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 - INPR A1 - Seehafer, Norbert A1 - Schumacher, Jörg T1 - Resistivity profile and instability of the plane sheet pinch N2 - The stability of the quiescent ground state of an incompressible, viscous and electrically conducting fluid sheet, bounded by stress-free parallel planes and driven by an external electric field tangential to the boundaries, is studied numerically. The electrical conductivity varies as cosh–2(x1/a), where x1 is the cross-sheet coordinate and a is the half width of a current layer centered about the midplane of the sheet. For a <~ 0.4L, where L is the distance between the boundary planes, the ground state is unstable to disturbances whose wavelengths parallel to the sheet lie between lower and upper bounds depending on the value of a and on the Hartmann number. Asymmetry of the configuration with respect to the midplane of the sheet, modelled by the addition of an externally imposed constant magnetic field to a symmetric equilibrium field, acts as a stabilizing factor. T3 - NLD Preprints - 44 Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14686 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 - INPR A1 - Seehafer, Norbert A1 - Schumacher, Jörg T1 - Squire‘s theorem for the magnetohydrodynamic sheet pinch N2 - The stability of the quiescent ground state of an incompressible viscous fluid sheet bounded by two parallel planes, with an electrical conductivity varying across the sheet, and driven by an external electric field tangential to the boundaries is considered. It is demonstrated that irrespective of the conductivity profile, as magnetic and kinetic Reynolds numbers (based on the Alfvén velocity) are raised from small values, two-dimensional perturbations become unstable first. T3 - NLD Preprints - 40 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14628 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 - TY - BOOK A1 - Schumacher, Jörg A1 - Kliem, Bernhard A1 - Seehafer, Norbert T1 - Three-dimensional spontaneous magnetic reconnection in neutral current sheets T3 - Preprint series / Astrophysikalisches Institut Potsdam Y1 - 1999 VL - 99,42 PB - AIP CY - Potsdam ER - TY - JOUR A1 - Zienicke, Egbert A1 - Seehafer, Norbert A1 - Li, B.-W. A1 - Schumacher, Jörg A1 - Politano, H. A1 - Thess, H. T1 - Voltage-driven instability of electrically conducting fluids Y1 - 2003 ER -