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100-лет со дня рождения И . Я . Померанчука ИТЭФ 5-6 июня 2013. Сверхмощные лазеры - инструмент для исследования свойств вакуума. Н.Б . Нарожный. Национальный Исследовательский Ядерный Университет МИФИ. Extreme Light Road Map. G. Mourou. F. Sauter. Vacuum Polarization. IZEST C 3. - PowerPoint PPT Presentation
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Сверхмощные лазеры - инструмент для исследования
свойств вакуума
НБ Нарожный
Национальный Исследовательский
Ядерный Университет МИФИ
100-лет со дня рождения ИЯ ПомеранчукаИТЭФ 5-6 июня 2013
Vacuum Polarization IZEST C3
Extreme Light Road MapF Sauter
G Mourou
HERCULES Petawatt Laser
Center for Ultrafast Optical Science (CUOS) Michigan USA
Victor Yanovsky
He directs the HERCULES laser - the highest intensity laser in the world and is interested in high intensity laser physics ultrahigh-intensity intensity interactions with solids particle acceleration and X-ray generation in laser-matter interaction
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 18MJ 192 beams 28MJ
I amp I L = 1023W=cv2I L =1023
ПЛАНИРУЕТСЯ
1 Создание TiSa лазера генерирующего импульсы длительностью 10 - 15-fs с энергией в районе 700 J (50 to 70 PW)
2 Активный фазовый контроль усиленных пучков и использование оптики с большой апертурой позволит получить интенсивность порядка
3 Комбинация10 одиночных 50 ndash 70-PW пучков приведет к пиковой мощности 500 ndash 700 PW и соответствующей интенсивности на мишени порядка или больше
(Proposal for an European Extreme Light Infrastructure wwwextreme-light-infrastructureeu)
ELI-Ultra High Field Facility
Место строительства еще дбопределено
laquoМеждународный центр исследованийэкстремальных световых полейraquo (ЦИЭС)
Комплекс будет включать 12 одинаковых каналов в каждом из которых будет генерироваться импульс с энергией 300-400 Дж длительностью 20-30 фс
максимальной интенсивностью при фокусировке более 10^23 Втсм2
F Sauter 1931W Heisenberg H Euler 1936J Schwinger 1951
QED is a nonlinear science at
The only experiment on Nonlinear QED ndash E144 (SLAC 1996 -1997)
Nonlinear Compton scattering
CBula et al PRL 76 3116 (1996)CBamber et al PRD 60 092004(1999)
schematic drawing of the experiment
IP1 ndash interaction pointECAL ndash silicon-tungsten calorimeterCCM1 ndash gas Čerenkov monitor
Final Focus Test Beam at SLAC
The multiphoton version of Breit-Wheeler process was observed
DLBurke et al PRL 79 1626 (1997)CBamber et al PRD 60 092004(1999)
Pair production two-step process
This was the first (and the only) laboratory evidence for inelastic light-by-light scattering involving only real photons
Laser λ=1054μm (infrared) and λ=0527μm (green) The laser intensity could be varied the maximum focused intensity
Electron beam
Parameters of E144 experiment
The field was close to a monochromatic plane wave field
Two Lorentz and gauge invariant parameters
Dimensionless intensity parameter
Dynamical parameter
(classical nonlinearity parameter)
(quantum nonlinearity parameter)
At the proper frame of electron
Parameters of E144 experiment
What we will have with new facilities
Fms optical pulses
Electrons
What does it mean experimentally
1 harmonics are undistinguishablelaser field works as a constant crossed field
2
e-m cascades will be observed
The effect was observed at SLAC experimentmultiplicity = 002
Analogue of cosmic-ray air showers
It could be the first experiment on laboratory astrophysics
3 Fms optical pulses
Electrons
Expansion parameter of perturbation theory at
Narozhny PRD 1980
Perturbation theory does not work
Nonlinear QED vacuum polarization effects have never been observed
Is it possible with new facilities
Vacuum in the presence of an external e-m field isa non-linear optical medium
Hans Heinrich Euler (1909ndash1941) Werner Karl Heisenberg (1901-1976)
The start of ldquoNonlinear Optics in Vacuumrdquo
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)
ldquoThis polarization of the vacuum to be studied below will give rise to a distinction between the vectors on the one hand and on the otherrdquo
F Sauter ZS f Phys 69 742 1931
permeability of vacuumpermittivity of vacuum
Vacuum polarization effects
1 Birefringence and dichroism of vacuumR Baier P Breitenlohner Acta Phys Austr 25 212 1967NB Narozhnyi Zh Eksp Teor Fiz 55 714 (1968) [Sov Phys JETP 28 371 1969]SL Adler Ann Phys (NY) 67 599 (1971) IA Batalin AE Shabad Zh Eksp Teor Fiz 60 894 (1971) [Sov Phys JETP 33 483 1971]
2 Photon splittingSL Adler Ann Phys (NY) 67 599 (1971)Z Bialynicka-Birula I Bialynicka-Birula PhysRev D 2 2341 (1971) VO Papanyan VI Ritus Zh Eksp Teor Fiz 61 2231 (1971) [Sov Phys JETP 33 483 1971]
3 Cherenkov radiation
T Erber Rev Mod Phys 38 626 1966VI Ritus Zh Eksp Teor Fiz 57 2176 (1969) [Sov Phys JETP 30 1181 (1970)]IM Dremin Pisrsquoma Zh Eksp Teor Fiz 76 185 (2002) [JETP Lett 76 151 (2002)]
4 Self-focusing in vacuum
M Soljacˇicacute and M Segev Phys Rev A 62 043817 (2000)D Kharzeev and K Tuchin Phys Rev A 75 043807 (2007)
NN Rozanov JETP 86 284 (1998)
5 Light-by-light scattering
A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)B E Lundstroumlm et alPhys Rev Lett 96 083602 (2006)
6 Harmonics generation
AE Kaplan and YJ Ding Phys Rev A 62 043805 (2000)A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)AMFedotov NB Narozhny Phys Lett A 362 1 (2007)
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
Vacuum Polarization IZEST C3
Extreme Light Road MapF Sauter
G Mourou
HERCULES Petawatt Laser
Center for Ultrafast Optical Science (CUOS) Michigan USA
Victor Yanovsky
He directs the HERCULES laser - the highest intensity laser in the world and is interested in high intensity laser physics ultrahigh-intensity intensity interactions with solids particle acceleration and X-ray generation in laser-matter interaction
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 18MJ 192 beams 28MJ
I amp I L = 1023W=cv2I L =1023
ПЛАНИРУЕТСЯ
1 Создание TiSa лазера генерирующего импульсы длительностью 10 - 15-fs с энергией в районе 700 J (50 to 70 PW)
2 Активный фазовый контроль усиленных пучков и использование оптики с большой апертурой позволит получить интенсивность порядка
3 Комбинация10 одиночных 50 ndash 70-PW пучков приведет к пиковой мощности 500 ndash 700 PW и соответствующей интенсивности на мишени порядка или больше
(Proposal for an European Extreme Light Infrastructure wwwextreme-light-infrastructureeu)
ELI-Ultra High Field Facility
Место строительства еще дбопределено
laquoМеждународный центр исследованийэкстремальных световых полейraquo (ЦИЭС)
Комплекс будет включать 12 одинаковых каналов в каждом из которых будет генерироваться импульс с энергией 300-400 Дж длительностью 20-30 фс
максимальной интенсивностью при фокусировке более 10^23 Втсм2
F Sauter 1931W Heisenberg H Euler 1936J Schwinger 1951
QED is a nonlinear science at
The only experiment on Nonlinear QED ndash E144 (SLAC 1996 -1997)
Nonlinear Compton scattering
CBula et al PRL 76 3116 (1996)CBamber et al PRD 60 092004(1999)
schematic drawing of the experiment
IP1 ndash interaction pointECAL ndash silicon-tungsten calorimeterCCM1 ndash gas Čerenkov monitor
Final Focus Test Beam at SLAC
The multiphoton version of Breit-Wheeler process was observed
DLBurke et al PRL 79 1626 (1997)CBamber et al PRD 60 092004(1999)
Pair production two-step process
This was the first (and the only) laboratory evidence for inelastic light-by-light scattering involving only real photons
Laser λ=1054μm (infrared) and λ=0527μm (green) The laser intensity could be varied the maximum focused intensity
Electron beam
Parameters of E144 experiment
The field was close to a monochromatic plane wave field
Two Lorentz and gauge invariant parameters
Dimensionless intensity parameter
Dynamical parameter
(classical nonlinearity parameter)
(quantum nonlinearity parameter)
At the proper frame of electron
Parameters of E144 experiment
What we will have with new facilities
Fms optical pulses
Electrons
What does it mean experimentally
1 harmonics are undistinguishablelaser field works as a constant crossed field
2
e-m cascades will be observed
The effect was observed at SLAC experimentmultiplicity = 002
Analogue of cosmic-ray air showers
It could be the first experiment on laboratory astrophysics
3 Fms optical pulses
Electrons
Expansion parameter of perturbation theory at
Narozhny PRD 1980
Perturbation theory does not work
Nonlinear QED vacuum polarization effects have never been observed
Is it possible with new facilities
Vacuum in the presence of an external e-m field isa non-linear optical medium
Hans Heinrich Euler (1909ndash1941) Werner Karl Heisenberg (1901-1976)
The start of ldquoNonlinear Optics in Vacuumrdquo
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)
ldquoThis polarization of the vacuum to be studied below will give rise to a distinction between the vectors on the one hand and on the otherrdquo
F Sauter ZS f Phys 69 742 1931
permeability of vacuumpermittivity of vacuum
Vacuum polarization effects
1 Birefringence and dichroism of vacuumR Baier P Breitenlohner Acta Phys Austr 25 212 1967NB Narozhnyi Zh Eksp Teor Fiz 55 714 (1968) [Sov Phys JETP 28 371 1969]SL Adler Ann Phys (NY) 67 599 (1971) IA Batalin AE Shabad Zh Eksp Teor Fiz 60 894 (1971) [Sov Phys JETP 33 483 1971]
2 Photon splittingSL Adler Ann Phys (NY) 67 599 (1971)Z Bialynicka-Birula I Bialynicka-Birula PhysRev D 2 2341 (1971) VO Papanyan VI Ritus Zh Eksp Teor Fiz 61 2231 (1971) [Sov Phys JETP 33 483 1971]
3 Cherenkov radiation
T Erber Rev Mod Phys 38 626 1966VI Ritus Zh Eksp Teor Fiz 57 2176 (1969) [Sov Phys JETP 30 1181 (1970)]IM Dremin Pisrsquoma Zh Eksp Teor Fiz 76 185 (2002) [JETP Lett 76 151 (2002)]
4 Self-focusing in vacuum
M Soljacˇicacute and M Segev Phys Rev A 62 043817 (2000)D Kharzeev and K Tuchin Phys Rev A 75 043807 (2007)
NN Rozanov JETP 86 284 (1998)
5 Light-by-light scattering
A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)B E Lundstroumlm et alPhys Rev Lett 96 083602 (2006)
6 Harmonics generation
AE Kaplan and YJ Ding Phys Rev A 62 043805 (2000)A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)AMFedotov NB Narozhny Phys Lett A 362 1 (2007)
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
HERCULES Petawatt Laser
Center for Ultrafast Optical Science (CUOS) Michigan USA
Victor Yanovsky
He directs the HERCULES laser - the highest intensity laser in the world and is interested in high intensity laser physics ultrahigh-intensity intensity interactions with solids particle acceleration and X-ray generation in laser-matter interaction
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 18MJ 192 beams 28MJ
I amp I L = 1023W=cv2I L =1023
ПЛАНИРУЕТСЯ
1 Создание TiSa лазера генерирующего импульсы длительностью 10 - 15-fs с энергией в районе 700 J (50 to 70 PW)
2 Активный фазовый контроль усиленных пучков и использование оптики с большой апертурой позволит получить интенсивность порядка
3 Комбинация10 одиночных 50 ndash 70-PW пучков приведет к пиковой мощности 500 ndash 700 PW и соответствующей интенсивности на мишени порядка или больше
(Proposal for an European Extreme Light Infrastructure wwwextreme-light-infrastructureeu)
ELI-Ultra High Field Facility
Место строительства еще дбопределено
laquoМеждународный центр исследованийэкстремальных световых полейraquo (ЦИЭС)
Комплекс будет включать 12 одинаковых каналов в каждом из которых будет генерироваться импульс с энергией 300-400 Дж длительностью 20-30 фс
максимальной интенсивностью при фокусировке более 10^23 Втсм2
F Sauter 1931W Heisenberg H Euler 1936J Schwinger 1951
QED is a nonlinear science at
The only experiment on Nonlinear QED ndash E144 (SLAC 1996 -1997)
Nonlinear Compton scattering
CBula et al PRL 76 3116 (1996)CBamber et al PRD 60 092004(1999)
schematic drawing of the experiment
IP1 ndash interaction pointECAL ndash silicon-tungsten calorimeterCCM1 ndash gas Čerenkov monitor
Final Focus Test Beam at SLAC
The multiphoton version of Breit-Wheeler process was observed
DLBurke et al PRL 79 1626 (1997)CBamber et al PRD 60 092004(1999)
Pair production two-step process
This was the first (and the only) laboratory evidence for inelastic light-by-light scattering involving only real photons
Laser λ=1054μm (infrared) and λ=0527μm (green) The laser intensity could be varied the maximum focused intensity
Electron beam
Parameters of E144 experiment
The field was close to a monochromatic plane wave field
Two Lorentz and gauge invariant parameters
Dimensionless intensity parameter
Dynamical parameter
(classical nonlinearity parameter)
(quantum nonlinearity parameter)
At the proper frame of electron
Parameters of E144 experiment
What we will have with new facilities
Fms optical pulses
Electrons
What does it mean experimentally
1 harmonics are undistinguishablelaser field works as a constant crossed field
2
e-m cascades will be observed
The effect was observed at SLAC experimentmultiplicity = 002
Analogue of cosmic-ray air showers
It could be the first experiment on laboratory astrophysics
3 Fms optical pulses
Electrons
Expansion parameter of perturbation theory at
Narozhny PRD 1980
Perturbation theory does not work
Nonlinear QED vacuum polarization effects have never been observed
Is it possible with new facilities
Vacuum in the presence of an external e-m field isa non-linear optical medium
Hans Heinrich Euler (1909ndash1941) Werner Karl Heisenberg (1901-1976)
The start of ldquoNonlinear Optics in Vacuumrdquo
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)
ldquoThis polarization of the vacuum to be studied below will give rise to a distinction between the vectors on the one hand and on the otherrdquo
F Sauter ZS f Phys 69 742 1931
permeability of vacuumpermittivity of vacuum
Vacuum polarization effects
1 Birefringence and dichroism of vacuumR Baier P Breitenlohner Acta Phys Austr 25 212 1967NB Narozhnyi Zh Eksp Teor Fiz 55 714 (1968) [Sov Phys JETP 28 371 1969]SL Adler Ann Phys (NY) 67 599 (1971) IA Batalin AE Shabad Zh Eksp Teor Fiz 60 894 (1971) [Sov Phys JETP 33 483 1971]
2 Photon splittingSL Adler Ann Phys (NY) 67 599 (1971)Z Bialynicka-Birula I Bialynicka-Birula PhysRev D 2 2341 (1971) VO Papanyan VI Ritus Zh Eksp Teor Fiz 61 2231 (1971) [Sov Phys JETP 33 483 1971]
3 Cherenkov radiation
T Erber Rev Mod Phys 38 626 1966VI Ritus Zh Eksp Teor Fiz 57 2176 (1969) [Sov Phys JETP 30 1181 (1970)]IM Dremin Pisrsquoma Zh Eksp Teor Fiz 76 185 (2002) [JETP Lett 76 151 (2002)]
4 Self-focusing in vacuum
M Soljacˇicacute and M Segev Phys Rev A 62 043817 (2000)D Kharzeev and K Tuchin Phys Rev A 75 043807 (2007)
NN Rozanov JETP 86 284 (1998)
5 Light-by-light scattering
A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)B E Lundstroumlm et alPhys Rev Lett 96 083602 (2006)
6 Harmonics generation
AE Kaplan and YJ Ding Phys Rev A 62 043805 (2000)A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)AMFedotov NB Narozhny Phys Lett A 362 1 (2007)
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
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 18MJ 192 beams 28MJ
I amp I L = 1023W=cv2I L =1023
ПЛАНИРУЕТСЯ
1 Создание TiSa лазера генерирующего импульсы длительностью 10 - 15-fs с энергией в районе 700 J (50 to 70 PW)
2 Активный фазовый контроль усиленных пучков и использование оптики с большой апертурой позволит получить интенсивность порядка
3 Комбинация10 одиночных 50 ndash 70-PW пучков приведет к пиковой мощности 500 ndash 700 PW и соответствующей интенсивности на мишени порядка или больше
(Proposal for an European Extreme Light Infrastructure wwwextreme-light-infrastructureeu)
ELI-Ultra High Field Facility
Место строительства еще дбопределено
laquoМеждународный центр исследованийэкстремальных световых полейraquo (ЦИЭС)
Комплекс будет включать 12 одинаковых каналов в каждом из которых будет генерироваться импульс с энергией 300-400 Дж длительностью 20-30 фс
максимальной интенсивностью при фокусировке более 10^23 Втсм2
F Sauter 1931W Heisenberg H Euler 1936J Schwinger 1951
QED is a nonlinear science at
The only experiment on Nonlinear QED ndash E144 (SLAC 1996 -1997)
Nonlinear Compton scattering
CBula et al PRL 76 3116 (1996)CBamber et al PRD 60 092004(1999)
schematic drawing of the experiment
IP1 ndash interaction pointECAL ndash silicon-tungsten calorimeterCCM1 ndash gas Čerenkov monitor
Final Focus Test Beam at SLAC
The multiphoton version of Breit-Wheeler process was observed
DLBurke et al PRL 79 1626 (1997)CBamber et al PRD 60 092004(1999)
Pair production two-step process
This was the first (and the only) laboratory evidence for inelastic light-by-light scattering involving only real photons
Laser λ=1054μm (infrared) and λ=0527μm (green) The laser intensity could be varied the maximum focused intensity
Electron beam
Parameters of E144 experiment
The field was close to a monochromatic plane wave field
Two Lorentz and gauge invariant parameters
Dimensionless intensity parameter
Dynamical parameter
(classical nonlinearity parameter)
(quantum nonlinearity parameter)
At the proper frame of electron
Parameters of E144 experiment
What we will have with new facilities
Fms optical pulses
Electrons
What does it mean experimentally
1 harmonics are undistinguishablelaser field works as a constant crossed field
2
e-m cascades will be observed
The effect was observed at SLAC experimentmultiplicity = 002
Analogue of cosmic-ray air showers
It could be the first experiment on laboratory astrophysics
3 Fms optical pulses
Electrons
Expansion parameter of perturbation theory at
Narozhny PRD 1980
Perturbation theory does not work
Nonlinear QED vacuum polarization effects have never been observed
Is it possible with new facilities
Vacuum in the presence of an external e-m field isa non-linear optical medium
Hans Heinrich Euler (1909ndash1941) Werner Karl Heisenberg (1901-1976)
The start of ldquoNonlinear Optics in Vacuumrdquo
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)
ldquoThis polarization of the vacuum to be studied below will give rise to a distinction between the vectors on the one hand and on the otherrdquo
F Sauter ZS f Phys 69 742 1931
permeability of vacuumpermittivity of vacuum
Vacuum polarization effects
1 Birefringence and dichroism of vacuumR Baier P Breitenlohner Acta Phys Austr 25 212 1967NB Narozhnyi Zh Eksp Teor Fiz 55 714 (1968) [Sov Phys JETP 28 371 1969]SL Adler Ann Phys (NY) 67 599 (1971) IA Batalin AE Shabad Zh Eksp Teor Fiz 60 894 (1971) [Sov Phys JETP 33 483 1971]
2 Photon splittingSL Adler Ann Phys (NY) 67 599 (1971)Z Bialynicka-Birula I Bialynicka-Birula PhysRev D 2 2341 (1971) VO Papanyan VI Ritus Zh Eksp Teor Fiz 61 2231 (1971) [Sov Phys JETP 33 483 1971]
3 Cherenkov radiation
T Erber Rev Mod Phys 38 626 1966VI Ritus Zh Eksp Teor Fiz 57 2176 (1969) [Sov Phys JETP 30 1181 (1970)]IM Dremin Pisrsquoma Zh Eksp Teor Fiz 76 185 (2002) [JETP Lett 76 151 (2002)]
4 Self-focusing in vacuum
M Soljacˇicacute and M Segev Phys Rev A 62 043817 (2000)D Kharzeev and K Tuchin Phys Rev A 75 043807 (2007)
NN Rozanov JETP 86 284 (1998)
5 Light-by-light scattering
A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)B E Lundstroumlm et alPhys Rev Lett 96 083602 (2006)
6 Harmonics generation
AE Kaplan and YJ Ding Phys Rev A 62 043805 (2000)A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)AMFedotov NB Narozhny Phys Lett A 362 1 (2007)
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
I amp I L = 1023W=cv2I L =1023
ПЛАНИРУЕТСЯ
1 Создание TiSa лазера генерирующего импульсы длительностью 10 - 15-fs с энергией в районе 700 J (50 to 70 PW)
2 Активный фазовый контроль усиленных пучков и использование оптики с большой апертурой позволит получить интенсивность порядка
3 Комбинация10 одиночных 50 ndash 70-PW пучков приведет к пиковой мощности 500 ndash 700 PW и соответствующей интенсивности на мишени порядка или больше
(Proposal for an European Extreme Light Infrastructure wwwextreme-light-infrastructureeu)
ELI-Ultra High Field Facility
Место строительства еще дбопределено
laquoМеждународный центр исследованийэкстремальных световых полейraquo (ЦИЭС)
Комплекс будет включать 12 одинаковых каналов в каждом из которых будет генерироваться импульс с энергией 300-400 Дж длительностью 20-30 фс
максимальной интенсивностью при фокусировке более 10^23 Втсм2
F Sauter 1931W Heisenberg H Euler 1936J Schwinger 1951
QED is a nonlinear science at
The only experiment on Nonlinear QED ndash E144 (SLAC 1996 -1997)
Nonlinear Compton scattering
CBula et al PRL 76 3116 (1996)CBamber et al PRD 60 092004(1999)
schematic drawing of the experiment
IP1 ndash interaction pointECAL ndash silicon-tungsten calorimeterCCM1 ndash gas Čerenkov monitor
Final Focus Test Beam at SLAC
The multiphoton version of Breit-Wheeler process was observed
DLBurke et al PRL 79 1626 (1997)CBamber et al PRD 60 092004(1999)
Pair production two-step process
This was the first (and the only) laboratory evidence for inelastic light-by-light scattering involving only real photons
Laser λ=1054μm (infrared) and λ=0527μm (green) The laser intensity could be varied the maximum focused intensity
Electron beam
Parameters of E144 experiment
The field was close to a monochromatic plane wave field
Two Lorentz and gauge invariant parameters
Dimensionless intensity parameter
Dynamical parameter
(classical nonlinearity parameter)
(quantum nonlinearity parameter)
At the proper frame of electron
Parameters of E144 experiment
What we will have with new facilities
Fms optical pulses
Electrons
What does it mean experimentally
1 harmonics are undistinguishablelaser field works as a constant crossed field
2
e-m cascades will be observed
The effect was observed at SLAC experimentmultiplicity = 002
Analogue of cosmic-ray air showers
It could be the first experiment on laboratory astrophysics
3 Fms optical pulses
Electrons
Expansion parameter of perturbation theory at
Narozhny PRD 1980
Perturbation theory does not work
Nonlinear QED vacuum polarization effects have never been observed
Is it possible with new facilities
Vacuum in the presence of an external e-m field isa non-linear optical medium
Hans Heinrich Euler (1909ndash1941) Werner Karl Heisenberg (1901-1976)
The start of ldquoNonlinear Optics in Vacuumrdquo
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)
ldquoThis polarization of the vacuum to be studied below will give rise to a distinction between the vectors on the one hand and on the otherrdquo
F Sauter ZS f Phys 69 742 1931
permeability of vacuumpermittivity of vacuum
Vacuum polarization effects
1 Birefringence and dichroism of vacuumR Baier P Breitenlohner Acta Phys Austr 25 212 1967NB Narozhnyi Zh Eksp Teor Fiz 55 714 (1968) [Sov Phys JETP 28 371 1969]SL Adler Ann Phys (NY) 67 599 (1971) IA Batalin AE Shabad Zh Eksp Teor Fiz 60 894 (1971) [Sov Phys JETP 33 483 1971]
2 Photon splittingSL Adler Ann Phys (NY) 67 599 (1971)Z Bialynicka-Birula I Bialynicka-Birula PhysRev D 2 2341 (1971) VO Papanyan VI Ritus Zh Eksp Teor Fiz 61 2231 (1971) [Sov Phys JETP 33 483 1971]
3 Cherenkov radiation
T Erber Rev Mod Phys 38 626 1966VI Ritus Zh Eksp Teor Fiz 57 2176 (1969) [Sov Phys JETP 30 1181 (1970)]IM Dremin Pisrsquoma Zh Eksp Teor Fiz 76 185 (2002) [JETP Lett 76 151 (2002)]
4 Self-focusing in vacuum
M Soljacˇicacute and M Segev Phys Rev A 62 043817 (2000)D Kharzeev and K Tuchin Phys Rev A 75 043807 (2007)
NN Rozanov JETP 86 284 (1998)
5 Light-by-light scattering
A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)B E Lundstroumlm et alPhys Rev Lett 96 083602 (2006)
6 Harmonics generation
AE Kaplan and YJ Ding Phys Rev A 62 043805 (2000)A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)AMFedotov NB Narozhny Phys Lett A 362 1 (2007)
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
laquoМеждународный центр исследованийэкстремальных световых полейraquo (ЦИЭС)
Комплекс будет включать 12 одинаковых каналов в каждом из которых будет генерироваться импульс с энергией 300-400 Дж длительностью 20-30 фс
максимальной интенсивностью при фокусировке более 10^23 Втсм2
F Sauter 1931W Heisenberg H Euler 1936J Schwinger 1951
QED is a nonlinear science at
The only experiment on Nonlinear QED ndash E144 (SLAC 1996 -1997)
Nonlinear Compton scattering
CBula et al PRL 76 3116 (1996)CBamber et al PRD 60 092004(1999)
schematic drawing of the experiment
IP1 ndash interaction pointECAL ndash silicon-tungsten calorimeterCCM1 ndash gas Čerenkov monitor
Final Focus Test Beam at SLAC
The multiphoton version of Breit-Wheeler process was observed
DLBurke et al PRL 79 1626 (1997)CBamber et al PRD 60 092004(1999)
Pair production two-step process
This was the first (and the only) laboratory evidence for inelastic light-by-light scattering involving only real photons
Laser λ=1054μm (infrared) and λ=0527μm (green) The laser intensity could be varied the maximum focused intensity
Electron beam
Parameters of E144 experiment
The field was close to a monochromatic plane wave field
Two Lorentz and gauge invariant parameters
Dimensionless intensity parameter
Dynamical parameter
(classical nonlinearity parameter)
(quantum nonlinearity parameter)
At the proper frame of electron
Parameters of E144 experiment
What we will have with new facilities
Fms optical pulses
Electrons
What does it mean experimentally
1 harmonics are undistinguishablelaser field works as a constant crossed field
2
e-m cascades will be observed
The effect was observed at SLAC experimentmultiplicity = 002
Analogue of cosmic-ray air showers
It could be the first experiment on laboratory astrophysics
3 Fms optical pulses
Electrons
Expansion parameter of perturbation theory at
Narozhny PRD 1980
Perturbation theory does not work
Nonlinear QED vacuum polarization effects have never been observed
Is it possible with new facilities
Vacuum in the presence of an external e-m field isa non-linear optical medium
Hans Heinrich Euler (1909ndash1941) Werner Karl Heisenberg (1901-1976)
The start of ldquoNonlinear Optics in Vacuumrdquo
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)
ldquoThis polarization of the vacuum to be studied below will give rise to a distinction between the vectors on the one hand and on the otherrdquo
F Sauter ZS f Phys 69 742 1931
permeability of vacuumpermittivity of vacuum
Vacuum polarization effects
1 Birefringence and dichroism of vacuumR Baier P Breitenlohner Acta Phys Austr 25 212 1967NB Narozhnyi Zh Eksp Teor Fiz 55 714 (1968) [Sov Phys JETP 28 371 1969]SL Adler Ann Phys (NY) 67 599 (1971) IA Batalin AE Shabad Zh Eksp Teor Fiz 60 894 (1971) [Sov Phys JETP 33 483 1971]
2 Photon splittingSL Adler Ann Phys (NY) 67 599 (1971)Z Bialynicka-Birula I Bialynicka-Birula PhysRev D 2 2341 (1971) VO Papanyan VI Ritus Zh Eksp Teor Fiz 61 2231 (1971) [Sov Phys JETP 33 483 1971]
3 Cherenkov radiation
T Erber Rev Mod Phys 38 626 1966VI Ritus Zh Eksp Teor Fiz 57 2176 (1969) [Sov Phys JETP 30 1181 (1970)]IM Dremin Pisrsquoma Zh Eksp Teor Fiz 76 185 (2002) [JETP Lett 76 151 (2002)]
4 Self-focusing in vacuum
M Soljacˇicacute and M Segev Phys Rev A 62 043817 (2000)D Kharzeev and K Tuchin Phys Rev A 75 043807 (2007)
NN Rozanov JETP 86 284 (1998)
5 Light-by-light scattering
A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)B E Lundstroumlm et alPhys Rev Lett 96 083602 (2006)
6 Harmonics generation
AE Kaplan and YJ Ding Phys Rev A 62 043805 (2000)A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)AMFedotov NB Narozhny Phys Lett A 362 1 (2007)
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
Комплекс будет включать 12 одинаковых каналов в каждом из которых будет генерироваться импульс с энергией 300-400 Дж длительностью 20-30 фс
максимальной интенсивностью при фокусировке более 10^23 Втсм2
F Sauter 1931W Heisenberg H Euler 1936J Schwinger 1951
QED is a nonlinear science at
The only experiment on Nonlinear QED ndash E144 (SLAC 1996 -1997)
Nonlinear Compton scattering
CBula et al PRL 76 3116 (1996)CBamber et al PRD 60 092004(1999)
schematic drawing of the experiment
IP1 ndash interaction pointECAL ndash silicon-tungsten calorimeterCCM1 ndash gas Čerenkov monitor
Final Focus Test Beam at SLAC
The multiphoton version of Breit-Wheeler process was observed
DLBurke et al PRL 79 1626 (1997)CBamber et al PRD 60 092004(1999)
Pair production two-step process
This was the first (and the only) laboratory evidence for inelastic light-by-light scattering involving only real photons
Laser λ=1054μm (infrared) and λ=0527μm (green) The laser intensity could be varied the maximum focused intensity
Electron beam
Parameters of E144 experiment
The field was close to a monochromatic plane wave field
Two Lorentz and gauge invariant parameters
Dimensionless intensity parameter
Dynamical parameter
(classical nonlinearity parameter)
(quantum nonlinearity parameter)
At the proper frame of electron
Parameters of E144 experiment
What we will have with new facilities
Fms optical pulses
Electrons
What does it mean experimentally
1 harmonics are undistinguishablelaser field works as a constant crossed field
2
e-m cascades will be observed
The effect was observed at SLAC experimentmultiplicity = 002
Analogue of cosmic-ray air showers
It could be the first experiment on laboratory astrophysics
3 Fms optical pulses
Electrons
Expansion parameter of perturbation theory at
Narozhny PRD 1980
Perturbation theory does not work
Nonlinear QED vacuum polarization effects have never been observed
Is it possible with new facilities
Vacuum in the presence of an external e-m field isa non-linear optical medium
Hans Heinrich Euler (1909ndash1941) Werner Karl Heisenberg (1901-1976)
The start of ldquoNonlinear Optics in Vacuumrdquo
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)
ldquoThis polarization of the vacuum to be studied below will give rise to a distinction between the vectors on the one hand and on the otherrdquo
F Sauter ZS f Phys 69 742 1931
permeability of vacuumpermittivity of vacuum
Vacuum polarization effects
1 Birefringence and dichroism of vacuumR Baier P Breitenlohner Acta Phys Austr 25 212 1967NB Narozhnyi Zh Eksp Teor Fiz 55 714 (1968) [Sov Phys JETP 28 371 1969]SL Adler Ann Phys (NY) 67 599 (1971) IA Batalin AE Shabad Zh Eksp Teor Fiz 60 894 (1971) [Sov Phys JETP 33 483 1971]
2 Photon splittingSL Adler Ann Phys (NY) 67 599 (1971)Z Bialynicka-Birula I Bialynicka-Birula PhysRev D 2 2341 (1971) VO Papanyan VI Ritus Zh Eksp Teor Fiz 61 2231 (1971) [Sov Phys JETP 33 483 1971]
3 Cherenkov radiation
T Erber Rev Mod Phys 38 626 1966VI Ritus Zh Eksp Teor Fiz 57 2176 (1969) [Sov Phys JETP 30 1181 (1970)]IM Dremin Pisrsquoma Zh Eksp Teor Fiz 76 185 (2002) [JETP Lett 76 151 (2002)]
4 Self-focusing in vacuum
M Soljacˇicacute and M Segev Phys Rev A 62 043817 (2000)D Kharzeev and K Tuchin Phys Rev A 75 043807 (2007)
NN Rozanov JETP 86 284 (1998)
5 Light-by-light scattering
A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)B E Lundstroumlm et alPhys Rev Lett 96 083602 (2006)
6 Harmonics generation
AE Kaplan and YJ Ding Phys Rev A 62 043805 (2000)A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)AMFedotov NB Narozhny Phys Lett A 362 1 (2007)
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
F Sauter 1931W Heisenberg H Euler 1936J Schwinger 1951
QED is a nonlinear science at
The only experiment on Nonlinear QED ndash E144 (SLAC 1996 -1997)
Nonlinear Compton scattering
CBula et al PRL 76 3116 (1996)CBamber et al PRD 60 092004(1999)
schematic drawing of the experiment
IP1 ndash interaction pointECAL ndash silicon-tungsten calorimeterCCM1 ndash gas Čerenkov monitor
Final Focus Test Beam at SLAC
The multiphoton version of Breit-Wheeler process was observed
DLBurke et al PRL 79 1626 (1997)CBamber et al PRD 60 092004(1999)
Pair production two-step process
This was the first (and the only) laboratory evidence for inelastic light-by-light scattering involving only real photons
Laser λ=1054μm (infrared) and λ=0527μm (green) The laser intensity could be varied the maximum focused intensity
Electron beam
Parameters of E144 experiment
The field was close to a monochromatic plane wave field
Two Lorentz and gauge invariant parameters
Dimensionless intensity parameter
Dynamical parameter
(classical nonlinearity parameter)
(quantum nonlinearity parameter)
At the proper frame of electron
Parameters of E144 experiment
What we will have with new facilities
Fms optical pulses
Electrons
What does it mean experimentally
1 harmonics are undistinguishablelaser field works as a constant crossed field
2
e-m cascades will be observed
The effect was observed at SLAC experimentmultiplicity = 002
Analogue of cosmic-ray air showers
It could be the first experiment on laboratory astrophysics
3 Fms optical pulses
Electrons
Expansion parameter of perturbation theory at
Narozhny PRD 1980
Perturbation theory does not work
Nonlinear QED vacuum polarization effects have never been observed
Is it possible with new facilities
Vacuum in the presence of an external e-m field isa non-linear optical medium
Hans Heinrich Euler (1909ndash1941) Werner Karl Heisenberg (1901-1976)
The start of ldquoNonlinear Optics in Vacuumrdquo
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)
ldquoThis polarization of the vacuum to be studied below will give rise to a distinction between the vectors on the one hand and on the otherrdquo
F Sauter ZS f Phys 69 742 1931
permeability of vacuumpermittivity of vacuum
Vacuum polarization effects
1 Birefringence and dichroism of vacuumR Baier P Breitenlohner Acta Phys Austr 25 212 1967NB Narozhnyi Zh Eksp Teor Fiz 55 714 (1968) [Sov Phys JETP 28 371 1969]SL Adler Ann Phys (NY) 67 599 (1971) IA Batalin AE Shabad Zh Eksp Teor Fiz 60 894 (1971) [Sov Phys JETP 33 483 1971]
2 Photon splittingSL Adler Ann Phys (NY) 67 599 (1971)Z Bialynicka-Birula I Bialynicka-Birula PhysRev D 2 2341 (1971) VO Papanyan VI Ritus Zh Eksp Teor Fiz 61 2231 (1971) [Sov Phys JETP 33 483 1971]
3 Cherenkov radiation
T Erber Rev Mod Phys 38 626 1966VI Ritus Zh Eksp Teor Fiz 57 2176 (1969) [Sov Phys JETP 30 1181 (1970)]IM Dremin Pisrsquoma Zh Eksp Teor Fiz 76 185 (2002) [JETP Lett 76 151 (2002)]
4 Self-focusing in vacuum
M Soljacˇicacute and M Segev Phys Rev A 62 043817 (2000)D Kharzeev and K Tuchin Phys Rev A 75 043807 (2007)
NN Rozanov JETP 86 284 (1998)
5 Light-by-light scattering
A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)B E Lundstroumlm et alPhys Rev Lett 96 083602 (2006)
6 Harmonics generation
AE Kaplan and YJ Ding Phys Rev A 62 043805 (2000)A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)AMFedotov NB Narozhny Phys Lett A 362 1 (2007)
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
The only experiment on Nonlinear QED ndash E144 (SLAC 1996 -1997)
Nonlinear Compton scattering
CBula et al PRL 76 3116 (1996)CBamber et al PRD 60 092004(1999)
schematic drawing of the experiment
IP1 ndash interaction pointECAL ndash silicon-tungsten calorimeterCCM1 ndash gas Čerenkov monitor
Final Focus Test Beam at SLAC
The multiphoton version of Breit-Wheeler process was observed
DLBurke et al PRL 79 1626 (1997)CBamber et al PRD 60 092004(1999)
Pair production two-step process
This was the first (and the only) laboratory evidence for inelastic light-by-light scattering involving only real photons
Laser λ=1054μm (infrared) and λ=0527μm (green) The laser intensity could be varied the maximum focused intensity
Electron beam
Parameters of E144 experiment
The field was close to a monochromatic plane wave field
Two Lorentz and gauge invariant parameters
Dimensionless intensity parameter
Dynamical parameter
(classical nonlinearity parameter)
(quantum nonlinearity parameter)
At the proper frame of electron
Parameters of E144 experiment
What we will have with new facilities
Fms optical pulses
Electrons
What does it mean experimentally
1 harmonics are undistinguishablelaser field works as a constant crossed field
2
e-m cascades will be observed
The effect was observed at SLAC experimentmultiplicity = 002
Analogue of cosmic-ray air showers
It could be the first experiment on laboratory astrophysics
3 Fms optical pulses
Electrons
Expansion parameter of perturbation theory at
Narozhny PRD 1980
Perturbation theory does not work
Nonlinear QED vacuum polarization effects have never been observed
Is it possible with new facilities
Vacuum in the presence of an external e-m field isa non-linear optical medium
Hans Heinrich Euler (1909ndash1941) Werner Karl Heisenberg (1901-1976)
The start of ldquoNonlinear Optics in Vacuumrdquo
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)
ldquoThis polarization of the vacuum to be studied below will give rise to a distinction between the vectors on the one hand and on the otherrdquo
F Sauter ZS f Phys 69 742 1931
permeability of vacuumpermittivity of vacuum
Vacuum polarization effects
1 Birefringence and dichroism of vacuumR Baier P Breitenlohner Acta Phys Austr 25 212 1967NB Narozhnyi Zh Eksp Teor Fiz 55 714 (1968) [Sov Phys JETP 28 371 1969]SL Adler Ann Phys (NY) 67 599 (1971) IA Batalin AE Shabad Zh Eksp Teor Fiz 60 894 (1971) [Sov Phys JETP 33 483 1971]
2 Photon splittingSL Adler Ann Phys (NY) 67 599 (1971)Z Bialynicka-Birula I Bialynicka-Birula PhysRev D 2 2341 (1971) VO Papanyan VI Ritus Zh Eksp Teor Fiz 61 2231 (1971) [Sov Phys JETP 33 483 1971]
3 Cherenkov radiation
T Erber Rev Mod Phys 38 626 1966VI Ritus Zh Eksp Teor Fiz 57 2176 (1969) [Sov Phys JETP 30 1181 (1970)]IM Dremin Pisrsquoma Zh Eksp Teor Fiz 76 185 (2002) [JETP Lett 76 151 (2002)]
4 Self-focusing in vacuum
M Soljacˇicacute and M Segev Phys Rev A 62 043817 (2000)D Kharzeev and K Tuchin Phys Rev A 75 043807 (2007)
NN Rozanov JETP 86 284 (1998)
5 Light-by-light scattering
A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)B E Lundstroumlm et alPhys Rev Lett 96 083602 (2006)
6 Harmonics generation
AE Kaplan and YJ Ding Phys Rev A 62 043805 (2000)A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)AMFedotov NB Narozhny Phys Lett A 362 1 (2007)
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
Nonlinear Compton scattering
CBula et al PRL 76 3116 (1996)CBamber et al PRD 60 092004(1999)
schematic drawing of the experiment
IP1 ndash interaction pointECAL ndash silicon-tungsten calorimeterCCM1 ndash gas Čerenkov monitor
Final Focus Test Beam at SLAC
The multiphoton version of Breit-Wheeler process was observed
DLBurke et al PRL 79 1626 (1997)CBamber et al PRD 60 092004(1999)
Pair production two-step process
This was the first (and the only) laboratory evidence for inelastic light-by-light scattering involving only real photons
Laser λ=1054μm (infrared) and λ=0527μm (green) The laser intensity could be varied the maximum focused intensity
Electron beam
Parameters of E144 experiment
The field was close to a monochromatic plane wave field
Two Lorentz and gauge invariant parameters
Dimensionless intensity parameter
Dynamical parameter
(classical nonlinearity parameter)
(quantum nonlinearity parameter)
At the proper frame of electron
Parameters of E144 experiment
What we will have with new facilities
Fms optical pulses
Electrons
What does it mean experimentally
1 harmonics are undistinguishablelaser field works as a constant crossed field
2
e-m cascades will be observed
The effect was observed at SLAC experimentmultiplicity = 002
Analogue of cosmic-ray air showers
It could be the first experiment on laboratory astrophysics
3 Fms optical pulses
Electrons
Expansion parameter of perturbation theory at
Narozhny PRD 1980
Perturbation theory does not work
Nonlinear QED vacuum polarization effects have never been observed
Is it possible with new facilities
Vacuum in the presence of an external e-m field isa non-linear optical medium
Hans Heinrich Euler (1909ndash1941) Werner Karl Heisenberg (1901-1976)
The start of ldquoNonlinear Optics in Vacuumrdquo
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)
ldquoThis polarization of the vacuum to be studied below will give rise to a distinction between the vectors on the one hand and on the otherrdquo
F Sauter ZS f Phys 69 742 1931
permeability of vacuumpermittivity of vacuum
Vacuum polarization effects
1 Birefringence and dichroism of vacuumR Baier P Breitenlohner Acta Phys Austr 25 212 1967NB Narozhnyi Zh Eksp Teor Fiz 55 714 (1968) [Sov Phys JETP 28 371 1969]SL Adler Ann Phys (NY) 67 599 (1971) IA Batalin AE Shabad Zh Eksp Teor Fiz 60 894 (1971) [Sov Phys JETP 33 483 1971]
2 Photon splittingSL Adler Ann Phys (NY) 67 599 (1971)Z Bialynicka-Birula I Bialynicka-Birula PhysRev D 2 2341 (1971) VO Papanyan VI Ritus Zh Eksp Teor Fiz 61 2231 (1971) [Sov Phys JETP 33 483 1971]
3 Cherenkov radiation
T Erber Rev Mod Phys 38 626 1966VI Ritus Zh Eksp Teor Fiz 57 2176 (1969) [Sov Phys JETP 30 1181 (1970)]IM Dremin Pisrsquoma Zh Eksp Teor Fiz 76 185 (2002) [JETP Lett 76 151 (2002)]
4 Self-focusing in vacuum
M Soljacˇicacute and M Segev Phys Rev A 62 043817 (2000)D Kharzeev and K Tuchin Phys Rev A 75 043807 (2007)
NN Rozanov JETP 86 284 (1998)
5 Light-by-light scattering
A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)B E Lundstroumlm et alPhys Rev Lett 96 083602 (2006)
6 Harmonics generation
AE Kaplan and YJ Ding Phys Rev A 62 043805 (2000)A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)AMFedotov NB Narozhny Phys Lett A 362 1 (2007)
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
The multiphoton version of Breit-Wheeler process was observed
DLBurke et al PRL 79 1626 (1997)CBamber et al PRD 60 092004(1999)
Pair production two-step process
This was the first (and the only) laboratory evidence for inelastic light-by-light scattering involving only real photons
Laser λ=1054μm (infrared) and λ=0527μm (green) The laser intensity could be varied the maximum focused intensity
Electron beam
Parameters of E144 experiment
The field was close to a monochromatic plane wave field
Two Lorentz and gauge invariant parameters
Dimensionless intensity parameter
Dynamical parameter
(classical nonlinearity parameter)
(quantum nonlinearity parameter)
At the proper frame of electron
Parameters of E144 experiment
What we will have with new facilities
Fms optical pulses
Electrons
What does it mean experimentally
1 harmonics are undistinguishablelaser field works as a constant crossed field
2
e-m cascades will be observed
The effect was observed at SLAC experimentmultiplicity = 002
Analogue of cosmic-ray air showers
It could be the first experiment on laboratory astrophysics
3 Fms optical pulses
Electrons
Expansion parameter of perturbation theory at
Narozhny PRD 1980
Perturbation theory does not work
Nonlinear QED vacuum polarization effects have never been observed
Is it possible with new facilities
Vacuum in the presence of an external e-m field isa non-linear optical medium
Hans Heinrich Euler (1909ndash1941) Werner Karl Heisenberg (1901-1976)
The start of ldquoNonlinear Optics in Vacuumrdquo
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)
ldquoThis polarization of the vacuum to be studied below will give rise to a distinction between the vectors on the one hand and on the otherrdquo
F Sauter ZS f Phys 69 742 1931
permeability of vacuumpermittivity of vacuum
Vacuum polarization effects
1 Birefringence and dichroism of vacuumR Baier P Breitenlohner Acta Phys Austr 25 212 1967NB Narozhnyi Zh Eksp Teor Fiz 55 714 (1968) [Sov Phys JETP 28 371 1969]SL Adler Ann Phys (NY) 67 599 (1971) IA Batalin AE Shabad Zh Eksp Teor Fiz 60 894 (1971) [Sov Phys JETP 33 483 1971]
2 Photon splittingSL Adler Ann Phys (NY) 67 599 (1971)Z Bialynicka-Birula I Bialynicka-Birula PhysRev D 2 2341 (1971) VO Papanyan VI Ritus Zh Eksp Teor Fiz 61 2231 (1971) [Sov Phys JETP 33 483 1971]
3 Cherenkov radiation
T Erber Rev Mod Phys 38 626 1966VI Ritus Zh Eksp Teor Fiz 57 2176 (1969) [Sov Phys JETP 30 1181 (1970)]IM Dremin Pisrsquoma Zh Eksp Teor Fiz 76 185 (2002) [JETP Lett 76 151 (2002)]
4 Self-focusing in vacuum
M Soljacˇicacute and M Segev Phys Rev A 62 043817 (2000)D Kharzeev and K Tuchin Phys Rev A 75 043807 (2007)
NN Rozanov JETP 86 284 (1998)
5 Light-by-light scattering
A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)B E Lundstroumlm et alPhys Rev Lett 96 083602 (2006)
6 Harmonics generation
AE Kaplan and YJ Ding Phys Rev A 62 043805 (2000)A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)AMFedotov NB Narozhny Phys Lett A 362 1 (2007)
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
This was the first (and the only) laboratory evidence for inelastic light-by-light scattering involving only real photons
Laser λ=1054μm (infrared) and λ=0527μm (green) The laser intensity could be varied the maximum focused intensity
Electron beam
Parameters of E144 experiment
The field was close to a monochromatic plane wave field
Two Lorentz and gauge invariant parameters
Dimensionless intensity parameter
Dynamical parameter
(classical nonlinearity parameter)
(quantum nonlinearity parameter)
At the proper frame of electron
Parameters of E144 experiment
What we will have with new facilities
Fms optical pulses
Electrons
What does it mean experimentally
1 harmonics are undistinguishablelaser field works as a constant crossed field
2
e-m cascades will be observed
The effect was observed at SLAC experimentmultiplicity = 002
Analogue of cosmic-ray air showers
It could be the first experiment on laboratory astrophysics
3 Fms optical pulses
Electrons
Expansion parameter of perturbation theory at
Narozhny PRD 1980
Perturbation theory does not work
Nonlinear QED vacuum polarization effects have never been observed
Is it possible with new facilities
Vacuum in the presence of an external e-m field isa non-linear optical medium
Hans Heinrich Euler (1909ndash1941) Werner Karl Heisenberg (1901-1976)
The start of ldquoNonlinear Optics in Vacuumrdquo
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)
ldquoThis polarization of the vacuum to be studied below will give rise to a distinction between the vectors on the one hand and on the otherrdquo
F Sauter ZS f Phys 69 742 1931
permeability of vacuumpermittivity of vacuum
Vacuum polarization effects
1 Birefringence and dichroism of vacuumR Baier P Breitenlohner Acta Phys Austr 25 212 1967NB Narozhnyi Zh Eksp Teor Fiz 55 714 (1968) [Sov Phys JETP 28 371 1969]SL Adler Ann Phys (NY) 67 599 (1971) IA Batalin AE Shabad Zh Eksp Teor Fiz 60 894 (1971) [Sov Phys JETP 33 483 1971]
2 Photon splittingSL Adler Ann Phys (NY) 67 599 (1971)Z Bialynicka-Birula I Bialynicka-Birula PhysRev D 2 2341 (1971) VO Papanyan VI Ritus Zh Eksp Teor Fiz 61 2231 (1971) [Sov Phys JETP 33 483 1971]
3 Cherenkov radiation
T Erber Rev Mod Phys 38 626 1966VI Ritus Zh Eksp Teor Fiz 57 2176 (1969) [Sov Phys JETP 30 1181 (1970)]IM Dremin Pisrsquoma Zh Eksp Teor Fiz 76 185 (2002) [JETP Lett 76 151 (2002)]
4 Self-focusing in vacuum
M Soljacˇicacute and M Segev Phys Rev A 62 043817 (2000)D Kharzeev and K Tuchin Phys Rev A 75 043807 (2007)
NN Rozanov JETP 86 284 (1998)
5 Light-by-light scattering
A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)B E Lundstroumlm et alPhys Rev Lett 96 083602 (2006)
6 Harmonics generation
AE Kaplan and YJ Ding Phys Rev A 62 043805 (2000)A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)AMFedotov NB Narozhny Phys Lett A 362 1 (2007)
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
Laser λ=1054μm (infrared) and λ=0527μm (green) The laser intensity could be varied the maximum focused intensity
Electron beam
Parameters of E144 experiment
The field was close to a monochromatic plane wave field
Two Lorentz and gauge invariant parameters
Dimensionless intensity parameter
Dynamical parameter
(classical nonlinearity parameter)
(quantum nonlinearity parameter)
At the proper frame of electron
Parameters of E144 experiment
What we will have with new facilities
Fms optical pulses
Electrons
What does it mean experimentally
1 harmonics are undistinguishablelaser field works as a constant crossed field
2
e-m cascades will be observed
The effect was observed at SLAC experimentmultiplicity = 002
Analogue of cosmic-ray air showers
It could be the first experiment on laboratory astrophysics
3 Fms optical pulses
Electrons
Expansion parameter of perturbation theory at
Narozhny PRD 1980
Perturbation theory does not work
Nonlinear QED vacuum polarization effects have never been observed
Is it possible with new facilities
Vacuum in the presence of an external e-m field isa non-linear optical medium
Hans Heinrich Euler (1909ndash1941) Werner Karl Heisenberg (1901-1976)
The start of ldquoNonlinear Optics in Vacuumrdquo
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)
ldquoThis polarization of the vacuum to be studied below will give rise to a distinction between the vectors on the one hand and on the otherrdquo
F Sauter ZS f Phys 69 742 1931
permeability of vacuumpermittivity of vacuum
Vacuum polarization effects
1 Birefringence and dichroism of vacuumR Baier P Breitenlohner Acta Phys Austr 25 212 1967NB Narozhnyi Zh Eksp Teor Fiz 55 714 (1968) [Sov Phys JETP 28 371 1969]SL Adler Ann Phys (NY) 67 599 (1971) IA Batalin AE Shabad Zh Eksp Teor Fiz 60 894 (1971) [Sov Phys JETP 33 483 1971]
2 Photon splittingSL Adler Ann Phys (NY) 67 599 (1971)Z Bialynicka-Birula I Bialynicka-Birula PhysRev D 2 2341 (1971) VO Papanyan VI Ritus Zh Eksp Teor Fiz 61 2231 (1971) [Sov Phys JETP 33 483 1971]
3 Cherenkov radiation
T Erber Rev Mod Phys 38 626 1966VI Ritus Zh Eksp Teor Fiz 57 2176 (1969) [Sov Phys JETP 30 1181 (1970)]IM Dremin Pisrsquoma Zh Eksp Teor Fiz 76 185 (2002) [JETP Lett 76 151 (2002)]
4 Self-focusing in vacuum
M Soljacˇicacute and M Segev Phys Rev A 62 043817 (2000)D Kharzeev and K Tuchin Phys Rev A 75 043807 (2007)
NN Rozanov JETP 86 284 (1998)
5 Light-by-light scattering
A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)B E Lundstroumlm et alPhys Rev Lett 96 083602 (2006)
6 Harmonics generation
AE Kaplan and YJ Ding Phys Rev A 62 043805 (2000)A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)AMFedotov NB Narozhny Phys Lett A 362 1 (2007)
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
Parameters of E144 experiment
What we will have with new facilities
Fms optical pulses
Electrons
What does it mean experimentally
1 harmonics are undistinguishablelaser field works as a constant crossed field
2
e-m cascades will be observed
The effect was observed at SLAC experimentmultiplicity = 002
Analogue of cosmic-ray air showers
It could be the first experiment on laboratory astrophysics
3 Fms optical pulses
Electrons
Expansion parameter of perturbation theory at
Narozhny PRD 1980
Perturbation theory does not work
Nonlinear QED vacuum polarization effects have never been observed
Is it possible with new facilities
Vacuum in the presence of an external e-m field isa non-linear optical medium
Hans Heinrich Euler (1909ndash1941) Werner Karl Heisenberg (1901-1976)
The start of ldquoNonlinear Optics in Vacuumrdquo
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)
ldquoThis polarization of the vacuum to be studied below will give rise to a distinction between the vectors on the one hand and on the otherrdquo
F Sauter ZS f Phys 69 742 1931
permeability of vacuumpermittivity of vacuum
Vacuum polarization effects
1 Birefringence and dichroism of vacuumR Baier P Breitenlohner Acta Phys Austr 25 212 1967NB Narozhnyi Zh Eksp Teor Fiz 55 714 (1968) [Sov Phys JETP 28 371 1969]SL Adler Ann Phys (NY) 67 599 (1971) IA Batalin AE Shabad Zh Eksp Teor Fiz 60 894 (1971) [Sov Phys JETP 33 483 1971]
2 Photon splittingSL Adler Ann Phys (NY) 67 599 (1971)Z Bialynicka-Birula I Bialynicka-Birula PhysRev D 2 2341 (1971) VO Papanyan VI Ritus Zh Eksp Teor Fiz 61 2231 (1971) [Sov Phys JETP 33 483 1971]
3 Cherenkov radiation
T Erber Rev Mod Phys 38 626 1966VI Ritus Zh Eksp Teor Fiz 57 2176 (1969) [Sov Phys JETP 30 1181 (1970)]IM Dremin Pisrsquoma Zh Eksp Teor Fiz 76 185 (2002) [JETP Lett 76 151 (2002)]
4 Self-focusing in vacuum
M Soljacˇicacute and M Segev Phys Rev A 62 043817 (2000)D Kharzeev and K Tuchin Phys Rev A 75 043807 (2007)
NN Rozanov JETP 86 284 (1998)
5 Light-by-light scattering
A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)B E Lundstroumlm et alPhys Rev Lett 96 083602 (2006)
6 Harmonics generation
AE Kaplan and YJ Ding Phys Rev A 62 043805 (2000)A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)AMFedotov NB Narozhny Phys Lett A 362 1 (2007)
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
1 harmonics are undistinguishablelaser field works as a constant crossed field
2
e-m cascades will be observed
The effect was observed at SLAC experimentmultiplicity = 002
Analogue of cosmic-ray air showers
It could be the first experiment on laboratory astrophysics
3 Fms optical pulses
Electrons
Expansion parameter of perturbation theory at
Narozhny PRD 1980
Perturbation theory does not work
Nonlinear QED vacuum polarization effects have never been observed
Is it possible with new facilities
Vacuum in the presence of an external e-m field isa non-linear optical medium
Hans Heinrich Euler (1909ndash1941) Werner Karl Heisenberg (1901-1976)
The start of ldquoNonlinear Optics in Vacuumrdquo
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)
ldquoThis polarization of the vacuum to be studied below will give rise to a distinction between the vectors on the one hand and on the otherrdquo
F Sauter ZS f Phys 69 742 1931
permeability of vacuumpermittivity of vacuum
Vacuum polarization effects
1 Birefringence and dichroism of vacuumR Baier P Breitenlohner Acta Phys Austr 25 212 1967NB Narozhnyi Zh Eksp Teor Fiz 55 714 (1968) [Sov Phys JETP 28 371 1969]SL Adler Ann Phys (NY) 67 599 (1971) IA Batalin AE Shabad Zh Eksp Teor Fiz 60 894 (1971) [Sov Phys JETP 33 483 1971]
2 Photon splittingSL Adler Ann Phys (NY) 67 599 (1971)Z Bialynicka-Birula I Bialynicka-Birula PhysRev D 2 2341 (1971) VO Papanyan VI Ritus Zh Eksp Teor Fiz 61 2231 (1971) [Sov Phys JETP 33 483 1971]
3 Cherenkov radiation
T Erber Rev Mod Phys 38 626 1966VI Ritus Zh Eksp Teor Fiz 57 2176 (1969) [Sov Phys JETP 30 1181 (1970)]IM Dremin Pisrsquoma Zh Eksp Teor Fiz 76 185 (2002) [JETP Lett 76 151 (2002)]
4 Self-focusing in vacuum
M Soljacˇicacute and M Segev Phys Rev A 62 043817 (2000)D Kharzeev and K Tuchin Phys Rev A 75 043807 (2007)
NN Rozanov JETP 86 284 (1998)
5 Light-by-light scattering
A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)B E Lundstroumlm et alPhys Rev Lett 96 083602 (2006)
6 Harmonics generation
AE Kaplan and YJ Ding Phys Rev A 62 043805 (2000)A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)AMFedotov NB Narozhny Phys Lett A 362 1 (2007)
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
3 Fms optical pulses
Electrons
Expansion parameter of perturbation theory at
Narozhny PRD 1980
Perturbation theory does not work
Nonlinear QED vacuum polarization effects have never been observed
Is it possible with new facilities
Vacuum in the presence of an external e-m field isa non-linear optical medium
Hans Heinrich Euler (1909ndash1941) Werner Karl Heisenberg (1901-1976)
The start of ldquoNonlinear Optics in Vacuumrdquo
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)
ldquoThis polarization of the vacuum to be studied below will give rise to a distinction between the vectors on the one hand and on the otherrdquo
F Sauter ZS f Phys 69 742 1931
permeability of vacuumpermittivity of vacuum
Vacuum polarization effects
1 Birefringence and dichroism of vacuumR Baier P Breitenlohner Acta Phys Austr 25 212 1967NB Narozhnyi Zh Eksp Teor Fiz 55 714 (1968) [Sov Phys JETP 28 371 1969]SL Adler Ann Phys (NY) 67 599 (1971) IA Batalin AE Shabad Zh Eksp Teor Fiz 60 894 (1971) [Sov Phys JETP 33 483 1971]
2 Photon splittingSL Adler Ann Phys (NY) 67 599 (1971)Z Bialynicka-Birula I Bialynicka-Birula PhysRev D 2 2341 (1971) VO Papanyan VI Ritus Zh Eksp Teor Fiz 61 2231 (1971) [Sov Phys JETP 33 483 1971]
3 Cherenkov radiation
T Erber Rev Mod Phys 38 626 1966VI Ritus Zh Eksp Teor Fiz 57 2176 (1969) [Sov Phys JETP 30 1181 (1970)]IM Dremin Pisrsquoma Zh Eksp Teor Fiz 76 185 (2002) [JETP Lett 76 151 (2002)]
4 Self-focusing in vacuum
M Soljacˇicacute and M Segev Phys Rev A 62 043817 (2000)D Kharzeev and K Tuchin Phys Rev A 75 043807 (2007)
NN Rozanov JETP 86 284 (1998)
5 Light-by-light scattering
A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)B E Lundstroumlm et alPhys Rev Lett 96 083602 (2006)
6 Harmonics generation
AE Kaplan and YJ Ding Phys Rev A 62 043805 (2000)A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)AMFedotov NB Narozhny Phys Lett A 362 1 (2007)
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
Nonlinear QED vacuum polarization effects have never been observed
Is it possible with new facilities
Vacuum in the presence of an external e-m field isa non-linear optical medium
Hans Heinrich Euler (1909ndash1941) Werner Karl Heisenberg (1901-1976)
The start of ldquoNonlinear Optics in Vacuumrdquo
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)
ldquoThis polarization of the vacuum to be studied below will give rise to a distinction between the vectors on the one hand and on the otherrdquo
F Sauter ZS f Phys 69 742 1931
permeability of vacuumpermittivity of vacuum
Vacuum polarization effects
1 Birefringence and dichroism of vacuumR Baier P Breitenlohner Acta Phys Austr 25 212 1967NB Narozhnyi Zh Eksp Teor Fiz 55 714 (1968) [Sov Phys JETP 28 371 1969]SL Adler Ann Phys (NY) 67 599 (1971) IA Batalin AE Shabad Zh Eksp Teor Fiz 60 894 (1971) [Sov Phys JETP 33 483 1971]
2 Photon splittingSL Adler Ann Phys (NY) 67 599 (1971)Z Bialynicka-Birula I Bialynicka-Birula PhysRev D 2 2341 (1971) VO Papanyan VI Ritus Zh Eksp Teor Fiz 61 2231 (1971) [Sov Phys JETP 33 483 1971]
3 Cherenkov radiation
T Erber Rev Mod Phys 38 626 1966VI Ritus Zh Eksp Teor Fiz 57 2176 (1969) [Sov Phys JETP 30 1181 (1970)]IM Dremin Pisrsquoma Zh Eksp Teor Fiz 76 185 (2002) [JETP Lett 76 151 (2002)]
4 Self-focusing in vacuum
M Soljacˇicacute and M Segev Phys Rev A 62 043817 (2000)D Kharzeev and K Tuchin Phys Rev A 75 043807 (2007)
NN Rozanov JETP 86 284 (1998)
5 Light-by-light scattering
A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)B E Lundstroumlm et alPhys Rev Lett 96 083602 (2006)
6 Harmonics generation
AE Kaplan and YJ Ding Phys Rev A 62 043805 (2000)A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)AMFedotov NB Narozhny Phys Lett A 362 1 (2007)
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
Vacuum in the presence of an external e-m field isa non-linear optical medium
Hans Heinrich Euler (1909ndash1941) Werner Karl Heisenberg (1901-1976)
The start of ldquoNonlinear Optics in Vacuumrdquo
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)
ldquoThis polarization of the vacuum to be studied below will give rise to a distinction between the vectors on the one hand and on the otherrdquo
F Sauter ZS f Phys 69 742 1931
permeability of vacuumpermittivity of vacuum
Vacuum polarization effects
1 Birefringence and dichroism of vacuumR Baier P Breitenlohner Acta Phys Austr 25 212 1967NB Narozhnyi Zh Eksp Teor Fiz 55 714 (1968) [Sov Phys JETP 28 371 1969]SL Adler Ann Phys (NY) 67 599 (1971) IA Batalin AE Shabad Zh Eksp Teor Fiz 60 894 (1971) [Sov Phys JETP 33 483 1971]
2 Photon splittingSL Adler Ann Phys (NY) 67 599 (1971)Z Bialynicka-Birula I Bialynicka-Birula PhysRev D 2 2341 (1971) VO Papanyan VI Ritus Zh Eksp Teor Fiz 61 2231 (1971) [Sov Phys JETP 33 483 1971]
3 Cherenkov radiation
T Erber Rev Mod Phys 38 626 1966VI Ritus Zh Eksp Teor Fiz 57 2176 (1969) [Sov Phys JETP 30 1181 (1970)]IM Dremin Pisrsquoma Zh Eksp Teor Fiz 76 185 (2002) [JETP Lett 76 151 (2002)]
4 Self-focusing in vacuum
M Soljacˇicacute and M Segev Phys Rev A 62 043817 (2000)D Kharzeev and K Tuchin Phys Rev A 75 043807 (2007)
NN Rozanov JETP 86 284 (1998)
5 Light-by-light scattering
A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)B E Lundstroumlm et alPhys Rev Lett 96 083602 (2006)
6 Harmonics generation
AE Kaplan and YJ Ding Phys Rev A 62 043805 (2000)A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)AMFedotov NB Narozhny Phys Lett A 362 1 (2007)
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
ldquoThis polarization of the vacuum to be studied below will give rise to a distinction between the vectors on the one hand and on the otherrdquo
F Sauter ZS f Phys 69 742 1931
permeability of vacuumpermittivity of vacuum
Vacuum polarization effects
1 Birefringence and dichroism of vacuumR Baier P Breitenlohner Acta Phys Austr 25 212 1967NB Narozhnyi Zh Eksp Teor Fiz 55 714 (1968) [Sov Phys JETP 28 371 1969]SL Adler Ann Phys (NY) 67 599 (1971) IA Batalin AE Shabad Zh Eksp Teor Fiz 60 894 (1971) [Sov Phys JETP 33 483 1971]
2 Photon splittingSL Adler Ann Phys (NY) 67 599 (1971)Z Bialynicka-Birula I Bialynicka-Birula PhysRev D 2 2341 (1971) VO Papanyan VI Ritus Zh Eksp Teor Fiz 61 2231 (1971) [Sov Phys JETP 33 483 1971]
3 Cherenkov radiation
T Erber Rev Mod Phys 38 626 1966VI Ritus Zh Eksp Teor Fiz 57 2176 (1969) [Sov Phys JETP 30 1181 (1970)]IM Dremin Pisrsquoma Zh Eksp Teor Fiz 76 185 (2002) [JETP Lett 76 151 (2002)]
4 Self-focusing in vacuum
M Soljacˇicacute and M Segev Phys Rev A 62 043817 (2000)D Kharzeev and K Tuchin Phys Rev A 75 043807 (2007)
NN Rozanov JETP 86 284 (1998)
5 Light-by-light scattering
A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)B E Lundstroumlm et alPhys Rev Lett 96 083602 (2006)
6 Harmonics generation
AE Kaplan and YJ Ding Phys Rev A 62 043805 (2000)A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)AMFedotov NB Narozhny Phys Lett A 362 1 (2007)
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
Vacuum polarization effects
1 Birefringence and dichroism of vacuumR Baier P Breitenlohner Acta Phys Austr 25 212 1967NB Narozhnyi Zh Eksp Teor Fiz 55 714 (1968) [Sov Phys JETP 28 371 1969]SL Adler Ann Phys (NY) 67 599 (1971) IA Batalin AE Shabad Zh Eksp Teor Fiz 60 894 (1971) [Sov Phys JETP 33 483 1971]
2 Photon splittingSL Adler Ann Phys (NY) 67 599 (1971)Z Bialynicka-Birula I Bialynicka-Birula PhysRev D 2 2341 (1971) VO Papanyan VI Ritus Zh Eksp Teor Fiz 61 2231 (1971) [Sov Phys JETP 33 483 1971]
3 Cherenkov radiation
T Erber Rev Mod Phys 38 626 1966VI Ritus Zh Eksp Teor Fiz 57 2176 (1969) [Sov Phys JETP 30 1181 (1970)]IM Dremin Pisrsquoma Zh Eksp Teor Fiz 76 185 (2002) [JETP Lett 76 151 (2002)]
4 Self-focusing in vacuum
M Soljacˇicacute and M Segev Phys Rev A 62 043817 (2000)D Kharzeev and K Tuchin Phys Rev A 75 043807 (2007)
NN Rozanov JETP 86 284 (1998)
5 Light-by-light scattering
A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)B E Lundstroumlm et alPhys Rev Lett 96 083602 (2006)
6 Harmonics generation
AE Kaplan and YJ Ding Phys Rev A 62 043805 (2000)A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)AMFedotov NB Narozhny Phys Lett A 362 1 (2007)
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
4 Self-focusing in vacuum
M Soljacˇicacute and M Segev Phys Rev A 62 043817 (2000)D Kharzeev and K Tuchin Phys Rev A 75 043807 (2007)
NN Rozanov JETP 86 284 (1998)
5 Light-by-light scattering
A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)B E Lundstroumlm et alPhys Rev Lett 96 083602 (2006)
6 Harmonics generation
AE Kaplan and YJ Ding Phys Rev A 62 043805 (2000)A Di Piazza KZ Hatsagortsyan CH Keitel Phys Rev D 72 085005 (2005)AMFedotov NB Narozhny Phys Lett A 362 1 (2007)
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
7 Pair creation by e-m field in vacuum
W Heisenberg and H Euler Zeitschr Phys 98 714 (1936)J Schwinger PhysRev 82 664 (1951)NB Narozhny AI Nikishov Yad Fiz 11 1072 (1970)NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
The most promising nonlinear vacuum effect is
PAIR PRODUCTION BY LASER FIELD
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
pair creation by a laser field in vacuum becomes observable at intensities
J Schwinger PhysRev 82 664 (1951)
The probability for vacuum to stay vacuum in a constant electric field
- the Heisenberg-Euler correction to em field Lagrangian
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
Laser pulse
- focal spot radius- pulse duration
at
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
Распространенная ошибка
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
The number of pairs created by an electromagnetic field
NB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)
In the reference frame where
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
Pair production by a single focused pulseNB Narozhny SS Bulanov VS Popov VD Mur PLA 330 1 (2004)AM Fedotov Las Phys 19 214 (2009)
Δ=01
Δ=005 Δ=01
41027 016 4010-11 4610-42 9610-23
11028 025
24 3110-19 2010-7
21028
035 30107
1410-7
16
61028
062 841013
19105 34109
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
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
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
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 and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
The number of created pairs and threshold energy
for different number of colliding pulses
S S Bulanov VD Mur NB Narozhny et al PRL 104 220404 (2010)
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
Pair creation from vacuum may be observed with laser fields of the strength 23 orders lower
than the critical (Sauter) field ES
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
What will happen after creation of a single pair
Particles are accelerated by the field and hellipMeeting
A R Bell and J G Kirk Phys Rev Lett 101 200403 (2008)AM Fedotov and NB Narozhny in Extreme Light Infrastructure Report on the GC Meeting 27-28 April 2009 Paris httpwwwextreme-light-infrastructureeuA M Fedotov N B Narozhny GMourou and G Korn Phys Rev Lett 105 080402 (2010)
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
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 fieldor for colliding laser pulses
Acceleration
Vacuum instability initiated by a seed particle
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
Estimation
An electron can be accelerated by the field many times for 1 period
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
The electron (positron) radiation lifetime (mean free pathc)
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
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 difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
The difference the laser field is not only a target for primary particles
but also an accelerator for slow particles
The self-sustaining e-m cascades strongly differ from cosmic ray air showers
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
FIG 2 Pair production as a function of The solid curve corresponds to the number 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
Fedotov A M Narozhny N B Mourou G Korn GPRL 105 080402 (2010)
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
The QED cascades (avalanche production of hard photons and electron-positron pairs) catalyzes
depletion of the initiating laser pulses
This confirms the N Bohrrsquos conjecture that the critical QED field strength can be never attained for a pair
creating electromagnetic field
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
QED cascade stops when the laser energy is almost completely converted into the cascade energy
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
Development of e-m cascade by itself leads to depletion of the laser pulse
СПАСИБО ЗА ВНИМАНИЕ
СПАСИБО ЗА ВНИМАНИЕ
