UNIVERSITY OF MARYLAND AT COLLEGE PARK
High-intensity optical slow-wave structure for direct laser electron
acceleration
H.M. Milchberg, B.D. Layer, A. York, J. Palastro, T, AntonsenUniversity of Maryland, College Park
HEDSA 2009
Conventional accelerators
high energy physics
27 km circumference
constraints: R > Rmin synchrotron radiation loss
Eaccel<106-7 V/m structure breakdown
LEP (CERN) (100 GeV)
SLAC (50 GeV)3 km
The SLAC structure is periodically modulated
50 GeV in 3.2 km
50 GeV/(1.7x107 V/m) ~ 2 miles
Solution: use ‘milder’ fields over longer distanceview from space
Ez
Etransverse
Btransverse
EM propagation& particle accel.
‘slow-wave’ structurewave phase velocity < c
internal breakdown (lightening!) and self-destructionif wave fields are greater than ~ 107 Volts/m
accelerator waveguide structure
relativistic electron beam
relativistic electron spectrometer
‘conventional’ laser-plasma wakefields: intense laser pulse enters gas jet and relativistic electron beam emerges
pulse speed is vg < c
150 m
Laser pond. force for >1018 W/cm2 pushes
electrons out of the way+-+- +-
E E E E E
Plasma oscillation: “wake-field”
~35 μm 1000
200
0 z (µm)-200
r (µ
m)
Radially modulated 100ps Nd:YAG laser
pulse
Axially modulated plasma waveguide
35 fs Ti:Sapphire laser pulse
(e)
(a)
50 fs transverse interferometer probe
13 µm
(e)
13µm
Axicon
(b)
(d)
300 µm
35µm
200µm
50µm
35 µm
50µm(c)
But can we imitate SLAC
using a plasma?
YES!
0radius (m)
104 barpressure
Plasma cross-sectionduring and immediately after pulse:
25
Principle of plasma waveguide: example of hydrodynamic shock generation
experimental electron densityprofiles after pulse:
blast waveexpansion“hollows”the Ne profile
nN r
Ne
cr
2 1 ( )
A hollow electron density profileacts as a focusing element
plasma index of refraction Ne(r) lower in middle results inindex n larger there focusing
k Lcoherence=Lcoherence
‘Slow wave’ structure quasi-phase matching
Particle acceleration EM wave generation
vparticle < vwave phase
Charged particle dephasing
Epump
z-vpumpt
Phase mismatch
vpump ≠ vgenerated
Ez
z-vphaset
vphase>c
electron
Slow wave picture
d
z
r
)exp(),,(),,( 0zikzuzE rr ),,(),,( zudzu rrwhere
Bloch-Floquet condition:
dmkm /20 Wave number of mth
axial harmonic
mth harmonic is ‘slow’ if cmmphase /,v
m
mm zikaudzu )exp(),(~),,( rr where dmkm /2
Electron acceleration: slow wave picture
L z
mm
m kkdziaudzedtEeU0
0 ))/('(exp~ vv
v/'dzdt dtzikatzkiuedtEeUm
mm vv ))exp(()(exp~0
Electron energy gain
0/0 vnkkFor the ‘matched’ case
LaeEU n0get
Accelerating region: low plasma density (high index)
Decelerating region: high plasma density (low index)
n1 > n2Mod period d=L1+L2
Ld1 Ld2
Example: density modulation
Quasi-phase matching picture
The driving wave speeds up and slows down in successive portions of the modulation so that the acceleration in the first part is not completely cancelled by deceleration in the second part.
Energy gain per period:
adeELELEeU dzdz 02211 )( where 1a
Outline
• reminder about clusters -heating and plasma formation with femtosecond pulses (PRLs <2005) -heating and plasma formation with long (many picosecond) pulses
• formation of axially modulated (corrugated) plasma fibres using long pulses - axially modulated heating pulse - tailored cluster flow
• direct laser acceleration
Clusters are essential!
Energetic electrons/ionsNeutrons
Cluster jet
X-rays: A. McPherson et al., PRL 72, 1810 (1994).EUV and x-rays: * E. Parra et al., PRE 62, R5931 (2000).Optical properties: Kim, Alexeev, Milchberg, PRLs 2003, 2005Fast electrons and ions: Y. L. Shao et al., PRL 77, 3343 (1996);
† V. Kumarappan et al., PRL 87, 085005 (2001).Nuclear fusion: T. Ditmire et al., Nature (London) 398, 489 (1999).
EUV spectrum*
X-ray signal*
X-rays
EUV
Clusters
few Å ~ 500 Å
~10-107 atoms—explode in < 1 ps
0 5 10 150
20
40
60 Electrons/photons
Ions
Sig
nal
Time (s)
TOF mass spectrum†
Laser pulse Scattering
>90% laser absorption
Why do 100ps pulses efficiently heat clusters?
•The far leading edge of the 100ps beam disassembles / ionizes the clusters, leaving a cool high Z plasma that the remainder of the pulse heats.
•Much more efficient than heating an unclustered gas (for same average Z in a plasma, up to 10x less pump energy required) -40-50% absorption
50 Å ~ 600 ÅSingle Ar cluster
Critical density layer
High Z, cool, under-dense
plasma
Sub-critical plasma
Super-critical plasmaa
H. Sheng et al, Phys. Rev. E 72, 036411 (2005)
•enhanced absorption, even for very long (100ps) pulses
• because absorption is local to a cluster, can ultimately form plasma channels with Ne ~ 1018 cm3 electron density* and lower
• efficiently makes plasma channels in anything that decently clusters
• Typically 10X more efficient than for equivalent vol. average pressures of unclustered gas
Cryogenic cluster jet
Controlled cryogenic cooling of the jet enhances clustering
2 cm
First modulation method- modulated Bessel beam and uniform cluster flow
Breakdown in Argon clustersBreakdown in atmosphere
100-300mj 100ps Nd:YAG pulse, axially modulated with diffractive optics, incident on
unmodulated cluster jet flows
Ex. ~2mm corrugation period
1.5cm
1.5 cm
Guiding in corrugated hydrogen plasma channels
• H2 jet cryogenically cooled to enhance clustering
• Electron densities of ~1.5*1018 cm-3 on axis and ~3*1018 cm-3 at channel wall for a delay of 1ns
15µm
1017 W/cm2
(b) (i) (ii) (iii)
700 µm
500 µm
200 mJ 300 mJ 500 mJ+ misalign.
Waveguide generation pulse energyand alignment controls modulation features
Extended high intensity guiding
1 mm
700µm
beads continuousNo injection No injection
injection injection
Pump scattering
Abel inversion Abel inversion
Pump scattering
2
4
6
8
1018cm-3
3 mm
660µm
Extended high intensity guiding
without injection
injection, 2x1017 W/cm2 at exit
laser
Propagation simulation using the code WAKE*
Energy flux
z
(b)
0.2
1.010
18 W
/cm
2
* P. Mora and T. M. Antonsen Jr., Phys. Plasmas 4, 217 (1997).
Simulation using experimental density
profiles
Attenuation from leakage at gaps
Second method: wire-tailored cluster flow, unmodulated laser pulse
uniform 500mj 100ps Nd:YAG pulse incident on axially modulated Argon cluster target
1mm corrugation period
1.5 cm
Features persist for the full life of the waveguide
Nitrogen cluster target @
-150 deg C, 25 m wiresArgon cluster target @
22 deg C, 25 m wires
160 μm 320 μm
0.5 ns
1.0 ns1.0 ns
2.0 ns
6.0 ns 6.0 ns
2.0 ns
0.5 ns
(200 consecutive shot averages)
600 μm 600 μm
B.D. Layer et. al, Opt Express 17, 4263 (2009)
Direct laser acceleration- inverse Cherenkov acceleration (ICA)
580-MW peak power 31 MeV/m.
10 TW peak powers are now routine, but the need for neutral-gas phase matching strongly limits peak intensities.
Nd:YAG laser pulseaxicon
Corrugated plasma waveguideRelativistic
electron bunch
Radially polarized fs laser pulseClustered H2 jet
Diffractive optic
Corrugated guide: simple estimates of dephasing lengths and acceleration gradients
n1 > n2One full dephasing cycle
Estimate acceleration gradients using index modulation:
Accelerating-phase region: low index
Decelerating-phase region: high index
λ = 800nm
Ne1 = 3*1018 cm-3
Ne2 = 6*1018 cm-3
wch = 12μm
p = 1, m = 0
} Ld1= ~260 μm
Ld2=~165 μm
For P = 1 TW, Ez =0.55 GV/cm, giving an effective gradient of 77 MV/cm
Wakefield comparison: Malka et al. used a 30 TW laser at λ = 0.8 μm to produce an acceleration gradient of ~0.66 GV/cm
This is a linear process with no threshold.
1 mJ regenerative amplifier alone
P = 20GW Effective accel. gradient: 11 MV/cm
,v vp,1 z o
• electrons distributed uniformly on axis 1 to 11 m behind pulse peak
• no transverse momentum
30 60
30 60time (ps) time (ps)
400 400
00
v p,1 c
m=1 phase velocity matched to initial electron velocity m=1 phase velocity set to c
o=1000
o=1000
o=100o=100
o=30o=30
Ideal scaling Ideal scaling
it is better when electrons catch up with a faster wave than to start them phase matched to a slower wave
Direct laser acceleration- energy gain
Comparing direct accel to other schemesComparing direct accel to other schemes
parameters used for comparison:
=800 nm
wch=15 m
ao=.25
no=7x1018 cm-3
=.9
m=.035 cm
o=100
z=300 fs*c
1
2 o oa
for direct accel we have:
= 1000
semi-infinite vacuum acceleration:
= 12.5
(best case scenario)
vacuum beat wave acceleration:2
2 2 2 1
1 2
8 1o chf i
a w
= 8.3 (1=22)
laser wakefield acceleration:
= 14.3
4a0
z
wch
p
2
12p
2
2wch2
2
a0
2
(1 a02 /2)1/ 2
p
2
1p
2
2wch2
2
Electron Beam Density Electron Beam Density
final electron density
-81m
81m 300
xf
zf -1 m
xf
number averaged final momentum
-11 m
0
0
1
nu
m. (a.u
.)p
z (me c
)
• density peaks off axis; beam has acquired sizeable transverse spread
81m
-81m
• off-axis peaks mostly composed of low energy electrons
• high energy electrons remain confined to center of beam
only the ponderomotive transverse force is significant for these electrons
• Can make modulated plasma waveguides with two distinct methods- modulating either the laser heating profile or the clustered target flow
• Can control nearly every aspect of the waveguide by varying cluster parameters and pump laser intensity
• Gas cluster channels can be more than 10X less dense than unclustered gas channels (1017’s-1018 ’s vs. 1019 ’s) and use 10X less laser energy for generation-
• Cluster-generated plasma waveguides are extremely stable (longitudinal AND transverse) and can support finely engineered structures.
Summary
One application:• Direct laser accelerator optical-frequency LINAC with no
damage threshold