Physics of the long-term evolution of the Weibel instability (WI) of an electron beam propagating through the plasma is described. Several phenomena occurring during the WI are identified: (i) the exponential growth stage resulting in beam breakup into small current filaments; (ii) merger of the small filaments and beam particles’ trapping inside them; (iii) filaments’ compression and expulsion of the ambient plasma from the filaments; (iv) formation of high-current filaments and their merger. It is shown that during the final stage these beam filaments can carry super-Alfvenic currents and form hollow current density profiles similar to the Hammer–Rostoker equilibrium. This explains why the initially increasing magnetic field energy eventually decreases during the late stage of the instability. Different computational approaches to modeling both collisionless and collisional WI are also described.

1.
E. W.
Weibel
,
Phys. Rev. Lett.
2
,
83
(
1959
).
2.
B. D.
Fried
,
Phys. Fluids
2
,
337
(
1959
).
3.
R. L.
Morse
and
C. W.
Nielson
,
Phys. Fluids
14
,
830
(
1971
).
4.
R. C.
Davidson
,
D. A.
Hammer
,
I.
Haber
, and
C. E.
Wagner
,
Phys. Fluids
15
,
317
(
1972
).
5.
R.
Lee
and
M.
Lampe
,
Phys. Rev. Lett.
31
,
1390
(
1973
).
6.
M. V.
Medvedev
and
A.
Loeb
,
Astrophys. J.
526
,
697
(
1999
).
7.
M. V.
Medvedev
,
M.
Fiore
,
R. A.
Fonseca
,
L. O.
Silva
, and
W. B.
Mori
,
Astrophys. J. Lett.
618
,
L75
(
2005
).
8.
A.
Gruzinov
,
Astrophys. J. Lett.
563
,
L15
(
2001
).
9.
L. O.
Silva
,
R. A.
Fonseca
,
J. W.
Tonge
,
W. B.
Mori
, and
J. M.
Dawson
,
Phys. Plasmas
9
,
2458
(
2002
).
10.
M.
Milosavljevic
,
E.
Nakar
, and
A.
Spitkovsky
,
Astrophys. J.
637
,
765
(
2006
).
11.
A.
Spitkovsky
,
Astrophys. J. Lett.
673
,
L39
(
2008
).
12.
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
).
13.
J. J.
Honrubia
and
J.
Meyer-ter-Vehn
,
Nucl. Fusion
46
,
L25
(
2006
).
14.
S.
Atzeni
and
J.
Meyer-ter-Vehn
,
The Physics of Inertial Fusion
(
Oxford University Press
,
New York
,
2004
), p.
409
.
15.
T.
Taguchi
,
T. M.
Antonsen
,
C. S.
Liu
, and
K.
Mima
,
Phys. Rev. Lett.
86
,
5055
(
2001
).
16.
R. A.
Fonseca
,
L. O.
Silva
,
J. W.
Tonge
,
W. B.
Mori
, and
J. M.
Dawson
,
Phys. Plasmas
10
,
1979
(
2003
).
17.
V. M.
Malkin
and
N. J.
Fisch
,
Phys. Rev. Lett.
89
,
125004
(
2002
).
18.
J. M.
Hill
,
M. H.
Key
,
S. P.
Hatchett
, and
R. R.
Freeman
,
Phys. Plasmas
12
,
082304
(
2005
).
19.
O.
Polomarov
,
A.
Sefkow
,
I.
Kaganovich
, and
G.
Shvets
,
Phys. Plasmas
14
,
043103
(
2007
).
20.
M.
Honda
,
J.
Meyer-ter-Vehn
, and
A.
Pukhov
,
Phys. Rev. Lett.
85
,
2128
(
2000
).
21.
L. O.
Silva
,
R. A.
Fonseca
,
J. W.
Tonge
,
J. M.
Dawson
,
W. B.
Mori
, and
M.
Medvedev
,
Astrophys. J. Lett.
596
,
L121
(
2003
).
22.
R. C.
Davidson
,
Physics of Nonneutral Plasmas
(
Addison-Wesley
,
Reading, MA
,
1990
), p.
122
.
23.
O.
Polomarov
,
I.
Kaganovich
, and
G.
Shvets
,
Phys. Rev. Lett.
101
,
175001
(
2008
).
24.
Ya. B.
Fainberg
,
V. D.
Shapiro
, and
V. I.
Shevchenko
,
Sov. Phys. JETP
30
,
528
(
1970
)
Ya. B.
Fainberg
,
V. D.
Shapiro
, and
V. I.
Shevchenko
, [
Zh. Eksp. Teor. Fiz.
57
,
966
(
1969
)].
25.
M.
Lampe
and
P.
Sprangle
,
Phys. Fluids
18
,
475
(
1975
).
26.
M. E.
Dieckmann
,
B.
Eliasson
,
P. K.
Shukla
,
N. J.
Sircombe
, and
R. O.
Dendy
,
Plasma Phys. Controlled Fusion
48
,
B303
(
2006
).
27.
A.
Bret
,
M. -C.
Firpo
, and
C.
Deutsch
,
Phys. Rev. Lett.
94
,
115002
(
2005
).
28.
B. I.
Cohen
,
A. B.
Langdon
,
D. W.
Hewett
, and
R. J.
Procassini
,
J. Comput. Phys.
81
,
151
(
1989
).
29.
LSP is a software product of ATK Mission Research, Albuquerque, NM 87110.
30.
T. N.
Kato
,
Phys. Plasmas
12
,
080705
(
2005
).
31.
D. A.
Hammer
and
N.
Rostoker
,
Phys. Fluids
13
,
1831
(
1970
).
32.
E. P.
Lee
,
S.
Yu
,
H. L.
Buchanan
,
F. W.
Chanbers
, and
M. N.
Rosenbluth
,
Phys. Fluids
23
,
2095
(
1980
).
33.
I. D.
Kaganovich
,
G.
Shvets
,
E.
Startsev
, and
R. C.
Davidson
,
Phys. Plasmas
8
,
4180
(
2001
).
34.
O.
Buneman
,
Proc. R. Soc. London, Ser. A
215
,
346
(
1952
).
You do not currently have access to this content.