Extreme Light – Matter Interactionthrough the Lenses

of the Relativistic Flying Mirror Concept

S. V. Bulanov

Advanced Photon Research Center,

Japan Atomic Energy Agency, Kizugawa-shi, Kyoto-fu, Japan

ELI Beamlines Scientific Challenges Workshop

26 – 27 April 2010

Prague

Czech Republic

Acknowledgment

M. Borghesi, L.-M. Chen, T. Zh. Esirkepov, A. Ya. Faenov,

Y. Fukuda, M. Kando, Y. Kato, T. Kawachi, K. Kawase,

H. Kiriyama, J. Koga, G. Korn, F. Pegoraro,

A. S. Pirozhkov, E. N. Ragozin, N. N. Rosanov, A. G. Zhidkov

OUTLINE

1. Receding Relativistic Mirrors in RPDA Regime of Ion

Acceleration

2. Flying Mirror for Femto-, Atto-, … Super Strong Fields

3. High Harmonic Generation in Underdense Relativistic

Plasma

4. Overdense Accelerating Mirror

5. Strong Field Limits

6. Applications & Conclusion

( )x t c t

2

1-

1 4

inref in ref

Co-Propagation

Configuration:

EM Wave

“Pushes”

Relativistic Mirror

“Receding Mirror”:

Ion Acceleration by

Radiation Pressure

ele

ctro

ns

ions2

11-

2ref in

in

ref

1. Receding Relativistic

Mirror

T. Esirkepov, M. Borghesi, S. Bulanov, G. Mourou, T. Tajima

Phys. Rev. Lett. 92, 175003 (2004)

s d d M M

M M

M M

( , , ), ( , , ), ( , , )x t y t z t

Surface element area

Unit normal

Conservation of the particle number

00 0s s

Surface

0s d d

Shell Evolution

0

1,

2 1

Lt i ijk j k

Ep x x

P P

2 2.i

t i

k k

cpx

m c p p

, , 1,2,3i j k

Final Ion Energy

/ toti lasN

Radiation pressure on the front part of the “cocoon” is equal to

22 2

0

'' 1

2 2 1

L L Mlas

M

E E

P

It yields

1/ 22 2 (0)2 (0)2(0) 2

1/ 22 2 (0)2 (0)2

0 02

pL

p

m c p pdp E

dt n l m c p p

Solution to this equation gives for energy balance

(0) 2 ( 1)

2 1p

p W W

m c W

Final ion energy depends on the laser pulse energy as

Efficiency of the laser energy conversion into the fast ion energy can be formally

up to 100%: 30 KJ laser pulse can accelerate 1012 protons up to the energy equal

to 200 GeV

/ 2

0 0

( )

2

t x c

L

i

x E dW t

c n l m c

FLUENCE

Energy Scaling

Nonrelativistic Limit

11 2 2

1 1

8 (10 / ) ( / )( /1 )tot p lasN M M J MeV

Ultrarelativistic Limit

11

1

62.5 (10 / )( / )( / )tot p lasN M M KJ GeV

221 /

lasacc las

ll l

v c

acceleration length

Efficiency and Luminosity Scaling

luminosity

If a thin foil target, is irradiated by the laser pulse

of 20 kJ focused in 0.01mm spot and of duration 100 fs.

protons are accelerated up to 100 GeV over the distance 60 cm.

24 3

0 010 , 1n cm l m

1210totN

efficiency

1 2

22 434 2 1

12

4

101

10

1

0

2

2

10

y z

to

e f

t

f

N Nf

Nf cmcm s

KHz

W

W

Stability of RPDA Ion Acceleration

For perturbations we have

where

(0) (1) (1) (1)

(1) (1)

(0)

(1) (1)

(0)

(0) 2

2

0 0 0

( ) ( )

2

( )

( ) 2

( )

( ) 2

( ) ( )( )

2

L

p x R y z

m c

m c y R x

p

m c z R x

p

x t Et R

c n l

,

Relativistic theory of RT instability of thin foil

1/ 2(0)3/ 2

1 3/ 2 2

0 0

(2 )

6RT

R

k

0

0

23 2

:

:

:

:

:

:

:

20

15

1

0.5

64

13 / 26.98

0 /

316

f

las

cr

i p

Focus spot

Pulse duration

Intensity

Dimensionless amplitude

Thicknes

r m

fs

s

Densi

I W

ty

A

n n

a

ml Z m

cm

LASER PULSE

PLASMA TARGET :

THIN FOIL

Plasma jets driven by Ultra-intense laser interaction with thin foils

VULCAN Nd-glass laser of Rutherford Appleton laboratory,

(60 J, 1ps & 250 J, 0.7 ps) interacts with foils (3, 5 mum, Al & Cu)

S. Kar, et al., Phys Rev Lett 100, 225004 (2008)

(0)

2

0

2 ( 1)2

2 1

( )1

2

p

p W WW

m c W

EW d

n l

Laser –Mass-Limited-Target Interaction in RPDA Regime

2D PIC Simulations

S. V. Bulanov et al., Phys. Rev. Lett. 104, 135003 (2010)

S. V. Bulanov et al., Phys. Plasmas 17, in press (2010)

Equations of shell element motion

Solution

with and ,

Ion energy

Efficiency

Non-Relativistic Limit

0

42 2

,0

0

1 112

tt i ijk j k

E ex

ex

x x xm

tx

l

v

( ) ( )y H t z H t ( ) 1ex

tH t

0

21 / ex

nn

t

2 4

,0 6

2

018

E exmt

l

v

22 2

2

0 0 0 0

2

18 3

L las laseff

ex ex

cE t tI

m n l m n l

2. Flying Mirror

for Femto-, Atto-, …

Super Strong Field Science

Kagami(“mirror” in Japanese)

2

0'' 4-

ph

ph

ph

c v

c v

2''6max

0

ph

I D

I

-3

ph

3D Particle-In-Cell Simulation

EM Pulse Intensification and Shortening

by the Flying Mirror

S.V.Bulanov,

T. Esirkepov,

T. Tajima,

PRL 91, 085001 (2003)

Ex

a

kpX20 10 0 10

4

3

21

0

ne

vph

(Driver laser, d )

vg

1D

3D

Cusps in density profile

A.I.Akhiezer & R.V.Polovin,

Sov. Phys. JETP 3, 696 (1956)

Paraboloidal shape

(due to dependence of wave

frequency on amplitude)

S.V.Bulanov & A.S.Sakharov, JETP Lett. 54, 203 (1991), N. H. Matlis, et al., Nature Physics 2, 749 (2006)

Optimal laser pulseduration p /2.

21

e e

eE eAa

m c m c

Nonlinear Plasma Wave

sL

sD

,s sIph phcv

2'' / 4s s phL L

'

''

phcev

'sL

sD

', 's sI0ph v

'

'

Laboratory

Frame

Moving

Frame

Laboratory

Frame

e

eEa inv

m e

2

1

1ph

ph

e phv v

1'

1 2

sph

s

ph ph

Focal spot diameter '

EM Pulse Length: '2

ss

ph

LL

Incident Pulse

Reflected Pulse2

1''

1 4

sph

s

ph ph

Focal region:

|| ''l

'l

Wake

Wave

Co

un

ter-p

rop

ag

atio

n in

tera

ctio

n

22

2

( )( ) 0,

d a gs a

d

0( ) ,

p

n Gn X

k X

2 1

p phg G k

1 2

(1 ) πsin

2 2

ig

s

2 22

2 2 2 2 π(1 ) sin

2 2

p p

ph

k kG

s s

R

2 2 22( ) ( ) ( )

ga s a a d

Amplitude eq:

Density: 0 1

2 2 2 2 0s c k

Reflection coefficient for n|X|

(integrable singulariy)

Multiply by and integrate:( )a

Use WKB approximation: and – bounded oscillating functions at .( )a ( )a

Reflected amplitude for large s:

Reflection coeff:

A.V.Panchenko, et al., Phys.Rev. E 78, 056402 (2008)

c)

Transverse Wake Wave Breaking

wf

2 200 0

2 20 0

0 00 2 2

0 0

0 00 2 2

0 0

( )

2 2 1 ( / ) ( / )

( )

1 ( / ) ( / )

( )

1 ( / ) ( / )

wf

y z y z

wf

y y z

wf

z y z

ry zx

R R y R z R

y ry y

R y R z R

y rz z

R y R z R

3D Regime of the Transverse Wake Wave Breaking:

3D Injection (Flat Beam)

The non-one-dimensional geometry of the electron motion results in their finite transverse

momentum along the axis. We suppose that the nonlinear displacement, in the nonlinear

wake wave is essentially perpendicular to the parabolic phase surfaces, which can be

derived in the linear approximation. Then, for the new position of the shifted phase surface in

the wave we have

Snapshots of laser wakefields

N. H. Matlis, et al., Nature Phys. (2006)

Exp

erim

en

t

Experiment setup

PIC

-Sim

ula

tion

Experiments on Relativistic Flying Mirror

M. Kando, et al., Phys. Rev. Lett. 99,135001 (2007)

A. S. Pirozhkov, et al., Phys. Plasmas 14, 080904 (2007)

Space-Time Overlapping of Driver and Source Pulses

tp = -750 fstp = -250 fstp = -150 fstp = -050 fstp = 0Driver

200 mJ, 76 fs

Source

12 mJ

Side View

Top View Relativistic Microlens

Vacuum

focus

Jet

center630 μm

In our experiments, narrow band XUV generation was

demonstrated

tp = -750 fstp = -250 fstp = -150 fstp = -050 fstp = 0

Detected signals

Proof of Principle Experiment

6 8 10 12 140

1x107

2x107

3x107

4x107

, nm

Nx, 1/sr

0.50.60.70.80.91p

-400 -200 0 200-20

-10

0

10

20

p

s, fs

z, m , arb. u.

0

0.25

0.50

0.75

1.0

180 fs

12 m

•x = 14.3 nm

•Δx = 0.3 nm, Δx /x = 0.02

• Wake wave parameters:

= 4.1, Δ/ = 0.01

•~ 4×107 photons/sr

•Reflected pulse duration:

x ~ 1.4 fs

(femtosecond pulse)

Flying Mirror in the Head-On Collision Experiment

M. Kando, et al., Phys. Rev. Lett., 103, 235003 (2009)

Two head-on colliding laser pulses

0 60000CCD Counts

m = -1 m = +1m = -2 m = +2

Within 12.5-20 nm:

1011 photons/sr

1.3 μJ/sr

(4000 times larger

than in 2007)

Detection angle:

Ω = 0.006 sr,

Energy at source:

EXUV = 7 nJ/pulse

J-KAREN laser:

0.5 J, 15 TW

12 14 16 18 20 220.0

1.0x10-7

2.0x10-7

3.0x10-7

4.0x10-7

dS/d,

J/sr/nm

, nm

Head-on collision of 2 pulses

cusps

ne~(y-y0)-2/3

xy

ne

f(x, y, py)

3. High Harmonic Generation

in Underdense Relativistic

Plasmalaser pulse

x

y

cusps, ne~(y-y0)-2/3

ne

cavity wall,

ne~(y-y0)-1/2

bow wave, ne~(y-y0)-1/2

A. S. Pirozhkov et al. (2010)

Experimental Setup (simplified)

Laser pulse

400 mJ, 27 fs, 9 TW

Ø25 μm @ 1/e2

6.5×1018 W/cm2

I-CCD

Electron

spectrometer

Be-

He

jet Toroidal mirror

Slit

Filters (Mo/C or Pd)

Spherical grating B-C

CD

Grazing-incidence spectrograph

(3.5-11 or 5-15 nm)

Acceptance angle Ω = 3×10-5 sr

60.0 64.50

200

400

600

800

1000

102.3 106.8 111.2 115.60

100

200

f = 0.885

0

Counts

/0

nH = 126*

/0

Counts

f = 0.885

0

100 150 2001

10

100

dE/(dħЧd, nJ/(eVЧsr)

ħ, eV

noise level

CCD Counts0a

200

bc

d

mλ, nm4 5 6 7 8 9 10 11 12 13 14 15 16 17 mλ, nm4 5 6 7 8 9 10 11 12 13 14 15 16 174 5 6 7 8 9 10 11 12 13 14 15 16 17

Bright resolved harmonics in the XUV

CCD Counts0 400

49.1 66.1 83.1 100.1 117.10

200

400

600

800 = 170

/0

Counts

74.3 83.0 91.70

200

400

600 f = 0.872

0

Counts

/0

CCD Counts0 150

mλ, nm4 5 6 7 8 9 10 11 12 13 14 15 16 17 mλ, nm4 5 6 7 8 9 10 11 12 13 14 15 16 174 5 6 7 8 9 10 11 12 13 14 15 16 17

a

b c

d

mλ, nm4 5 6 7 8 9 10 11 12 13 14 15 16 17 mλ, nm4 5 6 7 8 9 10 11 12 13 14 15 16 174 5 6 7 8 9 10 11 12 13 14 15 16 17

Modulated harmonics

BOW WAVE

wakefield

generated by

electron bow wave

wakefield

in the cavity

electron

bow wave

injected electrons

expelled

and

background

electrons

fill the cavity

second

bow wave

bow wave electronsbackground electrons

T. Zh. Esirkepov, et al., Phys. Rev. Lett. 101, 265001 (2008)

First Catastrophes

Electron density singularities

(folds & cusps)

from the Catastrophe Theory

Mechanism of harmonic generation

3D PIC

Robust mechanism based on wide-spread phenomena Relativistic self-focusing, a0

Wake wave, ω0

Folding of phase space, cusps in e density, ne

(mathematical Theory of Catastrophes)

Radiation of compact charge distribution

(mathematics similar to

the nonlinear Thomson scattering)

Collective effects in relativistic plasma

The photon number and X-ray pulse energy within the spectral range of 90-250 eV

reach (1.8±0.1)×1011 photons/sr and (3.2±0.2) μJ/sr, respectively

** 3

H 0

f

~n a

22 4 2 2 4 / 3 5/ 6 1/ 3

e 0 0 e 0 e 08

eW N a N P n

c

Conclusion (XUV Harmonics)

Bright XUV harmonics from relativistic underdense plasma

Resolved harmonic orders >120 (λx ≈ 7 nm)

Unresolved up to the “water window”

New, robust HHG mechanism:

relativistic plasma + theory of catastrophes

Convenient, simple setup with one laser pulse

Replenisheable, debris-free target (gas jet)

Max harmonic order scaling n ~ a03

a0 increased by the self-focusing

Bright coherent XUV/x-ray source

Many potential applications

4. Overdense Accelerating Mirror

T.Zh. Esirkepov, et al., Phys. Rev. Lett. 103, 025002 (2009)

Reflected light structure:

Fundamental mode

High harmonics

Shift due to acceleration

Ez

1st2nd

Reflected cycles

Source

tim

e

t

Field along x-axisSpectrum at fixed time

0

1 ( )(2 1), 1,2,3...

1 ( )n n

0

( )t d

– time of emissiontime of detection:

Dashed curves:

Accelerating Double-Sided Mirror: Boosted HOH

5. Strong Field Limits in the Ultra Relativistic

Interaction of Electrons with the Electro-Magnetic

Wave in PlasmasEquations of electron motion are:

Radiation friction force is given by

Here , is proper time:

4-velocity is

and is 4-tensor of EM field

i2 ik i

e k

du em c = F u + g

ds c

22 2 ii i k k

2 2

d u2e d ug = - u u

3c ds ds

0,1,2,3i

,i

i

e

dxu

ds m c

p

/ds cdt s

j iij i j

A AF

x x

Intensity of radiation emitted by electron is given by

In circularly polarized EM wave (in plasma), whose

amplitude is equal to electron energy

losses are

For linearly polarized wave we have

2

i i

2 3

e

2e dp dpI =

3m c ds ds

00

e 0

eEa =

m c2

2( ) 0 0

0

14

2 3

e e

2e E eE=

3m c m c

22

( ) 0 0

0

31

8

4

2 3

e e

e E eE=

3m c m c

L.D.Landau & E.M.Lifshitz

“The Classical Theory of Fields”

e

Pattern of field emitted by

electron. T.Shintake, 2003

The EM wave can provide energy gain rate not higher than

Energy Balance Condition yields

for c- polarization and for l- polarization

where is classical electron radius

For laser wavelength of we obtain

and , which corresponds to laser intensity

Emitted - photon energy: Ya. B. Zel‟dovich, Sov. Phys. Usp. 18, 79 (1975)

A. G. Zhidkov,etal, PRL 88, 185002 (2002)

S. V. Bulanov, etal., Plasma Phys. Rep. 30, 221 (2004)

3

0 (70 350)rad= a MeV

1/3

3 / 4c

rad 0 ea = r

( ) 2

0 e 0ω m c a

2 2 13/ 2.8 10e er e m c cm

0 0.8 m

408c

rada =

23 2

lasI =(4.5-7.0)×10 W/cm

( ) ( )

1/3

4 /l

rad 0 ea = r

713l

rada =

Energy balance between particle acceleration and slowing down due to the

radiation damping force:

In the limit of relatively low laser amplitude, when

i.e. particle momentum

dependence on the wave amplitude is given by

In the limit , i.e.

Cross section of nonlinear

Thomson scattering

2 42

2 2 2

2 2 20 0rade e e

p p pa = + ε a +

m c (m c + p ) m c

2

0 rad rad1 a a = ε 1/3

18 23 210 I 10 W/cm

e 0p = m ca

1/4

0e

rad

ap = m c

ε

0 rada a 23 26 2

las10 I 10 W/cm

Quantum Effects become important, when the recoil due to photon emission

becomes of the order of the electron momentum, i.e. At

For electron gamma-factor it yields

the quantum limit:

EM wave amplitude and intensity correspond to

and

Here is the Schwinger field

1/22

e Q e 0γ γ = m c ω /1/4

e 0 radγ = a /ε

2 2

e e

2Q

0 0

2e m c 2 m ca = =

3 ω 3 ω

2 2 2

e

2Q QED

2em c 2α e 1E = = E , α =

3 3 c 13724 2

lasI = 8.5× 10 W/cm

QEDE

2 3

eQED

m cE =

e

Energy balance equation

with and

gives

At , i.e. electron-positron pair creation in vacuum

comes into play with probability

E

V.I.Ritus (1979)

( )

2 8

2 2 2

0 rad

e e

p pa = + ε

m c m c

3/81/2

0

e 2

e rad

0.34 ahωm c

c p

m ε

29 2

lasI 3.6 10 W/cm

0

2

e e

ω p=

m c m c

232 Γ(2/3)

243

22/3e

2

m2

3e

exp

2

QED

2 4

C QED

πE1 c Ew = -

4π E E

QEDE E

00

2

2

2

1/3

2

3

3

4

e

eQED

eQM

pp

e

rade

eEa

m c

m ca

h

e m ca

h

ma

m

ar

a

2

+ -29

24

24

23

Amplitude Intensity Regime

W

cm

e ,e in vacuum2.4 × 10

quantum effects5.6 × 10

relativistic p1.3 × 10

radiation damping1× 10

1rel-18 relativistic e1.3 × 10

Cross section of nonlinear

Thomson scattering

When the radiation damping effects are important and when they are

unimportant?

1.Electron motion in EM wave in vacuum.

Electron kinetic energy is i.e.

for we have

Condition in the co-moving with electron reference frame ( )

yields

or

RDE are not important!

2 / 22 2

e e em c ( -1)= m c a2 1a

2 / 2e a

1/3

3 / 4rad ea = r

03 / 4 3 / 2 3 / 43 2

rad e e e rad ea = r r a r

inva

83 / 4 10rad ea = r

2. EM wave interaction with high density thick plasma slab

‟Snow Plow‟ mechanism of EM wave -plasma interaction

a=320, n=256 ncr

Ni (x,y) t= 125 t=187 t=250 t=300

Ion Energy Spectrum Ion Phase Plane (Px,x) Ez(x,y)

‟Snow Plow‟ approximation

Stationary „snow plow‟ regime

i.e. for

predicts sub-relativistic ion motion.

We can use condition which means for

A. G. Zhidkov,etal, PRL 88, 185002 (2002); N. M. Naumova etal., PRL (2009)

RDE are important !

1/ 22 2 2 22

00 1/ 2

2 2 2 2

1/ 22 2 2

2

p

p

p

m c p pd En x p

dt m c p p

dx pc

dt m c p

1/ 22

0 0

1/ 32 2

0 0

/ 2

/ 2

p

p p p

v E n m v c

p m c E n m c p m c

if

if

0

500p pe

e

ma

m

1/3

3 / 4rad ea = r 408rada >

3. RPDA ion acceleration regime in laser-thin-foil interaction

Slab is accelerated to relativistic energy

Condition in the rest frame of reference ( )

shows that

RDE become less and less significant !

T. Esirkepov, M. Borghesi, S. V. Bulanov, G. Mourou,

and T. Tajima Physical Review Letters, 92, 175003 (2004)

1/ 32

(0) 2 00

0

3

2

ep

p pe

m ctp m c a

m l

1/3

3 / 4rad ea = r inva

03 / 4 3 / 2 3 / 43

rad e e e pa = r r p r m c

Compact laser ion accelerators are expected for applications and for fundamental science.

a) Fast Ignition of thermonuclear targets

with laser accelerated ions with laser

accelerated ions M. Roth et al., (2001)

b) Hadron therapy in oncology:

(laser accelerator + optical gantry) SV Bulanov & VS Khoroshkov (2002)

c) Compact heavy ion RPDA collider T. Esirkepov et al., (2004)

d) Laboratory modeling of the laser propulsion of the “Photon Sail”

Applications (Ions)

c) probing relativistic plasmas,

for the nonlinear wave theory

& for charged particle acceleration

d) novel regimes of soft X ray - matter

interaction: dominant radiation friction

& quantum physics cooperative phenomena.

Such X-ray sources are expected for applications and for fundamental science.

a) biology and medicine - single-shot X-ray

imaging in a „water window‟ or shorter

wavelength range.

b) atomic physics and spectroscopy –

the multi-photon ionization

& high Z hollow atoms (and ions).

PRL 65, 159 (1990)

Nature 406, 752 (2000)

self-focusing

soliton

wake wave

ion acceleration

PRL 79, 1626 (1997)

Applications (Coherent XUV)

The driver and source must carry 10 kJ and 30 J, respectively

Reflected intensity can approach the Schwinger limit

It becomes possible to investigate such the fundamental problems of nowadays physics, as e.g. the electron-

positron pair creation in vacuum and the photon-photon scattering

The critical power for nonlinear vacuum effects is

Light compression and focusing with the FLYING MIRRORS yields

for with the driver power

FM for Laser Energy & Power to Achieve the Schwinger Field

2 3e

QED

m cE

e

Pcr=10 PW

242.5 10cr W

2

0 01 /4

phm

0 ph

30ph

2 2245

4QED

cr

cE

215 14

16 64F F F F F F F F

29 210 /QEDI W cm

Courtesy of N.B.Narozhny

eEx2mc

ee

22 / | |mc eE

x

2mc

0

2

42

2

1exp

, ,

Schw

Schwc

Schw c

e

Ec Ew

E E

eE E

c m c

W.Heisenberg, H.Euler (1936)

J. Schwinger (1951)

Brezin, Itzykson (1970)

V.S.Popov (2001)

Predicted by the FM theory parameters of the x-ray pulse compared

with the parameters of high power x-ray generated by other sources

Compact Coherent Ultrafast X-Ray Source

X-ray source Wavelength

Pulse

Duration

Pulse

Energy

Mono-

chromaticity

(/)

Coherence

XFEL (DESY) 13.8 nm 50 fs 100 μJ 10–3

spatial

good

Plasma XRL 13.9 nm 7 ps 10 μJ 10–4

spatial

good

Laser plasma

wide spectrum

1 nm – 40 nm 1 ps – 1 ns 10 μJ 10–2 – 10–3 No

HHG 5 – 200 nm 100 attosec 1 μJ 10–2 – 10–3

spatial and

temporal

good

Flying Mirror 0.1 – 20 nm < 1 fs 1 mJ 10–2 – 10–4

spatial and

temporal

good

28

2 2

1KeV 12 10

1J mm mrad 0.1% bandwidth

lasB

Brightness

Peak brightness of various light sources

NIF

HiPER

ELI

Wake Bow Wave Photon BubblesThe Mouse Pulsar Chandra image of M87 “Black Widow” pulsar

Matlis

et a

l, (2006)

Ion Wake

experiment

sim

ula

tion

Borg

hesi, e

t al, (2

005)

Electron Wake

Electron Bow Wave

“Kalmar” Submarine

RPDA

Esirkepov et al (2004)

Esirk

epov e

t al (2

008)

S. V. Bulanov, T. Zh. Esirkepov, D. Habs, F. Pegoraro, T. Tajima,

Relativistic Laser-Matter Interaction and Relativistic Laboratory

Astrophysics , Eur. Phys. J. D 55, 483 (2009)

Conclusion

In high power laser matter interaction the relativistic mirrors appear

naturally and robustly in breaking nonlinear waves, as the electron

or/and electron-ion shells moving with relativistic velocity.

We may control and use them for high energy particle and photon

generation

Thank You

For Listening

Me

Relativistic Laser Plasmas:

G. Mourou, T. Tajima, S. V. Bulanov

Optics in the Relativistic Regime

Rev. Mod. Phys. 78, 309 (2006)

Astrophysics:

V. S. Berezinskii, S. V. Bulanov, V. L. Ginzburg, V. A. Dogiel, V. S. Ptuskin

Astrophysics of cosmic rays

(North Holland Publ. Co. Elsevier Sci. Publ. Amsterdam, 1990)

Relativistic Laser Plasmas & Astrophysics:

S. V. Bulanov, T. Zh. Esirkepov, D. Habs, F. Pegoraro, T. Tajima,

Relativistic Laser-Matter Interaction and Relativistic Laboratory Astrophysics

Eur. Phys. J. D 55, 483 (2009)