1. UNIVERSITY OF MARYLAND AT COLLEGE PARK High-intensity optical slow-wave structure for direct laser electron acceleration H.M. Milchberg, B.D. Layer, A. York, J. Palastro, T, Antonsen University of Maryland, College Park HEDSA 2009

2. Conventional accelerators high energy physics 27 km circumference constraints: R > R min  synchrotron radiation loss E accel <10 6-7 V/m  structure breakdown LEP (CERN) (100 GeV) SLAC (50 GeV) 3 km

3. The SLAC structure is periodically modulated 50 GeV in 3.2 km 50 GeV/(1.7x10 7 V/m) ~ 2 miles Solution: use ‘milder’ fields over longer distance view from space EzEz E transverse B transverse EM propagation & particle accel. ‘slow-wave’ structure wave phase velocity < c internal breakdown (lightening!) and self-destruction if wave fields are greater than ~ 10 7 Volts/m accelerator waveguide structure

4. relativistic electron beam relativistic electron spectrometer ‘conventional’ laser- plasma wakefields: intense laser pulse enters gas jet and relativistic electron beam emerges pulse speed is v g < c 150  m Laser pond. force for >10 18 W/cm 2 pushes electrons out of the way + - + - + - E E E E E Plasma oscillation: “wake-field”

5. ~35 μm 1000 200 0 z (µm) -200 r (µm) Radially modulated 100ps Nd:YAG laser pulse Axially modulated plasma waveguide 35 fs Ti:Sapphire laser pulse (e) (a) 50 fs transverse interferometer probe 13 µm (e) 13µm Axicon (b) (d) 300 µm 35µm 200µm 50µm 35 µm 50µm (c) But can we imitate SLAC using a plasma? YES! 

6. 0 radius (  m) 10 4 bar pressure Plasma cross-section during and immediately after pulse: 25 Principle of plasma waveguide: example of hydrodynamic shock generation experimental electron density profiles after pulse: blast wave expansion “hollows” the N e profile A hollow electron density profile acts as a focusing element plasma index of refraction N e (r) lower in middle results in index n larger there focusing

7.  k  L coherence =  L coherence ‘Slow wave’ structure quasi-phase matching Particle accelerationEM wave generation v particle < v wave phase Charged particle dephasing E pump z-v pump t Phase mismatch v pump ≠ v generated EzEz z-v phase t v phase >c electron

8. Slow wave picture d z rr where Bloch-Floquet condition: Wave number of m th axial harmonic m th harmonic is ‘slow’ if where

9. Electron acceleration: slow wave picture Electron energy gain For the ‘matched’ case get

10. Accelerating region: low plasma density (high index) Decelerating region: high plasma density (low index) n 1 > n 2 Mod period d=L 1 +L 2 L d1 L d2 Example: density modulation Quasi-phase matching picture The driving wave speeds up and slows down in successive portions of the modulation so that the acceleration in the first part is not completely cancelled by deceleration in the second part. Energy gain per period: where

11. Outline reminder about clusters -heating and plasma formation with femtosecond pulses (PRLs <2005) -heating and plasma formation with long (many picosecond) pulses formation of axially modulated (corrugated) plasma fibres using long pulses - axially modulated heating pulse - tailored cluster flow direct laser acceleration

12. Clusters are essential! Energetic electrons/ions Neutrons Cluster jet X-rays: A. McPherson et al., PRL 72, 1810 (1994). EUV and x-rays: * E. Parra et al., PRE 62, R5931 (2000). Optical properties: Kim, Alexeev, Milchberg, PRLs 2003, 2005 Fast electrons and ions: Y. L. Shao et al., PRL 77, 3343 (1996); † V. Kumarappan et al., PRL 87, 085005 (2001). Nuclear fusion: T. Ditmire et al., Nature (London) 398, 489 (1999). EUV spectrum * X-ray signal* X-rays EUV Clusters few Å ~ 500 Å ~10-10 7 atoms— explode in < 1 ps TOF mass spectrum † Laser pulse Scattering >90% laser absorption

13. Why do 100ps pulses efficiently heat clusters? The far leading edge of the 100ps beam disassembles / ionizes the clusters, leaving a cool high Z plasma that the remainder of the pulse heats. Much more efficient than heating an unclustered gas (for same average Z in a plasma, up to 10x less pump energy required) -40-50% absorption 50 Å ~ 600 Å Single Ar cluster                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Critical density layer High Z, cool, under-dense plasma Sub-critical plasma Super-critical plasma a H. Sheng et al, Phys. Rev. E 72, 036411 (2005)

14. enhanced absorption, even for very long (100ps) pulses because absorption is local to a cluster, can ultimately form plasma channels with N e ~ 10 18 cm  3 electron density* and lower efficiently makes plasma channels in anything that decently clusters Typically 10X more efficient than for equivalent vol. average pressures of unclustered gas Cryogenic cluster jet Controlled cryogenic cooling of the jet enhances clustering 2 cm

15. First modulation method- modulated Bessel beam and uniform cluster flow Breakdown in Argon clustersBreakdown in atmosphere 100-300mj 100ps Nd:YAG pulse, axially modulated with diffractive optics, incident on unmodulated cluster jet flows Ex. ~2mm corrugation period 1.5cm

16. Guiding in corrugated hydrogen plasma channels H 2 jet cryogenically cooled to enhance clustering Electron densities of ~1.5*10 18 cm -3 on axis and ~3*10 18 cm -3 at channel wall for a delay of 1ns 15µm 10 17 W/cm 2 (b) (i) (ii) (iii) 700 µm 500 µm 200 mJ300 mJ500 mJ + misalign. Waveguide generation pulse energy and alignment controls modulation features

17. Extended high intensity guiding 1 mm 700µm beadscontinuous No injection injection Pump scattering Abel inversion Pump scattering

18. 2 4 6 8 10 18 cm -3 3 mm 660µm Extended high intensity guiding without injection injection, 2x10 17 W/cm 2 at exit laser

19. Propagation simulation using the code WAKE* 0.2 1.0 10 18 W/cm 2 * P. Mora and T. M. Antonsen Jr., Phys. Plasmas 4, 217 (1997). Simulation using experimental density profiles Attenuation from leakage at gaps

20. Second method: wire-tailored cluster flow, unmodulated laser pulse uniform 500mj 100ps Nd:YAG pulse incident on axially modulated Argon cluster target 1mm corrugation period 1.5 cm

21. Features persist for the full life of the waveguide Nitrogen cluster target @ -150 deg C, 25  m wires Argon cluster target @ 22 deg C, 25  m wires 160 μm 320 μm 0.5 ns 1.0 ns 2.0 ns 6.0 ns 2.0 ns 0.5 ns (200 consecutive shot averages) 600 μm B.D. Layer et. al, Opt Express 17, 4263 (2009)

22. Direct laser acceleration- inverse Cherenkov acceleration (ICA) 580-MW peak power  31 MeV/m. 10 TW peak powers are now routine, but the need for neutral- gas phase matching strongly limits peak intensities.

23. Nd:YAG laser pulse axicon Corrugated plasma waveguide Relativistic electron bunch Radially polarized fs laser pulse Clustered H 2 jet Diffractive optic

24. Corrugated guide: simple estimates of dephasing lengths and acceleration gradients n1 > n2 One full dephasing cycle Estimate acceleration gradients using index modulation: Accelerating-phase region: low index Decelerating-phase region: high index λ = 800nm N e1 = 3*10 18 cm -3 N e2 = 6*10 18 cm -3 w ch = 12μm p = 1, m = 0 } L d1 = ~260 μm L d2 =~165 μm For P = 1 TW, E z =0.55 GV/cm, giving an effective gradient of 77 MV/cm Wakefield comparison: Malka et al. used a 30 TW laser at λ = 0.8 μm to produce an acceleration gradient of ~0.66 GV/cm This is a linear process with no threshold. 1 mJ regenerative amplifier alone P = 20GW  Effective accel. gradient: 11 MV/cm

25. electrons distributed uniformly on axis 1 to 11  m behind pulse peak no transverse momentum  30 60 time (ps) 400 0 0 m=1 phase velocity matched to initial electron velocity m=1 phase velocity set to c  o =1000  o =100  o =30 Ideal scaling it is better when electrons catch up with a faster wave than to start them phase matched to a slower wave  Direct laser acceleration- energy gain

26. Comparing direct accel to other schemes parameters used for comparison: =800 nm w ch =15  m a o =.25 n o =7x10 18 cm -3  =.9 m =.035 cm  o =100  z =300 fs*c for direct accel we have:  = 1000 semi-infinite vacuum acceleration:  = 12.5 (best case scenario) vacuum beat wave acceleration:  = 8.3 ( 1 =2 2 ) laser wakefield acceleration:  = 14.3

27. Electron Beam Density final electron density -81  m 81  m 300 xfxf zfzf -1  m xfxf number averaged final momentum -11  m 0 0 1 num. (a.u.) p z (m e c) density peaks off axis; beam has acquired sizeable transverse spread 81  m -81  m off-axis peaks mostly composed of low energy electrons high energy electrons remain confined to center of beam only the ponderomotive transverse force is significant for these electrons

28. Can make modulated plasma waveguides with two distinct methods- modulating either the laser heating profile or the clustered target flow Can control nearly every aspect of the waveguide by varying cluster parameters and pump laser intensity Gas cluster channels can be more than 10X less dense than unclustered gas channels (10 17 ’s-10 18 ’s vs. 10 19 ’s) and use 10X less laser energy for generation- Cluster-generated plasma waveguides are extremely stable (longitudinal AND transverse) and can support finely engineered structures. Summary One application: Direct laser accelerator optical-frequency LINAC with no damage threshold