The ion‐temperature‐gradient‐driven instability is considered in this paper. Physical pictures are presented to clarify the nature of the instability. The saturation of a single eddy is modeled by a simple nonlinear equation. It is shown that eddies that are elongated in the direction of the temperature gradient are the most unstable and have the highest saturation amplitudes. In a sheared magnetic field, such elongated eddies twist with the field lines. This structure is shown to be an alternative to the usual Fourier mode picture in which the mode is localized around the surface where k =0. These elongated twisting eddies, which are an integral part of the ‘‘ballooning mode’’ structure, could survive in a torus. The elongated eddies are shown to be unstable to secondary instabilities that are driven by the large gradients in the long eddy. It is argued that the ‘‘mixing length’’ is affected by this nonlinear process, and is unlikely to be a linear eigenmode width.

1.
C.
Surko
,
Science
221
,
817
(
1983
).
2.
A. J.
Wooton
,
B. A.
Carreras
,
H.
Matsumoto
,
K.
McGuire
,
W. A.
Pibbles
,
Ch. P.
Ritz
,
P. W.
Terry
, and
S. J.
Zweben
,
Phys. Fluids B
2
,
2879
(
1990
).
3.
P. H. Rebut, M. Brusati, M. Hugon, and P. Lallia, in The Proceedings of the 11th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Kyoto, 1986 (IAEA, Vienna, 1987), Vol. 2, p. 187.
4.
A. B.
Rechester
and
M. N.
Rosenbluth
,
Phys. Rev. Lett.
40
,
38
(
1978
);
J. A.
Krommes
,
R. G.
Kleva
, and
C.
Oberman
,
J. Plasma Phys.
30
,
11
(
1983
).
5.
L. I.
Rudakov
and
R. Z.
Sagdeev
,
Dokl. Akad. Nauk. SSSR
138
,
581
(
1961
).
6.
B.
Coppi
,
M. N.
Rosenbluth
, and
R. Z.
Sagdeev
,
Phys. Fluids
10
,
582
(
1967
).
7.
J. F.
Drake
,
P. N.
Guzdar
, and
A. B.
Hassara
,
Phys. Rev. Lett.
61
,
2205
(
1988
).
8.
K. V.
Roberts
and
J. B.
Taylor
,
Phys. Fluids
8
,
315
(
1965
).
9.
S. C. Cowley, Ph.D. thesis, Princeton University, 1985.
10.
J. W.
Connor
,
R. S.
Hastie
, and
J. B.
Taylor
,
Proc. R. Soc. London Ser. A
365
,
1
(
1979
);
Y. C. Lee and J. W. Van Dam, in Proceedings of the Finite Beta Theory Workshop, edited by B. Coppi and W. Sadowski (U.S. Department of Energy, Washington, DC, 1979), p. 93;
A. H. Glasser, ibid., p. 35.
11.
J. W.
Connor
and
J. B.
Taylor
,
Phys. Fluids
30
,
3180
(
1987
).
12.
A. M.
Dimits
,
J. F.
Drake
,
A. B.
Hassam
, and
B.
Meerson
,
Phys. Fluids B
2
,
2591
(
1990
).
13.
G. S.
Lee
and
P. H.
Diamond
,
Phys. Fluids
29
,
3291
(
1986
).
14.
J. W.
Connor
,
Plasma Phys. Controlled Fusion
30
,
619
(
1988
).
15.
W. W.
Lee
,
J. A.
Krommes
,
C.
Oberman
, and
R.
Smith
,
Phys. Fluids
27
,
2652
(
1984
).
16.
J. F.
Federici
,
W. W.
Lee
,
W. M.
Tang
,
Phys. Fluids
30
,
425
(
1986
).
17.
W.
Horton
,
R. D.
Estes
, and
D.
Biskamp
,
Plasma Phys.
22
,
663
(
1980
).
18.
H.
Biglari
,
P. H.
Diamond
, and
M. N.
Rosenbluth
,
Phys. Fluids B
1
,
109
(
1989
).
19.
G.
Rewoldt
and
W. M.
Tang
,
Phys. Fluids B
2
,
318
(
1990
).
20.
R. D.
Sydora
,
T. S.
Hahm
,
W. W.
Lee
, and
J. M.
Dawson
,
Phys. Rev. Lett.
64
,
2015
(
1990
).
21.
T. Antonsen, A. M. Dimits, J. Q. Dong, J. F. Drake, P. N. Guzdar, A. B. Hassam, and C. S. Liu, in The Proceedings of Plasma Physics and Controlled Nuclear Fusion Research, Nice, France, 1988 (IAEA, Vienna, 1989), Vol. 2, p. 251.
22.
R.
Waltz
,
Phys. Fluids
31
,
1180
(
1988
).
23.
S.
Hamaguchi
and
W.
Horton
,
Phys. Fluids B
2
,
1833
(
1990
).
24.
S. Hamaguchi (private communication).
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