1. Electron acceleration in wake bubble by ultraintense laser interacting with plasma Bai-Song Xie and Hai-Cheng Wu College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875 People's Republic of China 19, Aug. 2010

2. Outline Modification of bubble core field by bubble interior residue electrons ( 空泡内部残余电子对空泡内部场 的修正） Optimizing electrons acceleration of wake bubble with dense-plasma wall ( 利用高密度等离子体壁优 化空泡加速中的电子加速 )

3. Laser-Plasma Wakefield Acceleration T. Tajima and J. M. Dawson, PRL 43, 267 (1979) Thomas and Katsouleas, Nature 431, 515 (2004).

4. Electrons acceleration in bubble Electrons void, higher acceleration field gradient Bubble is robust Wave-breaking and self- injection occurs at bubble bottom Linear scaling law of bubble core field Monoenergetic energy A. Pukhov and J. Meyer-Ter-Vehn, Appl. Phys. B 74, 355 (2002).

5. Linear scaling laws of bubble core fields I. Kostyukov et al. Phys. of Plasmas 11, 5256 (2004).

6. 6 Outlook Modification of bubble core field by bubble interior residue electrons Optimizing electrons acceleration of wake bubble with dense-plasma wall

7. Electrons density and velocity Plasma density Laser parameters

8. A: modification of bubble core fields based on Kostyukov model I. Kostyukov et al. Phys. of Plasmas 11, 5256 (2004).

9. Quasistatic approximation when ignoring

10. In bubble core region

11. Slope of longitudinal field ~1/2, slope of transverse’ are reduced. 3D cylindrical case 2D planar case

12. Approximately the bubble shape is given by the potential surface. Ratio of longitudinal to transverse radius Comparison by modification theory with PIC simulation results

14. Electrons charge and current density: Equi-potential surface: Moving frame: B: modification of bubble core fields based on elliptic bubble shape

15. In the condition of Lorenz gauge

16. Back transformation to laboratory frame

17. Similarly in 2D case

18. Quasistatic approximation, bubble velocity ~c, Lorenz gauge W. Lu et al. Phys. Plasmas 13, 056709 (2006). C: modification of bubble core fields based on Lu model

19. Electromagnetic fields solution:

20. Boundary conditions:ψ( r = ∞) = 0:

21. Electrons motion equation of bubble wall

22. When r b ≫ 1, and in bubble region of no laser pulse, no driving source and no self-injection e-bunch Comparison with elliptic equation Fields slope near to bubble core

23. Brief summary Electron that enter the bubble moves backward with ~c, which weaken the transverse fields, leads to reduction of ratio of longitudinal to transverse radius of bubble shape. Smaller ratio compensates the weakness of longitudinal field due to entered electrons so that the longitudinal field is hardly changed. The slope of transverse fields are reduced almost 2 times. This makes a possible to increase the accelerated e-bunch transverse emittance. For same transverse size bubble, because the longitudinally shrink, the corresponding de-phasing length is also shrunk that is disadvantage to get higher e-energy.

24. 24 Outline Modification of bubble core field by bubble interior residue electrons Optimizing electrons acceleration of wake bubble with dense-plasma wall

25. Introduction Two key points: electrons injection and acceleration optimization Lack of efficient scheme Rayleigh diffraction length, laser pulse depletion length, electrons acceleration de-phasing length Decreasing plasma density or/and enlarge the bubble size Enlongating the laser pulse depletion length as well electrons acceleration de-phasing length Continuous self-injection influnces energy peak and energy spread Two open problems: increasing of electrons acceleration de-phasing length and suppression of electrons continuous self-injection

26. Simulation parameters laser plasma I mm length homogenous underdense plasma with vacuum and preplasma in left dense plasma wall Wall density Wall thickness Wall inner radius is a little larger than the initial bubble transverse size

27. ZLP-laser, plasma with no dense- plasma wall (a) self-focus: (b) move a Z R again, back overtake fore, guiding loss, diffraction at two lateral side, e-bunch length ~48, 10 10 number. (c) move a 1.2 Z R again, e- bunch length ~ 40, 10 10 number. (some electrons overtake the centre so that e-bunch length is shorten) (d) large e-bunch spatial divergence, multi-peak energy spectrum, wide energy spreading.

28. (a): δa ≃ 24, σ = 0, Est. ~ 8.24, PIC ~ 9.1 (b): δa ≃ 32, σ = 2.18, Est. ~ 14.8, PIC ~ 15.4 Estimation of bubble transverse size

29. ZLP-laser with dense-plasma wall R w =11.31 (i) continuous self-injection; (ii) e-bunch tailoring; (iii) quasi stable phase acceleration As bubble grows it touches the dense- plasma wall, results in a thin layer high- density ions in the bubble transverse lateral side due to the wall layer electrons slightly move away wall. The high-density electrons near the wall screen quickly the fields of bubble that constitute a new wall and prevent the bubble further growth high-density positive charge layer enhances longitudinal field, half e-sheath at back is shorten and e-bunch is tailored The tailored e-bunch pushes the electrons at its front and drives out a 2nd bubble. It enhances the electrons density at bottom of 1st bubble and enforces furthermore longitudinal field

30. ZLP-laser with dense-plasma wall During 1ps - 2ps, the accelerated e numbers is less and less and almost unchanged after 2ps. The bubble bottom shorten and e-bunch tailored processes slows down until end. The bubble shrunk longitudinally slows down: (i) under a dense-plasma wall radius, the bubble size should be determined finally by consistent balance conditions; (ii) The accelerated e-bunch is shorten that make the transverse repulsion reduced; (iii) The tailored e-bunch is depleted continuously that leads its ability to push bottom electrons and enhancing longitudinal field becomes weaker and weaker

31. The tailored e-bunch pushes the electrons and enforces longitudinal field Some bottom electros follows the accelerated e- bunch to move forwardly. At t=3.5ps, e momentum ~ 10 3 mc. The accelerated e-bunch is always at botom so that it can be almost stable phase accelerated. Bubble longitudinally shrunk, high-density positive charge thin layer presence and high- density electrons of bottom enhance the longitudinal field, e.g. at t=2ps, the slope of longitudinal field ~ 1.7 > 0.5 High acceleration gradient +stable phase  high energy, narrow energy spread, high collimation. energy peak ~ 2GeV, energy spread ~ 4%, divergence angle < ±25mrad.

32. CP-laser Asymmetric transversely bubble shape is due to the phase of laser pulse envelop R w =12.25 a y =a z =20/sqrt(2) Peak energy 2GeV Energy spread 10% Electrons number 10 9 /2

33. YLP-laser R w =12.25 a y =20 Peak energy 1.2GeV Energy spread 4.4% Electrons number 10 9 /2

34. Brief summary A dense-plasma wall with radius about as between bubble initial and largest transverse sizes. The shrunk bubble tailors part self-injected e-bunch and suppresses further self-injection. It can increase the monoenergetic e-bunch production. Accelerated electrons stay almost at the bottom of bubble not only increase the average acceleration field gradient but also overcome the limit of electrons acceleration de-phasing length to some extent. Three key factors: longitudinal shrink, dense positive- charge thin layer, and very dense electrons at bottom of bubble.

35. Summary Analyzing theoretically the effect of electrons charge and current densities on the bubble core fields and bubble shape due to entering of electrons from bubble front into bubble core. Proposing an optimizing scheme by placing a dense- plasma wall with radius comparable to bubble transverse size that can suppress the electrons continuous self-injection and therefore it can increase acceleration gradient through a realization of quasi-stable phase.

36. Thanks