TY  - JOUR
A1  - Seehafer, Norbert
A1  - Schumacher, Jörg
T1  - Bifurcation analysis of an electrically driven fluid layer
N2  - The equilibrium states of electrically conducting fluids or plasmas have been a subject of intense study for a long time, motivated in particular by the interest in controlled thermonuclear fusion, as well as that in space and astrophysical phenomena such as plasma loops in the solar corona. If high temperatures prohibit solid walls, a conducting fluid can be held together by the action of an electric current passing through it with the pressure gradients being balanced by the Lorentz force. The resultant configuration is known as a pinch. In this paper we report on studies of the pinch in the geometry of a plane sheet.
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Schumacher, Jörg
A1  - Seehafer, Norbert
T1  - Bifurcation analysis of the plane sheet pinch
N2  - A numerical bifurcation analysis of the electrically driven plane sheet pinch is presented. The electrical conductivity varies across the sheet such as to allow instability of the quiescent basic state at some critical Hartmann number. The most unstable perturbation is the two-dimensional tearing mode. Restricting the whole problem to two spatial dimensions, this mode is followed up to a time-asymptotic steady state, which proves to be sensitive to three- dimensional perturbations even close to the point where the primary instability sets in. A comprehensive three- dimensional stability analysis of the two-dimensional steady tearing-mode state is performed by varying parameters of the sheet pinch. The instability with respect to three-dimensional perturbations is suppressed by a sufficiently strong magnetic field in the invariant direction of the equilibrium. For a special choice of the system parameters, the unstably perturbed state is followed up in its nonlinear evolution and is found to approach a three-dimensional steady state.
Y1  - 2000
UR  - http://publish.aps.org/abstract/PRE/v61/p2695
ER  - 
TY  - INPR
A1  - Schumacher, Jörg
A1  - Seehafer, Norbert
T1  - Bifurcation analysis of the plane sheet pinch
N2  - A numerical bifurcation analysis of the electrically driven plane sheet pinch is presented. The electrical conductivity varies across the sheet such as to allow instability of the quiescent basic state at some critical Hartmann number. The most unstable perturbation is the two-dimensional tearing mode. Restricting the whole problem to two spatial dimensions, this mode is followed up to a time-asymptotic steady state, which proves to be sensitive to three-dimensional perturbations even close to the point where the primary instability sets in. A comprehensive three-dimensional stability analysis of the two-dimensional steady tearing-mode state is performed by varying parameters of the sheet pinch. The instability with respect to three-dimensional perturbations is suppressed by a sufficiently strong magnetic field in the invariant direction of the equilibrium. For a special choice of the system parameters, the unstably perturbed state is followed up in its nonlinear evolution and is found to approach a three-dimensional steady state.
T3  - NLD Preprints - 56 
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14926
ER  - 
TY  - THES
A1  - Schumacher, Jörg
T1  - Numerische Untersuchung von MHD-Instabilitäten in koronalen Stromschichten
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Seehafer, Norbert
A1  - Schumacher, Jörg
T1  - Patterns in an electrically driven conducting fluid layer
N2  - The equilibrium states of electrically conducting fluids or plasmas have been a subject of intense study for a long time, motivated in particular by the interest in controlled thermonuclear fusion, as well as that in space and astrophysical phenomena such as plasma loops in the solar corona. If high temperatures prohibit solid walls, a conducting fluid can be held together by the action of an electric current passing through it with the pressure gradients being balanced by the Lorentz force. The resultant configuration is known as a pinch. In this paper we report on studies of the pinch in the geometry of a plane sheet.
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Seehafer, Norbert
A1  - Schumacher, Jörg
T1  - Resistivity profile and instability of the plane sheet pinch
Y1  - 1998
ER  - 
TY  - BOOK
A1  - Seehafer, Norbert
A1  - Schumacher, Jörg
T1  - Resistivity profile and instability of the plane sheet pinch
T3  - Preprint NLD
Y1  - 1998
SN  - 1432-2935
VL  - 44
PB  - Univ. Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Seehafer, Norbert
A1  - Schumacher, Jörg
T1  - Squire's theorem for the magnetohydrodynamic sheet pinch
Y1  - 1997
ER  - 
TY  - BOOK
A1  - Seehafer, Norbert
A1  - Schumacher, Jörg
T1  - Squire's theorem for the magnetohydrodynamic sheet pinch
T3  - Preprint NLD
Y1  - 1997
SN  - 1432-2935
VL  - 40
PB  - Univ. Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Schumacher, Jörg
A1  - Kliem, Bernhard
A1  - Seehafer, Norbert
T1  - Three-dimensional spontaneous magnetic reconnection in neutral current sheets
Y1  - 2000
ER  -