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Title: Poloidal velocity of impurity ions in neoclassical theory

Abstract

A formula for the poloidal velocity of impurity ions in a two-species plasma is derived from neoclassical theory in the banana regime, with corrections from the boundary layer separating the trapped and transiting ions. The formula is applicable to plasmas with toroidal rotations that can approach the thermal speeds of the ions. Using the formula to determine the poloidal velocity of C{sup +6} ions in a recently reported experiment [W. M. Solomon et al., Phys. Plasmas 13, 056116 (2006)] leads to agreement in the direction of the central region when it is otherwise from theories without strong toroidal rotations. Comparisons among these theories are made, demonstrating the degree of uncertainty of theoretical predictions.

Authors:
;  [1];  [2]
  1. General Atomics, P.O. Box 85608, San Diego, California 92186-5608 (United States)
  2. Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States)
Publication Date:
OSTI Identifier:
21120517
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 15; Journal Issue: 8; Other Information: DOI: 10.1063/1.2969438; (c) 2008 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; BOUNDARY LAYERS; CARBON IONS; COMPARATIVE EVALUATIONS; NEOCLASSICAL TRANSPORT THEORY; PLASMA; PLASMA IMPURITIES; VELOCITY

Citation Formats

Wong, S. K., Chan, V. S., and Solomon, W. M.. Poloidal velocity of impurity ions in neoclassical theory. United States: N. p., 2008. Web. doi:10.1063/1.2969438.
Wong, S. K., Chan, V. S., & Solomon, W. M.. Poloidal velocity of impurity ions in neoclassical theory. United States. doi:10.1063/1.2969438.
Wong, S. K., Chan, V. S., and Solomon, W. M.. 2008. "Poloidal velocity of impurity ions in neoclassical theory". United States. doi:10.1063/1.2969438.
@article{osti_21120517,
title = {Poloidal velocity of impurity ions in neoclassical theory},
author = {Wong, S. K. and Chan, V. S. and Solomon, W. M.},
abstractNote = {A formula for the poloidal velocity of impurity ions in a two-species plasma is derived from neoclassical theory in the banana regime, with corrections from the boundary layer separating the trapped and transiting ions. The formula is applicable to plasmas with toroidal rotations that can approach the thermal speeds of the ions. Using the formula to determine the poloidal velocity of C{sup +6} ions in a recently reported experiment [W. M. Solomon et al., Phys. Plasmas 13, 056116 (2006)] leads to agreement in the direction of the central region when it is otherwise from theories without strong toroidal rotations. Comparisons among these theories are made, demonstrating the degree of uncertainty of theoretical predictions.},
doi = {10.1063/1.2969438},
journal = {Physics of Plasmas},
number = 8,
volume = 15,
place = {United States},
year = 2008,
month = 8
}
  • Despite the importance of rotation in fusion plasmas, our present understanding of momentum transport is inadequate. The lack of understanding is in part related to the difficulty of performing accurate rotation measurements, especially for poloidal rotation. Recently, measurements of poloidal rotation for impurity ions (Z>1) have been obtained in the core of DIII-D [J. L. Luxon, Nucl. Fusion 42, 6114 (2002)] plasmas using charge exchange recombination spectroscopy. The inferred poloidal rotation is based on careful consideration of the effective energy-dependent cross section and of the gyromotion of the ions. The rotation measurements are found to be consistent with the radialmore » electric field determined independently from multiple impurity species as well as from motional Stark effect spectroscopic measurements. The poloidal rotation measurements have been compared with predictions based on the neoclassical theory of poloidal rotation from the code NCLASS [W. A. Houlberg et al., Phys. Plasmas 4, 3230 (1997)]. The comparison shows that the neoclassically predicted poloidal rotation is in general significantly smaller than the actual measurements.« less
  • Knowledge of poloidal velocity is necessary for the determination of the radial electric field, which along with its gradient is linked to turbulence suppression and transport barrier formation. Recent measurements of poloidal flow on conventional tokamaks have been reported to be an order of magnitude larger than expected from neoclassical theory. In contrast, poloidal velocity measurements on the NSTX spherical torus [Kaye et al., Phys. Plasmas 8, 1977 (2001)] are near or below neoclassical estimates. A novel charge exchange recombination spectroscopy diagnostic is used, which features active and passive sets of up/down symmetric views to produce line-integrated poloidal velocity measurementsmore » that do not need atomic physics corrections. Inversions are used to extract local profiles from line-integrated active and background measurements. Poloidal velocity measurements are compared with neoclassical values computed with the codes NCLASS[Houlberg et al., Phys. Plasmas 4, 3230 (1997)] and GTC-NEO[Wang et al., Phys. Plasmas 13, 082501 (2006)].« less
  • Here, predictive understanding of plasma transport is a long-term goal of fusion research. This requires testing models of plasma rotation including poloidal rotation. The present experiment was motivated by recent poloidal rotation measurements on spherical tokamaks (NSTX and MAST) which showed that the poloidal rotation of C +6 is much closer to the neoclassical prediction than reported results in larger aspect ratio machines such as TFTR, DIII-D, JT-60U and JET working at significantly higher toroidal field and ion temperature. We investigated whether the difference in aspect ratio (1.44 on NSTX versus 2.7 on DIII-D) could explain this. We measured Cmore » +6 poloidal rotation in DIII-D under conditions which matched, as best possible, those in the NSTX experiment; we matched plasma current (0.65 MA), on-axis toroidal field (0.55T), minor radius (0.6 m), and outer flux surface shape as well as the density and temperature profiles. DIII-D results from this work also show reasonable agreement with neoclassical theory. Accordingly, the different aspect ratio does not explain the previously mentioned difference in poloidal rotation results.« less
  • The damping rate of the poloidal flow {ital u}{sub {theta}} in a tokamak is determined in the banana regime as an initial value problem. The bounce averaged drift kinetic equation is solved analytically for early times and numerically for longer time scales of the order of the ion{endash}ion collision time {tau}{sub {ital ii}}. Initial conditions are chosen for the ion distribution function {ital f}{sub {ital i}}({ital t}=0) describing states with similar flows {ital u}{sub {theta}}({ital t}=0), but varying structures in pitch angle velocity space. At early times an analytical treatment shows that the damping characteristics of {ital u}{sub {theta}}({ital t})more » depend sensitively on whether or not the ions resposible for the flow are close to the trapped{endash}passing boundary. Initial decay is shown to be of the form {ital du}{sub {theta}}/{ital dt}{approximately}({nu}{sub {ital ii}}{epsilon}/{ital t}){sup 1/2}. A numerical treatment then confirms this early time result and extends the solution to the long term asymptotic decay, which is found to be independent of the initial preparation of the system. This long term evolution is also found to tend to independence of inverse aspect ratio {epsilon} as {ital t}{r_arrow}0. {copyright} {ital 1996 American Institute of Physics.}« less
  • Results from the first measurements of a core plasma poloidal rotation velocity (v{sub {theta}}) across internal transport barriers (ITB) on JET are presented. The spatial and temporal evolution of the ITB can be followed along with the v{sub {theta}} radial profiles, providing a very clear link between the location of the steepest region of the ion temperature gradient and localized spin-up of v{sub {theta}}. The v{sub {theta}} measurements are an order of magnitude higher than the neoclassical predictions for thermal particles in the ITB region, contrary to the close agreement found between the determined and predicted particle and heat transportmore » coefficients [K.-D. Zastrow et al., Plasma Phys. Controlled Fusion 46, B255 (2004)]. These results have significant implications for the understanding of transport barrier dynamics due to their large impact on the measured radial electric field profile.« less