The dispersive effects of vacuum polarization on the propagation of a strong circularly polarized electromagnetic wave through a cold collisional plasma are studied analytically. It is found that, due to the singular dielectric features of the plasma, the vacuum effects on the wave propagation in a plasma are qualitatively different and much larger than those in pure vacuum in the regime when the frequency of the propagating wave approaches the plasma frequency. A possible experimental setup to detect these effects in plasma is described.

1.
Y. I.
Salamin
,
S. X.
Hu
,
K. Z.
Hatsagortsyan
, and
C. H.
Keitel
,
Phys. Rep.
427
,
41
(
2006
).
2.
G. A.
Mourou
,
T.
Tajima
, and
S. V.
Bulanov
,
Rev. Mod. Phys.
78
,
309
(
2006
).
3.
P. A.
Norreys
,
M.
Zepf
,
S.
Moustaizis
 et al,
Phys. Rev. Lett.
76
,
1832
(
1996
);
[PubMed]
C.
Rischel
,
A.
Rousse
,
I.
Uschmann
,
P.-A.
Albouy
,
J.-P.
Geindre
,
P.
Audebert
,
J.-C.
Gauthier
,
E.
Fröster
,
J.-L.
Martin
, and
A.
Antonetti
,
Nature (London)
390
,
490
(
1997
);
A. L.
Cavalieri
,
D. M.
Fritz
,
S. H.
Lee
 et al,
Phys. Rev. Lett.
94
,
114801
(
2005
);
[PubMed]
H.
Schwoerer
,
B.
Liesfeld
,
H.-P.
Schlenvoigt
,
K.-U.
Amthor
, and
R.
Sauerbrey
,
Phys. Rev. Lett.
96
,
014802
(
2006
);
[PubMed]
B.
Dromey
,
M.
Zepf
,
A.
Gopal
 et al,
Nat. Phys.
2
,
456
(
2006
).
4.
S. P. D.
Mangles
,
C. D.
Murphy
,
Z.
Najmudin
 et al,
Nature (London)
431
,
535
(
2004
);
C. G. R.
Geddes
,
Cs.
Toth
,
J.
van Tilborg
,
E.
Esarey
,
C. B.
Schroeder
,
D.
Bruhwiler
,
C.
Nieter
,
J.
Cary
, and
W. P.
Leemans
,
Nature (London)
431
,
538
(
2004
);
J.
Faure
,
Y.
Glinec
,
A.
Pukhov
,
S.
Kiselev
,
S.
Gordienko
,
E.
Lefebvre
,
J.-P.
Rousseau
,
F.
Burgy
, and
V.
Malka
,
Nature (London)
431
,
541
(
2004
);
B. M.
Hegelich
,
B. J.
Albright
,
J.
Cobble
,
K.
Flippo
,
S.
Letzring
,
M.
Paffett
,
H.
Ruhl
,
J.
Schreiber
,
R. K.
Schulze
, and
J. C.
Fernández
,
Nature (London)
439
,
441
(
2006
);
H.
Schwoerer
,
S.
Pfotenhauer
,
O.
Jäckel
,
K.-U.
Amthor
,
B.
Liesfeld
,
W.
Ziegler
,
R.
Sauerbrey
,
K. W. D.
Ledingham
, and
T.
Esirkepov
,
Nature (London)
439
,
445
(
2006
);
J.
Fuchs
,
P.
Antici
,
E.
d’Humières
 et al,
Nat. Phys.
2
,
48
(
2006
);
B.
Hidding
,
K.-U.
Amthor
,
B.
Liesfeld
 et al,
Phys. Rev. Lett.
96
,
105004
(
2006
).
[PubMed]
5.
M.
Tabak
,
J.
Hammer
,
M. E.
Glinsky
,
W. L.
Kruer
,
S. C.
Wilks
,
J.
Woodworth
,
E. M.
Campbell
,
M. D.
Perry
, and
R. J.
Mason
,
Phys. Plasmas
1
,
1626
(
1994
);
P.
Mulser
and
D.
Bauer
,
Laser Part. Beams
22
,
5
(
2004
);
S.
Atzeni
and
J.
Meyer-ter-Vehn
,
The Physics of Inertial Fusion
(
Clarendon
,
Oxford
,
2004
).
6.
S.-W.
Bahk
,
P.
Rousseau
,
T. A.
Planchon
,
V.
Chvykov
,
G.
Kalintchenko
,
A.
Maksimchuk
,
G. A.
Mourou
, and
V.
Yanovsky
,
Opt. Lett.
29
,
2837
(
2004
).
7.
T.
Tajima
and
G.
Mourou
,
Phys. Rev. ST Accel. Beams
5
,
031301
(
2002
).
8.
W.
Dittrich
and
H.
Gies
,
Probing the Quantum Vacuum: Perturbative Effective Action Approach in Quantum Electrodynamics and its Application
(
Springer
,
Berlin
,
2000
).
9.
M.
Delbrück
,
Z. Phys.
84
,
144
(
1933
).
10.
W.
Heisenberg
and
H.
Euler
,
Z. Phys.
98
,
714
(
1936
).
11.
V.
Weisskopf
,
K. Dan. Vidensk. Selsk. Mat. Fys. Medd.
14
,
1
(
1936
).
12.
13.
J. J.
Klein
and
B. P.
Nigam
,
Phys. Rev.
135
,
B1279
(
1964
);
N. B.
Narozhnyĭ
,
Sov. Phys. JETP
28
,
371
(
1969
);
Z.
Bialynicka-Birula
and
I.
Bialynicki-Birula
,
Phys. Rev. D
2
,
2341
(
1970
);
E.
Brezin
and
C.
Itzykson
,
Phys. Rev. D
3
,
618
(
1971
);
I. A.
Batalin
and
A. E.
Shabad
,
Sov. Phys. JETP
33
,
483
(
1971
);
V. I.
Ritus
,
Ann. Phys. (Paris)
69
,
555
(
1972
);
J. K.
Daugherty
and
I.
Lerche
,
Phys. Rev. D
14
,
340
(
1976
);
L. F.
Urrutia
,
Phys. Rev. D
17
,
1977
(
1978
);
J. S.
Heyl
and
L.
Hernquist
,
J. Phys. A
30
,
6485
(
1997
).
14.
W.
Becker
and
H.
Mitter
,
J. Phys. A
8
,
1638
(
1975
).
15.
V. N.
Baier
,
A. I.
Mil’shtein
, and
V. M.
Strakhovenko
,
Sov. Phys. JETP
42
,
961
(
1975
).
16.
E. B.
Aleksandrov
,
A. A.
Ansel’m
, and
A. N.
Moskalev
,
Sov. Phys. JETP
62
,
680
(
1986
).
17.
A.
Di Piazza
,
K. Z.
Hatsagortsyan
, and
C. H.
Keitel
,
Phys. Rev. D
72
,
085005
(
2005
).
18.
T.
Heinzl
,
B.
Liesfeld
,
K.-U.
Amthor
,
H.
Schwoerer
,
R.
Sauerbrey
, and
A.
Wipf
,
Opt. Commun.
267
,
318
(
2006
).
19.
E.
Lundström
,
G.
Brodin
,
J.
Lundin
,
M.
Marklund
,
R.
Bingham
,
J.
Collier
,
J. T.
Mendonça
, and
P.
Norreys
,
Phys. Rev. Lett.
96
,
083602
(
2006
);
[PubMed]
E.
Lundström
,
J.
Collier
,
R.
Bingham
,
J. T.
Mendonça
, and
P.
Norreys
,
Phys. Rev. A
74
,
043821
(
2006
).
20.
A.
Di Piazza
,
K. Z.
Hatsagortsyan
, and
C. H.
Keitel
,
Phys. Rev. Lett.
97
,
083603
(
2006
).
21.
G.
Jarlskog
,
L.
Jönsson
,
S.
Prünster
,
H. D.
Schulz
,
H. J.
Willutzki
, and
G. G.
Winter
,
Phys. Rev. D
8
,
3813
(
1973
);
M.
Schumacher
,
F.
Smend
, and
I.
Borchert
,
Phys. Rev. C
13
,
2318
(
1976
);
Sh. Zh.
Akhmadaliev
,
G. Ya.
Kezerashvili
,
S. G.
Klimenko
 et al,
Phys. Rev. C
58
,
2844
(
1998
).
22.
Sh. Zh.
Akhmadaliev
,
G. Ya.
Kezerashvili
,
S. G.
Klimenko
 et al,
Phys. Rev. Lett.
89
,
061802
(
2002
).
23.
D.
Bakalov
,
G.
Cantatore
,
G.
Carugno
 et al,
Nucl. Phys. B
35
,
180
(
1994
); see also http://www.ts.infn.it/experiments/pvlas/pvlas.html
24.
E.
Zavattini
,
G.
Zavattini
,
G.
Ruoso
 et al,
Phys. Rev. Lett.
96
,
110406
(
2006
).
25.
F.
Moulin
,
D.
Bernard
, and
F.
Amiranoff
,
Z. Phys. C
72
,
607
(
1996
);
D.
Bernard
,
F.
Moulin
,
F.
Amiranoff
,
A.
Braun
,
J. P.
Chambaret
,
G.
Darpentigny
,
G.
Grillon
,
S.
Ranc
, and
F.
Perrone
,
Eur. Phys. J. D
10
,
141
(
2000
).
26.
A. V.
Borovski
,
A. L.
Galkin
,
O. B.
Shiryaev
, and
T.
Auguste
,
Laser Physics at Relativistic Intensities
(
Springer
,
Berlin
,
2003
).
27.
28.
M.
Marklund
and
P. K.
Shukla
,
Rev. Mod. Phys.
78
,
591
(
2006
).
29.
S. V.
Bulanov
,
T.
Esirkepov
, and
T.
Tajima
,
Phys. Rev. Lett.
91
,
085001
(
2003
);
[PubMed]
N. M.
Naumova
,
J. A.
Nees
,
I. V.
Sokolov
,
B.
Hou
, and
G. A.
Mourou
,
Phys. Rev. Lett.
92
,
063902
(
2004
);
[PubMed]
S.
Gordienko
,
A.
Pukhov
,
O.
Shorokhov
, and
T.
Baeva
,
Phys. Rev. Lett.
94
,
103903
(
2005
).
[PubMed]
30.
S. S.
Bulanov
,
A. M.
Fedotov
, and
F.
Pegoraro
,
JETP Lett.
80
,
734
(
2004
);
S. S.
Bulanov
,
A. M.
Fedotov
, and
F.
Pegoraro
,
Phys. Rev. E
71
,
016404
(
2005
).
31.
S.
Schmidt
,
D.
Blaschke
,
G.
Röpke
,
A. V.
Prozorkevich
,
S. A.
Smolyansky
, and
V. D.
Toneev
,
Phys. Rev. D
59
,
094005
(
1999
);
J. C. R.
Bloch
,
V. A.
Mizerny
,
A. V.
Prozorkevich
,
C. D.
Roberts
,
S. M.
Schmidt
,
S. A.
Smolyansky
, and
D. V.
Vinnik
,
Phys. Rev. D
60
,
116011
(
1999
);
R.
Alkofer
,
M. B.
Hecht
,
C. D.
Roberts
,
S. M.
Schmidt
, and
D. V.
Vinnik
,
Phys. Rev. Lett.
87
,
193902
(
2001
);
[PubMed]
C. D.
Roberts
,
S. M.
Schmidt
, and
D. V.
Vinnik
,
Phys. Rev. Lett.
89
,
153901
(
2002
).
[PubMed]
32.
Y. N.
Gnedin
,
G. G.
Pavlov
, and
Y. A.
Shibanov
,
JETP Lett.
27
,
305
(
1978
).
33.
P.
Mészáros
and
J.
Ventura
,
Phys. Rev. Lett.
41
,
1544
(
1978
).
34.
L.
Stenflo
,
G.
Brodin
,
M.
Marklund
, and
P. K.
Shukla
,
J. Plasma Phys.
71
,
709
(
2005
).
35.
M.
Marklund
,
P. K.
Shukla
,
L.
Stenflo
,
G.
Brodin
, and
M.
Servin
,
Plasma Phys. Controlled Fusion
47
,
L25
(
2005
).
36.
M.
Marklund
,
D. D.
Tskhakaya
, and
P. K.
Shukla
,
Europhys. Lett.
72
,
950
(
2005
).
37.
J.
Lundin
,
G.
Brodin
, and
M.
Marklund
,
Phys. Plasmas
13
,
102102
(
2006
).
38.
B.
Shen
,
M. Y.
Yu
, and
X.
Wang
,
Phys. Plasmas
10
,
4570
(
2003
).
39.
A. I.
Akhiezer
and
R. V.
Polovin
,
Sov. Phys. JETP
3
,
696
(
1956
).
40.
see also the book quoted therein,
S. R.
de Groot
,
W. A.
van Leeuwen
, and
C. G.
van Weert
,
Relativistic Kinetic Theory
(
Pergamon
,
London
,
1975
), pp.
18
24
.
41.
L. D.
Landau
and
E. M.
Lifshitz
,
Classical Theory of Fields
(
Pergamon
,
Oxford
,
1975
).
42.
P.
Elmfors
and
B.-S.
Skagerstam
,
Phys. Lett. B
348
,
141
(
1995
).
43.
J. I.
Kapusta
,
Finite-Temperature Field Theory
(
Cambridge University Press
,
Cambridge
,
1989
).
44.
D.
Cangemi
and
G.
Dunne
,
Ann. Phys. (Paris)
249
,
582
(
1996
).
45.
46.

The previous considerations hold at zero chemical potential. The effects of the chemical potential are more difficult to estimate because there are no expressions available for the two-loop effective Lagrangian at finite temperature and finite chemical potential. In this case, we proceed by estimating the chemical potential as that of an ideal gas, μ=kBTln[N(2πmekBT)32] (Ref. 47). At the densities we will be interested in 1023cm3 and at temperatures such that kBT100ω with ω in the optical regime [see the conditions below Eq. (11) on the laser frequency] then μkBT and it is sensible to assume that as for the temperature also the effects of the chemical potential can be neglected.

47.
L. D.
Landau
and
E. M.
Lifshitz
,
Statistical Physics—Part 1
(
Pergamon
,
Oxford
,
1980
), p.
134
.
48.
L. D.
Landau
and
E. M.
Lifshitz
,
Electrodynamics of Continuous Media
(
Pergamon
,
Oxford
,
1984
), p.
295
.
49.
P.
Mora
,
Plasma Phys. Controlled Fusion
43
,
A31
(
2001
).
50.
R. K.
Kirkwood
,
R. L.
Berger
,
C. G. R.
Geddes
,
J. D.
Moody
,
B. J.
MacGowan
,
S. H.
Glenzer
,
K. G.
Estabrook
, and
O. L.
Landen
,
Phys. Plasmas
10
,
2948
(
2003
);
C.
Rousseaux
,
L.
Gremillet
,
M.
Casanova
,
P.
Loiseau
,
M.
Rabec Le Gloahec
,
S. D.
Baton
,
F.
Amiranof
,
J. C.
Adam
, and
A.
Heron
,
Phys. Rev. Lett.
97
,
015001
(
2006
).
[PubMed]
51.
J. C.
Adam
,
A.
Heron
,
G.
Laval
, and
P.
Mora
,
Phys. Rev. Lett.
84
,
3598
(
2000
);
[PubMed]
C.
Rousseaux
,
M.
Rabec Le Gloahec
,
S. D.
Baton
,
F.
Amiranof
,
J.
Fuchs
,
L.
Gremillet
,
J. C.
Adam
,
A.
Heron
, and
P.
Mora
,
Phys. Plasmas
9
,
4261
(
2002
).
52.
F.
Cattani
,
A.
Kim
,
D.
Anderson
, and
M.
Lisak
,
Phys. Rev. E
62
,
1234
(
2000
).
53.
K.
Muroo
,
M.
Namikawa
, and
Y.
Takubo
,
Meas. Sci. Technol.
11
,
32
(
2000
).
54.
H.
Hora
,
Plasmas at High Temperature and Density: Applications and Implications of Laser-Plasma Interaction
(
Springer
,
Berlin
,
1991
), p.
110
.
55.

Since we are also considering the VPEs perturbatively up to first order in δvac it would be more correct to also set δvac=0. Nevertheless, the VPEs do not affect the zero-order Lorentz factors γ0,λ that are the only dynamical quantities entering the collision frequency because p0=meγ0,e21.

You do not currently have access to this content.