Erratum: “Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory” [Phys. Plasmas 20, 092104 (2013)]

Andreussi, T.; Morrison, P. J.; Pegoraro, F.

doi:10.1063/1.4916504

Title: Erratum: “Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory” [Phys. Plasmas 20, 092104 (2013)]

Authors:

^[1]; Morrison, P. J. ^[2];

^[3]

Alta S.p.A., Pisa 56121, Italy
Institute for Fusion Studies and Department of Physics, The University of Texas at Austin, Austin, Texas 78712-1060, USA
Dipartimento di Fisica E. Fermi, Pisa 56127, Italy

Publication Date:: Wed Mar 25 00:00:00 EDT 2015

Sponsoring Org.:: USDOE

OSTI Identifier:: 1228577

Grant/Contract Number:: FG05_80ET-53088

Resource Type:: Publisher's Accepted Manuscript

Journal Name:: Physics of Plasmas

Additional Journal Information:: Journal Name: Physics of Plasmas Journal Volume: 22 Journal Issue: 3; Journal ID: ISSN 1070-664X

Publisher:: American Institute of Physics

Country of Publication:: United States

Language:: English

Citation Formats


                    Andreussi, T., Morrison, P. J., and Pegoraro, F. Erratum: “Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory” [Phys. Plasmas 20, 092104 (2013)].  United States: N. p., 2015. 
Web.  doi:10.1063/1.4916504.

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                    Andreussi, T., Morrison, P. J., & Pegoraro, F. Erratum: “Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory” [Phys. Plasmas 20, 092104 (2013)].  United States.  https://doi.org/10.1063/1.4916504

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                    Andreussi, T., Morrison, P. J., and Pegoraro, F. Wed .  
"Erratum: “Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory” [Phys. Plasmas 20, 092104 (2013)]".  United States.  https://doi.org/10.1063/1.4916504.

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@article{osti_1228577,

  title        = {Erratum: “Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory” [Phys. Plasmas 20, 092104 (2013)]},

  author       = {Andreussi, T. and Morrison, P. J. and Pegoraro, F.},

  abstractNote = {},

  doi          = {10.1063/1.4916504},

  journal      = {Physics of Plasmas},

  number       = 3,

  volume       = 22,

  place        = {United States},

  year         = {Wed Mar 25 00:00:00 EDT 2015},

  month        = {Wed Mar 25 00:00:00 EDT 2015}

}

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https://doi.org/10.1063/1.4916504

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Works referenced in this record:

Hydromagnetic stability of a diffuse linear pinch
journal, June 1960

Newcomb, William A.
Annals of Physics, Vol. 10, Issue 2
DOI: 10.1016/0003-4916(60)90023-3

Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory
journal, September 2013

Andreussi, T.; Morrison, P. J.; Pegoraro, F.
Physics of Plasmas, Vol. 20, Issue 9
DOI: 10.1063/1.4819779

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Erratum: “Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory” [Phys. Plasmas 20, 092104 (2013)]

Journal Article Andreussi, T. ; Morrison, P. J. ; Pegoraro, F. - Physics of Plasmas

An algebraic mistake in the rendering of the Energy Casimir stability condition for a symmetric magnetohydrodynamics plasma configuration with flows made in the article Andreussi et al. “Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory,” Phys. Plasmas 20, 092104 (2013) is corrected.
https://doi.org/10.1063/1.4916504
Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory

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Stability conditions of magnetized plasma flows are obtained by exploiting the Hamiltonian structure of the magnetohydrodynamics (MHD) equations and, in particular, by using three kinds of energy principles. First, the Lagrangian variable energy principle is described and sufficient stability conditions are presented. Next, plasma flows are described in terms of Eulerian variables and the noncanonical Hamiltonian formulation of MHD is exploited. For symmetric equilibria, the energy-Casimir principle is expanded to second order and sufficient conditions for stability to symmetric perturbation are obtained. Then, dynamically accessible variations, i.e., variations that explicitly preserve invariants of the system, are introduced and the respectivemore »« less
https://doi.org/10.1063/1.4819779
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Because different constraints are imposed, stability conditions for dissipationless fluids and magnetofluids may take different forms when derived within the Lagrangian, Eulerian (energy-Casimir), or dynamically accessible frameworks. This is in particular the case when flows are present. These differences are explored explicitly here by working out in detail two magnetohydrodynamic examples: convection against gravity in a stratified fluid and translationally invariant perturbations of a rotating magnetized plasma pinch. In this second example, we show in explicit form how to perform the time-dependent relabeling introduced in Andreussi et al. [Phys. Plasmas 20, 092104 (2013)] that makes it possible to reformulate Eulerianmore »« less
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The formal stability analysis of Eulerian extended magnetohydrodynamics (XMHD) equilibria is considered within the noncanonical Hamiltonian framework by means of the energy-Casimir variational principle and the dynamically accessible stability method. Specifically, we find explicit sufficient stability conditions for axisymmetric XMHD and Hall MHD (HMHD) equilibria with toroidal flow and for equilibria with arbitrary flow under constrained perturbations. The dynamically accessible, second-order variation of the Hamiltonian, which can potentially provide explicit stability criteria for generic equilibria, is also obtained. Moreover, we examine the Lagrangian stability of the general quasineutral two-fluid model written in terms of MHD-like variables, by finding the actionmore »« less
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No abstract prepared.
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Similar Records

Title: Erratum: “Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory” [Phys. Plasmas 20, 092104 (2013)]

Citation Formats

Hydromagnetic stability of a diffuse linear pinch journal, June 1960

Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory journal, September 2013

Hydromagnetic stability of a diffuse linear pinch
journal, June 1960

Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory
journal, September 2013