High Harmonic Generation off a Tape Drive
as seed for the LPA-based FEL
Physics and Applications of High Brightness Beams:
Towards a Fifth Generation Light Source
Monday 2013-03-25
Jeroen van Tilborg
LOASIS program, LBNL
Acknowledgements
HHG experiments: Brian Shaw, Thomas Sokollik, Jeroen van Tilborg, and Wim Leemans
FEL concept & simulations: Carl Schroeder
Other LOASIS contributors: Sergey Rykovanov, Anthony Gonsalves, Kei Nakamura, Sven
Steiniger, Nicholas Matlis, Eric Esarey, Csaba Tóth, Carlo Benedetti, and Cameron Geddes
Collaborators
CEA Saclay:
LBNL, ALS:
LBNL, Metrology:
LDRD
Sylvain Monchocé, Fabien Quéré, Arnaud Malvache, and Philip Martin
Eric Gullikson
Valeriy Yashchuk, Wayne McKinney, and Nikolay Artemiev
Outline
 Efforts at LOASIS/Bella
 Introduction to Coherent Wake Emission
 Experimental setup and data
 Influence of tape and laser parameters
 FEL calculations
 Comparison CWE details to model
Each LOASIS/Bella system addresses
unique challenges
Godzilla Matlis, 10:50am
TREX
Bella
High-quality LPA e-beams: compact coherent light source
[energy, stability1, emittance2, (slice) spread3, charge]
1. Jet+Cap, Gonsalves et al. Nat. Phys 7 (2011)
2. Betatron X-rays: Plateau et al. PRL 109 (2012)
3. COTR: Lin et al. PRL 108 (2012)
Plateau et al. PRL 109 (2012)
Gonsalves et al. Nat. Phys 7 (2011)
Measured at LOASIS
Seeding the FEL has benefits
Goal: 53-nm LPA-driven seeded FEL
Schroeder et al., Proc. FEL (2006)
Schroeder et al., Proc. FEL (2008)
High-power lasers: trade-off
scale-length and HHG divergence
200 mJ Laser
gas-based HHG
Large spot (small HHG divergence)
ROM HHG
Small spot (large HHG divergence)
Coherent Wake Emission
 I~1x1017 W/cm2
 <2 meter delivery optics
 Target destruction: tape!
 Combiner, no transport
 Easy spatial overlap
 Quasi-linear regime
Step 1 & 2: Electrons are pulled out of
plasma into vacuum, and back into target
Step 1
 Laser 45o on high-n target
 Ionization
 Brunel electrons into vacuum
Step 2
 Restoring force turns electrons
around into target
 “Ejection phase” determines
return time and return velocity
 E-beam chirp leads to bunching
Heissler et al. Appl. Phys. B 101 (2010)
Hörlein, thesis MPQ (2008)
Step 3: Electron beamlets drive wake and
emit radiation at density step
electron beam
Plasma
ωp
 At density step, e-beam creates plasma wave
 Light emitted at plasma frequency
 Gradient density emits broad spectrum
 Maximum frequency given by maximum density
 Every cycle  Even and odd harmonics
 Atto-chirp present (high frequencies late)
Experimental Setup
 Focal length=2m, θ=35 mrad (FWHM)
 P-polarization after 3” waveplate
 Change energy, zfocus, compression
 Mylar, VHS, Kapton tape. Glass plate
 Silicon Brewster plate (X~100)
 100-nm-period transmission grating
 Double-stacked MCP
Borot et al. Opt. Lett.
36 (2011)
Orders up the 18th observed,
at divergences of 4-15 mrad
Shaw et al., submitted
Al foil
Table from Queré
(CEA Saclay)
Dependence spectrum on intensity
VHS tape (“front”, iron oxide side)
 15th and 16th only at higher intensities
 15th harmonic, x225 over-critical
 Lower intensity  density not high enough
70 mJ
150 mJ
300 mJ
15th
150 mJ
70 mJ
15th
15th
Divergence depends on tape material
Same laser conditions
different targets
different divergences
Glass
Kapton
VHS & Mylar
3.9 mrad (rms)
7.4 mrad (rms)
~13 mrad (rms)
Roughness plays role?
Roughness more complex than just “sigma”
Harvey et al. Opt. Eng. 51 (2012)
1/w0
Metrolog
y
1/λ
ALS reflectometry
k
Gold
627x470 μm 20 μm
Kapton
627x470 μm
20 μm
Power Spectral Density ~ FFT[ height distribution ]
Metrology reveals differences in roughness
(correlated to divergence)
Glass
Kapton
VHS & Mylar
3.9 mrad (rms)
7.4 mrad (rms)
~13 mrad (rms)
Quasi-linear CWE provides stability
VHS-front (iron-oxide
on Mylar)
 Pointing
fluctuation
0.2 mrad
 Divergence
fluctuation
2 mrad
 Fluctuations
total counts
~5%
30 mrad
Concave reflective grating 
order-specific divergence
VHS-front (iron-oxide on Mylar)
Integrated over entire spectrum
33 mrad (FWHM)
15
14th
th
13th
17 mrad (FWHM)
15 mrad (FWHM)
11.5 mrad (FWHM)
Absolute flux calibration:
megaWatts seed in 15th order
ALS CXRO beamline 6.3.2
(http://cxro.lbl.gov/reflectometer)
Flux
 Circa 20% in 15th order
 67 photons/count, 5x109
photons, 20 nJ
 Lose 40% Al foil,
35% Brewster plate
 50 nJ in 20 fs, is ~2.5 MW
 Laser energy on target ~ 70 mJ
 CE for 15th is 7x10-7
 Up to 250 mJ available
 Working on improvement
Borot et al. Opt. Lett. 36 (2011)
CWE
Easter et al. Opt. Lett. 35 (2010)
Seed:
15th harmonic
60 nJ in 20 fs
Focus 1 cm upstream
Divergence 5.7 mrad (rms)
Undulator & e-beam:
4.4 kA peak current
25 micron transverse size
Undulator period 2.18 cm
K=1.25
Wavelength 53 nm (15th)
Pierce parameter 0.012
Seed strength as
Measured seed parameters & FEL model
predict FEL gain
100 nJ
 ~  / w 0
 Z [m]
Model:
Mono-energetic e-beam
1d FEL radiation
Not included: slippage, wavefront curvature
Shaw et al., submitted
Phase electron
Energy electron
FEL radiation
Further seed source improvement
possible? Spectral details give insight
70 mJ
150 mJ
300 mJ
15th
150 mJ
70 mJ
15th
15th
Concentrate on 12th harmonic: higher
intensity broadening & blue-shifting
70 mJ
150 mJ
Focal scans
70 mJ
Always a red-shifted spectrum
Higher intensity  Broadening
Higher intensity  Less red-shifting
150 mJ
Energy scan
300 mJ
driver 800nm
order 820nm/q
Use of a model to predict attochirp:
dependent on intensity and density gradient
x 
t   
a0 
Density n(x)
1/ 3
Longer gradient  longer delay
Higher a  faster e’s  shorter delay
Leading edge: next cycle emits
faster then previous one  blue-shifting
Malvache et al., PRE 87 (2013)
Harmonic q
nc,ωq
Fundamental
nc,ωL
xω
x=0
x
Energy and Focal scans:
Model incomplete to match data
No red-shifting
Higher intensity
-Narrowing
-No shifts
Focal
scan
Energy
scan
van Tilborg et al., in preparation (LBNL)
70 mJ
150 mJ
Energy scan
300 mJ
Model
-No averaging over
spot-size
-No propagation to
diagnostic
150 mJ
Red-shifting
Higher intensity
-Broadening
-Less redshifting
Focal
scan
Expand the model: include
expanding plasma gradient
Increasing gradient length δ (distance ncr to ncr,q)
Density n(x)
 (t)   0  Cst
Warm plasma

Plasma expansion
 Saclay*: Pump 1e15 W/cm2  Cs=20 nm/ps
 We: Pump 3e17 W/cm2  Cs~100-1000 nm/ps
nmax
nq
Harmonic q
nc,ωq
Heissler et al., Appl. Phys. B 101 (2010)
Brunel orbits
Fundamental
nc,ωL
xω
x=0
x
Energy and Focal scans:
better agreement expanded model
Red-shifting
Energy
scan
Higher intensity
-Broadening
-Less redshifting
Red-shifting
70 mJ
150 mJ
Energy scan
300 mJ
Higher intensity
-Broadening
-Less redshifting
Focal
scan
150 mJ
Focal
scan
Conclusion
 Research towards compact (seeded) LPA-based FEL
 HHG from spooling tape
 Harmonics up to the 17th, 5-15 mrad divergence
 Tape roughness at micron-level is relevant
 MW-powers from VHS and Kapton
 FEL model predicts seed-induced bunching
 CWE model suggests plasma expansion relevant
 New round of CWE experiments planned
ALS data reveals <13 nm on most samples
(weak correlation divergence)
1/w0
1/λ
ALS reflectometry
k
Glass
Kapton
VHS & Mylar
3.9 mrad (rms)
7.4 mrad (rms)
~13 mrad (rms)
Laser chirp can compensate for
CWE femtochirp
ξ=0
ξ=1 (red
front)
Borot et al. Opt. Lett. 36 (2011)
  0 1 2
Blue-shifting
Red-shifting
ξ=-1 (blue
front)
Stable shot to shot performance
Experiment
Experiment
Scan
parameter
Model
Comparison Experiment to Model
 Insight in CWE physics
 Use insight for optimization
Scan
parameter
Questions
-Sergey, what drives the electrons back into the target. The laser, or the restoring
force of the plasma? If a density gradient exists, which electrons get pulled out?
Where is the field supposed to be zero? Where does density gradient come from?
Surface roughness? Plasma expansion into vacuum?
-Thomas Strehl Ratio
e-beam
Tape Drive
HHG drive laser
Bottom line: deliver seed strength 10-6-105 to undulator
Model:
1d-description FEL radiation
No wavefront effects
No slippage
Seed strength as
Seed:
60 nJ in 20 fs
100 nJ
2 nJ
2 mrad
Z [m]
Phase electron
Energy electron
FEL radiation
Notes on Sequoia Scan
Divergence 4-15
mrad (rms)
Notes on Compressor Data
  0 1 2
-In-vacuum optimum compression is at comp4=-0.1mm.
-Positive Comp4  Negative xi  Blue front, red back 
Makes femtochirp worse  Broad harmonics
-Scan 33 on 2012-07-09 (CWE day 2). Transmission
through Kapton (on fiber Hamamatsu).
-Reflectometry on 2012-10-04 scan (VHS-front) Chromax
-Also confirmed by 2012-06-28 (CWE day 1), compressor
scan

Sequoia data and Grenouille data where taken and
compared on 2012-09-05. By including temporal
resolution, nice fitting for both diagnostics is
retrieved
Scan33, 2012-07-09
Notes on spot size
-In-vacuum smallest spot is at z=+2 mm
-Positive z  focus downstream (more harmonics if
focused at z=2mm, but smaller divergence at z=>3mm,
see Day 2, scan 20)
-Guppy scan on 2012-06-26 (scan 16) gives a FWHM at
focus of 23 micron.
-Guppy Strehl ratio experiments on 2012-07-18 give a
FWHM of 23 micron (w0=19.5 micron), and a Strehl ratio
of 0.73.
-Use file “NotesSpotAveragedIntensity”. Based on 73%,
we calculate a 100 mJ, 47.7 fs (I-FWHM), we find an
Ipeak of 2.04e17 Wcm2.
-We fitted the max-counts versus z to calculated intensity
at other z’s.
ActualEnergy
47.7 fs
1
I peak  2.04 1017 
x
x
(z  2 103 ) 2 2
100m J
ActualPulseDuration
1
2Ppeak
2Energy
2
6 4
I peak 


19.5
10


r02
(  /2)r02
2012096026, scan 16
 
Roughness more complex than just “sigma”
FFT[h(x)
h(x)
FFT[
] ]
Same Sigma, Different regime
Critical is the spatial frequencies
λ
1/λ
CXRO
grazing
reflectometry
k [nm-1]
Assumption
Nevot-Croce
“single σ“
λ
1/λ
k [nm-1]
Conclusion
Gradient length δ
 (t)   0  Cst
Cs 
kTi
Mi
Function 1
Vdelta=1e-5
Time shift = 1e-5 ps per cycle, or 3nm per cycle, or 1100 nm/ps
Intro to Laser Plasma Accelerators (LPA’s)
laser
Godzilla
e- beam
TREX
LPA: Self injection + acceleration
Bella
High-power lasers: trade-off
scale-length and HHG divergence
General concept: More laser  More harmonics
Example, 200 mJ of laser, 50 fs
 Gas-based harmonics
Requirement: I~5x1014 W/cm2
Yields spotsize w0=0.7 mm, zR=1.9 m
At z=5 m:
w0=1.9 mm, Fluence=1900 mJ/cm2
At z=10 m: w0=3.7 mm, Fluence= 470 mJ/cm2
 ROM harmonics
Requirement: I~1x1019 W/cm2
Yields spotsize w0=5 μm, zR=100 μm, θ=50 mrad
Typically: Divergence harmonics ~ divergence laser
Coherent Wakefield Emission
 Intensities around I~1x1017 W/cm2
 <20-mrad laser divergence
 <2 meter delivery optics
 CHALLENGE: Target destroyed every shot!
Intensity regimes for
Laser-produced Harmonics
Gas-based HHG
 Intensity ~ Ionization
potential
 Laser on underdense
plasma
 Phase matching
(along z) important
Reflection off “relativistic mirror”
 Laser on overdense plasma
 a0>>1: longitudinal quiver
motion
Coherent Wakefield
Emission
 Laser on overdense
plasma
 Quasi-linear motion
of surface electrons
Laser chirp can compensate for
CWE femtochirp
Blue-shifting
Red-shifting
  0 1 2
ξ=1 (red front

Borot et al. Opt. Lett. 36 (2011)
ξ=-1 (blue front)
Coherent Wakefield Excitation: 3-step
model for laser-plasma interaction
Heissler et al. Appl. Phys. B 101 (2010)
1. Laser (p-polarized)
drives surface electrons
out-of-target
2. Laser & plasma restoring
force drive electrons
back.
3. E-bunches travel through
density gradient, emit
radiation at the plasma
frequency
Seed
 50 nJ in the 15th
 7 mrad (rms) divergence
 Source 1 cm from undulator
 20 fs (FWHM duration)
Electron beam
 307 MeV, λu=53 nm (15th)
 25 pC (5 fs flat-top from LPA)
 Transverse size ~20 micron
 Ideal 0.5% dE/E, upto 4% dE/E
 Include beam decompression
Undulator
 Six 22-period sections (now three)
 K=1.25
Comments
 Optimize simulations
Tapered undulator help
 Have energy up to 200 mJ
available
 Seen 5-mrad (rms)
divergence on VHS (Int)
 Kapton, integrated ~50%
of VHS (Int)
 Optimization underway
x10 decompression
seeded FEL
Energy
FEL simulation based on CWE source
Decompression
Time
no decompression
seeded FEL
Repeats every laser cycle:
odd and even harmonics
In a density ramp:
 Consider all n’s, each at specific location x
 Emission of continuous spectrum
 Low frequencies emitted first  Attochirp
 Happens every cycle: Even & odd harmonics
Hörlein, thesis MPQ (2008)
tL=2.67 fs