International Momiji School for Young Scientists
"High Field Science - Kyoto 2012"
Nikolay B. Narozhny
National Research Nuclear
University
MEPHI, Russia
What is vacuum?
In QFT the vacuum is the state with the lowest possible energy (ground state)
1. QED vacuum :
No particles (
2. QCD vacuum :
)
An example of a non-perturbative
vacuum state
Multiple vacuum states
can coexist
vacuum
emptiness
QED vacuum
Vacuum is “a boiling quantum liquid”!
(I.Ya. Pomeranchuk)
The size of the loop
- Compton length
- 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
The start of “Nonlinear Optics in Vacuum”
W. Heisenberg and H. Euler, Zeitschr. Phys. 98, 714 (1936)
Hans Heinrich Euler (1909–1941)
Werner Karl Heisenberg (1901-1976)
F. Sauter, ZS. f. Phys. 69, 742, 1931
“This polarization of the vacuum to be studied below will give rise to a distinction between the vectors
on the other”
on the one hand and
permittivity of vacuum
permeability of vacuum
Plane wave field (
The result is valid for a weakly variable field
) does not polarize vacuum!
Particles also polarize vacuum!
no e-m field
Real photon does not polarize vacuum
in the absence of e-m field
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: S.L. Adler, Ann. Phys. (NY) 67 212, 599 (1971)
I.A. Batalin, A.E. Shabad, Zh. Eksp. Teor. Fiz. 60, 894 (1971)
Constant e-m field of general configuration: [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 emission angle:
The condition for ChR:
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 is detectable at
!
the effect of stimulated emission of a photon
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)
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!)
This diagram dominates at distances
t
Vacuum is unstable in the presence of very strong
electromagnetic field!
x
x
F. Sauter, 1931
W. Heisenberg, H. Euler, 1936
J. Schwinger, 1951
QED scale:
length
- Compton length
energy
field
laser intensity
Existing laser facilities:
Question: Is it possible to observe vacuum polarization effects?
Most powerful facilities under construction or planning
LMJ (France)
240 beams, 2MJ
NIF (LLNL, US)
UFL-2M (VNIIEF, RF)
192 beams, 1.8MJ
192 beams, 2.8MJ
HiPER (GB)
Laser Fusion
High Field Sciense
ELI
XCELS (RF)
pair creation by a laser field in vacuum becomes observable at intensities
!
The probability for vacuum to stay vacuum in a constant electric field:
- the Heisenberg-Euler correction to em field Lagrangian
J. Schwinger, Phys.Rev., 82, 664 (1951)
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. R. Bell and J. G. Kirk, Phys. Rev. Lett. 101, 200403 (2008).
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 (2010).
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!
1. Processes initiated by a seed particle
a) photon emission
b) pair photoproduction
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
Arbitrary configuration of the field
:
Approximation of locally constant field (LCFA)
Let
and
be the space and time scale of variation of the field, and
Then in the domain of formation any field is constant!
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.
N.B. Narozhny, S.S. Bulanov, V.S. Popov, V.D. Mur, PLA 330, 1 (2004)
- local values of field invariants for the laser pulse
We can use the static field formula locally if
, or
Pair creation by laser fields
Invariants for a single focused laser pulse (focal plane, t=0)
TE- pulse
TM-pulse
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
4·1027
0.16
4.0·10-11
4.6·10-42
9.6·10-23
1·1028
0.25
24
!!
3.1·10-19
2.0·10-7
2·1028
0.35
3.0·107
1.4·10-7
16
6·1028
0.62
8.4·1013
1.9·105
3.4·109
Number of pairs is growing very fast after the
threshold value of intensity
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
Pair production by two colliding
S.S. Bulanov, N.B. Narozhny,
pulses
V.S. Popov, V.D. Mur, ZhETF 129, 14 (2006)
Δ=0.05
Δ=0.1
Δ=0.1
1.0·1026
2.5·10-2
4.5·10-12
6.0·10-9
7.1·10-13
2.0·1026
3.6·10-2
5.1·10-2
7.2
1.8·10-2
2.5·1026
4.0·10-2
1.2·103
6.0
5.5·108
1.8·107
5.0·1026
5.7·10-2
14
2.6·107
!!
1. The effect becomes observable at
2. Small difference between e- and h-pulses
The threshold can be lowered essentially at the expense of
MULTIPLE PULSES TECHNOLOGY
Collision geometry (linear polarization)
n=2
n=8
n=4
n=16
The number of created pairs Ne+e- and threshold energy Wth
for different number n of colliding pulses
S. S. Bulanov, V.D. Mur, N.B. Narozhny, et al., PRL, 104,
220404 (2010)
2. Vacuum instability initiated by a seed particle
Acceleration:
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
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!
Fedotov, A. M.; Narozhny, N. B.;
Mourou, G.; Korn, G.
PRL, 105, 080402 (2010)
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 ћω = 1 eV. The inset shows
the magnified region of intersection of the curves.
These results are supported by
N. V. Elkina, A. M. Fedotov, I. Yu. Kostyukov, et a
Phys.Rev. ST AB, 14, 054401 (2011)
where Monte-Carlo code for simulation of cascades in EM
field has been developed
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. ћω = 1eV.
The increment Γ as a function of the dimensionless field strength µ
for two rotation frequencies ћω = 1 eV and ћω = 0:66 eV
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
(2011)
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)
seed particle
QED cascade stops when the
laser energy is almost completely
converted into the cascade
energy.
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,
Expansion parameter of perturbation theory at
Narozhny, PRD, 1980
Perturbation theory does not work – high energy physics
in the presence of extreme laser field is an unexplored
branch of science!
THANK YOU FOR ATTENTION!