Magnetohydrodynamic motion of a two-fluid plasma
Here, the two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell’s equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally-exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, as well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-orders closure may be obtained in closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-orders bracket gives explicit expressions for a number of the full closure’s conservation laws.more »
- Publication Date:
- Grant/Contract Number:
- AC05-06OR23100
- Type:
- Accepted Manuscript
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Volume: 24; Journal Issue: 8; Journal ID: ISSN 1070-664X
- Publisher:
- American Institute of Physics (AIP)
- Research Org:
- Oak Ridge Inst. for Science and Education (ORISE), Oak Ridge, TN (United States)
- Sponsoring Org:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY
- OSTI Identifier:
- 1368063
- Alternate Identifier(s):
- OSTI ID: 1372123
Burby, Joshua W. Magnetohydrodynamic motion of a two-fluid plasma. United States: N. p.,
Web. doi:10.1063/1.4994068.
Burby, Joshua W. Magnetohydrodynamic motion of a two-fluid plasma. United States. doi:10.1063/1.4994068.
Burby, Joshua W. 2017.
"Magnetohydrodynamic motion of a two-fluid plasma". United States.
doi:10.1063/1.4994068. https://www.osti.gov/servlets/purl/1368063.
@article{osti_1368063,
title = {Magnetohydrodynamic motion of a two-fluid plasma},
author = {Burby, Joshua W.},
abstractNote = {Here, the two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell’s equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally-exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, as well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-orders closure may be obtained in closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-orders bracket gives explicit expressions for a number of the full closure’s conservation laws. Notably, the full closure, as well as any of its Hamiltonian truncations, admits a pair of independent circulation invariants.},
doi = {10.1063/1.4994068},
journal = {Physics of Plasmas},
number = 8,
volume = 24,
place = {United States},
year = {2017},
month = {7}
}