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Bifurcation analysis of the plane sheet pinch

  • 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.

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Author:Jörg Schumacher, Norbert Seehafer
Series (Serial Number):NLD Preprints (paper 056)
Document Type:Preprint
Year of Completion:1999
Publishing Institution:Universität Potsdam
Release Date:2007/08/15
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Zentrale und wissenschaftliche Einrichtungen / Interdisziplinäres Zentrum für Dynamik komplexer Systeme
Extern / Extern
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik