# 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 »

- Authors:

- Institut fuer Plasmaphysik, Forschungszentrum Juelich Gesellschaft mit beschraenkter Haftung (GmbH), Trilateral Euregio Cluster, European Atomic Energy Community (EURATOM) Association, D-52425 Juelich (Germany)
- (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}

}