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Bifurcations of magnetic topology by the creation or annihilation of null points

Published online by Cambridge University Press:  13 March 2009

E. R. Priest ,
D. P. Lonie  and
V. S. Titov
E. R. Priest
Affiliation:
School of Mathematical and Computational Sciences, University of St Andrews, St Andrews KYI6 9SS, Fife, Scotland
D. P. Lonie
Affiliation:
School of Mathematical and Computational Sciences, University of St Andrews, St Andrews KYI6 9SS, Fife, Scotland
V. S. Titov
Affiliation:
School of Mathematical and Computational Sciences, University of St Andrews, St Andrews KYI6 9SS, Fife, Scotland
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Abstract

Linear null points of a magnetic field may come together and coalesce at a secondorder null, or vice versa a second-order null may form and split, giving birth to a pair of linear nulls. Such local bifurcations lead to global changes of magnetic topology and in some cases release of magnetic energy. In two dimensions the null points are of X or O type and the flux function is a Hamiltonian; the magnetic field may undergo addle-centre, pitchfork or degenerate resonant bifurcations. In three dimensions the null points and their creation or annihilation by bifurcations are considerably more complex. The nulls possess a skeleton consisting of a spine curve and a fan surface and are of radial-type (proper or improper) or spiral-type; the type of null and the inclination of spine and fan depend on the magnitudes of the current components along and normal to the spine. In cylindrically symmetric fields a comprehensive treatment is given of the various types of saddle-node, Hopf and saddle-node—Hopfbifurcations. In fully three-dimensional situations examples are given of saddle-node and degenerate bifurcations, in which generically two nulls are created or destroyed and are joined by a separator field line, which is the intersection of the two fans. Furthermore, global bifurcations can create chaotic field lines that could perhaps trigger energy release in, for example, solar flares.

Type
Research Article
Information
Journal of Plasma Physics , Volume 56 , Issue 3: Special Issue: Honour of David Montgomery , December 1996 , pp. 507 - 530
Copyright
Copyright © Cambridge University Press 1996

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References

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