Driving laser wakefield acceleration with extremely short, near single-cycle laser pulses is crucial to the realization of an electron source that can operate at kHz-repetition rate while relying on modest laser energy. It is also interesting from a fundamental point of view, as the ponderomotive approximation is no longer valid for such short pulses. Through particle-in-cell simulations, we show how the plasma response becomes asymmetric in the plane of laser polarization, and dependent on the carrier-envelope phase (CEP) of the laser pulse. For the case of self-injection, this in turn strongly affects the initial conditions of injected electrons, causing collective betatron oscillations of the electron beam. As a result, the electron beam pointing, electron energy spectrum, and the direction of emitted betatron radiation become CEP dependent. For injection in a density gradient, the effect on beam pointing is reduced and the electron energy spectrum is CEP independent, as electron injection is mostly longitudinal and mainly determined by the density gradient. Our results highlight the importance of controlling the CEP in this regime for producing stable and reproducible relativistic electron beams and identify how CEP effects may be observed in experiments. In the future, CEP control may become an additional tool to control the energy spectrum or pointing of the accelerated electron beam.

1.
T.
Tajima
and
J. M.
Dawson
,
Phys. Rev. Lett.
43
,
267
(
1979
).
2.
E.
Esarey
,
C. B.
Schroeder
, and
W. P.
Leemans
,
Rev. Mod. Phys.
81
,
1229
(
2009
).
3.
J.
Faure
,
Y.
Glinec
,
A.
Pukhov
,
S.
Kiselev
,
S.
Gordienko
,
E.
Lefebvre
,
J.-P.
Rousseau
,
F.
Burgy
, and
V.
Malka
,
Nature
431
,
541
(
2004
).
4.
S. P. D.
Mangles
,
C. D.
Murphy
,
Z.
Najmudin
,
A. G. R.
Thomas
,
J. L.
Collier
,
A. E.
Dangor
,
E. J.
Divall
,
P. S.
Foster
,
J. G.
Gallacher
,
C. J.
Hooker
,
D. A.
Jaroszynski
,
A. J.
Langley
,
W. B.
Mori
,
P. A.
Norreys
,
F. S.
Tsung
,
R.
Viskup
,
B. R.
Walton
, and
K.
Krushelnick
,
Nature
431
,
535
(
2004
).
5.
C. G. R.
Geddes
,
C.
Toth
,
J.
van Tilborg
,
E.
Esarey
,
C. B.
Schroeder
,
D.
Bruhwiler
,
C.
Nieter
,
J.
Cary
, and
W. P.
Leemans
,
Nature
431
,
538
(
2004
).
6.
O.
Lundh
,
J.
Lim
,
C.
Rechatin
,
L.
Ammoura
,
A.
Ben-Ismaïl
,
X.
Davoine
,
G.
Gallot
,
J.-P.
Goddet
,
E.
Lefebvre
,
V.
Malka
, and
J.
Faure
,
Nat. Phys.
7
,
219
(
2011
).
7.
K.
Ta Phuoc
,
S.
Corde
,
R.
Fitour
,
R.
Shah
,
F.
Albert
,
J.-P.
Rousseau
,
F.
Burgy
,
A.
Rousse
,
V.
Seredov
, and
A.
Pukhov
,
Phys. Plasmas
15
,
073106
(
2008
).
8.
Z.-H.
He
,
B.
Hou
,
J. A.
Nees
,
J. H.
Easter
,
J.
Faure
,
K.
Krushelnick
, and
A. G. R.
Thomas
,
New J. Phys.
15
,
053016
(
2013
).
9.
B.
Mahieu
,
N.
Jourdain
,
K. T.
Phuoc
,
F.
Dorchies
,
J.-P.
Goddet
,
A.
Lifschitz
,
P.
Renaudin
, and
L.
Lecherbourg
,
Nat. Commun.
9
,
1
(
2018
).
10.
V.
Malka
,
J.
Faure
,
Y. A.
Gauduel
,
E.
Lefebvre
,
A.
Rousse
, and
K. T.
Phuoc
,
Nat. Phys.
4
,
447
(
2008
).
11.
K.
Behm
,
A.
Hussein
,
T.
Zhao
,
R.
Baggott
,
J.
Cole
,
E.
Hill
,
K.
Krushelnick
,
A.
Maksimchuk
,
J.
Nees
,
S.
Rose
,
A.
Thomas
,
R.
Watt
,
J.
Wood
,
V.
Yanovsky
, and
S.
Mangles
,
High Energy Density Phys.
35
,
100729
(
2020
).
12.
H.-P.
Schlenvoigt
,
K.
Haupt
,
A.
Debus
,
F.
Budde
,
O.
Jäckel
,
S.
Pfotenhauer
,
H.
Schwoerer
,
E.
Rohwer
,
J.
Gallacher
,
E.
Brunetti
 et al.,
Nat. Phys.
4
,
130
(
2008
).
13.
C. B.
Schroeder
,
E.
Esarey
,
C. G. R.
Geddes
,
C.
Benedetti
, and
W. P.
Leemans
,
Phys. Rev. Spec. Top. Accel. Beams
13
,
101301
(
2010
).
14.
L.
Rovige
,
J.
Huijts
,
I.
Andriyash
,
A.
Vernier
,
V.
Tomkus
,
V.
Girdauskas
,
G.
Raciukaitis
,
J.
Dudutis
,
V.
Stankevic
,
P.
Gecys
,
M.
Ouille
,
Z.
Cheng
,
R.
Lopez-Martens
, and
J.
Faure
,
Phys. Rev. Accel. Beams
23
,
093401
(
2020
).
15.
J.
Faure
,
D.
Gustas
,
D.
Guénot
,
A.
Vernier
,
F.
Böhle
,
M.
Ouillé
,
S.
Haessler
,
R.
Lopez-Martens
, and
A.
Lifschitz
,
Plasma Phys. Controlled Fusion
61
,
014012
(
2019
).
16.
F.
Salehi
,
A. J.
Goers
,
G. A.
Hine
,
L.
Feder
,
D.
Kuk
,
B.
Miao
,
D.
Woodbury
,
K. Y.
Kim
, and
H. M.
Milchberg
,
Opt. Lett.
42
,
215
(
2017
).
17.
D.
Guénot
,
D.
Gustas
,
A.
Vernier
,
B.
Beaurepaire
,
F.
Böhle
,
M.
Bocoum
,
M.
Lozano
,
A.
Jullien
,
R.
Lopez-Martens
,
A.
Lifschitz
, and
J.
Faure
,
Nat. Photonics
11
,
293
(
2017
).
18.
M.
Ouillé
,
A.
Vernier
,
F.
Böhle
,
M.
Bocoum
,
A.
Jullien
,
M.
Lozano
,
J.-P.
Rousseau
,
Z.
Cheng
,
D.
Gustas
,
A.
Blumenstein
,
P.
Simon
,
S.
Haessler
,
J.
Faure
,
T.
Nagy
, and
R.
Lopez-Martens
,
Light
9
,
1
(
2020
).
19.
P.
Mora
and
T. M.
Antonsen
, Jr.
,
Phys. Plasmas
4
,
217
(
1997
).
20.
A.
Baltuška
,
T.
Udem
,
M.
Uiberacker
,
M.
Hentschel
,
E.
Goulielmakis
,
C.
Gohle
,
R.
Holzwarth
,
V. S.
Yakovlev
,
A.
Scrinzi
,
T. W.
Hänsch
, and
F.
Krausz
,
Nature
421
,
611
(
2003
).
21.
N.
Ishii
,
K.
Kaneshima
,
K.
Kitano
,
T.
Kanai
,
S.
Watanabe
, and
J.
Itatani
,
Nat. Commun.
5
,
3331
(
2014
).
22.
E. N.
Nerush
and
I. Y.
Kostyukov
,
Phys. Rev. Lett.
103
,
035001
(
2009
).
23.
A.
Zhidkov
,
T.
Fujii
, and
K.
Nemoto
,
Phys. Rev. E
78
,
036406
(
2008
).
24.
A. F.
Lifschitz
and
V.
Malka
,
New J. Phys.
14
,
053045
(
2012
).
25.
P.
Valenta
,
T. Z.
Esirkepov
,
J. K.
Koga
,
A.
Nečas
,
G. M.
Grittani
,
C. M.
Lazzarini
,
O.
Klimo
,
G.
Korn
, and
S. V.
Bulanov
,
Phys. Rev. E
102
,
053216
(
2020
).
26.
S.
Xu
,
J.
Zhang
,
N.
Tang
,
S.
Wang
,
W.
Lu
, and
Z.
Li
,
AIP Adv.
10
,
095310
(
2020
).
27.
R.
Budriūnas
,
T.
Stanislauskas
,
J.
Adamonis
,
A.
Aleknavičius
,
G.
Veitas
,
D.
Gadonas
,
S.
Balickas
,
A.
Michailovas
, and
A.
Varanavičius
,
Opt. Express
25
,
5797
(
2017
).
28.
A.
Marcinkevičius
,
S.
Juodkazis
,
M.
Watanabe
,
M.
Miwa
,
S.
Matsuo
,
H.
Misawa
, and
J.
Nishii
,
Opt. Lett.
26
,
277
(
2001
).
29.
V.
Tomkus
,
V.
Girdauskas
,
J.
Dudutis
,
P.
Gečys
,
V.
Stankevič
, and
G.
Račiukaitis
,
Opt. Express
26
,
27965
(
2018
).
30.
R.
Lehe
,
M.
Kirchen
,
I. A.
Andriyash
,
B. B.
Godfrey
, and
J.-L.
Vay
,
Comput. Phys. Commun.
203
,
66
(
2016
).
31.
C. F. R.
Caron
and
R. M.
Potvliege
,
J. Mod. Opt.
46
,
1881
(
1999
).
32.
B.
Beaurepaire
,
A.
Lifschitz
, and
J.
Faure
,
New J. Phys.
16
,
023023
(
2014
).
33.
In Ref. 22 bubble asymmetry Λ(l) is defined as the sum of transverse momenta of two electrons born with initial position +l and −l in the polarization plane.
34.
A.
Modena
,
Z.
Najmudin
,
A. E.
Dangor
,
C. E.
Clayton
,
K. A.
Marsh
,
C.
Joshi
,
V.
Malka
,
C. B.
Darrow
,
C.
Danson
,
D.
Neely
, and
F. N.
Walsh
,
Nature
377
,
606
(
1995
).
35.
D.
Umstadter
,
S.-Y.
Chen
,
A.
Maksimchuk
,
G.
Mourou
, and
R.
Wagner
,
Science
273
,
472
(
1996
).
36.
W.
Lu
,
M.
Tzoufras
,
C.
Joshi
,
F. S.
Tsung
,
W. B.
Mori
,
J.
Vieira
,
R. A.
Fonseca
, and
L. O.
Silva
,
Phys. Rev. Spec. Top. Accel. Beams
10
,
061301
(
2007
).
37.
I.
Kostyukov
,
E.
Nerush
,
A.
Pukhov
, and
V.
Seredov
,
Phys. Rev. Lett.
103
,
175003
(
2009
).
38.
S.
Kalmykov
,
S. A.
Yi
,
V.
Khudik
, and
G.
Shvets
,
Phys. Rev. Lett.
103
,
135004
(
2009
).
39.
A.
Rousse
,
K. T.
Phuoc
,
R.
Shah
,
A.
Pukhov
,
E.
Lefebvre
,
V.
Malka
,
S.
Kiselev
,
F.
Burgy
,
J.-P.
Rousseau
,
D.
Umstadter
, and
D.
Hulin
,
Phys. Rev. Lett.
93
,
135005
(
2004
).
40.
D. H.
Whittum
,
W. M.
Sharp
,
S. S.
Yu
,
M.
Lampe
, and
G.
Joyce
,
Phys. Rev. Lett.
67
,
991
(
1991
).
41.
Calculated for each electron (macroparticle in the simulation) as θx=arctanux/uz, then averaged over the electron beam (taking into account the relative weights of the macroparticles).
42.
Calculated as ϵn=x2ux2xux2, where designates a beam average and ux=pxmc.
43.
Y.
Glinec
,
J.
Faure
,
A.
Lifschitz
,
J. M.
Vieira
,
R. A.
Fonseca
,
L. O.
Silva
, and
V.
Malka
,
Europhys. Lett.
81
,
64001
(
2008
).
44.
A.
Popp
,
J.
Vieira
,
J.
Osterhoff
,
Z.
Major
,
R.
Hörlein
,
M.
Fuchs
,
R.
Weingartner
,
T. P.
Rowlands-Rees
,
M.
Marti
,
R. A.
Fonseca
,
S. F.
Martins
,
L. O.
Silva
,
S. M.
Hooker
,
F.
Krausz
,
F.
Grüner
, and
S.
Karsch
,
Phys. Rev. Lett.
105
,
215001
(
2010
).
45.
D. E.
Mittelberger
,
M.
Thévenet
,
K.
Nakamura
,
A. J.
Gonsalves
,
C.
Benedetti
,
J.
Daniels
,
S.
Steinke
,
R.
Lehe
,
J.-L.
Vay
,
C. B.
Schroeder
,
E.
Esarey
, and
W. P.
Leemans
,
Phys. Rev. E
100
,
063208
(
2019
).
46.
K. T.
Phuoc
,
S.
Corde
,
R.
Shah
,
F.
Albert
,
R.
Fitour
,
J.-P.
Rousseau
,
F.
Burgy
,
B.
Mercier
, and
A.
Rousse
,
Phys. Rev. Lett.
97
,
225002
(
2006
).
47.
F.
Salehi
,
M.
Le
,
L.
Railing
, and
H. M.
Milchberg
, “
Laser-accelerated, low divergence 15 mev quasi-monoenergetic electron bunches at 1 kHz
,” arXiv:2010.15720 (
2020
).
48.
L.
Rovige
,
J.
Huijts
,
I. A.
Andriyash
,
A.
Vernier
,
M.
Ouillé
,
Z.
Cheng
,
T.
Asai
,
Y.
Fukuda
,
V.
Tomkus
,
V.
Girdauskas
,
G.
Raciukaitis
,
J.
Dudutis
,
V.
Stankevic
,
P.
Gecys
,
R.
Lopez-Martens
, and
J.
Faure
,
Phys. Plasmas
28
,
033105
(
2021
).
49.
S.
Bulanov
,
N.
Naumova
,
F.
Pegoraro
, and
J.
Sakai
,
Phys. Rev. E
58
,
R5257
(
1998
).
50.
C. G. R.
Geddes
,
K.
Nakamura
,
G. R.
Plateau
,
C.
Toth
,
E.
Cormier-Michel
,
E.
Esarey
,
C. B.
Schroeder
,
J. R.
Cary
, and
W. P.
Leemans
,
Phys. Rev. Lett.
100
,
215004
(
2008
).
51.
K.
Schmid
,
A.
Buck
,
C. M. S.
Sears
,
J. M.
Mikhailova
,
R.
Tautz
,
D.
Herrmann
,
M.
Geissler
,
F.
Krausz
, and
L.
Veisz
,
Phys. Rev. Spec. Top. Accel. Beams
13
,
091301
(
2010
).
52.
B.
Beaurepaire
,
A.
Vernier
,
M.
Bocoum
,
F.
Böhle
,
A.
Jullien
,
J.-P.
Rousseau
,
T.
Lefrou
,
D.
Douillet
,
G.
Iaquaniello
,
R.
Lopez-Martens
,
A.
Lifschitz
, and
J.
Faure
,
Phys. Rev. X
5
,
031012
(
2015
).
53.
S.
Corde
,
C.
Thaury
,
A.
Lifschitz
,
G.
Lambert
,
K.
Ta Phuoc
,
X.
Davoine
,
R.
Lehe
,
D.
Douillet
,
A.
Rousse
, and
V.
Malka
,
Nat. Commun.
4
,
1501
(
2013
).
54.
Despite the localized injection, broad energy spectra are observed. The reason is that towards the end of the simulation, as the laser pulse gets depleted, the rear part of the electron bunch starts driving its own wake
, thus losing energy with respect to the front of the bunch.
55.
J. D.
Jackson
,
Classical Electrodynamics
, 3rd ed. (
Wiley
,
New York
,,
1999
).
56.
I.
Andriyash
, see https://github.com/hightower8083/synchrad for “
Synchrad
,
2019
.”
57.
S.
Corde
,
K.
Ta Phuoc
,
G.
Lambert
,
R.
Fitour
,
V.
Malka
,
A.
Rousse
,
A.
Beck
, and
E.
Lefebvre
,
Rev. Mod. Phys.
85
,
1
(
2013
).

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