1. Prospects for generating high brightness and low energy spread electron beams through self-injection schemes Xinlu Xu*, Fei Li, Peicheng Yu, Wei Lu, Warren Mori and Chan Joshi University of California, Los Angeles Tsinghua University Oct 15, 2015 * xuxinlu04@gmail.com

2. Plasma-based acceleration Plasma-based acceleration 1 :  High gradient: ~ 100 GV/m  High efficiency: ~ 30%  High energy gain: ~ 10s GeV  Beam quality ? Emittance current energy spread Brightness 1 T. Tajima and J. M. Dawson, Phys. Rev. Lett., 43, 267 (1979); P. Chen et al., Phys. Rev. Lett., 54, 693 (1985); I. Blumenfeld, et al., Nature 445, 741-744 (2007); W. P. Leemans, et al., Phys. Rev. Lett., 113, 245002 (2014); M. Litos, et al., Nature 515, 92-95 (2014); and many other papers. 2 P. Emma et al., Nature Photonics 4, 641-647 (2010). Hard X-FEL at LCLS 2 ~0.4×10 17 A/m 2 /rad 2 (~3 kA, ~400 nm) < ρ ~ 0.001

3. Experimental results Question: How to generate an electron beam with both much higher brightness (>10 17 A/m 2 /rad 2 ) and much lower energy spread (<1%) in plasma- based accelerators?

4. Injection schemes What is injection? The electron is in the acceleration phase.

5. Injection schemes External Injection 1 : the electrons from other sources, e.g., RF-based accelerators Self Injection: the electrons from the plasma  Ionization Injection 2  Downramp Injection 3  Others 1 C. E. Clayton et al., Phys. Rev. Lett. 70,37 (1993); M. Everett et al., Nature 368, 527 (1994). 2 E. Oz et al., Phys. Rev. Lett. 98, 084801 (2007); A. Pak et al., Phys. Rev. Lett. 104, 025003 (2010). 3 C. G. R. Geddes et al., Phys. Rev. Lett. 100, 215004 (2008); A. J. Gonsalves, et al., Nature Phys. 7, 862-866 (2011); A. Buck, et al., Phys. Rev. Lett. 110, 18506 (2013).

6. Ionization injection – Different Scenarios

7. Ionization injection- The key physics Transverse Phase Mixing Longitudinal Phase Mixing X. Xu et al., Phys. Rev. Letts. 112, 035003 (2014).  Transverse phase mixing happens in each slice.  The slice energy spread is determined by the injection distance, ~ several MeV.

8. Ionization injection by transverse colliding pulses injection  Peak brightness: 1.7×10 19 A/m 2 /rad 2  Slice energy spread: 0.012 MeV F. Li et al., Phys. Rev. Letts. 111, 015003 (2013).

9. “Accordion effect”: S. Bulanov, et al., and H. Suk et al., studied the injection process using 1D analysis. We are studying downramp injection:  In the 3D blowout regime  With the aim of generating unprecedented beam quality ~ 10 20 A/m 2 /rad 2 + ~1 MeV ! Downramp injection T. Katsouleas, Phys. Rev. A 33, 2056 (1986); S. Bulanov, et al., Phys. Rev. E 58, R5257 (1998); H. Suk, et al., Phys. Rev. Lett. 86, 1011 (2001);

10. Downramp Injection – The phase velocity We focus on:  3D blowout regime  Gradual density ramp:  Injection condition: The phase velocity 1.5 n p0 n p0 W. Lu et al., PRL 96, 165002 (2006)

11. Downramp injection – transverse motion The transverse force for the particle at r=r b Defocusing Focusing

12. Downramp injection – General features of the injected electrons

13. Downramp injection – Beam Quality  Emittance ε n : determined by σ ri  Slice energy spread: determined by σ zi  Current:

14. How to generate a beam with high brightness? Scaling:  One stage Laser driver: n p ~ 10 19 cm -3 and higher

15. How to generate a beam with high brightness? Staging: ~ 0.8×10 21 A/m 2 /rad 2, < 2 MeV 50 um: 3.3×10 18 cm -3  2.6×10 18 cm -3 16 um: 2.3×10 20 cm -3  1.4×10 20 cm -3

16. How to generate a beam with low projected energy spread? initial energy chirp the chirp of acceleration gradient

17. How to generate a beam with low projected energy spread? Laser driver case: at z plasma = 0.17 mm

18. How to further reduce the relative projected energy spread? The ramp length L is increased from 17 c/ω p to 150 c/ω p. The beam duration is mainly determined by the density difference (n p,h - n p,l ).  Increase the ramp length to increase the initial energy chirp κ !

19. How to further reduce the relative projected energy spread? Generate an ultrashort beam. The plasma density is decreased from 1.05 n p to n p in 2 c/ω p. 10 18 cm -3 : ~20 nm

20. 10 17 cm -3 Other issues - Matching Parameters: OSIRIS results: Profile of the matching section X. Xu, et al., arXiv:1411.4386 (2014)

21. Conclusions We studied the density downramp injection in the 3D blowout regime driven by charged particle or laser pulses. The phase space dynamics of the injection beams are studied using 3D simulations and theoretical analysis. The current, emittance, beam length and initial energy chirp can be controlled by adjusting the driver intensity and the ramp parameters. Finally, electron beams with both high brightness and low energy spread can be generated.

22. Thanks for your attention!

23. Downramp injection – The particle velocity In a uniform plasma: with the quasi-static approximation 1 : P. Mora and T. M. Antonsen Jr, Physics of Plasma 4, 217 (1997). The distribution of Ψ 1 :

24. Downramp injection – The particle velocity In a uniform plasma:

25. Downramp injection – General features of the injected electrons