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Title: Effects of finite poloidal gyroradius, shaping, and collisions on the zonal flow residual

Abstract

Zonal flow helps reduce and regulate the turbulent transport level in tokamaks. Rosenbluth and Hinton have shown that zonal flow damps to a nonvanishing residual level in collisionless [M. Rosenbluth and F. Hinton, Phys. Rev. Lett. 80, 724 (1998)] and collisional [F. Hinton and M. Rosenbluth, Plasma Phys. Control. Fusion 41, A653 (1999)] banana regime plasmas. Recent zonal flow advances are summarized including the evaluation of the effects on the zonal flow residual by plasma cross-section shaping, shorter wavelengths including those less than an electron gyroradius, and arbitrary ion collisionality relative to the zonal low frequency. In addition to giving a brief summary of these new developments, the analytic results are compared with GS2 numerical simulations [M. Kotschenreuther, G. Rewoldt, and W. Tang, Comput. Phys. Commun. 88, 128 (1991)] to demonstrate their value as benchmarks for turbulence codes.

Authors:
; ;  [1];  [2]
  1. Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
  2. (United States)
Publication Date:
OSTI Identifier:
20975038
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 5; Other Information: DOI: 10.1063/1.2718519; (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; BANANA REGIME; BENCHMARKS; COLLISIONS; CONTROL; ELECTRONS; IONS; PLASMA; PLASMA CONFINEMENT; SIMULATION; TOKAMAK DEVICES; TURBULENCE; WAVELENGTHS

Citation Formats

Xiao Yong, Catto, Peter J., Dorland, William, and Department of Physics, University of Maryland, College Park, Maryland 20742. Effects of finite poloidal gyroradius, shaping, and collisions on the zonal flow residual. United States: N. p., 2007. Web. doi:10.1063/1.2718519.
Xiao Yong, Catto, Peter J., Dorland, William, & Department of Physics, University of Maryland, College Park, Maryland 20742. Effects of finite poloidal gyroradius, shaping, and collisions on the zonal flow residual. United States. doi:10.1063/1.2718519.
Xiao Yong, Catto, Peter J., Dorland, William, and Department of Physics, University of Maryland, College Park, Maryland 20742. Tue . "Effects of finite poloidal gyroradius, shaping, and collisions on the zonal flow residual". United States. doi:10.1063/1.2718519.
@article{osti_20975038,
title = {Effects of finite poloidal gyroradius, shaping, and collisions on the zonal flow residual},
author = {Xiao Yong and Catto, Peter J. and Dorland, William and Department of Physics, University of Maryland, College Park, Maryland 20742},
abstractNote = {Zonal flow helps reduce and regulate the turbulent transport level in tokamaks. Rosenbluth and Hinton have shown that zonal flow damps to a nonvanishing residual level in collisionless [M. Rosenbluth and F. Hinton, Phys. Rev. Lett. 80, 724 (1998)] and collisional [F. Hinton and M. Rosenbluth, Plasma Phys. Control. Fusion 41, A653 (1999)] banana regime plasmas. Recent zonal flow advances are summarized including the evaluation of the effects on the zonal flow residual by plasma cross-section shaping, shorter wavelengths including those less than an electron gyroradius, and arbitrary ion collisionality relative to the zonal low frequency. In addition to giving a brief summary of these new developments, the analytic results are compared with GS2 numerical simulations [M. Kotschenreuther, G. Rewoldt, and W. Tang, Comput. Phys. Commun. 88, 128 (1991)] to demonstrate their value as benchmarks for turbulence codes.},
doi = {10.1063/1.2718519},
journal = {Physics of Plasmas},
number = 5,
volume = 14,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}
  • Plasma shaping effects, such as elongation, triangularity, and Shafranov shift have long been considered important ingredients in improving tokamak performance. It is known that the growth rate of ion temperature gradient (ITG) turbulence can be regulated by these shaping effects and that the ITG turbulence level can also be regulated by zonal flow. Moreover, recent numerical simulation shows that the collsionless residual zonal flow level can be influenced by these shaping effects. An analytical approach is used to explicitly evaluate plasma shaping effects on the collisionless residual zonal flow. The results show that the residual zonal flow level increases withmore » elongation, triangularity and the Shafranov shift.« less
  • Sheared zonal flow helps to reduce the turbulent transport caused by the ion temperature gradient mode. Rosenbluth and Hinton (R-H) calculated the residual zonal flow level for radial wavelengths that are much larger than the ion poloidal gyroradius. Their calculation is extended to treat arbitrary radial wavelengths. For the radial wavelengths that approach the ion poloidal gyroradius, but are much larger than the ion gyroradius, an analytical formula is obtained. For radial wavelengths that are comparable or shorter than the poloidal ion gyroradius and the ion gyroradius a numerical solution is provided. These small radial wavelength results are then extendedmore » into the electron temperature gradient regime, where the residual zonal flow level is large but ineffective in regulating the turbulence, indicating that the conventional R-H explanation that zonal flow regulates turbulence is incomplete.« less
  • Finite Larmor radius (FLR) effects on nondiffusive transport in a prototypical zonal flow with drift waves are studied in the context of a simplified chaotic transport model. The model consists of a superposition of drift waves from the linearized Hasegawa-Mima equation and a zonal shear flow perpendicular to the density gradient. High frequency FLR effects are incorporated by gyroaveraging the ExB velocity. Transport in the direction of the density gradient is negligible and we therefore focus on transport parallel to the zonal flows. A prescribed asymmetry produces strongly asymmetric non-Gaussian probability distribution functions (PDFs) of particle displacements, with Levy flightsmore » in one direction only. For k{sub perpendicular}{rho}{sub th}=0, where k{sub perpendicular} is the characteristic wavelength of the flow and {rho}{sub th} is the thermal Larmor radius, a transition is observed in the scaling of the second moment of particle displacements: {sigma}{sup 2}{approx}t{sup {gamma}}. The transition separates ballistic motion ({gamma}{approx_equal}2) at intermediate times from superdiffusion ({gamma}=1.6) at larger times. This change of scaling is accompanied by the transition of the PDF of particle displacements from algebraic decay to exponential decay. However, FLR effects seem to eliminate this transition. In all cases, the Lagrangian velocity autocorrelation function exhibits nondiffusive algebraic decay, C{approx}{tau}{sup -{kappa}}, with {kappa}=2-{gamma} to a good approximation. The PDFs of trapping and flight events show clear evidence of algebraic scaling with decay exponents depending on the value of k{sub perpendicular}{rho}{sub th}. The shape and spatiotemporal self-similar anomalous scaling of the PDFs of particle displacements are reproduced accurately with a neutral ({alpha}={beta}), asymmetric, effective fractional diffusion model, where {alpha} and {beta} are the orders of the spatial and temporal fractional derivatives, respectively.« less
  • A code has been developed for calculating magnetohydrodynamic equilibria with poloidal-sonic flow and finite Larmor radius effects in high-beta tokamaks using an inverse aspect-ratio expansion and a reduced two-fluid model. The Grad-Shafranov equations governing the first- and second-order poloidal fluxes can be expressed in terms of five free profiles of the first-order poloidal flux. Sample equilibria, illustrating behaviors such as the deviation of pressure contours from the flux surfaces, and the criteria for the presence of the 'poloidal-sonic singularity' are presented.