It can be shown that in the presence of a toroidal magnetic field induced by poloidal coils, combined with the electromagnetic field induced by a central solenoid, no static equilibrium is possible within the MHD description, as soon as non-zero resistivity is assumed. The resulting dynamic equilibrium was previously discussed for the case of spatially homogeneous resisitivity. In the present work, it is shown how a spatial inhomogeneity of the viscosity and resisitivity coefficients influences this equilibrium. Parameters in both the stable, tokamak-like regime and unstable, reversed field pinch-like regime are considered. It is shown that, whereas the magnitudes of the velocity and magnetic field fluctuations are strongly modified by the spatial variation of the transport coefficients, the qualitative flow behaviour remains largely unaffected.

1.
X.
Shan
and
D.
Montgomery
, “
On the role of the Hartmann number in magnetohydrodynamic activity
,”
Plasma Phys. Controlled Fusion
35
,
619
(
1993
).
2.
X.
Shan
and
D.
Montgomery
, “
Global searches of Hartmann-number-dependent stability boundaries
,”
Plasma Phys. Controlled Fusion
35
,
1019
(
1993
).
3.
S.
Cappello
and
D. F.
Escande
, “
Bifurcation in viscoresistive MHD: The Hartmann number and the reversed field pinch
,”
Phys. Rev. Lett.
85
,
3838
(
2000
).
4.
M.
Onofri
,
F.
Malara
, and
P.
Veltri
, “
Compressibility effects in the dynamics of the reversed-field pinch
,”
Phys. Rev. Lett.
101
(
25
),
255002
(
2008
).
5.
M.
Onofri
,
F.
Malara
, and
P.
Veltri
, “
Effects of compressibility and heating in magnetohydrodynamics simulations of a reversed field pinch
,”
Phys. Plasmas
16
,
052508
(
2009
).
6.
J.
Morales
,
W.
Bos
,
K.
Schneider
, and
D.
Montgomery
, “
The effect of toroidicity on reversed field pinch dynamics
,”
Plasma Phys. Controlled Fusion
56
,
095024
(
2014
).
7.
S.
Cappello
,
D.
Bonfiglio
,
D.
Escande
,
S.
Guo
,
I.
Predebon
,
F.
Sattin
,
M.
Veranda
,
P.
Zanca
,
C.
Angioni
,
L.
Chacón
,
J.
Dong
,
X.
Garbet
, and
S.
Liu
, “
Equilibrium and transport for quasi-helical reversed field pinches
,”
Nucl. Fusion
51
,
103012
(
2011
).
8.
D.
Bonfiglio
,
M.
Veranda
,
S.
Cappello
,
D.
Escande
, and
L.
Chacón
, “
Experimental-like helical self-organization in reversed-field pinch modeling
,”
Phys. Rev. Lett.
111
(
8
),
085002
(
2013
).
9.
A.
Aydemir
, “
Shear flows at the tokamak edge and their interaction with edge-localized modes
,”
Phys. Plasmas
14
,
056118
(
2007
).
10.
A.
Aydemir
, “
Shear flows at the tokamak edge and their role in core rotation and the L-H transition
,”
Phys. Rev. Lett.
98
,
225002
(
2007
).
11.
S.
Pamela
,
G.
Huysmans
, and
S.
Benkadda
, “
Influence of poloidal equilibrium rotation in MHD simulations of edge-localized modes
,”
Plasma Physics Controlled Fusion
52
(
7
),
075006
(
2010
).
12.
J.
Freidberg
, “
Ideal magnetohydrodynamic theory of magnetic fusion systems
,”
Rev. Mod. Phys.
54
,
801
(
1982
).
13.
D.
Montgomery
,
H.
Chen
, and
X.
Shan
, “
Effects of uniform rotation on helically-deformed, resistive, magnetohydrodynamic equilibria
,”
Plasma Phys. Controlled Fusion
33
,
1871
(
1991
).
14.
J.
Bates
and
D.
Montgomery
, “
Toroidal visco-resisitive magnetohydrodynamic states contain vortices
,”
Phys. Plasmas
5
,
2649
(
1998
).
15.
L.
Kamp
and
D.
Montgomery
, “
Toroidal flows in resisitive magnetohydrodynamic states
,”
Phys. Plasmas
10
,
157
(
2003
).
16.
J.
Morales
,
W.
Bos
,
K.
Schneider
, and
D.
Montgomery
, “
Intrinsic rotation of toroidally confined magnetohydrodynamics
,”
Phys. Rev. Lett.
109
,
175002
(
2012
).
17.
J.
Morales
,
W.
Bos
,
K.
Schneider
, and
D.
Montgomery
, “
Magnetohydrodynamically generated velocities in confined plasma
,”
Phys. Plasmas
22
,
042515
(
2015
).
18.
P.
Angot
,
C.
Bruneau
, and
P.
Fabrie
, “
A penalization method to take into account obstacles in viscous flows
,”
Numer. Math.
81
,
497
(
1999
).
19.
J.
Morales
,
M.
Leroy
,
W.
Bos
, and
K.
Schneider
, “
Simulation of confined magnetohydrodynamic flows with Dirichlet boundary conditions using a pseudo-spectral method with volume penalization
,”
J. Comput. Phys.
274
,
64
(
2014
).
20.
D. F.
Escande
,
S.
Cappello
,
F.
D'Angelo
,
P.
Martin
,
S.
Ortolani
, and
R.
Paccagnella
, “
Single helicity: A new paradigm for the reversed field pinch
,”
Plasma Phys. Controlled Fusion
42
,
B243
(
2000
).
21.
X.
Litaudon
,
Y.
Sakamoto
,
P.
De Vries
,
A.
Salmi
,
T.
Tala
,
C.
Angioni
,
S.
Benkadda
,
M.
Beurskens
,
C.
Bourdelle
,
M.
Brix
 et al., “
Core transport properties in JT-60U and JET identity plasmas
,”
Nucl. Fusion
51
,
073020
(
2011
).
22.
J. M.
Finn
,
R.
Nebel
, and
C.
Bathke
, “
Single and multiple helicity Ohmic states in reversed-field pinches
,”
Phys. Fluids B
4
,
1262
1279
(
1992
).
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