On the Schwinger limit attainability with extreme power lasers

On the Schwinger limit attainability
with extreme power lasers
Sergey V. Bulanov
Kansai Photon Science Institute, JAEA, Kizugawa, Kyoto 619-0215, Japan

Acknowledgment
T.Esirkepov, Y.Hayashi, M.Kando, H.Kiriyama, J.Koga, K.Kondo, H.Kotaki, A.S.Pirozhkov
Kansai Photon Science Institute, JAEA, Kizugawa, Kyoto 619-0215, Japan
Y.Kato
The Graduate School for the Creation of New Photonics Industries, Hamamatsu, Japan
S.S.Bulanov
University of California, Berkeley, CA 94720, USA
A.G.R.Tomas
University of Michigan, Centre of Ultrafast Optical Sciences, Ann Arbor, MI 48109, USA
G.Korn
Max Plank Institute of Quantum Optics, Garching, Germany
A.G.Zhidkov
Central Research Institute of Electric Power Industry, Yokosuka, Kanagawa, Japan

Preface
The critical electric field of quantum electrodynamics, called also the Schwinger field, is so
strong that it produces electron-positron pairs from vacuum, converting the energy of light
into matter. Since the dawn of quantum electrodynamics there has been a dream on how to
reach it on Earth. With the rise of the laser technologies this field becomes feasible through
construction of extreme power lasers or with the sophisticated usage of nonlinear processes
in relativistic plasmas.
Recently there were raised doubts on whether or not the Schwinger field can be reached
with lasers. It was claimed that the laser with intensity well below the Schwinger limit creates
an avalanche of electron-positron pairs similar to a discharge, and the focused laser pulse
exhausts its energy before attaining the Schwinger field. This reasoning weakens one of the
most attractive motivations for extreme power laser development, i.e. producing matter from
vacuum by pure light in fundamental process of quantum electrodynamics in the
nonperturbative regime.
•A. R. Bell and J. G. Kirk, “Possibility of Prolific Pair Production with High-Power Lasers ” Phys. Rev. Lett. 101, 200403 (2008)
•A. M. Fedotov, N. B. Narozhny, G. Mourou, G. Korn, “Limitations on the Attainable Intensity of High Power Lasers” Phys. Rev. Lett. 105, 080402 (2010)

Introduction
Outline
What is better, circular or linear table top accelerators,
for reaching the quantum limits?
Towards antimatter creation in vacuum in experiments
with present day lasers
Conclusion

Introduction

e - - e + pairs created in the trident type process
• e - - e + generation in laser-solid target interaction
(trident mechanism of the e - - e + pair generation)
C.Gahn, et al., Phys. Plasmas 9, 987 (2002)
H.Chen, et al., Phys. Plasmas 16, 122702 (2009)
H.Chen, et al., Phys. Rev. Lett. 105, 015003 (2010)
28
e N e
e e
2 2
re( Z)
ln 1
27
mc e
r e / m c , e / c
1/137
2 2 2
e e
p
2

Breit-Wheeler process of e - - e +
generation 'e e with
if
' e mc
2 2 4
Multiphoton inverse Compton
&
Multiphoton B-W processes
50 GeV
Breit-Wheeler process of e - - e + generation
30GeV
G. Breit, J. A. Wheeler, Phys. Rev. 46, 1087 (1934)
D. L. Burke, et al., Phys. Rev. Lett. 79, 1627 (1997)
e N
e
0
N e e
1.6 ps a0 0.3
0
( E/ E ) 0.3
e S e
r
ee
2
( E / ES)( / mec) 0.15
2 2
e

“Schwinger” mechanism of e - - e + pair creation
The energy is plotted against the momentum and
coordinate (the electric field is parallel z-axis). The
solution to the Dirac equation shows that the -
function is large only in the regions I and III. In the
region II, it decreases exponentially. Therefore the
transmission coefficient through region II, which gives
the pair creation probability, has the order of
2 3
magnitude exp m c / | e | E
.
e
Quasiclassical regime ( F. Sauter, 1931)
2 z2 mec
/ eE
2
w Aexp
| p( z) | dz
z m
c / eE
1
2
e
2 3 1
4mc
e
2
Aexp
1 d
| e | E
ES
exp
E
w
0
Probability
( W.Heisenberg, H.Euler, 193 6)
2
1 2 3
2 3
| e | E mec mec mec
exp
3
2 3
4
m c
| e | E
e

We reach a limit when the nonlinear QED with the electron-positron pair creation in the
vacuum comes into play, at the “Schwinger electric field”, which corresponds to so strong
electric field that it starts to create the electron-positron pairs at the Compton length
/ mc
C e
, i.e.
2 3 2
e e
It corresponds to the intensity410
W / cm
O. Klein (1929)
N. Bohr (1931)
F. Sauter (1931)
W.Heisenberg, H.Euler (1936)
J. Schwinger (1951)
E.Brezin, C.Itzykson (1970)
V. S. Popov (1971)
V.I.Ritus (1979)
A. Ringwald (2001)
Upper Limit on the EM wave amplitude
E
S
m c m c
e e
29 2
C
V. S. Popov, Phys. Lett. A 298, 83 (2002)
N. B. Narozhny et al., Phys. Lett. A 330, 1 (2004)
S. S. Bulanov et al., Phys. Rev E 71, 016404 (2005)
S. S. Bulanov et al., JETP, 102, 9 (2006)
A. Di Piazza et al., Phys. Rev. Lett. 103, 170403 (2009)
R. Schutzhold, Adv. Sci. Lett. 2, 121 (2009)
G. V. Dunne et al., Phys. Rev. D 80, 111301(R) (2009)
C. K. Dumlu, G. V. Dunne, Phys. Rev. Lett. 104, 250402 (2010)
R. Ruffini et al., Phys. Rep. 487, 1 (2010)

2 2 2
E B F F F
*
F inv, G ( EB) inv
2 4 4
2 2 2 2
E F G F, B F G F
are the electric and magnetic fields in the frame where they are parallel
W
ee
for e 0probability W 0
2 2
eES
b
ebcoth
exp
3 3
4
c e e
b = B/ E , e E/ E
ee
S S
2 2
eESchw
2
at b 0 probability W
e exp
ee 2 3
4
c e
+ -
The number
of eepairs
Dimensionless parameters
c lxl ylz 4
N W dVdt
exp
e e e
e e
4 4 m 64
C em

Laser Power to Achieve the Schwinger Field
If the laser intensity approaches the Schwinger limit
being focused into the “lambda-cube” volume, the required power is
Vacuum polarization with the cross-focusing due to nonlinear terms in the H-E Lagrangian
becomes seen at i.e. at
cr
I 410 29 2
W/cm
2
1
FF 5FF14FFFF 16 64
2 2 2
45
cE
24 S
cr
2.510
W
4
1μm
2
2 3
2 3
1 | e | E mecmec mc
e
w
exp
3
2 3
4 mc
| e| E
Huge pre-exponential factor lowers the intensity (and power) at which the pairs occur
e
QED
2
21
cr
10
W
1μm
2
G. Mourou, T. Tajima, S.V. Bulanov, Rev. Mod. Phys. 78, 309 (2006)

The number of electron-positron pairs produced in
the focus of a single pulse or two colliding pulses
I, W/cm 2 E 0/E s N e , single
pulse
N e , two
pulses
2.5x10 26 4x10 -2 - 14
5x10 26 5.7x10 -2 - 2.6x10 7
5x10 27 0.18 25
1x10 28 0.25 3x10 7
S. S. Bulanov, N. B. Narozhny, V. D. Mur, V.S. Popov, JETP, 102, 9 (2006)

Multiple Colliding EM pulses:
The scheme of
interaction
S. S. Bulanov, V. D. Mur, N. B. Narozhny, J. Nees, V. S. Popov, Phys. Rev. Lett. 104, 220404 (2010)
A Way to Lower the Threshold
of Pair Production from
Vacuum
N pulses N ± at W=10 kJ W(kJ)
to produce one pair
2 9.0 x 10 -19 40
4 3.0 x 10 -9 20
8 4.0 10
16 1.8 x 10 3 8
24 4.2 x 10 6 5.1

In the case of time - dependent field :
2 2mc
e
Here K with K0
K e
0
Nonadiabatic Pair Production
2
p|| p
W
exp g K b1Kb2K ee
mecmec
e
In adiabatic regime (tunneling), 1,
8 2 4
2 2 2
K K K
K g K 1 , b1K, b2K1
4
In nonadiabatic
regime (multiphoton), K 1, g K
K
1
1ln 0.386 ,
2 K
8
K
2
b1K
ln K
2
0.386 , b2K
ln K 1.39
K K
5/ 2
4 2K0
1 mc e
4
K
The probability W
w
ee n 3/ 2 3 2 V. S. Popov, “Tunnel and multiphoton
nK 2 c m 0
ec
e ionization of atoms and ions in an intense
laser field (Keldysh theory)”
Phys.-Usp. 47 855 (2004)

What is better, circular or linear table top accelerators,
for reaching the quantum limits?
S. S. Bulanov, T. Zh. Esirkepov, A. G. R. Thomas, J. K. Koga, S. V. Bulanov,
“On the Schwinger limit attainability with extreme power lasers”
Phys. Rev. Lett. 105, 220407 (2010)

Electromagnetic cascades induced by pairs
2
e F p E E
1
n n
m c E 4e
e 3 4
e
e S
I 2.510 W / cm
26 2
0
D.L.Burke et al., PRL 79, 1626 (1997)
0.3, 0.15
e
+
e
•W.Heisenberg, H.Euler (1936)
•N. B. Narozhny, “Extreme Power Photonics: New Phenomena” ISTC-ELI/HiPER/PETAL Workshop, 2008
•A. R. Bell and J. G. Kirk, “Possibility of Prolific Pair Production with High-Power Lasers ” Phys. Rev. Lett. 101, 200403 (2008)
•A. M. Fedotov, N. B. Narozhny, G. Mourou, G. Korn, “Limitations on the Attainable Intensity of High Power Lasers” Phys. Rev. Lett. 105, 080402 (2010)
-
e
-
e
-
e

e - - e + , -ray plasma
generation via the multi-photon B-W process
Key dimensionless Lorentz invariant parameters are
e A eE
a
m cmc 2
e e
e e
F
3
p
4
2
e
E
2
p B
p E
2
E p
e S e S e S S e
m c E m cE m cE E m c
2
e F k
2
2
0
3 4
mec 2 4
mec 0
a
Nee

Probability of pair creation
2 2 3
3/ 2
3 e me c
8
|| 3 for
32 2 3
W ( ) exp 1
7
2 2 3
2/3
27 (2 / 3) e m 3 e c
||
5 3 for
56 2
W ( ) 1
The number of absorbed laser photons:
N a
0 0
Photon mean - free -path before the pair is created: lm..
f p 220
l
0.2
a a
H. Reiss, J. Math. Phys. 3, 59 (1962)
A. I. Nikishov, and V. I. Ritus, „Interaction of Electrons and Photons with a Very Strong Electromagnetic Field‟, Sov. Phys. Usp. 13, 303 (1970)
V. I. Ritus, „Quantum Effects of the Interaction of Elementary Particles with an Intense Electromagnetic Field‟, Tr. Fiz. Inst. Akad. Nauk SSSR 111, 5 (1979)
K. T. McDonald, “Fundamental Physics During Violent Acceleration”, AIP Conf. Proceed. 130, 23 (1985)

, 1at I 10
e
Avalanche
1/ 4
1/ 2
2
mecES
0
2
E mec 24
2( E / E ) a
e S
W/cm
+ -
The number of e - e pairs grows exponentially :
0
N exp( t)
"... even a single electron-positron
pair
created by a superstrong laser field
in vacuum would cause development of an avalanchelike QED cascade which
rapidly depletes the incoming laser pulse.
... the electric field of the critical QED strength E S could never be created...
...destruction of the laser pulse will take place much earlier than discussed..."
A. M. Fedotov, N. B. Narozhny, G. Mourou, G. Korn, “Limitations on the Attainable Intensity of High Power Lasers” Phys. Rev. Lett. 105, 080402 (2010)
2
ee

Avalanche discharge as the Geiger Counter
It can indicate on the Schwinger process provided the laser intensity required for the
avalanche is small enough, I*

Colliding EM Waves:
Circularly Polarized v.s. Linearly Polarized
Credit: T. Shintake
power emitted by electron
rotating in CP wave :
2r
P m c ( 1)
3
maximum frequency :
e 2 2 2 4
C, 0 e e e e
0.29
max 0
3
e
power emitted by electron
oscillating in LP wave :
r
P m c ( 1)
3
maximum frequency :
e
2 2 2
L, 0 e e e
2
max 0
2
e

Radiation friction effects (LAD):
Circularly Polarized v.s. Linearly Polarized
energy balance
a
2 2 2 6
0 e rad e
0
( 1)(1 ),
1
tan
1/
3
rad
3
rad e
radiation friction important at :
a
400, 23 2
i.e. at I 4.510 W/cm
quantum recoil important at :
a ( m c /
)
e
2 1/ 2
0
24 2
i.e. at I 410 W/cm
,
energy balance
mca= mc
+ 2 -
2 2
0 e 0
rad 0 e e
= 2r/ 10
rad
a
0
2
e
1
rad
8
radiation friction important at :
i.e. at E m c e E
2 4 3
3 e / 3 137 S
quantum recoil important at :
mci.e. a mc/
0. 21
2 2
m e e
e
i.e. at I 10
29
W/cm
2
0

Threshold for the e - - e + Avalanche:
Circularly Polarized v.s. Linearly Polarized
1/ 4
E p
E a
sin 1,
0
e
ES mec ES
rad
where
0
with a
S
I*
610 3
sin 1/
rad e ,
at a a 5.510 2 3
rad S
mc e 5.110
avalanche threshold :
25
0
W/cm
2
5
E
e no any avalanches
E
INSTABILITY
OF ELECTRON
TRAJECTORY
??!!
S
when particle velocity is parallel
to its acceleration
We must take into account
small but finite magnetic
field

The scheme of
interaction
S. S. Bulanov, V. D. Mur, N. B. Narozhny, J. Nees, V. S. Popov, Phys. Rev. Lett. 104, 220404 (2010)
Multiple Colliding EM pulses
Near the origine
in the limit N
E e a cos( t) e 0.1 a k r z cos( t)
Be z 0 0 r 0
2
0 0
a0 k0rsin( 0t)
8
pulse
∞
electric and magnetic field
can be approximated
in cylindrical coordinates as :

Bφ
1
0
1
F a
TM /
2
3D EM configuration
TM - mode
The vector field shows r- and z-components of the poloidal electric field in the plane (r,z):
The color density shows the toroidal magnetic field distribution B ( r, z)
The first Poincare invariant
2 2 2 2
F / a ( E B
) / 2a
TM 0 0
TM
configuration :
Magnetic field
B(
R,
)
e
a sin( t) J ( k R) L (cos )
0 0
1/ 2
8 R
Electric fied l
0
B
E ik
n1/ 2 0
l
n
E(
rz , )

Eφ
1
0
1
3D EM configuration
TE - mode
F a
TE /
2
The vector field shows r- and z-components of the poloidal magnetic field in the plane (r,z):
The color density shows the toroidal electric field distribution, E ( r, z)
The first Poincare invariant : c) 2 2 2 2
F / a ( E B
) / 2a
TE 0 0
TE configuration
Electric field
E(
R,
)
e
a sin( t) J ( k R) L (cos )
0 0
1/ 2
8 R
Magnetic field 0
B ik E
n1/ 2 0
l
n
B(
rz , )

Threshold for the e - - e + avalanche
in 3D TM configuration
- +
INSTABILIT
Y : e (e )trajectory in r, z - plane t 1, a 1
p ( t) m c a t,
z e
0 0
0 0
a0k0r00t 0t
pr( t) mec I 3/ 2 1 , 3/ 2
2 2
a0r0 0t a0r0 0t 0t 0t
r( t) I 3/ 2 1 I 3/ 2
0 + I 3/ 2 2 3/ 2
2 2 16
2 2
with kr
(2. 5 a / a ) ; growth rate : = / 2
0
1/ 2 3/ 2
0 S
0
a / a 0.105
S
27 2
which corresponds to I*
410W/cm 0
0 0
THRESHOLD
: assuming t 0.1
we find that the avalanche
will start at

The pairs are created in a small 4-volume near the electric field maximum
(maximum of F ) with the characteristic size
TM
Here normalized Schwinger field is
5 a
16 aS 3/ 2 4
2 0 0
0 0 0 5
r z ct
2
mc e 5.110
Integrating over the 4-volume the probability of the pair creation
we obtain the number of pairs produced per wave period,
a
S
0
3/ 2
5 4 a S
N W
dVdt a 3 0 exp
e e e e
4
a
The first pairs can be observed for an one-micron wavelength laser intensity of the order of
27 2
10 W/cm , which corresponds to a0 / aS0.05 , i.e. a characteristic size, 0 ,
Is approximately equal to
r
0.04
0
5
2
F a
TM /
0
2
z0
r0

Towards antimatter creation in vacuum
by present day lasers
(experiments to conduct in next few years)
S. V. Bulanov, T. Zh. Esirkepov, M. Kando, J. K. Koga, A. S. Pirozhkov, Y. Kato, S. S. Bulanov, G. Korn, A. G. Zhidkov
“Extreme Field Limits in the Ultra-Relativistic Interaction of Electromagnetic Waves with Plasmas”
Proceed. of XRL-2010 Conf.

Multi-photon creation of e - - e + , -ray plasma
during ultrarelativistic electron beam collision
with the EM pulse
2 2 2 1/ 2 2 2 2 1/ 2
E ( mecp0) | p0 |
0 ( mecp0) | p0
|
e
a
,
2
E
S mec
mec
mec
The electron is not scattered aside by the PW, 30 fs laser ponderomotive force if
eclasa/ 2w 500
For 1mPW laser pulse focused to a few micron focus spot the amplitude is
2
a 10
3
the parameter e becomes equal to unity for 0 2.510, i.e. for the electron energy of
about of 1.3 GeV.

Gamma-ray photon generation via
the nonlinear Thomson scattering
When a counter-propagating electron collides with the laser pulse its longitudinal momentum
decreases:
2
a mec px | p0 | mec2221/
2
2[( m c p ) |
p |]
In the boosted frame of reference where the electron is at the rest the laser frequency is
related to the laser frequency in the laboratory frame as
0 1
0
0
2
1 a 1
0
The energy of emitted photon is
The number of emitted photons during one wave period is
e
0.3 a
0
0 0
3
3
Na 4
J. Koga, T. Esirkepov, S. V. Bulanov, „Nonlinear Thomson scattering in the strong radiation damping regime‟, Phys. Plasmas 12, 093106, 2005
Cross section of nonlinear
Thomson scattering

What the values of e and for the parameters of
JKAREN-PW + Microtron electrons are?
We assume 1 PW, a=100 and 150 MeV electron energy (JAEA Microtron)
&
2 2 2 1/ 2
0 ( mec p0 ) | p0
| 02100300
e a 2a
2 2 e
5
mec
mec
0.12
mec 5.110 The number of electrons colliding
with the laser pulse is about 300.
2
2 4 2 2
0
2 2
0 1.2 (3)
10 (10 )
-3
a 1.2
2 2 2 e a 2
4 10
11
S e e e e 2.510 E
E m c m c m c m c
H. Kiriyama et al., Applied Optics, 49, 2105 (2010)

What the values of e and for the parameters of
JKAREN-PW +LWFA electrons are?
We assume 1 PW, a=150 and 1.25 GeV (LWFA ) electron energy:
&
2 2 2 1/ 2
0 ( mec p0 ) | p0
| 021502500
e a 2a
2 2 e
5
mec
mec
1.5
mec 5.110 2
2 6 2 2
0
2 2
0 1.2 (2.5) 10 (1.5 10
)
a 1.2
2 2 2 e a 2
11
S e e e e
2.510 E
0.4
E m c m c m c mc The number of electrons colliding
with the laser pulse is about 10 8 .

T. Tajima, J. M. Dawson (1979)
Theory
LWFA
Experiment

What values of e and for the parameters
of FM generated EM pulse +LWFA electrons are?
We assume 1 PW, a=150, 1.25 GeV (LWFA ) electron energy, ph=5 (E=2 phE 0, =4 2 ph 0):
2 2 2 1/ 2
E ( mec p0) | p0 | E 2 150 2500
e 2 e ph 10
5
E
S mec
15
ES
5.110
& (in multi-photon inverse Compton scattering regime)
E
1.2 5 10 2.510 3
E m c m c
The number of electrons colliding
with the laser pulse is about 10 6 .
2 3
S e
2 1.2 e pha
e
0
2 5
5.110

EM Pulse Intensification and Shortening by Flying Mirror
cvph '' 4
c-v ph
2
ph 0
''
2
max 6
ph
I0
I D
Theory
paraboloidal relativistic mirrors formed by the
wake wave left behind the laser driver pulse
S.V.Bulanov, T. Esirkepov, T. Tajima, Phys.Rev.Lett. 91, 085001 (2003)
N x , 1/sr
4x10 7
3x10 7
2x10 7
1x10 7
p
1
0.9
0.8
0.7
0.6
0.5
0
6 8 10 12 14
Experiment
, nm
z, m
20
10
0
-10
12 m
-20
-400 -200 0
180 fs
200 , fs s
x = 14.3 nm
Δ x = 0.3 nm, Δ x / x = 0.02
Reflected pulse duration: x ~ 1.4 fs
(femtosecond pulse)
, arb. u.
1.0
M. Kando, et al., Phys. Rev. Lett. 99, 135001 (2007)
A. S. Pirozhkov, et al., Phys. Plasmas 14, 080904 (2007)
M. Kando, et al., Phys. Rev. Lett., 103, 235003 (2009)
0.75
0.50
0.25
0
p

These estimations are too optimistic….
What is the role of the radiation damping?

Radiation friction effects
du 2e
ds 3c
2
2
mec
eFu
g
The radiation friction force in the Landau-Lifshitz form is given by
Retaining the main order terms, we obtain equation for the x-component of the electron
momentum
2
dpx 2 px re
rad0 a (2 t)
, rad
dt m c 3
Its solution is
2
2
2e
Fe g u u F F u F u F u u
3 2
3mec
x
mec
p (0) m c m c
p ( t) , p ( t)
x e e
x t
2
mec rad0px(0) a (2t ') dt '
0
x
t
2
rad0lasa0 L. D. Landau, and E. M. Lifshitz, The Classical Theory of Fields, Pergamon, 1975
I. Pomeranchuk, “Maximum Energy that Primary Cosmic-ray Electrons Can Acquire on the Surface of the Earth as a Result of Radiation in the Earth's Magnetic
Field”, J. Phys. USSR, 2, 65 – 69, 1940
e

Numerical solution of the equations of the electron motion in the
laser field with the radiation friction effects taken into account
Time dependence of the electron and photon parameters for a 1.25 GeV electron beam
interaction with a PW (a=150, 9 fs) laser pulse. a) Gaussian pulse; b) Super-Gaussian
(m=4) pulse. The electron energy before and after the interaction with the laser pulse
equals 1.25 GeV and 0.25 GeV, respectively. The parameter e
reaches the
maximum value 0.5 and
is equal to 0.3.

H. Kotaki et al.,
Phys. Rev. Lett. (2009)
Experimental setup
M. Kando, et al.,
Phys. Rev. Lett., 103, 235003 (2009)

Years
Parameters
e
a 0
e
Schedule of planned experiments
I II&III IV&V
300 2500 2500
100 100 10
0.05 0.5 2.5
a rad =(/ e -1/3 60 30 6

Conclusion

Linearly polarized pulses save room for the Schwinger limit attainability. In a linearly
polarized electric field an electron moves with parallel velocity and acceleration
emitting much less photons with substantially lower energy, suffering much less
from the radiation friction and quantum recoil effects. Thus as a result of enabling
the increase of laser intensity without an avalanche onset, for a sufficiently small
amount of residual electrons, linearly polarized tightly focused pulses will reveal
“pure” Schwinger electron-positron pair creation.
One can see an analogy with circular and linear electron accelerators where the
constraining role of synchrotron radiation losses for the former is reduced in the
latter.
The experiments in this field will allow modelling the state of matter in the Universe,
the cosmic Gamma Ray Bursts, and will open a way for developing new type of hard
EM radiation sources:
20 MeV, several fs, gamma-ray burst.

Thank you for listening me!