10. 1) Mode conversion + + An EM wave obliquely propagates into a plasma with density gradient. An oscillatory current can cause space charge oscillations. EM wave → ES wave

11. 2) Beat wave excitation –Two long laser pulses –Plasma wave excitation possible if, –Maximum saturated amplitude of the plasma wave due to relativistic mass effect (Rosenbluth and Liu, PRL, 1972) Backscattering, Forward scattering,

12. Nonlinear frequency-amplitude relation

13. Laser light: Scattered light: 3) Raman Scattering by Plasma Wave Plasma: Current: Feed back Instability Growth rate:

14. Raman heated electrons

15. Raman scattering causes electron acceleration

16. Maximum electric field of the plasma wave 4) Relativistic wake plasma wave excitation by electron beam or short pulse laser

17. Acceleration of a SLAC electron beam Hogan et.al. Phys. Rev. Lett. 95, 054802 (2005) Demonstration of acceleration in beam driven wakefield (SLAC)

18. Mono-energetic electron beam by short pulse laser Mangles et.al, Nature, 431, 535 (2004), Faure et.al., Nature, 431, 541 (2004), Geddes et.al., Nature, 431, 538 (2004) Observation of mono-energetic beam of electrons with energy 50-170 MeV by three groups.

19. Chen, et.al.(Particle accelerator group, Academia Sinica, NCU) First direct measurement of acceleration gradient; eE=2.5 GeV/m ~ 10 3 of linac.

20. Micro magnetosphere Relativistic self focusing whereLaser power, Relativistic dielectric constant Relativistic effect increases Ponderomotive effect decreases Resultant effect ion channel formation Laser wakefield acceleration and ion channel formation in laser

21. Electron trajectories

22. Number density of electrons on axis

23. Wake field on axis

24. Injection and acceleration of mono-energetic electrons by a self-modulated laser pulse Experiments at Academia Sinica (PRL, 2006) OOPIC (object-oriented particle-in-cell) code –two spatial and three velocity components –pre-ionized electron-proton plasma –linearly polarized Gaussian laser pulse –s-polarization (normal to the density perturbation) –moving window –immobile ions Parameters –Peak laser intensity: I 0 = 8x10 18 W/cm 2 (a 0 = 2.) –Laser wavelength: = 0.81  m –Pulse duration:  = 45 fs –Gas density: n = 4x10 19 /cm 3 (  p /  L = 0.15) –Initial waist size: w 0 = 4  m –Chirp bandwidth: 27 nm

25. Initial Plasma Density

26. Time = 0.735ps

27. Time = 0.829 ps

28. Time = 1 ps

29. Time = 1.1 ps 50 MeV mono energetic electron beam

30. The wake field bunches the electrons in real space. Time = 1.1 ps

31. The modulated laser field traps electrons and push electrons moving with the laser pulse. Time = 1.1 ps

32. The modulated laser field traps electrons and push electrons moving with the laser pulse. (The plasma is turned off at time = 1.33 ps) Time = 1.43 ps 50 MeV mono energetic electron beam E z of laser pulse

33. Distribution function

34. p x - x phase space

35. Weibel instability kxkx EyEy BzBz u+u+ u-u- Growth rate:

36. Thank you

37. Outline Plasma universe Plasma wave excitation and trapping of resonant electrons Laser driven acceleration and production of the mono-energetic electrons beam Ion acceleration Concluding remark

38. Plasma universe Three minutes after Big Bang ----- Plasma dominated universe Radio jets, X-ray sources,  -ray bursts, pulsar, accretion disk etc…. We observe our universe mostly by EM waves. Its dispersion relation,

39. Ion bubble formation by different a