The nonlinear evolution of the resistive tearing mode exhibits an abrupt growth after an X-point collapse once the magnetic island exceeds a certain critical width Δwc for large instability parameter Δ, leading to a current sheet formation [N. F. Loureiro et al., Phys. Rev. Lett. 95, 235003 (2005)]. In this work, we investigate the underlying mechanism of the X-point collapse as well as the current sheet formation including the viscosity effects, based on a secondary instability analysis. The secondary instability is excited due to the quasilinear current modification by the zonal current. In particular, it is identified that the current peaking effect is plausibly responsible for the onset of the X-point collapse and the current sheet formation, leading to the explosive growth of reconnected flux. In the presence of finite viscosity, the Δwc scaling with the resistivity gets modified. A transition behavior is revealed at Pr1 for the viscosity dependence of Δwc and the linear tearing instability. However, the explosive growth seems to be independent of the viscosity in the magnetic Prandtl number Pr<1 regime, while large viscosity plays a strong dissipation role.

1.
H. P.
Furth
,
J.
Killeen
, and
M. N.
Rosenbluth
,
Phys. Fluids
6
,
459
(
1963
).
2.
K.
Shibata
and
T.
Magara
,
Living Rev. Solar Phys.
8
,
6
(
2011
).
3.
A.
Retino
,
D.
Sundkvist
,
A.
Vaivads
,
F.
Mozer
,
M.
Andre
, and
C. J.
Owen
,
Nature Phys.
3
,
236
(
2007
).
4.
R. J.
Hastie
,
Astro Phys. Space Sci.
256
,
177
(
1997
).
5.
P. H.
Rutherford
,
Phys. Fluids
16
,
1903
(
1973
).
6.
S.
Migliuolo
,
F.
Pegoraro
, and
F.
Porcelli
,
Phys. Fluids B
3
,
1338
(
1991
).
7.
F. L.
Waelbroeck
,
Phys. Rev. Lett.
70
,
3259
(
1993
).
8.
B. D.
Jemella
,
M. A.
Shay
, and
J. F.
Drake
.
Phys. Rev. Lett.
91
,
125002
(
2003
).
9.
N. F.
Loureiro
,
S. C.
Cowley
,
W. D.
Dorland
,
M. G.
Haines
, and
A. A.
Schekochihin
,
Phys. Rev. Lett.
95
,
235003
(
2005
).
10.
P. A.
Sweet
, in
Proceedings of the IAU Symposium 6:Electromagnetic Phenomena in Cosmical Physics
(
Cambridge University Press
,
Cambridge, England
,
1958
), p.
123
.
11.
E. N.
Parker
,
J. Geophys. Res.
62
,
509
, doi: (
1957
).
12.
D. A.
Uzdensky
,
N. F.
Loureiro
, and
A. A.
Schekochihin
,
Phys. Rev. Lett.
105
,
235002
(
2010
).
13.
Y. M.
Huang
,
A.
Bhattacharjee
, and
B. P.
Sullivan
,
Phys. Plasmas
18
,
072109
(
2011
).
14.
N. F.
Loureiro
,
R.
Samtaney
,
A. A.
Schekochihin
, and
D. A.
Uzdensky
.
Phys. Plasmas
19
,
042303
(
2012
).
15.
M.
Janvier
,
Y.
Kishimoto
, and
J.
Li
,
Phys. Rev. Lett.
107
,
195001
(
2011
).
16.
Y.
Ishii
,
M.
Azumi
,
G.
Kurita
, and
T.
Tuda
,
Phys. Plasmas
7
,
4477
(
2000
).
17.
Y.
Ishii
,
M.
Azumi
, and
Y.
Kishimoto
,
Phys. Rev. Lett.
89
,
205002
(
2002
).
18.
Z. X.
Wang
,
X. G.
Wang
,
J. Q.
Dong
,
Y. A.
Lei
,
Y. X.
Long
,
Z. Z.
Mou
, and
W. X.
Qu
,
Phys. Rev. Lett.
99
,
185004
(
2007
).
19.
Z. X.
Wang
,
X. G.
Wang
,
J. Q.
Dong
,
Y.
Kishimoto
, and
J. Q.
Li
,
Phys. Plasmas
15
,
082109
(
2008
).
20.
F.
Militello
,
M.
Romanelli
,
R. J.
Hastie
, and
N. F.
Loureiro
,
Phys. Plasmas
16
,
032101
(
2009
).
21.
R. E.
Waltz
,
J.
Candy
,
F. L.
Hinton
,
C.
Estrada-Mila
, and
J. E.
Kinsey
,
Nucl. Fusion
45
,
741
(
2005
).
22.
M.
Janvier
,
Y.
Kishimoto
, and
J.
Li
,
Nucl. Fusion
51
,
083016
(
2011
).
23.
K.
Itoh
,
S.-I.
Itoh
,
A.
Fukuyama
,
M.
Yagi
, and
M.
Azumi
,
J. Phys. Soc. Jpn.
62
,
4269
(
1993
).
24.
A.
Furuya
,
S.
Itoh
, and
M.
Yagi
,
J. Phys. Soc. Jpn.
70
,
407
(
2001
).
25.
F.
Pocelli
,
Phys. Fluids
30
,
1734
(
1987
).
26.
S. C.
Guo
,
R.
Paccagnella
, and
F.
Romanelli
,
Phys. Plasmas
1
,
2741
(
1994
).
27.
L.
Spitzer
,
Physics of Fully Ionized Gases
(
Inter-Science
,
New York
,
1956
).
28.
K.
Takeda
,
O.
Agullo
,
S.
Benkadda
,
A.
Sen
,
N.
Bian
, and
X.
Garbet
,
Phys. Plasmas
15
,
022502
(
2008
).
29.
D.
Grasso
,
R. J.
Hastie
,
F.
Porcelli
, and
C.
Tebaldi
,
Phys. Plasmas
15
,
072113
(
2008
).
30.
F.
Militello
,
D.
Borgogno
,
D.
Grasso
,
C.
Marchetto
, and
M.
Ottaviani
,
Phys. Plasmas
18
,
112108
(
2011
).
31.
G.
Einaudi
and
F.
Rubini
,
Phys. Fluids B
1
,
2224
(
1989
).
32.
L.
Ofman
,
X. L.
Chen
, and
P. J.
Morrison
,
Phys. Fluids B
3
,
1364
(
1991
).
33.
W.
Park
,
D. A.
Monticello
, and
R. B.
White
,
Phys. Fluids
27
,
137
(
1984
).
34.
F.
Porcelli
,
D.
Borgogno
,
F.
Califano
,
D.
Grasso
,
M.
Ottaviani
, and
F.
Pegoraro
,
Plasma Phys. Controlled Fusion
44
,
B389
(
2002
).
You do not currently have access to this content.