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

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

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

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 modeObservation of microbunching: Sears et al. PRST-AB 11, 061301 (2008)

Net acceleration: Sears et al. PRST-AB 11, 101301 (2008)

Free-space accelerating structure

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

At UCLA, we are designing an optical accelerator consisting of a diffractive optic coupling structure and a partial reflector

Courtesy G. Travish

A long term goal is to develop a mm-scale, laser-powered, disposable, relativistic particle source

MAP: Micro Accelerator Platform

Courtesy G. Travish

xyz

laserbeam

cylindrical lensvacuum

channel

electron beam

cylindrical lens

top view

/2

xyz

laserbeam

cylindrical lensvacuum

channel

electron beam

cylindrical lens

top view

/2

top view

/2

More slab/grating structures

• Slab structures tend to use gratings: Gratings induce phase shifts for matching to a particle beam

Courtesy T. Plettner

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

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

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 (ω, kz) are prohibited for all 2D propagation vectors

Geometry, mode and gap map of fiber structure from X. E. Lin, PRST-AB 4, 051301 (2001)

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)

Goals:1. Design fibers to

confine vphase = c defect modes within their bandgaps

2. Understand how to optimize accelerating mode properties: ZC, vgroup, Eacc/Emax ,…

Codes:3. RSOFT – commercial

photonic fiber code using Fourier transforms

4. 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 vphase=c line and significant field intensity at defect edge. • Tunable by changing details of defect boundary.

Rinner(µm) λ(µm) Eacc/Emax ZC(Ω) Loss (db/mm)

5.00 1.8946 0.0493 0.136 0.227

5.10 1.8872 0.0660 0.250 0.035

5.20 1.8767 0.0788 0.371 0.029

Ez of 1.89 µm accel. mode

in Crystal Fibre

HC-1550-02

Modified X.E. Lin hollow core silica

fiber with improved ratio Eacc/Ez matrix

obtained by filling the first layer holes

with εr = 1.5 material

Modifying Accel. Mode via Defect Radius:Increasing the Accel. Field:

HC-1550-02Band Gaps

Courtesy R. Noble et al.

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 (εr = 12.1)

Vacuum

Axial field

PRST-AB 11, 011301 (2008)

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-1 Stuart et al., PRB 53, 1749 (1996)

(For THz measurements see Thompson et al., PRL 100, 214801 (2008))

Si

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 laserpulse slips 1 ps relative toparticle beam in 100 μm– Frequent coupling & compact

coupler needed

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

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

Beam dynamics considerations

• Structure has small aperture: 1.55 μm × 1.41 μm• 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 π/2 out of phase as focusing elements

– Adjust waveguide geometry to suppress quadrupole fields during acceleration

• Geometry is key

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

suppressedFocusing mode with octupole field suppressed:~ 831 kT/m magnet

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

m1009.1

m,102.99

10

y

x

Emittance requirement:

87% energy gain

Dynamic aperture, on-crest particles

Computational issues

• Computing properties of photonic crystal structures is hard– High-order mode– Large computational area

• For n “cladding” layers:– Computational cell size ~ n2

– Mode number ~ n2

• Computations can be orders ofmagnitude more intensive than formetal-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

field emitter tip

Field emission tip properties1. laser-assisted tunneling of

electrons from the atom to free space

2. Highly nonlinear3. Potential for timed sub-optical

cycle electron emission

metal vacuum

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)

radm 10~ 10 tip

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

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

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

Step 2: Compute an accelerating mode

Mode parameters (with Si structure parameters for comparison):Si Diamond

Normalized frequency a/λ 0.367076 0.426313

Loss < 0.48 dB/cm

35.3 dB/cm

Damage impedance 6.10 5.56

Characteristic impedance 460 241

Group velocity 0.253c 0.108c

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