1. 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

2. C. Schroeder, FLS2012 Up to 4 GeV now

3. C. Schroeder, FLS2012

4. M. Hogan, FEL2015 Projected energy spread is still on the order of % ?

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

6. off-energy particle  For efficient FEL interaction, the resonant wavelength spread caused by the energy spread over a gain length << 1     -3 for short-wavelength FELs  This is a local energy spread requirement not projected (for LPAs, bunch length ~ slippage length (SXR), local E spread ~ projected E spread)  TGU compensates this effect with K(x)/  (x) off-energy particle in TGU Effects of Energy Spread

7. Effects of energy spread on gain length Gain length ratio = TGU: trade energy spread with horizontal beam size effective FEL paramater Emittance matters here! normal undulator TGU TGU improve gain when Normal undulator Z. Huang, Y. Ding, C. Schroeder, PRL109, 204801 (2012)

8. Transverse gradient undulator in reality Hybrid undulator, use Halbach formula e.g.,  7.5 deg, u = 2 cm, g >7mm   = 50 m -1 SINAP 1.5-m TGU (Courtesy D. Wang)

9. Superconducting TGU  = 330 m -1

10. 1GeV, 10kA, 1% energy spread; 0.1um emittance; 5 fs (50 pC) 5-m SC undulator u = 1 cm, K = 2; Transverse gradient  = 150 m -1 Radiation wavelength r = 3.9 nm For TGU, dispersion  = 0.01 m, trans. beam size 100um x 15um Compact soft x-ray FELs Z. Huang, Y. Ding, C. Schroeder, PRL109, 204801 (2012)

11. 3D effects and analysis No TGU SASE TGU SASE P. Baxevanis et al., PRSTAB 17, 020701 (2014) P. Baxevanis et al., PRSTAB 18, 010701 (2015)  = 0.01 m degree of transverse coh.

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

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

14. High-quality high-energy electron beams from a cascaded LPA Peak energy: 0.4-0.6 GeV Energy spread: ~1% Beam charge : up to 82.5 pC Divergence: 0.4-1.0 mrad Peak energy: 0.4-0.6 GeV Energy spread: ~1% Beam charge : up to 82.5 pC Divergence: 0.4-1.0 mrad Peak energy398 MeV Energy spread (rms)0.8% Divergence (rms)0.8 mrad Beam charge82.5 pC J.S. Liu et al., Phys. Rev. Lett. 107, 035001 (2011). Courtesy J.S. Liu (Shanghai Institute of Optics and Fine Mechanics)

15. LPA FEL with TGU (SIOM/SINAP) Beam transport LPA chamber TGU Focusing optics Plan a demonstration experiment at 30 nm (400 MeV, 6 m TGU) SIOM LPA setup (J.-S. Liu)SINAP TGU assembly (D. Wang)

16. T. Liu (SINAP) single dipole

17. T. Liu (SINAP)

18. Assume 30 nm seeding

19. 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.