The rotational instability almost always appears in dynamically formed field-reversed configurations (FRC). It generally appears as an m=2 mode (azimuthal mode number). Driven by the gravitylike centrifugal effect in rotating plasmas, it is akin to a gravitational mode. On the other hand, translated FRCs often do not exhibit this instability. A recent analysis [H. Y. Guo et al, Phys. Rev. Lett.95, 17001 (2005)] suggested that magnetic shear effects associated with a modest toroidal field can stabilize it. Here the stabilizing effect of a modest toroidal field is investigated numerically using the NIMROD code [C. R. Sovinec et al, J. Comput. Phys.195, 355 (2004)] and analytically using the modified energy principle. The analysis predicts the growth rate as a function of toroidal field strength, as well as a stability condition. The three-dimensional numerical calculations are in basic agreement with the analysis, although complete stability is not predicted due to the appearance of a distinct mode structure that persists in the open field-line region.

1.
H. Y.
Guo
,
A. L.
Hoffman
,
L. C.
Steinhauer
, and
K. E.
Miller
,
Phys. Rev. Lett.
95
,
175001
(
2005
).
2.
M.
Tuszewski
,
Nucl. Fusion
28
,
2033
(
1988
).
3.
A.
Eberhagen
and
W.
Grossmann
,
Z. Phys.
248
,
130
(
1971
).
4.
A. G.
Es’kov
,
R. Kh.
Kurtmullaev
,
A. I.
Malyutin
,
V. N.
Semenov
, and
A. L.
Chernyakov
, in “
Contr. Fusion and Plasma Phys.
,”
Proceedings of the 6th European Conference
,
Moscow
,
1973
(
European Physical Society
,
France
,
1973
), p.
595
.
5.
A. G.
Es’kov
,
R. Kh.
Kurtmullaev
,
A. P.
Kreschchuk
,
Ya. N.
Laukhin
,
A. I.
Malyutin
,
A. I.
Markin
,
Yu. S.
Martyushov
,
B. N.
Mironov
,
M. M.
Orlov
,
A. P.
Proshletsov
,
V. N.
Semenov
, and
Yu. B.
Sosunov
, in “
Plasma Physics and Controlled Nuclear Fusion Research, 1978
,”
Proceedings of the 7th International Conference
,
Innsbruck
,
1978
(
IAEA
,
Vienna
,
1979
), Vol.
2
, p.
187
.
6.
S.
Ohi
,
T.
Minato
,
Y.
Kawakami
,
M.
Tanjyo
,
S.
Okada
,
Y.
Ito
,
M.
Kako
,
S.
Goto
,
T.
Ishimura
, and
H.
Ito
,
Phys. Rev. Lett.
51
,
1042
(
1983
).
7.
M.
Ohnishi
,
A.
Ishida
, and
T.
Akasaka
,
Phys. Fluids B
5
,
1842
(
1993
).
8.
T.
Ishimura
,
Phys. Fluids
27
,
2139
(
1984
).
9.
R. J.
Goldston
and
P. H.
Rutherford
,
Introduction to Plasma Physics
(
IOP
,
Bristol
,
2000
), Chap. 19.1.
10.
See, e.g.,
W. M.
Manheimer
and
C.
Lashmore-Davies
,
MHD Instabilities in Simple Plasma Configuration
(
Naval Research Laboratory
,
Washington, D.C.
,
1984
), p.
71
.
11.
C. R.
Sovinec
,
T. A.
Gianakon
,
E. D.
Held
,
S. E.
Kruger
, and
D. D.
Schnack
, and
The NIMROD Team
,
Phys. Plasmas
10
,
1727
(
2003
).
12.
C. R.
Sovinec
,
A. H.
Glasser
,
T. A.
Gianakon
,
D. C.
Barnes
,
R. A.
Nebel
,
S. E.
Kruger
,
D. D.
Schnack
,
S. J.
Plimpton
,
A.
Tarditi
, and
M. S.
Chu
and
the NIMROD Team
,
J. Comput. Phys.
195
,
355
(
2004
).
13.
E.
Frieman
and
M.
Rotenberg
,
Rev. Mod. Phys.
32
,
898
(
1960
).
14.
A. I. D.
Macnab
,
R. D.
Milroy
,
C. C.
Kim
, and
C. R.
Sovinec
,
Phys. Plasmas
14
,
092503
(
2007
).
You do not currently have access to this content.