Ideal relaxation of the Hopf fibration

Christopher Berg Smiet, Simon Candelaresi, Dirk Bouwmeester

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Abstract

Ideal magnetohydrodynamics relaxation is the topology-conserving reconfiguration of a magnetic field into a lower energy state where the net force is zero. This is achieved by modeling the plasma as perfectly conducting viscous fluid. It is an important tool for investigating plasma equilibria and is often used to study the magnetic configurations in fusion devices and astrophysical plasmas. We study the equilibrium reached by a localized magnetic field through the topology conserving relaxation of a magnetic field based on the Hopf fibration in which magnetic field lines are closed circles that are all linked with one another. Magnetic fields with this topology have recently been shown to occur in non-ideal numerical simulations. Our results show that any localized field can only attain equilibrium if there is a finite external pressure, and that for such a field a Taylor state is unattainable. We find an equilibrium plasma configuration that is characterized by a lowered pressure in a toroidal region, with field lines lying on surfaces of constant pressure. Therefore, the field is in a Grad-Shafranov equilibrium. Localized helical magnetic fields are found when plasma is ejected from astrophysical bodies and subsequently relaxes against the background plasma, as well as on earth in plasmoids generated by, e.g., a Marshall gun. This work shows under which conditions an equilibrium can be reached and identifies a toroidal depression as the characteristic feature of such a configuration.

Original languageEnglish
Article number072110
Pages (from-to)1-11
Number of pages11
JournalPhysics of Plasmas
Volume24
Issue number7
Early online date6 Jul 2017
DOIs
Publication statusPublished - Jul 2017

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magnetic fields
plasma equilibrium
topology
astrophysics
configurations
viscous fluids
magnetohydrodynamics
fusion
conduction
simulation
energy

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Smiet, Christopher Berg ; Candelaresi, Simon ; Bouwmeester, Dirk. / Ideal relaxation of the Hopf fibration. In: Physics of Plasmas. 2017 ; Vol. 24, No. 7. pp. 1-11.
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Smiet, CB, Candelaresi, S & Bouwmeester, D 2017, 'Ideal relaxation of the Hopf fibration', Physics of Plasmas, vol. 24, no. 7, 072110, pp. 1-11. https://doi.org/10.1063/1.4990076

Ideal relaxation of the Hopf fibration. / Smiet, Christopher Berg; Candelaresi, Simon; Bouwmeester, Dirk.

In: Physics of Plasmas, Vol. 24, No. 7, 072110, 07.2017, p. 1-11.

Research output: Contribution to journalArticle

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