Gyrokinetic equations and full f solution method based on Dirac’s constrained Hamiltonian and inverse Kruskal iteration

Jukka A. Heikkinen, M. Nora

Research output: Contribution to journalArticleScientificpeer-review

10 Citations (Scopus)

Abstract

Gyrokinetic equations of motion, Poisson equation, and energy and momentum conservation laws are derived based on the reduced-phase-space Lagrangian and inverse Kruskal iteration introduced by Pfirsch and Correa-Restrepo [J. Plasma Phys. 70, 719 (2004)]. This formalism, together with the choice of the adiabatic invariant J=⟨p⃗ ⋅∂x⃗ /∂ϕ⟩ as one of the averaging coordinates in phase space, provides an alternative to the standard gyrokinetics. Within second order in gyrokinetic parameter, the new equations do not show explicit ponderomotivelike or polarizationlike terms. Pullback of particle information with an iterated gyrophase and field dependent gyroradius function from the gyrocenter position defined by gyroaveraged coordinates allows direct numerical integration of the gyrokinetic equations in particle simulation of the field and particles with full distribution function. As an example, gyrokinetic systems with polarization drift either present or absent in the equations of motion are considered.
Original languageEnglish
Article number022310
Number of pages13
JournalPhysics of Plasmas
Volume18
Issue number2
DOIs
Publication statusPublished - 2011
MoE publication typeA1 Journal article-refereed

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iteration
equations of motion
energy conservation
Poisson equation
conservation laws
numerical integration
distribution functions
formalism
momentum
polarization
simulation

Cite this

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title = "Gyrokinetic equations and full f solution method based on Dirac’s constrained Hamiltonian and inverse Kruskal iteration",
abstract = "Gyrokinetic equations of motion, Poisson equation, and energy and momentum conservation laws are derived based on the reduced-phase-space Lagrangian and inverse Kruskal iteration introduced by Pfirsch and Correa-Restrepo [J. Plasma Phys. 70, 719 (2004)]. This formalism, together with the choice of the adiabatic invariant J=⟨p⃗ ⋅∂x⃗ /∂ϕ⟩ as one of the averaging coordinates in phase space, provides an alternative to the standard gyrokinetics. Within second order in gyrokinetic parameter, the new equations do not show explicit ponderomotivelike or polarizationlike terms. Pullback of particle information with an iterated gyrophase and field dependent gyroradius function from the gyrocenter position defined by gyroaveraged coordinates allows direct numerical integration of the gyrokinetic equations in particle simulation of the field and particles with full distribution function. As an example, gyrokinetic systems with polarization drift either present or absent in the equations of motion are considered.",
author = "Heikkinen, {Jukka A.} and M. Nora",
year = "2011",
doi = "10.1063/1.3552140",
language = "English",
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journal = "Physics of Plasmas",
issn = "1527-2419",
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Gyrokinetic equations and full f solution method based on Dirac’s constrained Hamiltonian and inverse Kruskal iteration. / Heikkinen, Jukka A.; Nora, M.

In: Physics of Plasmas, Vol. 18, No. 2, 022310, 2011.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Gyrokinetic equations and full f solution method based on Dirac’s constrained Hamiltonian and inverse Kruskal iteration

AU - Heikkinen, Jukka A.

AU - Nora, M.

PY - 2011

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N2 - Gyrokinetic equations of motion, Poisson equation, and energy and momentum conservation laws are derived based on the reduced-phase-space Lagrangian and inverse Kruskal iteration introduced by Pfirsch and Correa-Restrepo [J. Plasma Phys. 70, 719 (2004)]. This formalism, together with the choice of the adiabatic invariant J=⟨p⃗ ⋅∂x⃗ /∂ϕ⟩ as one of the averaging coordinates in phase space, provides an alternative to the standard gyrokinetics. Within second order in gyrokinetic parameter, the new equations do not show explicit ponderomotivelike or polarizationlike terms. Pullback of particle information with an iterated gyrophase and field dependent gyroradius function from the gyrocenter position defined by gyroaveraged coordinates allows direct numerical integration of the gyrokinetic equations in particle simulation of the field and particles with full distribution function. As an example, gyrokinetic systems with polarization drift either present or absent in the equations of motion are considered.

AB - Gyrokinetic equations of motion, Poisson equation, and energy and momentum conservation laws are derived based on the reduced-phase-space Lagrangian and inverse Kruskal iteration introduced by Pfirsch and Correa-Restrepo [J. Plasma Phys. 70, 719 (2004)]. This formalism, together with the choice of the adiabatic invariant J=⟨p⃗ ⋅∂x⃗ /∂ϕ⟩ as one of the averaging coordinates in phase space, provides an alternative to the standard gyrokinetics. Within second order in gyrokinetic parameter, the new equations do not show explicit ponderomotivelike or polarizationlike terms. Pullback of particle information with an iterated gyrophase and field dependent gyroradius function from the gyrocenter position defined by gyroaveraged coordinates allows direct numerical integration of the gyrokinetic equations in particle simulation of the field and particles with full distribution function. As an example, gyrokinetic systems with polarization drift either present or absent in the equations of motion are considered.

U2 - 10.1063/1.3552140

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