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Title: Nonlinear gyrokinetic theory for finite-BETA plasmas

Abstract

A self-consistent and energy-conserving set of nonlinear gyrokinetic equations, consisting of the averaged Vlasov and Maxwell's equations for finite-..beta.. plasmas, is derived. The method utilized in the present investigation is based on the Hamiltonian formalism and Lie transformation. The resulting formation is valid for arbitrary values of k/perpendicular//rho//sub i/ and, therefore, is most suitable for studying linear and nonlinear evolution of microinstabilities in tokamak plasmas as well as other areas of plasma physics where the finite Larmor radius effects are important. Because the underlying Hamiltonian structure is preserved in the present formalism, these equations are directly applicable to numerical studies based on the existing gyrokinetic particle simulation techniques. 31 refs.

Authors:
; ;
Publication Date:
Research Org.:
Princeton Univ., NJ (USA). Plasma Physics Lab.
OSTI Identifier:
5044420
Report Number(s):
PPPL-2498
ON: DE88009358; TRN: 88-021317
DOE Contract Number:
AC02-76CH03073
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; LOW-BETA PLASMA; KINETIC EQUATIONS; NONLINEAR PROBLEMS; EQUATIONS OF MOTION; LARMOR RADIUS; MAGNETIC FIELDS; MAXWELL EQUATIONS; PLASMA MICROINSTABILITIES; PLASMA SIMULATION; TOKAMAK DEVICES; CLOSED PLASMA DEVICES; DIFFERENTIAL EQUATIONS; EQUATIONS; INSTABILITY; PARTIAL DIFFERENTIAL EQUATIONS; PLASMA; PLASMA INSTABILITY; SIMULATION; THERMONUCLEAR DEVICES; 700103* - Fusion Energy- Plasma Research- Kinetics; 700107 - Fusion Energy- Plasma Research- Instabilities

Citation Formats

Hahm, T.S., Lee, W.W., and Brizard, A.. Nonlinear gyrokinetic theory for finite-BETA plasmas. United States: N. p., 1988. Web. doi:10.2172/5044420.
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Hahm, T.S., Lee, W.W., & Brizard, A.. Nonlinear gyrokinetic theory for finite-BETA plasmas. United States. doi:10.2172/5044420.
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Hahm, T.S., Lee, W.W., and Brizard, A.. Mon . "Nonlinear gyrokinetic theory for finite-BETA plasmas". United States. doi:10.2172/5044420. https://www.osti.gov/servlets/purl/5044420.
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@article{osti_5044420,
title = {Nonlinear gyrokinetic theory for finite-BETA plasmas},
author = {Hahm, T.S. and Lee, W.W. and Brizard, A.},
abstractNote = {A self-consistent and energy-conserving set of nonlinear gyrokinetic equations, consisting of the averaged Vlasov and Maxwell's equations for finite-..beta.. plasmas, is derived. The method utilized in the present investigation is based on the Hamiltonian formalism and Lie transformation. The resulting formation is valid for arbitrary values of k/perpendicular//rho//sub i/ and, therefore, is most suitable for studying linear and nonlinear evolution of microinstabilities in tokamak plasmas as well as other areas of plasma physics where the finite Larmor radius effects are important. Because the underlying Hamiltonian structure is preserved in the present formalism, these equations are directly applicable to numerical studies based on the existing gyrokinetic particle simulation techniques. 31 refs.},
doi = {10.2172/5044420},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Mon Feb 01 00:00:00 EST 1988},
month = {Mon Feb 01 00:00:00 EST 1988}
}
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Technical Report:
View Technical Report (0.62 MB)
DOI:  10.2172/5044420
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  • ; ; - Phys. Fluids; (United States)
    A self-consistent and energy-conserving set of nonlinear gyrokinetic equations, consisting of the averaged Vlasov and Maxwell's equations for finite-beta plasmas, is derived. The method utilized in the present investigation is based on the Hamiltonian formalism and Lie transformation. The resulting formulation is valid for arbitrary values of k/sub perpendicular/rho/sub i/ and, therefore, is most suitable for studying linear and nonlinear evolution of microinstabilities in tokamak plasmas as well as other areas of plasma physics where the finite Larmor radius effects are important. Because the underlying Hamiltonian structure is preserved in the present formalism, these equations are directly applicable to numericalmore » studies based on the existing gyrokinetic particle simulation techniques.« less

  • ;
    The influence of sheared equilibrium flows on the confinement properties of tokamak plasmas is a topic of much current interest. A proper theoretical foundation for the systematic kinetic analysis of this important problem has been provided here by presented the derivation of a set of nonlinear electromagnetic gyrokinetic equations applicable to low frequency microinstabilities in a rotating axisymmetric plasma. The subsonic rotation velocity considered is in the direction of symmetry with the angular rotation frequency being a function of the equilibrium magnetic flux surface. In accordance with experimental observations, the rotation profile is chosen to scale with the ion temperature.more » The results obtained represent the shear flow generalization of the earlier analysis by Frieman and Chen where such flows were not taken into account. In order to make it readily applicable to gyrokinetic particle simulations, this set of equations is cast in a phase-space-conserving continuity equation form.« less

  • A set of the electrostatic toroidal gyrokinetic Vlasov equation and the Poisson equation, which explicitly includes the polarization drift, is derived systematically by using Lie-transform method. The polarization drift is introduced in the gyrocenter equations of motion, and the corresponding polarization density is derived. Contrary to the wide-spread expectation, the inclusion of the polarization drift in the gyrocenter equations of motion does not affect the expression for the polarization density significantly. This is due to modification of the gyrocenter phase-space volume caused by the electrostatic potential [T. S. Hahm, Phys. Plasmas 3, 4658 (1996)] .

  • ; ; ; ... - Phys. Fluids, v. 17, no. 2, pp. 419-427