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Title: Collisionless kinetic-fluid model of zonal flows in toroidal plasmas

Abstract

A novel kinetic-fluid model is presented, which describes collisionless time evolution of zonal flows in tokamaks. In the new zonal-flow closure relations, the parallel heat fluxes are written by the sum of short- and long-time-evolution parts. The former part is given in the dissipative form of the parallel heat diffusion and relates to collisionless damping processes. The latter is derived from the long-time-averaged gyrocenter distribution and plays a major role in describing low-frequency or stationary zonal flows, for which the parallel heat fluxes are expressed in terms of the parallel flow as well as the nonlinear-source and initial-condition terms. It is shown analytically and numerically that, when applied to the zonal flow driven by either ion or electron temperature gradient turbulence, the kinetic-fluid equations including the new closure relations can reproduce the same long-time zonal-flow responses to the initial condition and to the turbulence source as those obtained from the gyrokinetic model.

Authors:
; ;  [1];  [2]
  1. National Institute for Fusion Science, Graduate University for Advanced Studies, Toki 509-5292 (Japan)
  2. (United States)
Publication Date:
OSTI Identifier:
20974832
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 2; Other Information: DOI: 10.1063/1.2435329; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; DAMPING; DIFFUSION; DISTRIBUTION; ELECTRON TEMPERATURE; HEAT; HEAT FLUX; ION TEMPERATURE; IONS; NONLINEAR PROBLEMS; PLASMA; PLASMA CONFINEMENT; PLASMA FLUID EQUATIONS; PLASMA SIMULATION; TEMPERATURE GRADIENTS; TOKAMAK DEVICES; TURBULENCE

Citation Formats

Sugama, H., Watanabe, T.-H., Horton, W., and Institute for Fusion Studies, University of Texas at Austin, Austin, Texas 78712. Collisionless kinetic-fluid model of zonal flows in toroidal plasmas. United States: N. p., 2007. Web. doi:10.1063/1.2435329.
Sugama, H., Watanabe, T.-H., Horton, W., & Institute for Fusion Studies, University of Texas at Austin, Austin, Texas 78712. Collisionless kinetic-fluid model of zonal flows in toroidal plasmas. United States. doi:10.1063/1.2435329.
Sugama, H., Watanabe, T.-H., Horton, W., and Institute for Fusion Studies, University of Texas at Austin, Austin, Texas 78712. Thu . "Collisionless kinetic-fluid model of zonal flows in toroidal plasmas". United States. doi:10.1063/1.2435329.
@article{osti_20974832,
title = {Collisionless kinetic-fluid model of zonal flows in toroidal plasmas},
author = {Sugama, H. and Watanabe, T.-H. and Horton, W. and Institute for Fusion Studies, University of Texas at Austin, Austin, Texas 78712},
abstractNote = {A novel kinetic-fluid model is presented, which describes collisionless time evolution of zonal flows in tokamaks. In the new zonal-flow closure relations, the parallel heat fluxes are written by the sum of short- and long-time-evolution parts. The former part is given in the dissipative form of the parallel heat diffusion and relates to collisionless damping processes. The latter is derived from the long-time-averaged gyrocenter distribution and plays a major role in describing low-frequency or stationary zonal flows, for which the parallel heat fluxes are expressed in terms of the parallel flow as well as the nonlinear-source and initial-condition terms. It is shown analytically and numerically that, when applied to the zonal flow driven by either ion or electron temperature gradient turbulence, the kinetic-fluid equations including the new closure relations can reproduce the same long-time zonal-flow responses to the initial condition and to the turbulence source as those obtained from the gyrokinetic model.},
doi = {10.1063/1.2435329},
journal = {Physics of Plasmas},
number = 2,
volume = 14,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}
  • Fluid simulation of linear zonal flow damping is done with a closure model based on the collisionless gyrokinetics [Sugama et al., Phys. Plasmas 14, 022502 (2007)]. Simulation results of residual zonal flow for low radial wavenumbers are compared with theoretical formulas for circular and non-circular tokamaks. The effects of the elongation and the triangularity are shown to be properly treated in the closure model. Effects of initial parallel flows on zonal flow evolution are also clarified. An appropriate choice of the initial parallel flow gives a much higher residual level than the conventional result with no initial parallel flow. Besides,more » the zonal flow simulations are done with the E Multiplication-Sign B nonlinearity as initial sources, which is evaluated from linear gyrokinetic microinstabilities such as ion temperature gradient modes, trapped electron modes, and electron temperature gradient modes, in order to estimate efficiency of zonal flow generation by the source instabilities.« less
  • Zonal flows in tokamak plasmas with toroidal rotation are theoretically investigated. It is found that the low-frequency branch of zonal flows, which is linearly stable in a nonrotating system, becomes linearly unstable in a rotating tokamak, and that the high-frequency branch of zonal flows, the geodesic acoustic mode, can propagate in the poloidal direction with the frequency significantly lower than the frequency of the standing wave geodesic acoustic mode in the nonrotating system.
  • Gyrokinetic {delta}f particle simulation is used to investigate the nonlinear saturation mechanisms in collisionless trapped electron mode (CTEM) turbulence. It is found that the importance of zonal flow is parameter-sensitive and is well characterized by the shearing rate formula. The effect of zonal flow is empirically found to be sensitive to temperature ratio, magnetic shear, and electron temperature gradient. For parameters where zonal flow is found to be unimportant, zonal density (purely radial density perturbations) is generated and expected to be the dominant saturation mechanism. A toroidal mode-coupling theory is presented that agrees with simulation in the initial nonlinear saturationmore » phase. The mode-coupling theory predicts the nonlinear generation of the zonal density and the feedback and saturation of the linearly most unstable mode. Inverse energy cascade is also observed in CTEM turbulence simulations and is reported here.« less
  • Collisionless time evolution of zonal flows in helical systems is investigated. An analytical expression describing the collisionless response of the zonal-flow potential to the initial potential and a given turbulence source is derived from the gyrokinetic equations combined with the quasineutrality condition. The dispersion relation for the geodesic acoustic mode (GAM) in helical systems is derived from the short-time response kernel for the zonal-flow potential. It is found that helical ripples in the magnetic-field strength as well as finite orbit widths of passing ions enhance the GAM damping. The radial drift motions of particles trapped in helical ripples cause themore » residual zonal-flow level in the collisionless long-time limit to be lower for longer radial wavelengths and deeper helical ripples. On the other hand, a high-level zonal-flow response, which is not affected by helical-ripple-trapped particles, can be maintained for a longer time by reducing their radial drift velocity. This implies a possibility that helical configurations optimized for reducing neoclassical ripple transport can simultaneously enhance zonal flows which lower anomalous transport. The validity of our analytical results is verified by gyrokinetic Vlasov simulation.« less
  • The collisionless time evolution of zonal flows in stellarator systems is investigated. An analytical solution of the kinetic and quasineutrality equations describing the residual zonal flow is derived for arbitrary three-dimensional systems without approximations in the magnetic geometry. The theory allows for an arbitrary number of particle species. It has been found that in stellarators the residual zonal flows are not in general steady but oscillate with a certain frequency. This frequency is determined by the speed of the bounce-averaged radial drifts of the particles trapped in the magnetic field and vanishes in tokamaks, where such net drifts are absent.more » A reduction of the bounce-averaged radial drifts in configurations optimized with respect to neoclassical transport results in a smaller zonal-flow frequency.« less