A differential-geometric perspective on magneto-hydrodynamic equilibria

David Perrella

doi:10.26182/3x78-k926

A differential-geometric perspective on magneto-hydrodynamic equilibria

David Perrella

School of Physics, Mathematics and Computing

Research output: Thesis › Doctoral Thesis

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Abstract

We consider the mathematical foundations of magneto-hydrodynamic (MHD) equilibria from adifferential-geometric perspective. We treat flux-coordinates in a very general way, prove a resultrelated to Grad's Conjecture, and establish a non-vanishing result about integrable vacuum fields.Lastly, we develop a generalisation of the Stefan-Sussman Theorem, making comments about therelationship to MHD equilibria.

Original language	English
Qualification	Doctor of Philosophy
Awarding Institution	The University of Western Australia
Supervisors/Advisors	Pfefferle, David, Supervisor Stoyanov, Luchezar, Supervisor
Thesis sponsors	Australian Government Research Training Program
Award date	11 Jun 2024
DOIs	https://doi.org/10.26182/3x78-k926
Publication status	Unpublished - 2024

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10.26182/3x78-k926

THESIS - DOCTOR OF PHILOSOPHY - PERRELLA David Alexander - 2024_
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1 Abstract/Meeting Abstract

A Differential-geometric Perspective on Magneto-hydrodynamic Equilibria
Perrella, D., 20 Nov 2024, In: Bulletin of the Australian Mathematical Society. 2 p.
Research output: Contribution to journal › Abstract/Meeting Abstract › peer-review

Cite this

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abstract = "We consider the mathematical foundations of magneto-hydrodynamic (MHD) equilibria from adifferential-geometric perspective. We treat flux-coordinates in a very general way, prove a resultrelated to Grad's Conjecture, and establish a non-vanishing result about integrable vacuum fields.Lastly, we develop a generalisation of the Stefan-Sussman Theorem, making comments about therelationship to MHD equilibria.",

keywords = "MHD equilibria, differential geometry, differential topology, Riemannian manifolds, Riemannian geometry, de Rham cohomology, plasma physics, magnetic confinement fusion",

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AB - We consider the mathematical foundations of magneto-hydrodynamic (MHD) equilibria from adifferential-geometric perspective. We treat flux-coordinates in a very general way, prove a resultrelated to Grad's Conjecture, and establish a non-vanishing result about integrable vacuum fields.Lastly, we develop a generalisation of the Stefan-Sussman Theorem, making comments about therelationship to MHD equilibria.

KW - MHD equilibria

KW - differential geometry

KW - differential topology

KW - Riemannian manifolds

KW - Riemannian geometry

KW - de Rham cohomology

KW - plasma physics

KW - magnetic confinement fusion

U2 - 10.26182/3x78-k926

DO - 10.26182/3x78-k926

M3 - Doctoral Thesis

ER -

A differential-geometric perspective on magneto-hydrodynamic equilibria

Abstract

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Research output

A Differential-geometric Perspective on Magneto-hydrodynamic Equilibria

Cite this