1. Laser-structure accelerators B. Cowan, M.-C. Lin, B. Schwartz, Tech-X Corporation E. Colby, J. England, C. McGuinness, C. Ng, R. Noble, J. Spencer, SLAC R. Byer, Stanford University

2. Outline Motivation A tour of structure types –Macroscopic structures –Grating-enabled slab structures –Photonic bandgap structures Laser-structure concepts –Gradient –Efficiency –Beam dynamics –Microfabrication Ongoing work –Computation –Beam experiments –Injectors

3. Motivation: Laser-driven acceleration using dielectric structures High gradient –Take advantage of intense laser fields –High dielectric breakdown thresholds Efficiency –Laser wall-plug to optical efficiency continues to improve –Optics have low loss Operate in stable, linear regime –Many concepts carry over from RF Generate attosecond bunches

4. Macroscopic structures: Demonstration of microbunching and acceleration Optically bunch the beam in IFEL, follow with accelerating structure First observed by Kimura et al. at ATF with 2 IFELs Net acceleration using linear structure demonstrated at SLAC Structure used tilted free-space mode Observation of microbunching: Sears et al. PRST-AB 11, 061301 (2008) Net acceleration: Sears et al. PRST-AB 11, 101301 (2008) Free-space accelerating structure

5. What’s next for structures? Want to develop scalable structure – accelerate over many Rayleigh lengths Need to generate axial electric field Speed-of-light phase velocity for matching to high-energy beam How do we scale down RF structures to optical wavelengths? –Ideally, use waveguide: Similar to RF, high efficiency –But for index-guiding (as in conventional fiber-optics) fields in vacuum are slow waves: Waveguides get complicated

6. At UCLA, we are designing an optical accelerator consisting of a diffractive optic coupling structure and a partial reflector Courtesy G. Travish

7. A long term goal is to develop a mm-scale, laser- powered, disposable, relativistic particle source MAP: Micro Accelerator Platform Courtesy G. Travish

8. More slab/grating structures Slab structures tend to use gratings: Gratings induce phase shifts for matching to a particle beam Courtesy T. Plettner

9. Interlude: Photonic bandgaps (PBGs) A photonic crystal is a structure with periodic dielectric constant Like electronic states in solids, EM modes form bands Band gaps can form, in which propagation is prohibited

10. Benefits of photonic bandgaps Provide confinement in “defect” — an interruption in the lattice Can confine a speed-of-light mode in all-dielectric structure – impossible with index (total internal reflection) guiding Only confines modes in bandgap frequency range – automatic HOM damping Axial field

11. PBGs with reduced dimension: Fibers PBGs can be made with periodic structure in some dimensions, uniform in others Ex. PBG fibers: Periodic in transverse dimension; longitudinally uniform Certain dispersion points ( , k z ) are prohibited for all 2D propagation vectors Geometry, mode and gap map of fiber structure from X. E. Lin, PRST-AB 4, 051301 (2001)

12. PBGs: They’re not just for optical structures! HOM damping motivated PBG structure development in the RF regime Geometry and modes of metallic PBG structure based on triangular transverse lattice. From Smirnova et al., PRL 95, 074801 (2005) Dielectric Bragg structure, from Jing et al, NIM A 594, 132 (2008)

13. Goals: 1.Design fibers to confine v phase = c defect modes within their bandgaps 2.Understand how to optimize accelerating mode properties: Z C, v group, E acc /E max,… Codes: 1.RSOFT – commercial photonic fiber code using Fourier transforms 2.CUDOS – Fourier-Bessel expansion from Univ of Sydney Modeling Photonic Band Gap Fibers and Defect Modes Accelerating Modes in Photonic Band Gap Fibers Accelerating modes identified as special type of defect mode called “surface modes”: dispersion relation crosses the v phase =c line and significant field intensity at defect edge. Tunable by changing details of defect boundary. R inner (µm)λ(µm)E acc /E max Z C (Ω)Loss (db/mm) 5.001.89460.04930.1360.227 5.101.88720.06600.2500.035 5.201.87670.07880.3710.029 E z of 1.89 µm accel. mode in Crystal Fibre HC-1550-02 Modified X.E. Lin hollow core silica fiber with improved ratio E acc /E z matrix obtained by filling the first layer holes with ε r = 1.5 material Modifying Accel. Mode via Defect Radius:Increasing the Accel. Field: HC-1550-02 Band Gaps Courtesy R. Noble et al.

14. 3D “woodpile”-based structure Has complete bandgap; requires high index Lithographic fabrication can allow incorporation of features, e.g. coupling elements Supports speed-of-light, near-lossless accelerating mode Si (ε r = 12.1) Vacuum Axial field PRST-AB 11, 011301 (2008)

15. Key structure concept: Sustainable gradient (Also not just for optical structures!) Gradient fundamentally limited by breakdown of material Huge unexplored territory: What are best parameters? –5 orders of magnitude in frequency (RF to optical) –Lots of materials –Relatively little data One conclusion: Short pulses are good (at least down to ~1 ps) Simanovskii et al., PRL 91, 107601 (2003) Proc. SPIE 6720, 67201M-1Stuart et al., PRB 53, 1749 (1996) (For THz measurements see Thompson et al., PRL 100, 214801 (2008)) Si

16. Woodpile gradient example Based on damage threshold of bulk silicon, sustainable gradient is 300 MeV/m at  = 1550 nm, 1 ps pulse width –Could get to 400 MeV/m at longer wavelength; GeV/m challenging in silicon –Higher-bandgap materials could allow higher gradient Achievable with 500 W peak laser power –Commercially available in fiber systems Low group velocity  laser pulse slips 1 ps relative to particle beam in 100  m –Frequent coupling & compact coupler needed

17. Optical accelerator efficiency Bunch charge and optical-to-beam efficiency limited by wakefields Embed accelerator in optical resonator to recycle energy; use multiple bunches Beam can consist of a single optical bunch or a train of optical bunches spaced by  From Y. C. Neil Na et al., PRST-AB 8, 031301 (2005) IFEL + chicane RF electron bunch Optically- bunched beam

18. Efficiency optimization Optimize resonator beamsplitter reflectivity and bunch charge for optimum efficiency Efficiency 37% for single bunch, 76% for 100 bunches Bunch charge ~few fC, so rep rate must be high Energy spread could be problem efficiency reflectivity charge

19. Beam dynamics considerations Structure has small aperture: 1.55  m × 1.41  m Structure is not azimuthally symmetric  has strong transverse focusing and nonlinear forces for off-crest particles Perturb woodpile structure by adjusting central bar Two problems ⇒ one solution –Idea: Use the optical structures  /2 out of phase as focusing elements –Adjust waveguide geometry to suppress quadrupole fields during acceleration Geometry is key

20. Effect of geometry change 2 modes available; suppress quadrupole field in accelerating mode and octupole field in focusing mode We can now use thin lenses Out of guideInto guide Original mode Quadrupole field suppressed Focusing mode with octupole field suppressed: ~ 831 kT/m magnet

21. Beam confinement Use accelerating and focusing structures to create thin-lens F0D0 lattice Resulting design has high dynamic aperture, low emittance growth Results for full 6D tracking simulation over 3 m Emittance requirement: 87% energy gain Dynamic aperture, on-crest particles

24. Computational issues Computing properties of photonic crystal structures is hard –High-order mode –Large computational area For n “cladding” layers: –Computational cell size ~ n 2 –Mode number ~ n 2 Computations can be orders of magnitude more intensive than for metal-bounded structures for similar resolution High-performance computing is beginning to be brought to bear –Advanced dielectric algorithms –Frequency extraction techniques from time-domain simulation PBG lattice defect

26. field emitter tip Field emission tip properties 1.laser-assisted tunneling of electrons from the atom to free space 2.Highly nonlinear 3.Potential for timed sub-optical cycle electron emission metalvacuum e P. Hommelhoff et al, Kasevich group, Stanford University laser beam P. Hommelhoff, Y. Sortais, A. Aghajani-Talesh, M. A. Kasevich, “Field Emission Tip as a Nanometer Source of Free Electron Femtosecond Pulses”, PRL 96, 077401 (2006)

27. Summary Optical structures hold great promise for laser-driven acceleration Groundwork in place further exploration –Linear acceleration in vacuum demonstrated –Several structure designs simulated –Efficiency and beam focusing concepts described Fabrication and experimentation underway Much work remains to be done and many exciting ideas to explore –Many concepts carry over to other frequency ranges

28. Acknowledgments Collaborators at SLAC/Stanford J. Rosenzweig, G. Travish (UCLA) A. Chao, A. Wachsmann (SLAC) S. Fan, D. Simanovskii (Stanford) M. Tang (SNF) Work supported by Department of Energy contracts DE- AC02-76SF00515 (SLAC), DE-FG06-97ER41276 (LEAP), and DE-SC0000839 (SBIR), and by Tech-X Corporation. Bob

29. Diamond structure Simulate woodpile structure based on diamond: n = 2.395 at λ = 1.55 μm First, optimize the lattice: Adjust rod width w for largest bandgap; optimum at w = 0.37a w a Omnidirectional bandgap: 5.4% width-to-center ratio

30. Step 2: Compute an accelerating mode Mode parameters (with Si structure parameters for comparison): SiDiamond Normalized frequency a/λ 0.3670760.426313 Loss < 0.48 dB/cm 35.3 dB/cm Damage impedance 6.10  5.56  Characteristic impedance 460  241  Group velocity0.253c0.108c For diamond, electronic bandgap is 5.5 eV, requiring 7  absorption for ionization at λ = 1.55 μm Frequency near bandgap edge; loss might be reduced by altering waveguide to bring frequency into the gap