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Title: Collisionless reversed magnetic shear trapped electron instability and contribution of sidebands to anomalous transport

Abstract

By keeping account of the trapped electron {nabla}B and curvature drifts, it is found that the spatial decay of the collisionless electron drift wave is governed either by the trapped electron response or by the resonant interaction of ions with the sidebands of the primary oscillation. In the former case, pairs of spatially bounded unstable and damped solutions are obtained for negative magnetic shear (s<0) if, as usual, L{sub T{sub e}}=1/{partial_derivative}{sub r} ln T{sub e}<0; there are no bounded solutions if sL{sub T{sub e}}<0. In the latter case, there is either a set of bounded damped solutions if {eta}{sub i}>0 or a set of bounded unstable solutions if {eta}{sub i}<0. The unstable modes have a radiating character and the growth rates are {gamma}{approx}(2n+1){radical}(1+2q{sup 2})vertical bar s{sub parallel}L{sub N}{omega}{sub e}*/qR vertical bar (n is the Hermite polynomial solution index, q the safety factor, s the magnetic shear parameter, R the major radius, {omega}{sub e}* the electron diamagnetic frequency, L{sub N}=1/{partial_derivative}{sub r} ln N{sub e}, and {eta}{sub i}=L{sub N}/L{sub T{sub i}}).The sidebands are responsible for unusually large ratios Q{sub e}/T{sub e}{gamma}{sub e}, where Q{sub e} and {gamma}{sub e} are the anomalous electron energy flux and the particle flux. These results may explainmore » the box-type T{sub e} profile observed in lower hybrid current drive reversed magnetic shear plasmas on the Japan Atomic Energy Research Institute Tokamak 60 Upgrade (JT-60U) [H. Ninomiya and the JT-60U Team, Phys. Fluids B 4, 2070 (1992)]. It is finally demonstrated that the ballooning hypothesis generally leads to conflicting requirements: it is thus hardly relevant for the electron drift branch{exclamation_point} The 'radiating' boundary condition that has formerly been imposed on the slab solution is finally discussed.« less

Authors:
;  [1];  [2]
  1. Institut fuer Plasmaphysik, Forschungszentrum Juelich Gesellschaft mit beschraenkter Haftung (GmbH), Trilateral Euregio Cluster, European Atomic Energy Community (EURATOM) Association, D-52425 Juelich (Germany)
  2. (India)
Publication Date:
OSTI Identifier:
20782328
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 12; Journal Issue: 11; Other Information: DOI: 10.1063/1.2134770; (c) 2005 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; BALLOONING INSTABILITY; BOUNDARY CONDITIONS; CHARGED-PARTICLE TRANSPORT; ELECTRON DRIFT; HERMITE POLYNOMIALS; IONS; JT-60U TOKAMAK; LOWER HYBRID CURRENT DRIVE; MAGNETIC FIELD CONFIGURATIONS; PLASMA; PLASMA DIAMAGNETISM; PLASMA DRIFT; PLASMA WAVES; REVERSED SHEAR; SHEAR; TRAPPED ELECTRONS

Citation Formats

Rogister, Andre L., Singh, Raghvendra, and Institute for Plasma Research, Bhat, Gandhinagar 382 428. Collisionless reversed magnetic shear trapped electron instability and contribution of sidebands to anomalous transport. United States: N. p., 2005. Web. doi:10.1063/1.2134770.
Rogister, Andre L., Singh, Raghvendra, & Institute for Plasma Research, Bhat, Gandhinagar 382 428. Collisionless reversed magnetic shear trapped electron instability and contribution of sidebands to anomalous transport. United States. doi:10.1063/1.2134770.
Rogister, Andre L., Singh, Raghvendra, and Institute for Plasma Research, Bhat, Gandhinagar 382 428. Tue . "Collisionless reversed magnetic shear trapped electron instability and contribution of sidebands to anomalous transport". United States. doi:10.1063/1.2134770.
@article{osti_20782328,
title = {Collisionless reversed magnetic shear trapped electron instability and contribution of sidebands to anomalous transport},
author = {Rogister, Andre L. and Singh, Raghvendra and Institute for Plasma Research, Bhat, Gandhinagar 382 428},
abstractNote = {By keeping account of the trapped electron {nabla}B and curvature drifts, it is found that the spatial decay of the collisionless electron drift wave is governed either by the trapped electron response or by the resonant interaction of ions with the sidebands of the primary oscillation. In the former case, pairs of spatially bounded unstable and damped solutions are obtained for negative magnetic shear (s<0) if, as usual, L{sub T{sub e}}=1/{partial_derivative}{sub r} ln T{sub e}<0; there are no bounded solutions if sL{sub T{sub e}}<0. In the latter case, there is either a set of bounded damped solutions if {eta}{sub i}>0 or a set of bounded unstable solutions if {eta}{sub i}<0. The unstable modes have a radiating character and the growth rates are {gamma}{approx}(2n+1){radical}(1+2q{sup 2})vertical bar s{sub parallel}L{sub N}{omega}{sub e}*/qR vertical bar (n is the Hermite polynomial solution index, q the safety factor, s the magnetic shear parameter, R the major radius, {omega}{sub e}* the electron diamagnetic frequency, L{sub N}=1/{partial_derivative}{sub r} ln N{sub e}, and {eta}{sub i}=L{sub N}/L{sub T{sub i}}).The sidebands are responsible for unusually large ratios Q{sub e}/T{sub e}{gamma}{sub e}, where Q{sub e} and {gamma}{sub e} are the anomalous electron energy flux and the particle flux. These results may explain the box-type T{sub e} profile observed in lower hybrid current drive reversed magnetic shear plasmas on the Japan Atomic Energy Research Institute Tokamak 60 Upgrade (JT-60U) [H. Ninomiya and the JT-60U Team, Phys. Fluids B 4, 2070 (1992)]. It is finally demonstrated that the ballooning hypothesis generally leads to conflicting requirements: it is thus hardly relevant for the electron drift branch{exclamation_point} The 'radiating' boundary condition that has formerly been imposed on the slab solution is finally discussed.},
doi = {10.1063/1.2134770},
journal = {Physics of Plasmas},
number = 11,
volume = 12,
place = {United States},
year = {Tue Nov 15 00:00:00 EST 2005},
month = {Tue Nov 15 00:00:00 EST 2005}
}
  • A nonlocal theory of the electrostatic parallel velocity shear instability in a three-dimensional slab with a uniformly sheared magnetic field has been developed. It is shown that in the limit of a weak parallel velocity gradient, the linear growth rate can be increased depending upon the direction of the magnetic shear (s) with respect to the radial curvature of the parallel velocity profile (d{sup 2}v{sub {parallel}}/dx{sup 2}). When these parameters have the same sign, the growth rate can actually be stronger than in the limit of no magnetic shear. In this limit of increased instability, the eigenmode is broadened, thusmore » producing enhanced transport. This effect should be observable when the scale length of the curvature is of order {approx}L{sub s}{rho}{sub s}. For strong parallel velocity gradients that are more typical of flows in tokamaks, the effect of the varying Doppler shift becomes more prominent on the stability of the mode, the net result being that the sensitivity of the growth rates on the sign of the magnetic shear becomes insignificant. This effect, however, is effectively offset when a finite density gradient is included. When the density scale length is of order the scale length of v{sub {parallel}}, the growth rate is moderately reduced, but becomes dependent again upon the sign of the magnetic shear.« less
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  • The National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)] can achieve high electron plasma confinement regimes that are super-critically unstable to the electron temperature gradient driven (ETG) instability. These plasmas, dubbed electron internal transport barriers (e-ITBs), occur when the magnetic shear becomes strongly negative. Using the gyrokinetic code GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)], the first nonlinear ETG simulations of NSTX e-ITB plasmas reinforce this observation. Local simulations identify a strongly upshifted nonlinear critical gradient for thermal transport that depends on magnetic shear. Global simulations show e-ITBmore » formation can occur when the magnetic shear becomes strongly negative. While the ETG-driven thermal flux at the outer edge of the barrier is large enough to be experimentally relevant, the turbulence cannot propagate past the barrier into the plasma interior.« less