Ellipticity conditions for the extended MHD Grad-Shafranov-Bernoulli equilibrium equations

Kaltsas, D. A.; Throumoulopoulos, G. N.; Morrison, P. J.

doi:10.1063/1.5080997

Title: Ellipticity conditions for the extended MHD Grad-Shafranov-Bernoulli equilibrium equations

Journal Article · 07 February 2019 · Physics of Plasmas

DOI: https://doi.org/10.1063/1.5080997 · OSTI ID:1614604

^[1];

^[2];

^[3]

Univ. of Ioannina (Greece); DOE/OSTI
Univ. of Ioannina (Greece)
Univ. of Texas, Austin, TX (United States)

In this study, we find the points of transition between elliptic and hyperbolic regimes for the axisymmetric extended magnetohydrodynamic (MHD) equilibrium equations. The ellipticity condition is expressed via a single inequality but is more involved than the corresponding two-fluid ones due to the imposition of the quasineutrality condition and is also more complicated than the Hall MHD ellipticity condition, due to electron inertia. In fact, the inclusion of electron inertia is responsible for peculiar results; namely, even the static equilibrium equations can become hyperbolic.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: FG05-80ET53088

OSTI ID:: 1614604

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 2 Vol. 26; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (15)

Über die Ausbreitung von Wellen in einem Plasma Lüst, Reimar Fortschritte der Physik, Vol. 7, Issue 9 https://doi.org/10.1002/prop.19590070902	journal	January 1959
Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles Kaltsas, D. A.; Throumoulopoulos, G. N.; Morrison, P. J. Journal of Plasma Physics, Vol. 84, Issue 3 https://doi.org/10.1017/S0022377818000338	journal	May 2018
Ellipticity criterion for flowing two-fluid high β equilibria Ishida, Akio; Harahap, Caesar O.; Steinhauer, Loren C. Physics of Plasmas, Vol. 11, Issue 11 https://doi.org/10.1063/1.1804533	journal	November 2004
Variational principles for stationary one- and two-fluid equilibria of axisymmetric laboratory and astrophysical plasmas Goedbloed, J. P. Physics of Plasmas, Vol. 11, Issue 12 https://doi.org/10.1063/1.1808453	journal	December 2004
On Hall magnetohydrodynamics equilibria Throumoulopoulos, G. N.; Tasso, H. Physics of Plasmas, Vol. 13, Issue 10 https://doi.org/10.1063/1.2358111	journal	October 2006
Ellipticity of axisymmetric equilibria with flow and pressure anisotropy in single-fluid and Hall magnetohydrodynamics Ito, Atsushi; Ramos, Jesús J.; Nakajima, Noriyoshi Physics of Plasmas, Vol. 14, Issue 6 https://doi.org/10.1063/1.2741391	journal	June 2007
Ertel's vorticity theorem and new flux surfaces in multi-fluid plasmas Hameiri, Eliezer Physics of Plasmas, Vol. 20, Issue 9 https://doi.org/10.1063/1.4820769	journal	September 2013
Traveling waves in Hall-magnetohydrodynamics and the ion-acoustic shock structure Hagstrom, George I.; Hameiri, Eliezer Physics of Plasmas, Vol. 21, Issue 2 https://doi.org/10.1063/1.4862035	journal	February 2014
A model for transonic plasma flow Guazzotto, Luca; Hameiri, Eliezer Physics of Plasmas, Vol. 21, Issue 2 https://doi.org/10.1063/1.4866600	journal	February 2014
On energy conservation in extended magnetohydrodynamics Kimura, Keiji; Morrison, P. J. Physics of Plasmas, Vol. 21, Issue 8 https://doi.org/10.1063/1.4890955	journal	August 2014
Translationally symmetric extended MHD via Hamiltonian reduction: Energy-Casimir equilibria Kaltsas, D. A.; Throumoulopoulos, G. N.; Morrison, P. J. Physics of Plasmas, Vol. 24, Issue 9 https://doi.org/10.1063/1.4986013	journal	September 2017
The equilibrium and stability of rotating plasmas Hameiri, Eliezer Physics of Fluids, Vol. 26, Issue 1 https://doi.org/10.1063/1.864012	journal	January 1983
Radial discontinuities in tokamak magnetohydrodynamic equilibria with poloidal flow Betti, R.; Freidberg, J. P. Physics of Plasmas, Vol. 7, Issue 6 https://doi.org/10.1063/1.874083	journal	June 2000
Second Order Elliptic Systems of Differential Equations Morrey, C. B. Proceedings of the National Academy of Sciences, Vol. 39, Issue 3 https://doi.org/10.1073/pnas.39.3.201	journal	March 1953
On energy conservation in extended magnetohydrodynamics Kimura, Keiji; Morrison, P. J. arXiv https://doi.org/10.48550/arxiv.1406.2745	text	January 2014

Cited By (2)

Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria Kaltsas, D. A.; Throumoulopoulos, G. N.; Morrison, P. J. Physics of Plasmas, Vol. 27, Issue 1 https://doi.org/10.1063/1.5125573	journal	January 2020
Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria Kaltsas, D. A.; Throumoulopoulos, G. N.; Morrison, P. J. arXiv https://doi.org/10.48550/arxiv.1908.08821	text	January 2019

Similar Records

Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles

Journal Article · 2018 · Journal of Plasma Physics · OSTI ID:1538937

Kaltsas, D. A.; Throumoulopoulos, G. N.; Morrison, P. J.

Ellipticity of axisymmetric equilibria with flow and pressure anisotropy in single-fluid and Hall magnetohydrodynamics

Journal Article · 2007 · Physics of Plasmas · OSTI ID:20975113

Ito, Atsushi; Ramos, Jesus J; Nakajima, Noriyoshi

Translationally symmetric extended MHD via Hamiltonian reduction: Energy-Casimir equilibria

Journal Article · 2017 · Physics of Plasmas · OSTI ID:2567726

Kaltsas, D. A.; Throumoulopoulos, G. N.; Morrison, P. J.

Related Subjects

Speed of sound
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Physics
Plasma confinement

Title: Ellipticity conditions for the extended MHD Grad-Shafranov-Bernoulli equilibrium equations

Citation Formats

References (15)

Cited By (2)

Similar Records

Related Subjects