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, FLS2012
Up to 4 GeV now
C. Schroeder, FLS2012
M. Hogan, FEL2015
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
Sort e-beam energy by dispersion h so that
y
g+
g-
x
Resonance can be satisfied for all energies if
T. Smith et al., J. App. Phys. 50, 4580 (1979)
Effects of Energy Spread
off-energy
off-energyparticle
particle in TGU
 For efficient FEL interaction, the resonant wavelength spread
caused by the energy spread over a gain length << 1
u


<<
 4r
g
2r
2 LG
g
 sd << r~10-3 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)/g(x)
Effects of energy spread on gain length
Gain length ratio =
Normal undulator
normal undulator
TGU
TGU improve gain when
TGU: trade energy spread with horizontal beam size
effective FEL paramater
Emittance
matters here!
Z. Huang, Y. Ding, C. Schroeder, PRL109, 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, u = 2 cm, g >7mm  a = 50 m-1
Superconducting TGU
a = 330 m-1
Compact soft x-ray FELs
1GeV, 10kA, 1% energy spread;
0.1um emittance; 5 fs (50 pC)
5-m SC undulator u = 1 cm, K = 2;
Transverse gradient a = 150 m-1
Radiation wavelength r = 3.9 nm
For TGU, dispersion h = 0.01 m, trans. beam size 100um x 15um
Z. Huang, Y. Ding, C. Schroeder, PRL109, 204801 (2012)
3D effects and analysis
h = 0.01 m
No TGU SASE
TGU SASE
degree of transverse coh.
P. Baxevanis et al., PRSTAB 17, 020701 (2014)
P. Baxevanis et al., PRSTAB 18, 010701 (2015)
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 GeV
Energy spread: ~1%
Beam charge : up to 82.5 pC
Divergence: 0.4-1.0 mrad
dN/dE(pC/MeV)
0.2
0.15
0.1
0.05
0
350
400
450
500
Energy(MeV)
Peak energy
398 MeV
Energy spread (rms)
0.8%
Divergence (rms)
0 .8 mrad
Beam charge
82.5 pC
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 MeV, 6 m TGU)
SIOM LPA setup (J.-S. Liu)
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.