radiation reaction of electrons at laser intensities up to
TRANSCRIPT
X. K. ZHOU* and S. X. HU
Radiation Reaction of Electrons at Laser Intensities up to 1025 W/cm2
University of Rochester, Laboratory for Laser Energetics*Webster Schroder High School and Summer High School Program
The radiation-reaction force can signifi cantly alter electron trajectories at laser intensities above 1023 W/cm2
Summary
TC12751
• Highly charged ion scenario
– little difference with and without RR
• Counter-propagating electron-beam scenario
– signifi cant difference with and without RR
The effects of the radiation-reaction (RR)force have been simulated for two scenarios
Proposed laser developments promise to deliverultrahigh laser intensities above 1023 W/cm2
I2205a
*D. D. Meyerhofer et al., presentedat the 56th Annual Meeting of the APSDivision of Plasma Physics, New Orleans,LA, 27–31 October 2014.
**G. A. Mourou et al., Opt. Commun.285, 720 (2012).
• OMEGA EP optical parametric amplifi er line (OPAL)*
– pulse energy: E = 1.6 kJ
– pulse duration: x = 20 fs
– wavelength: m = 910 nm
– focused intensity:I = 1024 W/cm2
• ELI and beyond**
– pulse energy: E = 10 kJ
– pulse duration: x = 20 fs
– wavelength: m = 1250 nm
– focused intensity:I > 1025 W/cm2
QCD . 1035 W/cm2
Nonlinear QED: E • e mc = 2m0c21 PeV
1 TeV
1 MeV
1 eV
Ultrarelativistic optics
Relativistic optics
EQ = mpc2
EQ = m0c2
ELI
CUOS
CPA
Mode lockingQ switching
1960 1980 2000 2020
Focu
sed
inte
nsi
ty (
W/c
m2 )
1025
1030
1020
1015
1010
OPCPA
C3
OPCPAor CPA
Bound electronsBound electrons
ILE
Year
CPA: chirped-pulse amplifi cationOPCPA: optical parametric chirped-pulse amplifi cationCUOS: Center for Ultrafast Optical Science, University of MichiganILE: Institute of Laser Engineering, University of OsakaELI: Extreme Light Infrastructure (Europe)QED: quantum electrodynamicsQCD: quantum chromodynamics
from Mourou et al.**
The electron stays bound to the highly charged ion until the laser pulse reaches its peak intensity
TC12753
• The electron also experiences the Coulomb force of the ion
+Ze–
e–
E
B
x
z
y
20 fsm = 910 nm
Ionizationtime
20 nm
i
Electron trajectories were calculatedusing the relativistic equation of motionincluding the radiation-reaction force
TC12752
*L. D. Landau and E. M. Lifshitz, in The Classical Theory of Fields, 3rd rev. ed.(Pergamon Press, Oxford, 1971), Vol. 2, Chap. 9, pp. 170–224.
**S. X. Hu and A. F. Starace, Phys. Rev. E 73, 066502 (2006).
/mF e c v E v B c E v c2 3RR e4 2 5 2 2 2 2# :--, c +_ ^ ^i h h8 B
The radiation-reaction force* is given by
A fi fth-order expansion of Maxwell’s equations was usedfor the focused laser fi eld (EL, BL)**
/d d e B m c Fp t E E pL C L e RR#- c= + + +_ i
Coulomb fi eld if present
Single-trajectory simulations of electron accelerations from highly charged ions show little difference evenat laser intensities of 1024 W/cm2
TC12754
100 102 1040
2
4
6
8
10
12
Time (fs)
En
erg
y (G
eV)
1024 W/cm2, Tc42+
Electron becomesin phase and seesa strong field
Electron leavesthe focal spot
Electron becomesout of phase withthe electromagneticwave
RR offRR on
The radiation-reaction effects are just noticeableat 1025 W/cm2
TC12755
100 102 1040
10
20
30
40
50
60
Interaction time (fs)
En
erg
y (G
eV)
1025 W/cm2, Gd63+
RR offRR on
Abstract
Recent developments in high-power laser technology make focused laser intensities from 1022 W/cm2 to 1025 W/cm2 feasible in the near future, opening up the study of the superintense laser acceleration of electrons to tens of GeV energies. Previous work on this subject has not accounted for the radiation-reaction force, which is the recoil force caused by the electromagnetic radiation emitted by an accelerating charged particle. In this work, two possible scenarios (an electron originally bound in a highly charged ion and a counter-propagating 1-GeV electron pulse) were simulated. In the fi rst scenario, little difference was found between simulations with and without the radiation-reaction force. In contrast, the second scenario, involving the counter-propagating 1-GeV electron pulse, showed the electrons losing signifi cant amounts of energy when the radiation-reaction force was taken into account.
Monte Carlo simulations at 1025 W/cm2 also show little difference when radiation reaction is included
TC12756
• The ions are located randomlyin the shaded area
0
10
20
30
40
50
60
Ele
ctro
n e
ner
gy
(GeV
)
Ejection angle i (°)
The highest-energy electronshave small ejection angles
0.0 1.0 2.0 3.02.51.50.5
20 nm
4 nm
Laser
e–i
RR offRR on
z
A 1-GeV beam of electrons is aimed to meet the peakof the laser pulse at z = 0
TC12757
E
B
x
z
y
20 fsm = 910 nm
20 nme– (1 GeV)
Single-trajectory simulations show signifi cant differences at 1023 W/cm2 with or without radiation reaction
TC12758
1023 W/cm2
0.0
0.5
1.0
Ele
ctro
n e
ner
gy
(GeV
)
0–20 20Time (fs)
RR on
RR off
The electron is turned around and reacceleratedat 1024 W/cm2 with radiation reaction included
TC12759
0.0
0.5
1.0
Ele
ctro
n e
ner
gy
(GeV
)
102 1041000
2
4
6
8
Time (fs)
Ele
ctro
n e
ner
gy
(GeV
)
1060–20 20Time (fs)
RR off
RR onRR off
RR on
Monte Carlo simulations at 1023 W/cm2 with radiation reaction show the scattering of electrons
TC12760
• The electrons were chosen to meet the peak of the laser pulseat random points within the same 20 × 4-nm region
• The electrons were also given a 2% momentum spreadin the z direction
No
rmal
ized
co
un
to
f el
ectr
on
s
0Energy (GeV)
1 2 3
RR off
0.0
0.2
0.4
0.6
0.8
1.0
No
rmal
ized
co
un
to
f el
ectr
on
s
0.0
0.2
0.4
0.6
0.8
1.0
RR on
RR off
1023 W/cm2 1023 W/cm2
Undeflected electronsRR onRR on
0 9045
Ejection angle i (°)
135 180
Most electrons are turned around at 1024 W/cm2
TC12761
No
rmal
ized
co
un
to
f el
ectr
on
s
0Energy (GeV)
1 2 3
RR off
0 90450.0
0.2
0.4
0.6
0.8
1.0
No
rmal
ized
co
un
to
f el
ectr
on
s
0.0
0.2
0.4
0.6
0.8
1.0
Ejection angle i (°)
135 180
RR onRR off
1024 W/cm2 1024 W/cm2
Undeflectedelectrons RR onRR on
Counterpropagating Electron BeamHighly Charged Ion
The radiation-reaction force can significantly alter electron trajectories at laser intensities above 1023 W/cm2
Summary
TC12751
• Highly charged ion scenario
– little difference with and without RR
• Counter-propagating electron-beam scenario
– significant difference with and without RR
The effects of the radiation-reaction (RR) force have been simulated for two scenarios
Proposed laser developments promise to deliver ultrahigh laser intensities above 1023 W/cm2
I2205a
*D. D. Meyerhofer et al., presented at the 56th Annual Meeting of the APS Division of Plasma Physics, New Orleans, LA, 27–31 October 2014.
**G. A. Mourou et al., Opt. Commun. 285, 720 (2012).
• OMEGA EP optical parametric amplifier line (OPAL)*
– pulse energy: E = 1.6 kJ
– pulse duration: x = 20 fs
– wavelength: m = 910 nm
– focused intensity: I = 1024 W/cm2
• ELI and beyond**
– pulse energy: E = 10 kJ
– pulse duration: x = 20 fs
– wavelength: m = 1250 nm
– focused intensity: I > 1025 W/cm2
QCD . 1035 W/cm2
Nonlinear QED: E • e mc = 2m0c21 PeV
1 TeV
1 MeV
1 eV
Ultrarelativistic optics
Relativistic optics
EQ = mpc2
EQ = m0c2
ELI
CUOS
CPA
Mode lockingQ switching
1960 1980 2000 2020
Focu
sed
inte
nsi
ty (
W/c
m2 )
1025
1030
1020
1015
1010
OPCPA
C3
OPCPAor CPA
Bound electronsBound electrons
ILE
Year
CPA: chirped-pulse amplificationOPCPA: optical parametric chirped-pulse amplificationCUOS: Center for Ultrafast Optical Science, University of MichiganILE: Institute of Laser Engineering, University of OsakaELI: Extreme Light Infrastructure (Europe)QED: quantum electrodynamicsQCD: quantum chromodynamics
from Mourou et al.**
Electron trajectories were calculated using the relativistic equation of motion including the radiation-reaction force
TC12752
*L. D. Landau and E. M. Lifshitz, in The Classical Theory of Fields, 3rd rev. ed. (Pergamon Press, Oxford, 1971), Vol. 2, Chap. 9, pp. 170–224.
**S. X. Hu and A. F. Starace, Phys. Rev. E 73, 066502 (2006).
/mF e c v E v B c E v c2 3RR e4 2 5 2 2 2 2# :--, c +_ ^ ^i h h8 B
The radiation-reaction force* is given by
A fifth-order expansion of Maxwell’s equations was used for the focused laser field (EL, BL)**
/d d e B m c Fp t E E pL C L e RR#- c= + + +_ i
Coulomb field if present
Abstract
Recent developments in high-power laser technology make focused laser intensities from 1022 W/cm2 to 1025 W/cm2 feasible in the near future, opening up the study of the superintense laser acceleration of electrons to tens of GeV energies. Previous work on this subject has not accounted for the radiation-reaction force, which is the recoil force caused by the electromagnetic radiation emitted by an accelerating charged particle. In this work, two possible scenarios (an electron originally bound in a highly charged ion and a counter-propagating 1-GeV electron pulse) were simulated. In the first scenario, little difference was found between simulations with and without the radiation-reaction force. In contrast, the second scenario, involving the counter-propagating 1-GeV electron pulse, showed the electrons losing significant amounts of energy when the radiation-reaction force was taken into account.
The electron stays bound to the highly charged ion until the laser pulse reaches its peak intensity
TC12753
• The electron also experiences the Coulomb force of the ion
+Ze–
e–
E
B
x
z
y
20 fsm = 910 nm
Ionizationtime
20 nm
i
Single-trajectory simulations of electron accelerations from highly charged ions show little difference even at laser intensities of 1024 W/cm2
TC12754
100 102 1040
2
4
6
8
10
12
Time (fs)
En
erg
y (G
eV)
1024 W/cm2, Tc42+
Electron becomesin phase and seesa strong field
Electron leavesthe focal spot
Electron becomesout of phase withthe electromagneticwave
RR offRR on
The radiation-reaction effects are just noticeable at 1025 W/cm2
TC12755
100 102 1040
10
20
30
40
50
60
Interaction time (fs)
En
erg
y (G
eV)
1025 W/cm2, Gd63+
RR offRR on
Monte Carlo simulations at 1025 W/cm2 also show little difference when radiation reaction is included
TC12756
• The ions are located randomly in the shaded area
0
10
20
30
40
50
60
Ele
ctro
n e
ner
gy
(GeV
)
Ejection angle i (°)
The highest-energy electronshave small ejection angles
0.0 1.0 2.0 3.02.51.50.5
20 nm
4 nm
Laser
e–i
RR offRR on
z
A 1-GeV beam of electrons is aimed to meet the peak of the laser pulse at z = 0
TC12757
E
B
x
z
y
20 fsm = 910 nm
20 nme– (1 GeV)
Single-trajectory simulations show significant differences at 1023 W/cm2 with or without radiation reaction
TC12758
1023 W/cm2
0.0
0.5
1.0
Ele
ctro
n e
ner
gy
(GeV
)
0–20 20Time (fs)
RR on
RR off
The electron is turned around and reaccelerated at 1024 W/cm2 with radiation reaction included
TC12759
0.0
0.5
1.0
Ele
ctro
n e
ner
gy
(GeV
)
102 1041000
2
4
6
8
Time (fs)
Ele
ctro
n e
ner
gy
(GeV
)1060–20 20
Time (fs)
RR off
RR onRR off
RR on
Monte Carlo simulations at 1023 W/cm2 with radiation reaction show the scattering of electrons
TC12760
• The electrons were chosen to meet the peak of the laser pulse at random points within the same 20 × 4-nm region
• The electrons were also given a 2% momentum spread in the z direction
No
rmal
ized
co
un
to
f el
ectr
on
s
0Energy (GeV)
1 2 3
RR off
0.0
0.2
0.4
0.6
0.8
1.0
No
rmal
ized
co
un
to
f el
ectr
on
s
0.0
0.2
0.4
0.6
0.8
1.0
RR on
RR off
1023 W/cm2 1023 W/cm2
Undeflected electronsRR onRR on
0 9045
Ejection angle i (°)
135 180
Most electrons are turned around at 1024 W/cm2
TC12761
No
rmal
ized
co
un
to
f el
ectr
on
s
0Energy (GeV)
1 2 3
RR off
0 90450.0
0.2
0.4
0.6
0.8
1.0
No
rmal
ized
co
un
to
f el
ectr
on
s0.0
0.2
0.4
0.6
0.8
1.0
Ejection angle i (°)
135 180
RR onRR off
1024 W/cm2 1024 W/cm2
Undeflectedelectrons RR onRR on