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