Transverse Gradient Undulator and its applications to PlasmaAccelerator

Transverse Gradient Undulator and its applications to Plasma-Accelerator Based FELs Zhirong Huang (SLAC) Introduction TGU concept, theory, technology Soft XFEL example Ideal beam Simulated LPA beam EUV POP experiment Summary

C. Schroeder, FLS 2012 Up to 4 Ge. V now

C. Schroeder, FLS 2012

M. Hogan, FEL 2015 Projected energy spread is still on the order of % ?

Transverse Gradient Undulator (TGU) FEL resonant condition By canting the undulator poles, generate a linear field gradient N Sort e-beam energy by dispersion h so that y g+ Resonance can be satisfied for all energies if g- x S T. Smith et al. , J. App. Phys. 50, 4580 (1979)

Effects of Energy Spread off-energyparticle in TGU Ø For efficient FEL interaction, the resonant wavelength spread caused by the energy spread over a gain length << 1 sd << r~10 -3 for short-wavelength FELs Ø This is a local energy spread requirement not projected (for LPAs, bunch length ~ slippage length (SXR), local E spread ~ projected E spread) Ø TGU compensates this effect with K(x)/g(x)

Effects of energy spread on gain length Gain length ratio = Normal undulator normal undulator TGU improve gain when TGU: trade energy spread with horizontal beam size effective FEL paramater Emittance matters here! Z. Huang, Y. Ding, C. Schroeder, PRL 109, 204801 (2012)

Transverse gradient undulator in reality Hybrid undulator, use Halbach formula SINAP 1. 5 -m TGU (Courtesy D. Wang) e. g. , f = 7. 5 deg, lu = 2 cm, g >7 mm a = 50 m-1

Superconducting TGU a = 330 m-1

Compact soft x-ray FELs 1 Ge. V, 10 k. A, 1% energy spread; 0. 1 um emittance; 5 fs (50 p. C) 5 -m SC undulator lu = 1 cm, K = 2; Transverse gradient a = 150 m-1 Radiation wavelength lr = 3. 9 nm For TGU, dispersion h = 0. 01 m, trans. beam size 100 um x 15 um Z. Huang, Y. Ding, C. Schroeder, PRL 109, 204801 (2012)

3 D effects and analysis h = 0. 01 m No TGU SASE P. Baxevanis et al. , PRSTAB 17, 020701 (2014) P. Baxevanis et al. , PRSTAB 18, 010701 (2015) TGU SASE degree of transverse coh.

TGU FEL using simulated LPA beams correlated energy spread transverse phase space C. Benedetti, C. Schroeder (LBNL)

FEL power profile FEL gain curve FEL spectrum Z. Huang et al. , to be published in the proceedings of 2014 AAC conference

High-quality high-energy electron beams from a cascaded LPA Courtesy J. S. Liu (Shanghai Institute of Optics and Fine Mechanics) Peak energy: 0. 4 -0. 6 Ge. V Energy spread: ~1% Beam charge : up to 82. 5 p. C Divergence: 0. 4 -1. 0 mrad Peak energy 398 Me. V Energy spread (rms) 0. 8% Divergence (rms) 0. 8 mrad Beam charge 82. 5 p. C J. S. Liu et al. , Phys. Rev. Lett. 107, 035001 (2011).

LPA FEL with TGU (SIOM/SINAP) Plan a demonstration experiment at 30 nm (400 Me. V, 6 m TGU) Focusi ng opti cs LPA ch amber SIOM LPA setup (J. -S. Liu) Beam transpo rt TGU SINAP TGU assembly (D. Wang)

single dipole T. Liu (SINAP)

T. Liu (SINAP)

Assume 30 nm seeding T. Liu (SINAP)

Summary Transverse Gradient Undulator appears to be a good fit for plasma accelerator based FELs with relatively large energy spread Two orders of magnitude power enhancement has been obtained in EUV and soft x-ray simulations. Transporting beams from plasma accelerators to undulators with desired optics properties is a challenge. Various techniques are developed to address it.