Exawatt-class Laser-Plasma Acceleration

Kazuhisa NakajimaKazuhisa NakajimaKEK

SJTU/SIOM

ILE meetingILE meetingDec. 13, 2010

KEK, Tsukuba, Japan

Electron accelerationElectron acceleration

OutlineOutline

HadronHadron accelerationacceleration

Laser focusing and Laser Micro Collider Laser focusing and Laser Micro Collider

PairPair--beam production and acceleration beam production and acceleration

Race of plasma-based particle acceleration Race of plasma-based particle acceleration

M.Borghesi et al, Fusion Science and Technology, 49, 412 (2006)

M.J. Hogan, AAC2010

Evolution of the maximum electron Evolution of the maximum electron energy by single-stage laser-plasma

accelerators since 1990

Evolution of the maximum proton Evolution of the maximum proton energy by laser-foil interaction

since 2000

First observation of Multi-Mev proton emission in superintense interaction with metallic targets was reported in 2000

First observation of Multi-Mev proton emission in superintense interaction with metallic targets was reported in 2000

LMU /MPQ LMU /MPQ RPA

RAL RPARAL RPA

42 GeV42 GeV

1.8 GeV1.8 GeV

68 MeV68 MeV

Laser pulse Bubble

Self-injected electrons

C. D. Murphy et al., Phys. Plasmas 13, 033108 (2006)

Z=0.3 mm

Z=2.0 mm

Z=5.7 mm

Z=7.5 mm

W. Lu, PRST-AB 10, 061301 (2007)

Bubble formation

Electron injection

Acceleration

Laser depletion

Electron self-injection and acceleration Electron self-injection and acceleration in a nonlinear wake so-called “Bubble”

3D-PIC simulation

ɑ0 >>1

mW/cm10855.02

0

2219

21

52

2

0

2

0

I

cm

Iea

e

34

0

32

3-

1831

m

8.0

cm

10

100

TW7.1GeV

pn

PW

100

TW8.3GeV

32

P

P

PW

c

3132

0

216.0

e

c

r n

n

P

P

w

cmcW

0aRk bp

Linear LWFALinear LWFA

Nonlinear LWFA: Lu’s modelNonlinear LWFA: Lu’s model

Nonlinear LWFA: Gordienko’s modelNonlinear LWFA: Gordienko’s model

W. Lu et al., PRST-AB 10, 061301 (2007)

S. Gordienko et al., Phys. Plasmas 12, 043109 (2005)

3

1

3182maxcm10

TW36.0GeV

pn

PE

for =0.8 m

Pr m

e

2c5 e2 8.7 GW

Lu’s modelLu’s model

323/1

p

c

r n

n

P

P

323/1

23.0

p

c

r n

n

P

P

Energy scaling of LWFA Energy scaling of LWFA

00 2 awkRk pbp

3-

18

2

0

2

0

2

cm

10

m

TW353.1GeV

pp

clinear

nr

P

n

namcW

3231

2

0

2

3

2

p

c

rp

cdpav

n

n

P

Pmc

n

namcLEeW

KEK/SIOM capillaryKEK/SIOM capillary

LBNL/Oxford capillaryLBNL/Oxford capillary

UCLA/LLNLUCLA/LLNLGas cell

Capillary enhances energy Capillary enhances energy gain by a factor of 2

A B C D E

Laser intensitya0

3.4 1.7 2 5.8 1.4

Spot radius w0 [mm]

44 31 43 50 90

Pulse duration L [fs]

100 70 100 110 57

Peak power P [TW}

756 94 250 2800 563

Pulse energy EL [J]

76 6.6 25 308 32

Plasma density ne [cm-3 ]

2x1017 2x1017 1.2x1017 2.7x1017 1.0x1017

Plasma lengthLp [cm]

25.5 18 43 22 ~100

Challenge toward 10 GeV single-stage LWFAChallenge toward 10 GeV single-stage LWFA

p

c

n

na0

3

2

p

c

n

na0

3

4

Martins, Nature Phys. 6, 311 (2010)Self-guiding

W. Lu et al., PRST-AB 10,

061301 (2007)

C.G.R. Geddes, LPAW2009

GeV-regime LWFA driven by PW lasers - 3D PIC simulation

S. F. Martins et al., Nature Phys. 6, 311 (2010)

Bubble-LWFAin the laboratory frame

Bubble-LWFAin the laboratory frame

ɑ =53, =33fs, w =10mɑ0=53, L=33fs, w0=10mne= 1.5x1019 cm-3

Lacc = 2.5 mm

9.4 PWSelf injection

9.4 PWSelf-guiding/Self-injection

E = 3.4 GeV Q=25 nCE = 3.4 GeV Q=25 nCE/E = 11%

e=0.5x103 mm mrad

2.8 PWSelf injection

2.8 PWSelf-guiding/Self-injection

Blowout-LWFAin the Lorentz boosted frame

Blowout-LWFAin the Lorentz boosted frame

ɑ =5.8, =110fs, w =50mɑ0=5.8, L=110fs, w0=50mne= 2.7x1017 cm-3

Lacc = 22 cm

E =5- 13GeV Q=0.6 20%

E =5- 13GeV Q=0.6-2.2 nCE/E = 8-20%

Weakly Nonlinear LWFAin the Lorentz boosted frame

Weakly Nonlinear LWFAin the Lorentz boosted frame

1.4 PWPlasma channel/External

1.4 PWPlasma channel/External-injection

ɑ =2.0, =160fs, w =100mɑ0=2.0, L=160fs, w0=100mne= 2.2x1016 cm-3

Lacc = 528 cm

E =40 GeV

E/E = 20% at 40GeV

E =40 GeVQ=0.3 nC

E/E = 20% at 40GeV

TeV single-stage acceleration by ExawattTeV single-stage acceleration by Exawatt

Hzcm

G105.2cm

2

0193

RFH

pf

Bn

R. W. Boswell, Plasma Phys. and Controlled Flusion, 26, 1147 (1984)

peei

B0

Helicon wave long acceleratorHelicon wave long magnetoplasma accelerator

For Excitation RF frequency: fRF = 1MHz Helicon wavelength: H = 1 cmResonance solenoidal magnetic field B0

T4cm101 0

318 Bnp

kG4cm101 0

317 BnpG400cm101 0

316 Bnp

G40cm101 0

315 Bnp

r

r

Azimuthal mode2j

2j

Gas jet injector

Capillary injector

Gas jet injectoror

Capillary injector

LaserLaser

Helicon wave Helicon wave excitation antenna

80 m80 m1 EW 1ps 1MJ1 EW 1ps 1MJ

1 TeV1 TeV

SolenoidSolenoid

Superconducting Superconducting solenoid

10 PW 300fs 3kJ10 PW 300fs 3kJ

10 PW 300fs 3kJ10 PW 300fs 3kJ

500 GeV x 500 GeV LPA 500 GeV x 500 GeV LPA collider experiment

Final focusFinal focus

4 particle detector4 particle detector

PIC simulation suggests PIC simulation suggests advent of Radiation Pressure Acceleration mechanism

L. O. Silva et al., PRL 92, 015002 (2004)

RPA:Acceleration

RPA:Acceleration force ~ 2I/c

From rear side in the forward direction

From rear side in the forward direction

From front side in the backward direction

From front side in the backward direction

From front side in the forward direction

From front side in the forward direction

T. Esirkepov et al., PRL 175003 (2004)

At I =10 W/cmRPA dominates over TNSAAt I =1023 W/cm2

RPA dominates over TNSA

RPAAcceleration

RPAAcceleration force ~ I1/2

At I =5x1020 W/cm2 RPA becomes comparable to TNSAAt I =5x1020 W/cm2 RPA becomes comparable to TNSA

Accelerated ion population Accelerated ion population in the phase space

1D model for Radiation Pressure Acceleration1D model for Radiation Pressure Acceleration“Light Sail” or “Laser Piston” mode

pcp

pcp

c

I

c

I

dt

dp

222

2222

1

12

The relativistic equation of motion for the foilThe relativistic equation of motion for the foil

Solution for constant intensitySolution for constant intensity

I: light intensitypn

I: light intensityp: areal momentum of the foil: areal mass of the foil mi: ion mass ni: ion density l: foil thickness

4

2

LcEI

lnm ii

sinh4

1sinhcp

2

6sinh

3

12

1

lcnm

It

ii

V

NIi

rr NI

Incident pulse

Reflected pulse

Moving foil

1

1r cV

Energy transfer efficiency between the foil over the light

1

2

i

ri

I

II

The final velocity:The final velocity: 11

112

2

e

e f

A.P.L. Robinson et al., New Journal Physics 10 (2008) 013021; A. Macchi et al., PRL 103, 085003 (2009)

e L

p

e a

m

m

A

Z 2

02

l

n

n

c

0

Very weak dependence on wavelength or ion charge

ee

12

12

f

The final kinetic energy:The final kinetic energy: Energy scales as Il ,1

Underdense plasmadensity: ni = 0.1nc

Z/A = 1/3

10s GeV quasi-monoenergetic proton beams10s GeV quasi-monoenergetic proton beamsby RPA-LWFA hybrid mechanism

L.L. Yu et al., New Journal of Phys. 12, 045021 (2010)

I = 6.9x1021-1.7x1023 Wcm-2

ɑ0 = 50 -250, R0=8mL = 25(2/)

I = 6.9x1021-1.7x1023 Wcm-2

ɑ0 = 50 -250, R0=8mL = 25(2/)

Overdense proton plasma layer n0L~ɑ0nc0/2

np =15nc L=10 size: 1m x 4m

Overdense proton plasma layer n0L~ɑ0nc0/2

np =15nc L=10 size: 1m x 4m

1D PICɑ0 = 200

1D PICɑ0 = 200

1D PICɑ0 = 200

2D PICɑ0 = 200

Laser energy

Electrostatic field

0max aThe maximum proton energy

270 PW 70 fs19 kJ

270 PW 70 fs19 kJ

60 GeVProtons60 GeVProtons

Plasma thickness ~ 1 mmPlasma thickness ~ 1 mm

Virtual photonVirtual photon

e-e- e-e-

e in the laser e- in the laser field

e+e+

Coulomb fieldCoulomb fieldof nuclear charge Z

Virtual photonVirtual photon

mec2

0

E

V0

V0 -mec2

V0 +mec2

e+

e-e-

dNp

dt

9.6 2

104

c

l3 2 Z2

Zi

ne

nc

2

3 3.6 2 1

1 2

e Z e ee

Ei 3mec2

It 2.61019

L m 2 W/cm

2

Pair creation in plasmaPair creation in plasma

• Trident process in the nuclear field

• Threshold intensity for pair production

• Pair-production rate in a plasma

Pair creation via spontaneous Pair creation via spontaneous breakdown of the vacuum

Ic cEc

2

4 4.7 10

29W/cm

2

• Critical field and Intensity:

for

cmV1032.1 1632

e

cmE ec

Schwinger fieldSchwinger field

(Shearer, J.W. et al., Phys. Rev. A8, 1582, 1973)

• Pair production probability for ɑ0≫1

E

EEw c

exp

2

(E. Brezin and C. Itzykson, Phys. Rev. D, 2, 1191, 1970)Tunneling Tunneling

regime

Electrons bound in vacuum with binding

energy V0~2mec2

Electrons bound in vacuum with binding

energy V0~2mec2

Klein’s Paradox; electrons tunnel through a potential barrier with V0>2mec2, leading to positron current flowing in the potential region.

Klein’s Paradox; electrons tunnel through a potential barrier with V0>2mec2, leading to positron current flowing in the potential region.

-mec2

Relativistic pair-beam production schemesRelativistic pair-beam production schemes

＋

＋＋

＋

＋＋

＋

＋

＋

＋

＋

＋

＋

＋

＋

----

-

--

--

-

----

++

+

IonIon

AcceleratedAcceleratedelectrons

ProducedProducede+e- pair

Plasma

Trident process in ion nuclear fields

Trident process in ion nuclear fields

----

-

--

--

-

----

++

+

AcceleratedAcceleratedelectrons

ProducedProducede+e- pair

Plasma

Laser pulsefor electronacceleration

Laser pulsefor electronacceleration

Laser pulsefor pair-

production

Trident processin counter propagating

Trident processin counter-propagating

laser fields

Electron-positron pairs can be accelerated by . Electron-positron pairs can be accelerated by direct laser fields (RPA) or plasma wakefields.

Electron acceleration by ultra-relativistic laser fields in plasma

• For initially stationary plasma electrons, the final accelerated energy by RPA:

2 g21 L L 1 a0

22

1 21

Assuming relativistic transparency of laser propagation,

g L

p

Lnc

ne0

1 2

nc m 2

4e2

reL2

• The accelerated energy of electrons is given by

L 2 g2 1 2 L

2 nc

ne0

L

To produce electron-positron pairs in plasma, initially plasma electrons must be To produce electron-positron pairs in plasma, initially plasma electrons must be accelerated up to relativistic energy.

a02 nc

ne0

• The final Electron density:ne 2 Lnc ne0 2a0nc

• Electron bunch length: lb ne0

2 Lnc

ne0

2a0nc

ne0 : the plasma electron density

for linear polarization

: plasma thickness

0

2

0max6

1

e

c

n

na

X. Q. Yan, 5th ASSS 2010, Shanghai

ProtonProton

ElectronElectron

EEx

Trident process in plasma ions Trident process in plasma ions

Pair-beam production yieldsPair-beam production yields

22

0

2

0

38

0

6108.0

r

n

nZaN

e

cp

For >> 3

r0 : the laser spot radius : the plasma thickness

mmcm

W/cm108.2

22

0

32

0

24345

rn

IZN

e

p

e.g.

Np 4.4 1014

Z = 54 (Xe)I nr

Z = 54 (Xe)I = 1022 W/cm2

ne0 = 1020 cm-3

r0 = 10 m = 100 m

Trident process in counter-Trident process in counter-propagating laser fields

31

0

22312

3

00

3

0

2

0

0

cmW/cm1038.3

44

e

e

C

c

nI

n

aa

E

E

exp8

exp8

0

3

0

2

0

4

0

3

00

2

0

L

LCep

cra

caNN

expfsm

mW/cm105 2

0

2233

L

p rIN

I = 1022 W/cm2

nr

I = 1022 W/cm2

ne0 = 1020 cm-3

r0 = 10 mL = 20 fs = 100 m

34 Np 9 1016

e.g.

Pair-production yieldsPair-production yields

1020 1021 1022 1023 1024 1025

Laser Intensity [W/cm2]

1010

1014

1018

1022

1026

Nu

mb

er

of e

+e

-p

air

s

Pair-production Pair-production in nuclear field

of Z=54 (Xe)

Pair productionPair-productionin laser field of

L = 20 fs

ne0 1020 cm3

r0 10m

100m

• Plasma density:

• Laser spot radius:

• Target thickness:

-ray radiation scattered from a pair-beam-ray radiation scattered from a pair-beamThomson scattering radiation power from an accelerated pair-beam:

Prad 64

3re

2 2INp 64

3re

2a04INp

Irad 5123re

2a08

302 I

0

c L

0

exp

Prad 1.551092 I 5 W/cm 2 04 m r0

2 m m L fs exp

e.g.

For

512 3re

2a08

3I

r02

03

c L

0

exp

Irad 5 1085 I5 W/cm2 04 m m L fs exp

----

-

--

--

-

----

++

+

-ray

I = 10nr

I = 1022 W/cm2

ne0 = 1020 cm-3

0 = 0.8 mr0 = 10 mL = 20 fs = 100 m

= 34NPI

= 34Np = 9×1016

Prad = 1.2×1023 WIrad = 4×1028 W/cm2

Intensity

Radius

ElectronElectron

Fpond Fpond

Scattering of the electrons

x

z

x

x-z plane

x-y plane

z

x

y

x

TEM(0,0)

y

TEM(1,0)

x

y

TEM(1,0)+TEM(0,1)

U0 r, z,t a02 0

2

2 exp

r2

22

z ct 2

2 z2

U1 r, z,t a1

2 r202

4 exp

r2 02

24

z ct 2

2 z2

TEM ponderomotive potentialTEM00 ponderomotive potential TEM +TEM ponderomotive potentialTEM10 +TEM01 ponderomotive potential

Intensity

Radius

FpondFpond

Electrons confinement

Potential well

S. Kawata, S. Miyazaki, Utsunomiya Univ.

Beam focusing by combined Hermite-Gaussian modes

Focusing strength at r=0, and z-ct=0

KF Ft

mc2r

2a12 a0

2

02

• The beam envelope equation on the rms beam radius rb

02 3

2

322

2

rb

b

rbzb

erbF

rb NrK

dz

d

e

where N : number of electrons in the bunch,zb : rms bunch length, eb : geometric emittance,en : normalized emittancere : the classical electron radius.

eb en

Space charge forceSpace charge force Thermal emittanceThermal emittance

The focusing forceThe focusing force

2

2

2

2

6

2

0

32

14

2

02

0

2

12 22exp2

ctzrra

raa

r

U

mc

Fr

-3 -2 -1 1 2 3

0.2

0.4

0.6

0.8

1

1.2

1.4

U0U1

U=U0 +U1

r 0

Combined ponderomotivepotential for beam focusingCombined ponderomotivepotential for beam focusing

0 : rms beam size

ZR :the Rayleigh length z :beam pulse length

0 1 z2

ZR2

Estimate of a focused beam sizeEstimate of a focused beam size- Picometer beam would be created -

0

21412

0

2

1

4122

zb

erb

aa

Nr

a1 a0Assuming 0 r0 2 zb 0

rb 2 1 4

2

r0

a05 2

reN

0

rb pm 2 1024 N

I5 4 W/cm2 r0 m 0

3 m

e.g.10

00 101 m,10 m,8.0 Nr

45

2

25

cmW

1006.12.0pm

I

rb

Assuming a1 a0

rb en0

a0

1

2a02

0r0

eb en en a02 a0

4

0 r0 2

rb pm 4 1023

I W/cm2 r0

0

rb eb

KF1 4

1 4 eb0

2a12 a0

2 1 4

e.g.

The space chrage force would be neglected for a charge-neutralized pair beam.

m10 m,8.0 00 r

2

25

cmW

1006.113.0pm

Irb

Space-charge-force dependent beam sizeSpace-charge-force dependent beam size Emittance dependent beam sizeEmittance dependent beam size

Laser Micro ColliderLaser Micro ColliderTwo counter propagating laser-accelerated beams turn to a micro collider.

• The space-charge-limited luminosity: L Np

2 frep

4 rb2

a050Np frep

2 3 2rer02

L cm2s1 2 1030 I5 2 W/cm2 06 m r0

2 m N p frep

25

2

C.M.101.06

cmW5TeVI

E

e.g.

25

25

24012

1006.1

cmW102scm

I

fL rep

• Required peak power and pulse energy

• The final energy is approximately assumed as f a02

E f GeV 0.37 1021 I W/cm2 02 m

10

00 101 m,10 m,8.0 pNr

at

25

2

101.06

cmW17EW

IP

25

2

101.06

cmW42kJI

EL

e+e- Pair-beam Laser Micro Collidere+e- Pair-beam Laser Micro Collider

Two counter-propagating laser-accelerated pair beams would createe+e-, e-e-, e+e+ micro-size collider without beam disruption at collision.

L Np

2 frep

4 rb2

a04 Np

2 frep

0r0

• The emittance-limited luminosity is given by

where Np : the number of accelerated e+e- pairs frep : the repetition rate of laser pulses.

L cm2s1 5.31027 I2 W/cm2 03 m r0

1 m Np2 frep[Hz]

e.g.

2

25

24212

101.06

cmW103scm

I

fL rep

10

00 101 m,10 m,8.0 pNr

EC.M.[GeV] I [W/cm2] P [PW/pulse] EL [J] L [cm-2s-1] *

1 2.1・1021 3.3 1.6 1.2・1035

4 8.4・1021 13 6.4 2・1036

10 2.1・1022 33 16 1.2・1037

500 1.1・1024 1700 800 3・1040

1000 2.1・1024 3300 1600 1.2・1041

5000 1.1・1025 17000 8000 3・1042

10000 2.1・1025 33000 16000 1.2・1043

* frep = 1 HzPair-beam micro-collider conceptPair-beam micro-collider concept

Tenuous plasmaTarget Target

Strawman design of Pair-beam Laser Micro Collider

Pair beam

pulse

Pair beam production

pulse

Pair beam

pulse

Pair beam production

pulse

Acceleration & Final Focus

pulse

Acceleration & Final Focus

pulse

Acceleration & Final Focus

pulse

Acceleration & Final Focus

pulse

Laser beam

sLaser b

eams La

ser

bea

ms

Lase

r b

eam

sPair be

ams

Pair be

ams Pa

ir b

eam

sPa

ir b

eam

s

Cartoon of Multi-Beam Laser Micro Collider

N beams coherent combination multiples N beams coherent combination multiples N times increase of the luminosity

Luminosity of laser micro-collidersLuminosity of laser micro-colliders

1042

1039

1036

1033

1030

1027

Lum

inosity a

t 1 H

z [cm

-2s

-1]

100

110

C.M

. E

nerg

y [

GeV

]

100010000

1020 1021 1022 1023 1024 1025

Laser Intensity [W/cm2]

C.M. energyC.M. energy

Emittance-limitedEmittance-limitedluminosity

Space charge-limitedSpace charge-limitedluminosity

0 0.8m r0 10m Np 11010

ELIをASIAにELIをASIAに日中を軸に超高強度場科学研究センターをアジアに創設

３つの超高強度レーザー科学•

•

•

３つの超高強度レーザー科学•超高エネルギー科学（加速、放射、核素粒子物理）

•超高速光学（フェムト、アト、…科学）

•超高強度エネルギー科学（核融合、宇宙物理、n-QED、QCD)

ねらい•

•

真にグローバルサイエンスの先進拠点の構築が求められている。

ねらい•旧来科学を打破する橋頭堡•一国一所の村興し的計画から脱却し、真にグローバルサイエンスの先進拠点の構築が求められている。

CAS-IOP, ChinaCAEP-LFRC, China

300TW760TW

GIST-APRI, Korea

500TW

JAEA-KPSI, Japan

100TW

RRCAT, India150TW

NCU, Taiwan

100TW

CAS-SIOM, China

890TW

A big potential for laser A big potential for laser plasma acceleration in Asia

200TW

SJTU, China

Shenguang II (神光 貳) at SIOMShenguang II (神光 貳) at SIOM

New Optical Science Lab at 上海交通大学New Optical Science Lab at 上海交通大学 5 Asia Summer School & Symposium in 上海5th Asia Summer School & Symposium in 上海