Other
Scientific paper
Aug 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993jgr....9813225o&link_type=abstract
Journal of Geophysical Research (ISSN 0148-0227), vol. 98, no. A8, p. 13,225-13,231.
Other
33
Magnetic Fields, Magnetic Flux, Magnetohydrodynamics, Plasma Interactions, Differential Equations, Evolution (Development), Magnetic Field Configurations, Nonlinear Equations
Scientific paper
We study the nonlinear self-similar evolution of a cylindrical magnetic flux tube with two components of the magnetic field, axial and azimuthal. We restrict ourselves to the case of a plasma of low beta. Introducing a special class of configurations we call 'separable fields', we reduce the problem to an ordinary differential equation. Two cases are to be distinguished: (1) when the total field minimizes on the symmetry axis, the magnetic configuration inexorably collapses, and (2) when, on the other hand, the total field maximizes on the symmetry axis, the magnetic configuration behaves analogously to a nonlinear oscillator. Here we focus on the latter case. The effective potential of the motion contains two terms: a strong repulsive term and a weak restoring term associated with the pinch. We solve the nonlinear differential equation of motion numerically and find that the period of oscillations grows exponentially with the energy of the oscillator. Our treatment emphasizes the role of the force-free configuration as the lowest potential energy state about which the system oscillates.
Burlaga Leonard Francis
Farrugia Charles J.
Osherovich Vladimir A.
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