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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)