An Energy Principle for Ideal MHD Equilibria with Flows

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In the standard ideal MHD energy principle for equilibria with no flows, the stability criterion, which is the defi niteness of the perturbed potential energy, is usually constructed from the linearized equation of motion. Equivalently while more straightforwardly, it can also be obtained from the second variation of the Hamiltonian calculated with proper constraints. For equilibria with flows, a stability criterion was proposed from the linearized equation of motion, but not explained as an energy principle1. In this paper, the second variation of the Hamiltonian is found to provide a stability criterion equivalent to, while more straightforward than, what was ... continued below

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Qin, Yao Zhou and Hong March 11, 2013.

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In the standard ideal MHD energy principle for equilibria with no flows, the stability criterion, which is the defi niteness of the perturbed potential energy, is usually constructed from the linearized equation of motion. Equivalently while more straightforwardly, it can also be obtained from the second variation of the Hamiltonian calculated with proper constraints. For equilibria with flows, a stability criterion was proposed from the linearized equation of motion, but not explained as an energy principle1. In this paper, the second variation of the Hamiltonian is found to provide a stability criterion equivalent to, while more straightforward than, what was constructed from the linearized equation of motion. To calculate the variations of the Hamiltonian, a complete set of constraints on the dynamics of the perturbations is derived from the Euler-Poincare structure of the ideal MHD. In addition, a previous calculation of the second variation of the Hamiltonian was claimed to give a different stability criterion2, and in this paper we argue such a claim is incorrect.

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  • Physics of Plasmas (March 2013)

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  • Report No.: PPPL-4858
  • Grant Number: DE-AC02-09CH11466
  • DOI: 10.2172/1072366 | External Link
  • Office of Scientific & Technical Information Report Number: 1072366
  • Archival Resource Key: ark:/67531/metadc838467

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  • March 11, 2013

Added to The UNT Digital Library

  • May 19, 2016, 9:45 a.m.

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  • July 18, 2016, 5:24 p.m.

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Qin, Yao Zhou and Hong. An Energy Principle for Ideal MHD Equilibria with Flows, report, March 11, 2013; Princeton, New Jersey. (digital.library.unt.edu/ark:/67531/metadc838467/: accessed November 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.