Neoclassical toroidal viscosity for an axisymmetric toroidal equilibrium with multiple trapping of particles
Abstract
A method is illustrated on how to apply existing formulas to the neoclassical toroidal plasma viscosity for an axisymmetric toroidal equilibrium with an arbitrary aspect ratio that has multiple trapping states. The effect of the energy scattering on the viscosity in the {nu} regime is presented using an approximate collision operator. Here, {nu} is the collision frequency. The explicit expressions for the steady state toroidal flow speed resulting from the neoclassical toroidal flow damping in both the 1/{nu} and the {nu} regime are also presented. The physics origin of the toroidal viscous force is the broken toroidal symmetry induced by the error fields and the amplification of these fields by stable or unstable resistive wall modes, or other asymmetric magnetic field perturbations.
 Authors:
 Department of Engineering Physics, University of Wisconsin, Madison, Wisconsin 53706 (United States)
 (United States)
 Publication Date:
 OSTI Identifier:
 20974851
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 2; Other Information: DOI: 10.1063/1.2437119; (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; AMPLIFICATION; ASPECT RATIO; ASYMMETRY; AXIAL SYMMETRY; COLLISIONS; CONFINEMENT; DAMPING; EQUILIBRIUM; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; NEOCLASSICAL TRANSPORT THEORY; PLASMA; PLASMA INSTABILITY; STEADYSTATE CONDITIONS; TOKAMAK DEVICES; TRAPPING; VISCOSITY; WALL EFFECTS
Citation Formats
Shaing, K. C., Sabbagh, S. A., Peng, M., Department of Applied Physics and Applied Mechanics, Columbia University, New York, New York 10027, and Fusion Energy Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831. Neoclassical toroidal viscosity for an axisymmetric toroidal equilibrium with multiple trapping of particles. United States: N. p., 2007.
Web. doi:10.1063/1.2437119.
Shaing, K. C., Sabbagh, S. A., Peng, M., Department of Applied Physics and Applied Mechanics, Columbia University, New York, New York 10027, & Fusion Energy Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831. Neoclassical toroidal viscosity for an axisymmetric toroidal equilibrium with multiple trapping of particles. United States. doi:10.1063/1.2437119.
Shaing, K. C., Sabbagh, S. A., Peng, M., Department of Applied Physics and Applied Mechanics, Columbia University, New York, New York 10027, and Fusion Energy Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831. Thu .
"Neoclassical toroidal viscosity for an axisymmetric toroidal equilibrium with multiple trapping of particles". United States.
doi:10.1063/1.2437119.
@article{osti_20974851,
title = {Neoclassical toroidal viscosity for an axisymmetric toroidal equilibrium with multiple trapping of particles},
author = {Shaing, K. C. and Sabbagh, S. A. and Peng, M. and Department of Applied Physics and Applied Mechanics, Columbia University, New York, New York 10027 and Fusion Energy Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831},
abstractNote = {A method is illustrated on how to apply existing formulas to the neoclassical toroidal plasma viscosity for an axisymmetric toroidal equilibrium with an arbitrary aspect ratio that has multiple trapping states. The effect of the energy scattering on the viscosity in the {nu} regime is presented using an approximate collision operator. Here, {nu} is the collision frequency. The explicit expressions for the steady state toroidal flow speed resulting from the neoclassical toroidal flow damping in both the 1/{nu} and the {nu} regime are also presented. The physics origin of the toroidal viscous force is the broken toroidal symmetry induced by the error fields and the amplification of these fields by stable or unstable resistive wall modes, or other asymmetric magnetic field perturbations.},
doi = {10.1063/1.2437119},
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}
}

A method is illustrated on how to apply existing formulas to the neoclassical toroidal plasma viscosity for an axisymmetric toroidal equilibrium with an arbitrary aspect ratio that has multiple trapping states. The effect of the energy scattering on the viscosity in the nu regime is presented using an approximate collision operator. Here, nu is the collision frequency. The explicit expressions for the steady state toroidal flow speed resulting from the neoclassical toroidal flow damping in both the 1/nu and the nu regime are also presented. The physics origin of the toroidal viscous force is the broken toroidal symmetry induced bymore »

Toroidal viscosity and ambipolarity in the neoclassical transport theory of axisymmetric tori
To selfconsistently evaluate both the toroidal rotation and the radial electric field in a tokamak the two distinct constraints of toroidal angular momentum conservation and ambipolarity must be invoked. A gyrokinetic derivation of the neoclassical transport equations that permits a large toroidal rotation speed is employed. Explicit forms for the toroidal viscosity are obtained so that both constraints can be imposed. To keep the E x B drift speed smaller than the ion thermal speed and still consider large toroidal rotation, the ratio of the poloidal to toroidal magnetic field components is assumed to be small. For larger poloidal fieldsmore » 
Observation of Plasma ToroidalMomentum Dissipation by Neoclassical Toroidal Viscosity
Dissipation of plasma toroidal angular momentum is observed in the National Spherical Torus Experiment due to applied nonaxisymmetric magnetic fields and their plasmainduced increase by resonant field amplification and resistive wall mode destabilization. The measured decrease of the plasma toroidal angular momentum profile is compared to calculations of nonresonant drag torque based on the theory of neoclassical toroidal viscosity. Quantitative agreement between experiment and theory is found when the effect of toroidally trapped particles is included. 
Peak neoclassical toroidal viscosity at low toroidal rotation in the DIIID tokamak
Observation of a theoretically predicted peak in the neoclassical toroidal viscous (NTV) force as a function of toroidal plasma rotation rate {Omega} is reported. The NTV was generated by applying n=3 magnetic fields from internal (I)coils to low {Omega} plasmas produced with nearly balanced neutral beam injection. Locally, the peak corresponds to a toroidal rotation rate {Omega}{sub 0} where the radial electric field E{sub r} is near zero as determined by radial ion force balance. 
Neoclassical and anomalous transport in axisymmetric toroidal plasmas with electrostatic turbulence
Neoclassical and anomalous transport fluxes are determined for axisymmetric toroidal plasmas with weak electrostatic fluctuations. The neoclassical and anomalous fluxes are defined based on the ensembleaveraged kinetic equation with the statistically averaged nonlinear term. The anomalous forces derived from that quasilinear term induce the anomalous particle and heat fluxes. The neoclassical bananaplateau particle and heat fluxes and the bootstrap current are also affected by the fluctuations through the parallel anomalous forces and the modified parallel viscosities. The quasilinear term, the anomalous forces, and the anomalous particle and heat fluxes are evaluated from the fluctuating part of the drift kinetic equation.more »