LASER-PLASMA ACCELERATORS: PRODUCTION OF HIGH-CURRENT

ULTRA-SHORT e--BEAMS, BEAM CONTROL AND RADIATION

GENERATION

I.Yu. Kostyukov, E.N. Nerush (IAP RAS, Russia)

A. Pukhov, S. Kiselev (Düsseldorf University, Germany)

OUTLINE INTRODUCTION• Electron Acceleration• Bubble Regime• Experiments BUBBLE REGIME: PHENOMENOLOGICAL THEORY • Electromagnetic field in plasma cavity• Plasma electron trapping and acceleration• Beam control ELECTROMAGNETIC RADIATION • Spectrum of betatron radiation• Laser-plasma x-ray source • Radiation effects SUMMARY

ELECTRON ACCELERATION Ya.B. Fainberg, UFN 93, 617, (1967) acceleration by relativistic electron bunch in plasma

T. Tajima and J.M. Dawson, PRL 43, 267, (1979) acceleration by laser pulse in plasma

20

-20-30 0 x-t

y

electron density

grv grv

vv

ccvv pgrph )2/1( 22

][96.0/ 300

ñìnñìÂE

3190 10 смn мГВE /3000

ELECTRON ACCELERATION

Plasma cavity

100 m1 m

RF cavity

V. Malka, Dream beam, 2007

ELECTRON ACCELERATION

NBNL2006

E-167:Energy Doubling of 42GeV Electrons

ELECTRON ACCELERATION

K. Nakajima, HEEAUP 2005

ELECTRON ACCELERATION

Scheme of principle

Experimental set upV. Malka, Dream beam, 2007

LASER-PLASMA PARAMETERS

• laser intensity ~~2 2

WeAa

mc mc

ratio of electron quiver energy to the energy at rest

• laser pulse duration

1a relativistically strong laser field

2 crl p l

p

nccT

n

short pulse

2

22

4 e

mncr

critical density

• plasma density crn n

• hot spot sizepr

22 4p

e n

m

plasma frequency

ELECTRON ACCELERATION 100% ENERGY SPREAD IN EARLY EXPERIMENTS

V.Malka et al., Science 298, 1596 (2002)

150 a

S.P.D. Mangles et al., PRL 94, 245001 (2005)

160 J, 650 fs, 6 μm

I 3 x 1018 W/cm2 1 J, 30 fs, 10 Hz

(Total Charge : 5 nC)

Nu

mb

er o

f E

lect

ron

s

Electron Energy (MeV)

10 6

10 10

10 8

100 200

DetectionThreshold

T ~ 18 MeV

5.10 a

QUASI-MONOENERGETIC e- -BEAM

1) T. Katsouleas, Nature 431, 515 (2004)

2) S.P.D. Mangles et al., Nature 431, 535 (2004) 3) C.G.R. Geddes et al., Nature 431, 538 (2004) 4) J.Faure et al., Nature 431, 541 (2004)

Extremely collimated beams with 10 mrad divergence and 0.5±0.2nC of charge at 170±20MeV have been produced.

[J.Faure et al., Nature 431, 541 (2004)]

BUBBLE REGIME

20

-20-30 0 x-t

y

plasma wave bubble

310

1

A. Pukhov and J. Meyer-ter-Vehn, Applied Physics B, 74, 355 (2002)

Ponderomotive force of laser pulse push out plasma electrons from region where laser intensity is high, while heavy ions can be considered as immobile.

BUBBLE REGIME

2

2

2

2

0 exp),(LL T

x

r

rAzrAcircular polarization

,10/ 20 mceA,82.0 mL ,/5 pL cr 01.0/0 cnn,/2 pL cT

GEV: CHANNELING OVER CM-SCALELNBL EXPERIMENT

0.5 GEV BEAM GENERATION

E. Esarey, Dream beam, 2007

1 GEV BEAM GENERATION

E. Esarey, Dream beam, 2007

TUNABLE e--ACCELERATOR: USING COLLIDING PULSE pump injection

pump injection

late injection

early injection

pump injection

middle injection

Zinj=225 μm

Zinj=125 μm

Zinj=25 μm

Zinj=-75 μm

Zinj=-175 μm

Zinj=-275 μm

Zinj=-375 μm

J. Faure et al., Nature december 2006

PW LASER SYSTEM IN INSTITUTE OF APPLIED PHYSICS

0 11.4a 0.911 ,m 43 ,fs 12 ,R m24 ,W J 0.56 ,P PW 20 21.1 10 / ,I W cm

E=30 TeV/m

CONCLUSIONS

Rapid progress in laser-plasma acceleration: GEV in 3 cm, tunable quasi-monoenergetic e--bunches

BUBBLE REGIME: PHENOMENOLOGICAL

THEORY

QUASISTATIC APPROXIMATION

tvx gr

QUASISTATIC APPROXIMATION

x

v = c ,

2

11

2

3

A

xpnn

,2

1

p

AA n

xA - gauge

xA - wakefield potential

1|| 0 ncme

tvx gr1/1 222 cvgrgr

relativistic electron hole in plasma (not relativistic ion ball)

x

v = c

,0 iee jjn constnni 0

441

2222 zyR

,2/xE ,4/yBE zy 4/zBE yz

2

3

ELECTROMAGNETIC FIELD IN BUBBLE

I. Kostyukov, A. Pukhov, S. Kiselev, Phys. Plasmas, 2004, 11, 5256 (LASER-PLASMA INTERACTION)

К.V. Lotov, Phys. Rev. E, 2004 69, 046405 (e--BEAM-PLASMA INTERACTION)

ELECTRON TRAPPING

constttatH grgrLgr vrvrvrAP 221

Hamiltonian of electron

tvxx gr ,),,( PvrPr ttS gr

canonical transformation

,constpvH xgr cvgr

x - t

y

bubble

cvgr

plasma

,0v 0t

trapping condition

2

|| grgrgrgr vpvp vvgr Potential from PIC,

441

2222 zyR ,Rr

,1 Rr 0R

ELECTRON ACCELERATION

,,2 2|| rgr

xpH

1x

p

p

2/2 222 Rgrgr

21/1 grgr v

22/11 grgrr vv 22/ grrbubxaccx vLeELeE

,2 2

gr

tR

20 22

4 gr

tR

t

x - t

y

bubble

cvgr

plasma

grgrx vmpp ,

BETATRON OSCILLATIONS

42

22y

tp

pH

x

y

,022

2

yBy pt

dt

pd/ 2B p

x - t

y

bubble

plasma

cvgr

t

B dttt

ry0

4/1

00 )(cos

2/yBEF zyy

x - t

y

BEAM CONTROL BY PLASMA PROFILING

laser pulse

plasma wave

ev

grv

Dephasing: The accelerated electrons slowly outrun the plasma wave and leave the accelerating phase.

1 1

( )p gr

d

dx x c v

0

2/3( )1 / inh

nn x

x L

3/2

0 2

3inhp c

ncL

n

T. Katsouleas, Phys. Rev. A 33, 2056 (1986).

Choosing a proper density gradient one can uplift the dephasing limitation and keep the phase synchronism between the bunch of relativistic particles and the plasma wave over extended distances.

LAYERED PLASMA

plasma wake

electron bunch

laser pulse

2.5 10∙ -2

2.5 10∙ -3

0 xωp0/c 150000

0

2/3( ) ,1 / inh

nn x

x L

( )n x inhx Lat

A. Pukhov, I. Kostyukov, Phys. Rev. E, 77, 025401 (2008)

( )n x

Putting electrons into the n-th wake period behind the driving laser pulse, the maximum energy gain is increased by the factor 2πn over that in the case of uniform plasma.

ENERGY SPREAD REDUCTION

energy spread mechanism

peak acceleration

min acceleration

1.15

1.451

2

3

4

0 2x/λL

ε (GeV)

0 500000

n/nc

0.001

0.006

x/λL

1.5

0

ε (GeV)

0 50000x/λL

1 2

energy spread reduction peak

deceleration

min deceleration

CONCLUSIONS

1. The Bubble produces a quasi-monoenergetic e-−beams.

2. The Bubble is an efficient energy converter: 10..20% laser energy is transformed to the e- −beam.

3. Self-guiding over many Rayleigh lengths.

4. Plasma density profiling for beam control

BETATRON RADIATION

DIPOLE RADIATION

/ 1p mc 1/

/p

22 B

1/

electron betatron orbit

electron velocity deflection angle

electron emission angle

plasma

ion channel

/ 2B p - betatron frequency

dipole regime of emission

- radiation frequency

SYNHROTRON RADIATION

/ 1p mc 1/ synchrotron regime of emission

10.92

0.5

0c0 0.3 1 2 3

quasi-continuous spectrum

2 3 20 03 /c B r c n r - critical frequency

2222 cossin

K

c

BETATRON RADIATION SPECTRUM

cossinsincossin zyxc

eeek

qKqK

c

e

cNPspon

23/2

23/1

22

2

222sinsin

32

1K

I. Kostyukov, S. Kiselev, A. Pukhov, Phys. Plasmas, 2003, 10, 4818

,sinsin1 22

2

cq

3

2/3

P

x

K

1

y

sinsiny

cossinx

SYNCHROTRON RADIATION

100 – 400 m

undulator

Advanced Photon Source, Argonne National Laboratory, http://www.aps.anl.gov/

LASER-PLASMA X-RAY SOURCE

S. Kiselev, A. Pukhov, I. Kostyukov, Phys. Rev.Lett., 2004, 93, 135004

• simultaneous acceleration and x-ray generation

• laser pulse propagates in plasma a few centimeters

• laser systems sizes – several meters

• COMPACTNESS

22

3

2 FPe

20,

,

pe peLPS

FEL He He

rF

F c

Òë,1FELB,ñì10 -3190 npecr /0

610FEL

LPS

P

P

F2

• HIGH POWER

• PHOTON ENERGY

• X-RAY PULSE DURATION fs505

plasma

bubble radiatio

n

RADIATION OF EXTERNAL e--BEAM

QUANTUM EFFECTS IN STRONG PLASMA FIELD

'ple V e plV e e

E. Nerush, I. Kostyukov, Phys. Rev. E 75, 057401 (2007)

quantum photon emission e-e+ pair production

PLASMA FIELD INSTEAD OF CRYSTALLINE FIELD

plasmabubble

z

r

k

plasmabubble

k

2Bmc

2mc 1) electron motion is semiclassical

2) photon emission is quantum

V.N.Baier, V.M.Katkov, V.M.Strakhovenko, Electromagnetic Processes at High Energies in Oriented Single Crystals (Singapore, World Scientific 1998).

Semiclassical operator method

RADIATION REACTION

ik

iki

guFc

e

ds

dumc

3 4 4

3 2 5 2 5

2 2 2

3 3 3

iki l il k l km i

k kl kl ml

e F e eg u u F F u F u F u u

mc x m c m c

P. Michel, et al., Phys. Rev.E 74, 026501 (2006).I. Kostyukov, E. Nerush, and A.Pukhov, JETP 103, 800 (2006)

rF

fF

aF radiation

BETATRON RADIATION

A. Rousse et al., Phys. Rev.Lett. 2004, 93, 135005

LASER-PLASMA SYNCHROTRON

H.-P. Schlenvoigt et al, Nature Physics 4, 130 - 133 (2008)

INTENSE COHERENT THZ RADIATION GENERATION

CONCLUSIONS

Compact and powerful laser-plasma radiation sources: X-ray, optical and THz radiation

SUMMARY

• Laser-plasma accelerators: GEV in 3 cm, tunable quasi-monoenergetic e--bunches

• The Bubble produces a quasi-monoenergetic e--beams with efficiency conversion 10..20%

• Laser plasma can be a compact and powerful source of X-rays, optical radiation and THz pulses.