### Abstract

Original language | English |
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Article number | 20150012 |

Number of pages | 12 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 471 |

Issue number | 2178 |

DOIs | |

Publication status | Published - 3 Jun 2015 |

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### Keywords

- Coronal heating
- Magnetic topology
- Magnetohydrodynamics
- Plasma relaxation

### Cite this

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**Physical role of topological constraints in localized magnetic relaxation.** / Yeates, A. R. (Lead / Corresponding author); Russell, A. J. B.; Hornig, G.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Physical role of topological constraints in localized magnetic relaxation

AU - Yeates, A. R.

AU - Russell, A. J. B.

AU - Hornig, G.

PY - 2015/6/3

Y1 - 2015/6/3

N2 - Predicting the final state of turbulent plasma relaxation is an important challenge, both in astro-physical plasmas such as the Sun's corona and in controlled thermonuclear fusion. Recent numerical simulations of plasma relaxation with braided magnetic fields identified the possibility of a novel constraint, arising from the topological degree of the magnetic field-line mapping. This constraint implies that the final relaxed state is drastically different for an initial configuration with topological degree 1 (which allows a Taylor relaxation) and one with degree 2 (which does not reach a Taylor state). Here, we test this transition in numerical resistive-magnetohydrodynamic simulations, by embedding a braided magnetic field in a linear force-free background. Varying the background force-free field parameter generates a sequence of initial conditions with a transition between topological degree 1 and 2. For degree 1, the relaxation produces a single twisted flux tube, whereas for degree 2 we obtain two flux tubes. For predicting the exact point of transition, it is not the topological degree of the whole domain that is relevant, but only that of the turbulent region.

AB - Predicting the final state of turbulent plasma relaxation is an important challenge, both in astro-physical plasmas such as the Sun's corona and in controlled thermonuclear fusion. Recent numerical simulations of plasma relaxation with braided magnetic fields identified the possibility of a novel constraint, arising from the topological degree of the magnetic field-line mapping. This constraint implies that the final relaxed state is drastically different for an initial configuration with topological degree 1 (which allows a Taylor relaxation) and one with degree 2 (which does not reach a Taylor state). Here, we test this transition in numerical resistive-magnetohydrodynamic simulations, by embedding a braided magnetic field in a linear force-free background. Varying the background force-free field parameter generates a sequence of initial conditions with a transition between topological degree 1 and 2. For degree 1, the relaxation produces a single twisted flux tube, whereas for degree 2 we obtain two flux tubes. For predicting the exact point of transition, it is not the topological degree of the whole domain that is relevant, but only that of the turbulent region.

KW - Coronal heating

KW - Magnetic topology

KW - Magnetohydrodynamics

KW - Plasma relaxation

UR - http://www.scopus.com/inward/record.url?scp=84930860615&partnerID=8YFLogxK

U2 - 10.1098/rspa.2015.0012

DO - 10.1098/rspa.2015.0012

M3 - Article

VL - 471

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 1364-5021

IS - 2178

M1 - 20150012

ER -