Nikolay B. Narozhny

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Nov 16, 2013 (3 years and 10 months ago)

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N
ikolay

B
.
Narozhny

National Research Nuclear
University

MEPHI, Russia

International
Momiji

School for Young Scientists
"High Field Science
-

Kyoto 2012"



What is vacuum?

vacuum emptiness

In QFT the vacuum is the state with the lowest possible energy (ground state)

1.
QED vacuum

:

No particles ( )

2.
QCD vacuum

:

Multiple vacuum states

can coexist

An example of a non
-
perturbative


vacuum state

QED
vacuum

Vacuum is “a boiling quantum liquid”!

(
I.Ya
.
Pomeranchuk
)

-

Compton length

The size of the loop

-

Compton time

An external electromagnetic field polarizes vacuum!

Vacuum in the presence of an external e
-
m
field
is
a
non
-
linear optical medium


Experimentally verified effects of vacuum polarization:



Spontaneous emission,
Casimir

effect, Lamb shift

Hans Heinrich Euler (1909

1941)

Werner Karl Heisenberg (1901
-
1976)


The start of “Nonlinear Optics in Vacuum”

W. Heisenberg and H. Euler, Zeitschr.
Phys. 98, 714 (1936)

“This polarization of the vacuum to be studied below will give rise to a distinction between the vectors

on the one hand and

on the other”

F. Sauter, ZS. f. Phys. 69, 742, 1931

permeability of vacuum

permittivity of vacuum


Plane wave field (

)
does not polarize vacuum!



The result is valid for a weakly variable field


Particles also polarize vacuum!

no e
-
m field

e
-
m field

Real photon
does not polarize vacuum

in the absence of e
-
m field

Real photon
does polarize vacuum

in the presence of e
-
m field!

Vacuum birefringence

Crossed field:

N.B.
Narozhnyi
,
Zh
.
Eksp
.
Teor
.
Fiz
.
55
, 714 (1968)

[
Sov
. Phys. JETP
28
, 371, 1969]

Vacuum is a dispersive, absorptive and
dichroic

medium at

R.
Baier
, P.
Breitenlohner
,
Acta

Phys.
Austr
.
25
, 212, 1967

Constant magnetic field:

C
onstant e
-
m field of general configuration
:

S.L. Adler, Ann. Phys. (NY)
67

212, 599 (1971)


I.A.
Batalin
, A.E.
Shabad
,
Zh
.
Eksp
.
Teor
.
Fiz
.
60
, 894 (1971)

[
Sov
. Phys. JETP
33
, 483, 1971]

The PVLAS experiment to measure the effect of vacuum birefringence is under way


(Ferrara University, Italy)

Cherenkov radiation

T.
Erber
, Rev. Mod. Phys.
38
, 626, 1966

V.I.
Ritus
,
Zh
.
Eksp
.
Teor
.
Fiz
.
57
, 2176 (1969) [
Sov
. Phys. JETP
30
, 1181, (1970)]

I.M.
Dremin
,
Pis’ma

Zh
.
Eksp
.
Teor
.
Fiz
.
76
, 185 (2002) [JETP
Lett
.
76
, 151, (2002)]



The condition for
ChR
:

The emission angle:

At:

at

For

and

focused to the diffraction limit

in the presence of the background due to Compton scattering

Harmonics generation

1.
A.E. Kaplan and Y.J. Ding, Phys. Rev. A
62
, 043805 (2000)

Harmonics generation by a laser beam propagating in an external magnetic field

2.
A. Di Piazza, K.Z. Hatsagortsyan, C.H. Keitel, Phys. Rev. D
72
, 085005 (2005)

Harmonics generation by two

colliding laser beams in vacuum

3.
A.M.Fedotov, N.B. Narozhny, Phys. Lett. A 362, 1 (2007)

Harmonics generation by a
focused


laser beam in vacuum

the effect of stimulated emission of a photon

The effect is detectable at !

Self
-
focusing

1.
M.
Soljacˇic
´

and M.
Segev
, Phys. Rev A,
62
, 043817 (2000)


A superposition of two plane waves, modified by a slowly varying envelope is considered. It is
shown that modified Maxwell equations in vacuum give rise to spatial
solitons
. The
solitons

exist
because the diffraction, which tends to expand the pulse, is exactly balanced by the nonlinear effect
of self
-
focusing that is trying to shrink the pulse. The peak intensity needed to support the
soliton

is

about
!




2.
D.
Kharzeev

and K.
Tuchin
, Phys. Rev A,
75
, 043807
(
2007
)

This diagram dominates at distances

Attractive two
-
photon exchange

Since the transverse size of a laser beam is

the self
-
focusing effect must exist!

The focusing angle

For a laser with :

(though the estimates of does not look very reliable!)

F.
Sauter
, 1931

W.
Heisenberg
, H.
Euler
, 1936

J.
Schwinger
,

1951

t

x

x



Vacuum is unstable in the presence of very strong

electromagnetic field!

QED scale:





length




energy




field





laser intensity

-


Compton
length

Question:

Is it possible to observe vacuum polarization effects?

Existing laser facilities:

NIF (LLNL, US)

UFL
-
2M (VNIIEF, RF)

LMJ (France)

HiPER

(GB)

ELI

XCELS (RF)

Most powerful facilities under construction or planning

Laser Fusion

High Field
Sciense

240 beams, 2MJ

192 beams, 1.8MJ

192 beams, 2.8MJ

pair creation by a laser field in vacuum becomes observable at intensities

J.
Schwinger,
Phys.Rev
., 82, 664
(1951)

The probability for vacuum to stay vacuum in a
constant electric field
:

-

the Heisenberg
-
Euler correction to
em

field
Lagrangian

!

Focused laser
pulse:

-

focal spot

radius,
-

pulse
duration

The ideal vacuum is stable in the presence of a laser field until the process of

pairs creation starts

However, even a single charged particle located in the focal area of an intense
laser pulse may lead to vacuum instability

Particles are accelerated by the field and …

A.M.
Fedotov

and N.B.
Narozhny
, in Extreme Light Infrastructure: Report on the GC Meeting, 27
-
28 April 2009,
Paris,
http://www.extreme
-
light
-
infrastructure.eu

A. M.
Fedotov
, N. B.
Narozhny
,
G.Mourou

and G.
Korn
, Phys. Rev.
Lett
.
105
, 080402
(20
10
).

A. R. Bell and J. G. Kirk, Phys. Rev.
Lett
.
101
, 200403
(2008).

Vacuum instability may be caused by:

a) A strong focused laser pulse

b) A “seed particle” inside a strong focused laser pulse

seed particle

To describe vacuum instability we should be able

to calculate probabilities of elementary processes!

a) photon emission

b) pair
photoproduction

1. Processes initiated by a seed particle

The probabilities are known for a monochromatic plane wave field

a)

b)

-


classical limit

-

the process is essentially quantum

Domain of formation

The space
-
time area where the functions which determine the probability amplitude

for a quantum process are formed

The formation length:

A.I.
Nikishov
, V.I.
Ritus
, 1964

Classically:

circular polarization

cone of radiation

the cone angle

PWF:

crossed field = constant field with

A.I.
Nikishov
, V.I.
Ritus
, 1964


Let and be the
space and time scale of variation of the
field, and

Arbitrary configuration of the field :

Then in the domain of formation any field is constant!

Approximation of locally constant field (LCFA)

at

A.I.
Nikishov
, V.I.
Ritus
, 1964

2. Pair creation by an e
-
m field in vacuum

Constant e
-
m field:

The number of
pais

created
per unit
volume and unit time

Pairs can be created if

A.I.
Nikishov
, 1969

The formation length (coherence length) for pair production in a constant field

A.I.Nikishov
,

ZhETF
, 57, 1210 (1969)

formation
length

and
time

The formula for the constant field can be applied to a
field
which is not static
and uniform
if


and
are space and time scale of variation of the
field.

-

local values of field invariants for the laser pulse

N.B.
Narozhny
, S.S.
Bulanov
, V.S. Popov, V.D. Mur, PLA 330, 1 (2004)

,
or

We can use the static field formula locally if

Pair creation by laser fields

Invariants for a single focused laser pulse

TE
-

pulse


TM
-
pulse


(focal plane, t=0)

An analytical model for a focused laser pulse was used

N.B.Narozhny
,

M.S.Fofanov
, 2000


Pair
production by a single focused pulse

N.B.
Narozhny
, S.S.
Bulanov
,
V.S
. Popov, V.D. Mur, PLA 330, 1 (2004
)

A.M.
Fedotov
, Las. Phys., 19, 214 (2009)





Δ
=
0.1




Δ
=
0.05



Δ
=
0.1




4·10
27



0.16


4.0·10
-
11


4.6·10
-
42


9.6·10
-
23



1·10
28


0.25



24


3.1·10
-
19


2.0·10
-
7




2·10
28




0.35


3.0·10
7




1.4·10
-
7




16




6·10
28




0.62


8.4·10
13




1.9·10
5


3.4·10
9


!!

Compare the total energy of produced pairs

with the energy of the laser pulse

COLLAPSE OF THE LASER PULSE

PAIR CREATION IMPOSES LIMITATION ON ATTAINABLE LASER INTENSITY

Number of pairs is growing very fast after the
threshold value of intensity



Pair
production by two colliding
pulses




Δ
=
0.1




Δ
=
0.05



Δ
=
0.1




1.0·10
26



2.5·10
-
2


4.5·10
-
12


6.0·10
-
9



7.1·10
-
13



2.0·10
26


3.6·10
-
2




5.1·10
-
2


7.2


1.8·10
-
2



2.5·10
26



4.0·10
-
2



14




1.2·10
3




6.0




5.0·10
26



5.7·10
-
2


2.6·10
7




5.5·10
8




1.8·10
7


!!

S.S.
Bulanov
, N.B.
Narozhny
,

V.S. Popov, V.D. Mur,
ZhETF

129, 14 (2006)

1.
The effect becomes observable at



2.
Small difference between e
-

and h
-
pulses

Collision geometry (linear polarization)

n=2

n=4

n=8

n=16

The threshold can be lowered essentially at the expense of

MULTIPLE PULSES TECHNOLOGY

The number of created pairs
N
e+e
-

and threshold
energy
W
th


f
or
different number
n

of colliding pulses

S. S.
Bulanov
, V.D. Mur, N.B.
Narozhny
,
et al.,
PRL, 104
,
2
20404

(20
10
)


Cascade can be self
-
sustained if the field accelerates charged particles

It is not the case for PWF or constant electromagnetic field,


where is an integral of motion,

The

self
-
sustained cascade can arise only in a focused laser field,

or for colliding laser pulses

Acceleration:

2. Vacuum instability initiated by a seed particle

The same result is valid for the case of 2 colliding linearly

polarized laser pulses

I.
Kostyukov
, 2012

The same result is valid for the case of 2 colliding linearly

polarized laser pulses

I.
Kostyukov
, 2012

The electron (positron) radiation lifetime (mean free path/c)

The photon lifetime

The escape time

The following hierarchy of time scales

should be respected for occurrence of electromagnetic cascade

(for optical frequencies)

-

determines a natural threshold for electromagnetic cascades.

The effect reminds the cosmic
-
ray air showers

The difference: the laser field is not only a target for

primary particles,

but also an accelerator for slow particles

Development of e
-
m cascade needs

a
seed

particle inside laser pulse

seed

particle

It can be a component of a pair created either
i
) by a photon,

or ii) by the field itself

Pairs are created by a focused laser pulse at

The theory of e
-
m cascades works!

FIG. 2. Pair production as a function of . The solid curve corresponds to the number Ne
of pairs produced by a single cascade process. The dotted curve shows the number of pairs
produced by multiple cascades generated by pairs created by two colliding circularly
polarized 10
fs

laser pulses. The branching point corresponds to the threshold value of
where the spontaneous pair production begins. The dash line shows the limit for
determined by the energy of the laser pulse. The laser frequency
ћ
ω

= 1
eV
. The inset shows
the magnified region of intersection of the curves.

Fedotov
,

A.

M.;
Narozhny
,

N.

B.;

Mourou
,

G.;
Korn
,

G.

PRL,
105, 080402 (2010)

where Monte
-
Carlo code for simulation of cascades in EM
field has been developed

N. V. Elkina, A. M. Fedotov, I. Yu. Kostyukov,
et al
.,

Phys.Rev
. ST A
B, 14, 054401
(2011)

These results are supported by

The cascade equations for a uniformly rotating homogeneous
electric field

The
μ

dependence of the mean values of energy , dynamical quantum parameter
χ
,
and the angle
θ

between the momentum of an electron and the field, over the estimated
values.
ћ
ω

= 1eV.

The increment
Γ

as a function of the dimensionless field strength µ
for two rotation frequencies
ћ
ω

= 1
eV

and
ћ
ω

= 0:66
eV

The cascade is initiated by a single electron located

at x = y = 0 with zero initial momentum for t = 0

(e.g., electron belongs to a pair created by a high
-
energy photon)

Pair creation, e
-
m cascades and their combination

are mechanisms for of laser field depletion!

BACK REACTION

SHOULD BE TAKEN INTO ACCOUNT

E
.
N.
Nerush

et

al
.
, PRL
106
, 035001

(20
11
)

QED cascade stops when the
laser energy is almost completely
converted into the cascade
energy.

seed particle

At the initial stage of the cascade development, the number of
created particles is growing exponentially. Then the growth
substantially slows down.





These results

confirm the N. Bohr’s conjecture
that the critical QED field strength can be
never attained for a pair creating
electromagnetic field!

e
-
m cascade can be initiated by
ultrarelativistic

particles

The effect was observed at SLAC
E144 experiment

D.L.Burke
, et al., PRL, 79, 1626 (1997)

Laser:


Energy of particles:

No of steps of the cascade/laser shot

Excellent agreement with experiment!

Present days PW laser + LWFA

-

LCFA works!

?
NO!

Particles loose energy very quickly!

Mechanism of acceleration begins

to work, if the field is strong enough.

Acceleration gives start to cascade development

which leads to depletion of the laser field.

Depletion of laser field can be observed at intensities

lower than the threshold intensity for pair creation!


ELI:

LCFA, the crossed field
,

Perturbation theory
does
not
work


high energy physics

in the presence of extreme laser field is an unexplored

branch of science!

Expansion parameter of perturbation theory at

Narozhny
, PRD, 1980

THANK YOU FOR ATTENTION!