1. Laser-Plasma Accelerators as Sources of Electron Beams at 1 MeV to 1 GeV
Eric Esarey
W. Leemans, C. Geddes, C. Schroeder, S. Toth,
Gonsalzas, J. van Tilborg, K. Nakamura, M. Chen and others
LOASIS Program
Lawrence Berkeley National Laboratory
FLS Workshop, March 1 -5, 2010

2. Laser-plasma accelerators: Outline
Self-modulated LWFAs: Status Prior to 2004
LWFAs: High quality e-beam production at 100 MeV-level (2004)
LWFAs: High quality e-beam production at 1 GeV-level (2006)
Downramp injection at 1 MeV-level (2008)
Integrated gas jet+capillary structure (2009)
Colliding pulse injection at 100 MeV-level (2006, 2009)
Ionization injection at 100 MeV-level (2008, 2010)

3. Laser Wakefield Accelerator (LWFA)
Standard regime (LWFA): pulse duration matches plasma period
B.A. Shadwick et al., IEEE PS. 2002
Ultrahigh axial electric fields
Ez > 10 GV/m, fast waves
Ultrashort plasma wavelength
lp ~ 30 mm (100 fs)
Plasma channel: Guides laser pulse
and supports plasma wave
Tajima, Dawson (79); Gorbunov, Kirsanov (87); Sprangle, Esarey et al. (88)

4. Basic design of a laser-plasma accelerator: single-stage limited by laser energy
Laser pulse length determined by plasma density
kp sz ≤ 1, sz ~ lp ~ n-1/2
Wakefield regime determined by laser intensity
Linear (a0<1) or blowout (a0>1)
Determines bunch parameters via beam loading
Ex: a0 = 1 for I0 = 2x1018 W/cm2 and 0 = 0.8 m
Accelerating field determined by density and laser intensity
Ez ~ (a02/4)(1+a02/2)-1/2 n1/2 ~ 10 GV/m
Energy gain determined by laser energy via depletion*
Laser: Present CPA technology 10’s J/pulse
laser
Ez wake
*Shadwick, Schroeder, Esarey, Phys. Plasmas (2009)

5. State-of-the-Art Prior to 2004:
Self-Modulated Laser Wakefield Accelerator (SM-LWFA)
Self-modulated regime:
Laser pulse duration > plasma period
Laser power > critical power for self-guiding
High-phase velocity plasma waves by
• Raman forward scattering
• Self-modulation instability
0.75
0.50
laser pulse
0.25
0.00
-0.25
Plasma density wave
-0.50
Sprangle et al. (92); Antonsen, Mora (92); Andreev et al. (92); Esarey et al. (94); Mori et al. (94)
-0.75
-40
-20 20 40
SM-LWFA experiments routinely produce electrons with:
1-100 MeV (100% energy spread), multi-nC, ~100 fs, ~10 mrad divergence
Modena et al. (95); Nakajima et al. (95); Umstadter et al. (96); Ting et al. (97); Gahn et al. (99); Leemans et al. (01); Malka et al. (01)
Red: 1000 psi He
Blue: 500 psi He
Laser beam
Energy Distribution
Mirror
CCD
e- beam
Few TW
Gas jet
nC’s
Parabolic
mirror
1020 cm-3
Detection Threshold
Leemans et al. (02)

6. Breakthrough Results: High Quality Bunches
30 Sep 2004 issue of nature:
Three groups report production of high quality e-bunches
Approach 1: Plasma channel
LBNL/USA: Geddes et al.
Plasma Channel: 1-4x1019 cm-3
Laser: 8-9 TW, 8.5 m, 55 fs
E-bunch: 2109 (0.3 nC), 86 MeV, E/E=1-2%, 3 mrad
Approach 2: No channel, larger spot size
RAL/IC/UK: Mangles et al.
No Channel: 21019 cm-3
Laser: 12 TW, 40 fs, 0.5 J, 2.51018 W/cm2, 25 m
E-bunch: 1.4108 (22 pC), 70 MeV, E/E=3%, 87 mrad
LOA/France: Faure et al.
No Channel: 0.5-2x1019 cm-3
Laser: 30 TW, 30 fs, 1 J, 18 m
E-bunch: 3109 (0.5 nC), 170 MeV, E/E=24%,10 mrad
Channel allows higher e-energy with lower laser power

7. GeV: channeling over cm-scale
Increasing beam energy requires increased dephasing length and power:
Scalings indicate cm-scale channel at ~ 1018 cm-3 and ~50 TW laser for GeV
Laser heated plasma channel formation is inefficient at low density
Use capillary plasma channels for cm-scale, low density plasma channels
Capillary
Plasma channel technology: Capillary
1 GeV
e- beam
Laser:
TW, 40 fs 10 Hz
3 cm

8. 1 Tesla magnetic spectrometer Optical diagnostics (not shown)
GeV Beams in 3cm
40TW laser
Capillary discharge
1 Tesla magnetic spectrometer
Optical diagnostics (not shown)
3cm
This technology allowed us to extend the acceleration length and produce GeV beams in a LPA for the first time. This was achieved in an acc of just 3cm in length by
focusing 40TW laser pulses onto the entrance of the waveguide. The acc e- bunch was then dispersed using a 1Tesla magnet onto lanex screens imaged by ccd cams. Here is an image from the Lanex screen, with angle on vert, and energy on hor. We can see we prod a GeV beam with less than 2mrad divergence and energy spread of 2.5%, although this measurement may have been resolution limited.
Here is a photo of one of our accelerators, the bright line in the middle showing the plasma channel.
Divergence(rms): 1.6 mrad
Energy spread (rms): 2.5%
Resolution: 2.4%
Leemans et al., Nature Physics 2006

9. Geddes et al., Nature (2004) & Phys. Plasmas (2005)
Wake Evolution and Dephasing Yield Low Energy Spread Beams in PIC Simulations
WAKE FORMING
200
Longitudinal
Momentum
Propagation Distance
INJECTION
200
Longitudinal
Momentum
Propagation Distance
200
DEPHASING
DEPHASING
Longitudinal
Momentum
Propagation Distance
Geddes et al., Nature (2004) & Phys. Plasmas (2005)

10. LWFA: Production of a Monoenergetic Beam
Excitation of wake (e.g., self-modulation of laser)
Onset of self-trapping (e.g., wavebreaking)
Termination of trapping (e.g., beam loading)
Acceleration
If > dephasing length: large energy spread
If ≈ dephasing length: monoenergetic gv
Momentum
Dephasing distance:
z-vgt
Phase 1
2-3 4
Trapping
Acceleration: Laccel ~Ldephase
Wake Excitation

11. GeV Beams Repeatable but not Stable – Available Controls not Sufficient
GeV repeatable but not stable shot to shot. We have observed regions of stability as I’ll show in a moment, but as we vary the laser and plasma parameters such as…. to optimize beam performance. We see that optimizing injection does not optimize guiding, and the two need to be separated.
Laser energy, pulse width, plasma density, discharge delay, plasma channel density, depth, and length, degree of ionization
Accelerator performance
But optimizing injection does not optimize guiding (accelerating structure)
Need to separate injection and acceleration

12. Reducing energy spread and emittance requires controlled injection
Self-injection experiments have been in bubble regime:
Cannot tune injection and acceleration separately
Emittance degraded due to off-axis injection and high transverse fields.
Energy spread degraded due to lack of control over trapping
Y[µm]
X[µm] 5 -5
800
2000
Transverse motion
However, as you heard from Wim and will hear in more detail from Carl and Eric, both the energy spread and emittance need to be improved for applications such as an x-ray FEL. All our experiments thus far have been relying on injection and acceleration in a single stage, so the two cannot be tuned independently. In this bubble regime, there are high transverse fields, and injection is off-axis, leading to increased transverse momentum and emittance. Furthermore, the lack of control over the injection process limits the energy spread that can be achieved. To improve beam quality further we propose an injector based on controlled trapping at lower wake amplitude and then a separately tunable acceleration stage.
⇒ Use injector based on controlled trapping at lower wake amplitude and separately tunable acceleration stage to reduce emittance and energy spread

13. Basic physics of downramp injection
Bucket length ~ 1/√n
Phase velocity drop enables trapping ne
x1018 5 1
Laser
z [mm]
-0.5
0.5
1.0
30.0

14. Laser transmission 70% and mode still good for driving wakefield
Down-ramp Injector Demonstrated: Simulations Show Injector Coupled to Low Density Accelerator Produces Low Energy Spread Beams
MeV beam produced with
Low divergence (20 mrad)
Good stability
Central energy (760keV/c ± 20keV/c rms)
Momentum spread (170 keV/c ± 20keV/c rms)
Beam pointing (1.5 mrad rms)
Laser transmission 70% and mode still good for driving wakefield
Laser focused on down-ramp of gas jet density profile
Laser
10TW
Cameron Geddes has developed an injector with good stability and low absolute energy spread by focusing 10TW laser pulses on the downramp of a gas jet. Focusing on the downramp has the added advantage of reducing self-modulation of the laser pulse, meaning the laser still has the energy and mode quality for producing a large amplitude wakefield. This cartoon on the left shows what this allows for. Both the e beam and laser can propagate to a lower density accelerating structure, where the laser pulse continues to drive a plasma wave and accelerate the e- bunch. These simulations on the right, produced using Vorpal show that the low absolute energy spread of the bunch can be preserved, so as we increase the energy, the relative energy spread decreases.
Momentum spread 200keV/c
Energy 1.5MeV
delta Px ~ 0.2 MeV
Py ~ 50 keV
10 TW laser pulse
plasma density profile in ramp gaussian with peak ne =1.8e19, – ~900um FWHM density, laser focused downstream of center, in expt. range for MeV beams
Consistent with experimental stability, the simulation parameters
were scanned and MeV-class beams were observed
for plasma lengths 0.5–1 mm, densities
1:8–2: cm 3, and laser powers 8–10 TW.
Exeriment
The peak power was 10 TW (0.5 J in
47 fs FWHM), focused to a 7:5 m FWHM spot. The
plasma density profile along the laser propagation direction,
measured by an interferometer [21], was approximately
Gaussian with a peak density of 2:2 0: cm 3 and a FWHM of 750 m m.
2D sim 545b shows trap, acel: Py = 160 keV/c FWHM , DPx = 200keV /c at energy = 20MeV
large transverse domain to resolve focus through jet
plasma density profile in ramp gaussian – ~900um FWHM density, laser focused downstream of center, in expt. range for MeV beams
merges into channel at:
channel density 3.5e17, radial profile ~ matched to guide 8um spot
propagates 2mm to gain 20 MeV
coming soon:
3D simulation with Envelope model (Ben Cowan, )
high order particle/force weighting for improved momentum spread accuracy
Just for your background:
There is little growth in delta_pX
delta py does grow but is still very low - grows about 3-fold ; combination of numerics (particle push error), and channel tuning
2D simulation done in VORPAL* of injector + accelerator up to 3mm
Injector peak density 2x1019 cm-3, FWHM 900μm
Accelerator density 3x1017 cm-3
Narrow energy spread of beam at output of injector preserved during acceleration in lower density region e-
Jet
Inject low ∆E: ∆E conserved during acceleration so as E , ∆E/E 
Energy Spectrum at
Ramp Exit
#/Pz (MeV/c)
P 1.5MeV/c
∆P 200keV/c
3mm
Pz (MeV/c)
P 20MeV/c
Accelerator:
cm; n~ cm-3 n z
Plasma ramp injector:
1mm; 1019 cm-3
laser
Geddes et al., PRL V 100, (2008)
*Nieter et al., JCP 2004

15. Density profile in jet region
Gas Jet Nozzle Machined Into Capillary Can Provide Local Density Perturbation
laser
1mm
Laser-machined gas jet
laser
e- beam
Axis of the capillary
0.2mm
Measured surface profile
Density profile in jet region
Now I’ll talk about our initial expts on separating inj and acc by laser machining a gas jet nozzle into the waveguide. Images of the nozzle machined by one of our grad students are shown on the left, and the image on the right shows the density profile in the jet region. The jet here is vertical and the cap hor. The color map shows the density with red being highest and blue lowest. We can see that a local rise in density can be produced within the waveguide.
Capillary size 200 micron. Gas jet inlet tube 1mm diameter (cant be right). Outlet 1.8mm diameter. Jet throat diameter 0.32mm throat length 0.35mm. Approx mach1. Linearish ramp over 200um up to high10^19 then 100um flat and then symmetric down-ramp.

16. Jet Improves Beam Stability
laser
Jet Improves Beam Stability
Stability with jet
Input Parameters: Pjet≈145psi,
Ne ≈ 2x1018 cm-3,a0≈1 (25TW),
Laser pulse length≈ 45 fs
The initial results from this design show a significant increase in beam stability compared with previous experiments that did not employ a jet. The two plots on the right show an averaged electron spectrum in black for about 30 sequential shots. The rms fluctuation is shown by the grey shaded area. The jet has significantly stabilized the electron spectrum with the central energy fluctuation improving from 20% to 2%. As well as the spectrum, the pointing improved by factor 2 to less than mrad and the charge fluc has improved from nearly 80% to 25%. Furthermore, the charge is corr with shot to shot laser energy with 5% change in laser energy leading to a factor of 2 difference in charge, so by improving laser stability we can improve beam stability even further.
150psi data 21st july sub 13 subsequent shots
Pointing ± 0.8 mrad
Divergence 1mrad
Energy 300MeV ± 7MeV
ΔE/E 6% ± 0.7%
Q 7.3pC ± 1.7pC
Best stability
without jet
Input Parameters: no jet in cap,
Ne ≈ 2x1018 cm-3,a0≈1 (25TW),
Laser pulse length≈ 45 fs
Pointing ± 1.8 mrad
Divergence 1mrad
Energy 440MeV ± 95MeV
ΔE/E 4% ± 2%
Q 2.6pC ± 2.0pC
NB: Both data sets show subsequent shots

17. Colliding pulse allows control of injection
Add two counter-propagating laser pulses
Collision produces laser beat wave with slow phase velocity
3-pulse colliding pulse [Esarey et al. PRL (1997), Schroeder et al., PRE (1999)]
1. control of injection position: delay between pump and trailing pulses
2. control injected charge: laser intensities and pulse durations
3. control beat phase velocity: different laser frequencies
2-pulse version: Pump + backward [Fubiani et al., PRE (2004)]
Phase Space
3-pulse Colliding Pulse Injection
2.0
Trapped + Focused Wake Orbit
1.5
1.0
Beat Wave Separatrices
Momentum spread 170 keV/c
Central momentum ±20 keV/c
Pointing ± 2mrad
Divergence implies p ~ 20 keV/c
0.5
Untrapped Wake Orbit
-0.5
-1.0
-1.5
kpz -2 -1 1 2 3

18. Controlled injection via colliding laser pulses improves beam quality
Theory:
Experiment:
trapped orbits 
Esarey et al. PRL (1997); Schroeder et al. PRE (1999); Fubiani et al. PRE (2004);
Leemans et al. AAC (2002); (2004);
Faure et al. Nature (2006);
Rechatin et al. PRL (2009);
Kotaki et al. PRL (2009)
untrapped orbits  e-
laser
laser
kp (z-ct)
laser
a=0.35
a=1.2
Gas jet: 7x1018 cm-3
Pump laser (drives wake)
Colliding laser pulse
3 mm
Rechatin et al. Phys. Rev. Lett. (2009)
LOA (France): Faure et al., Nature (2006)
Experimental demonstration (2-pulse):
1% FWHM energy spread

19. Colliding pulse experiments at LBNL
Colliding pulse experimental setup online
Experimental plan:
Step1: demonstrate reliable injector
Step 2: accelerator/laser control for high energy
Step 3: tune for high quality beam
12 TW system

20. Colliding pulses produce stable, reproducible beam
Scan timing of collider
Charge measured on phosphor screen, ICT
Timing window as expected from simulation
~20% rms charge stability
QICT ~ O[40pC]
Charge vs. collision timing
Phosphor
Simulation
at a=0.5
3351 &3587
e-beam image
Geddes et al., ongoing

21. Ionization-induced trapping using high-Z gas (nitrogen)
Ionization-induced trapping using integrated gas jet + capillary (LBNL)
Theory:
Umstadter et al. PRL (1996); M. Chen et al. JAP (2006); Schroeder et al. (in progress)
laser n H2 z
trapped e- orbit
Injection region, <mm, n~1018 cm-3 (mixture of H2 + high Z gas)
Trapped charge determined by length of injection region (<< dephasing length) and probability of ionization

22. Ionization injection experiments
Oz et al. PRL (2007);
Rowlands-Rees et al. PRL (2008);
Pak et al. PRL (2010)
A. Pak, K.A. Marsh, et al., PRL (2010)
2-mm gas jet: He/Nitrogen (10%)

23. Ionization injection: improve beam quality with gas jet+capillary
M. Chen, C. Schroeder et al. (in progress)
PIC simuation: a=2.0, wr=15.0, f=75l, Gaussian pulse, L=0.4lp , ne=0.001,
laser n
H H80%, N20% H
x/l

24. 10 GeV laser-plasma accelerator with BELLA (40 J laser)
Plasma density scalings:
Energy gain:
low density plasmas (~1017 cm-3)
long plasma channels (~m)
Accelerator length:
Laser energy/power:
more laser energy (~10 J)
a0 =1.5
P/Pc = 1.1
UL=40 J
TL=130 fs
rL=63 micron
Plasma channel
1.11017 cm-3
10 GeV
X-ray FEL
79 cm
lp = 110 mm

25. Laser-plasma accelerators: Summary
Self-modulated LWFAs: Status Prior to 2004
100% energy spread, max energy > 100 MeV, nC’s of charge
LWFAs: High quality e-beam production at 100 MeV-level (2004)
Narrow energy spread, small divergence, 100 MeV, 100’s pC
LWFAs: High quality e-beam production at 1 GeV-level (2006)
Narrow energy spread (few %), small divergence (few mrad), 1 GeV, 10’s pC
Few-cm long plasma channel guiding (capillary discharge)
Downramp injection at 1 MeV-level (2008)
Good stability, narrow absolute momentum spread (170 keV/c), 100’s pC
Integrated gas jet+capillary structure (2009)
Improved stability, few % energy spread, 0.5 GeV, few pC (ongoing)
Colliding pulse injection at 100 MeV-level (2006, 2009)
Good stability, narrow energy spread (1%), 180 MeV, 10 pC
Ionization injection at 100 MeV-level (2008, 2010)