Beatification: Flattening the Poisson bracket for two-dimensional fluid and plasma theories
Abstract
A perturbative method called beatification is presented for a class of two-dimensional fluid and plasma theories. The Hamiltonian systems considered, namely, the Euler, Vlasov-Poisson, Hasegawa-Mima, and modified Hasegawa-Mima equations, are naturally described in terms of noncanonical variables. The beatification procedure amounts to finding the correct transformation that removes the explicit variable dependence from a noncanonical Poisson bracket and replaces it with a fixed dependence on a chosen state in the phase space. As such, beatification is a major step toward casting the Hamiltonian system in its canonical form, thus enabling or facilitating the use of analytical and numerical techniques that require or favor a representation in terms of canonical, or beatified, Hamiltonian variables.
- Authors:
-
[1];
[2]
- Univ. of São Paulo, São Paulo (Brazil). Inst. of Physics
- Univ. of Texas, Austin, TX (United States). Inst. for Fusion Studies and Department of Physics
- Publication Date:
- Research Org.:
- Univ. of Texas, Austin, TX (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1535301
- Alternate Identifier(s):
- OSTI ID: 1348950
- Grant/Contract Number:
- FG02-04ER54742; 402163/2012-5; 470380/2012-8; 2011/19296-1; 2012/20452-0; FG02-04ER-54742
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Volume: 24; Journal Issue: 3; Journal ID: ISSN 1070-664X
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Physics
Citation Formats
Viscondi, Thiago F., Caldas, Iberê L., and Morrison, Philip J. Beatification: Flattening the Poisson bracket for two-dimensional fluid and plasma theories. United States: N. p., 2017.
Web. doi:10.1063/1.4977451.
Viscondi, Thiago F., Caldas, Iberê L., & Morrison, Philip J. Beatification: Flattening the Poisson bracket for two-dimensional fluid and plasma theories. United States. https://doi.org/10.1063/1.4977451
Viscondi, Thiago F., Caldas, Iberê L., and Morrison, Philip J. Thu .
"Beatification: Flattening the Poisson bracket for two-dimensional fluid and plasma theories". United States. https://doi.org/10.1063/1.4977451. https://www.osti.gov/servlets/purl/1535301.
@article{osti_1535301,
title = {Beatification: Flattening the Poisson bracket for two-dimensional fluid and plasma theories},
author = {Viscondi, Thiago F. and Caldas, Iberê L. and Morrison, Philip J.},
abstractNote = {A perturbative method called beatification is presented for a class of two-dimensional fluid and plasma theories. The Hamiltonian systems considered, namely, the Euler, Vlasov-Poisson, Hasegawa-Mima, and modified Hasegawa-Mima equations, are naturally described in terms of noncanonical variables. The beatification procedure amounts to finding the correct transformation that removes the explicit variable dependence from a noncanonical Poisson bracket and replaces it with a fixed dependence on a chosen state in the phase space. As such, beatification is a major step toward casting the Hamiltonian system in its canonical form, thus enabling or facilitating the use of analytical and numerical techniques that require or favor a representation in terms of canonical, or beatified, Hamiltonian variables.},
doi = {10.1063/1.4977451},
journal = {Physics of Plasmas},
number = 3,
volume = 24,
place = {United States},
year = {Thu Mar 02 00:00:00 EST 2017},
month = {Thu Mar 02 00:00:00 EST 2017}
}
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