1. Nonlinear Optics in Plasmas

2. What is relativistic self-guiding? Ponderomotive self-channeling resulting from expulsion of electrons on axis Relativistic self-focusing resulting from relativistic modification of electron mass

3. What is relativistic self-guiding? the combinational effect of relativistic self-focusing and ponderomotive self-channeling overcomes the natural diffraction, leading to the self-guiding of the laser pulse. At

4. What is Raman forward scattering in a plasma?

6. Setup for characterizing relativistic self-guiding and Raman forward scattering

8. Side imaging of Thomson scattering for various laser powers

9. Transverse profiles of the self-guided laser beam

10. Channel length vs. laser pulse duration and chirp A longer self-guiding channel is observed for longer pulse duration. Chirp has no effect.

11. Breakup of the laser pulse due to a lower contrast contrast at -1 ns <5x10 5 Low contrast produces a longitudinal plasma density gradient which results in bifurcation of the laser beam. N e = 1.3x10 19 cm -3, E = 310 mJ

12. Raman spectra for various plasma densities The frequency shift is equal to plasma frequency

13. Raman spectra for various laser powers The frequency shift is independent of laser power. We can conclude that the frequency shift is due to RFS.

14. Dependence of RFS on the chirp of a laser pulse Raman forward scattering is expected to be assisted by a positively chirped pulse and suppressed by a negatively chirped pulse.

15. Raman intensity vs. laser pulse duration and chirp The intensity of the Raman Stokes satellite is observed to be stronger for positively chirped pulse in comparison to negatively chirped pulse.

16. Raman spectra vs. laser pulse duration and chirp The narrowing and spread of the Stokes satellite spectrum for positively and negatively chirped pulses respectively confirms that Raman forward scattering is enhanced by positive chirp and inhibited by negative chirp.

17. Setup for producing a collinearly-propagating second-harmonic probe pulse

18. Setup for time-resolving the phase modulation

19. Blue shift of the probe pulse wavelength versus delay High contrast results in a significant ionization at within 1 ps prior to the peak of the pulse. Such an ionization front excites a plasma wave to seed the growth of Raman forward scattering. (nm) when strong Raman satellite is observed  when no Raman satellite is observed. Blue shift of the probe occurs due to the rapid change of plasma density at the ionization front.

20. Summary Relativistic self-guiding can be enhanced by increasing pulse duration. Raman forward scattering is enhanced by positive chirp and suppressed by negative chirp. Channel bifurcation of relativistic self-guiding can be suppressed by raising the nanosecond-scale temporal contrast. Raman forward scattering is suppressed when the picosecond-scale temporal contrast falls below a threshold of 10 ⁴.

21. Laser-Plasma-Based Electron Accelerator

22. Acceleration of electrons by an electron plasma wave + - + - + - + - + - pump pulse plasma wave driven by Raman forward scattering instability electrons injected by Raman backscattering instability Raman forward scattering instability can drive an electron plasma wave with a phase velocity close to c. Electrons with initial energy higher than a threshold can be trapped and accelerated by the plasma wave.

23. Use collective Thomson scattering to measure an electron plasma wave Scattering efficiency of the probe into the first Stokes and anti-Stokes satellites is Scanning the probe delay maps out the the temporal evolution of the electron plasma wave.

24. 2×10 19 cm -3 1.8×10 19 cm -3 1.5×10 19 cm -3 1.3×10 19 cm -3 pump pulse: 260 mJ, 275 fs (  -)  t = 0 Thomson satellites vs. plasma density The frequency shift is equal to plasma frequency

25. Thomson satellites vs. probe delay pump pulse: 260 mJ, 275 fs (  -) N e = 2×10 19 cm -3

26. Temporal evolution of the amplitude of the plasma wave pump pulse: 260 mJ, 275 fs (  -) N e = 2×10 19 cm -3 The decay rate of the electron plasma wave driven by Raman forward scattering is measured to be about 1 ps -1. Since the plasma wave lasts for only 1 ps, the macro-bunch duration of the accelerated electrons should be less than 1 ps.

27. Acceleration of electrons by an electron plasma wave The same dependence of the electron number and Raman satellite energy on laser pulse duration and chirp proves that the electrons are accelerated by the plasma wave driven by Raman forward scattering instability. 250 mJ, 55 fs 3x10 19 cm -3

28. Total number of electrons accelerated vs. plasma density and laser peak power Above an appearance threshold the total number of electrons accelerated increases exponentially with plasma density and laser peak power, and saturates at >1x10 9. 3.3x10 19 cm -3 250 mJ 55 fs laser focus at the front edge of the gas jet

29. Divergence of the electron beam Since the source size should be smaller than the laser channel size (10  m), the transverse emittance is lower than 0.1  -mm-mrad, better than that of a state-of-the-art electron gun.

30. Low-energy electron spectrum The dispersion of the image on the LANEX under magnetic field identifies that it is indeed from electrons. The electron energy spectrum can be fitted into an exponetial decay with a characteristic temperature of 1.8 MeV 250 mJ, 55 fs 3.3x10 19 cm -3 focus at front edge

31. High-energy electron spectrometer The existence of electrons of a certain energy can be confirmed by checking if they indeed move in the path expected.

32. High-energy electron spectrum Electrons with kinetic energy up to 45 MeV was observed. The energy spectrum can be fitted into an exponetial decay with a characteristic temperature of 8.5 MeV, a flat region, and a high-energy cut-off. 250 mJ, 55 fs 3.3x10 19 cm -3 focus at front edge

33. Laser channel and electron beam profile vs. gas jet position 0: laser focus at the center of the gas jet 400: laser focus at the front edge of the gas jet The electron beam with smaller divergence angle is produced when the laser focus is positioned at near the front edge of the gas jet. It is correlated with the onset of relativistic self-guiding. 3.3x10 19 cm -3

34. Laser channel and electron beam profile vs. plasma density and laser peak power 55 fs laser focus at the front edge of the gas jet Once the small-divergence electron beam appears, its divergence angle shows little variation with increasing plasma density and laser peak power.

35. Laser channel and electron beam profile vs. laser pulse duration and chirp The large-divergence electron beam is stronger for positive chirp, while the small-divergence electron beam is stronger for negative chirp. The onset of the small-divergence electron beam does not correspond to a sudden decrease of the large-divergence electron beam. 250 mJ, 55 fs 3.1x10 19 cm -3

36. Summary The decay rate of the electron plasma wave driven by Raman forward scattering instability is measured to be about 1 ps -1 using probing collective Thomson scattering. The generated electron beam has a total electron number of >10 9, a divergence angle of 1.8º, and a maximum electron energy exceeding 40 MeV. The same dependence of the electron number of the large- divergence electron beam and Raman satellite energy on laser pulse duration and chirp proves that these electrons are accelerated by the plasma wave driven by Raman forward scattering instability. The appearance of an electron beam with small divergence angle is correlated with the onset of relativistic self-guiding, possibly resulting from a direct laser acceleration mechanism.