Abstract
Under due consideration of anomalous transport phenomena resulting from electromagnetics field fluctuations a 2D drift-kinetic equation for impurity ions is formulated in toroidal coordinates assuming the usual model for the helical magnetic field in axisymmetric tokamak configurations. A general solution for T,,{ne} Tperpendicular to (different kinetic temperatures for longitudinal and cross-field thermal motion) can be constructed in the form of a series expansion in Hermite polynomials with respect to {nu},, and in laguerre polynomials with respect to v perpendicular to, which in the limit T,, = T perpendicular to is equivalent to a gyro-averaged version of Grad`s expansion in tensorial Hermite polynomials. The lowest order approximations with respect to the Laguerre polynomials lead to kinetic equations for the reduced guiding-centre distribution functions 2{pi}{sub 0} {integral} d{nu}{sub perpendicular} {sub to}{theta}{sub perpendicular} {sub to} (1, {nu}{sup 2}{sub perpendicular} {sub to}) {chi}, {theta}`,, ({nu}{sub perpendicular} {sub to}), which in the presence of anomalous transport can be more easily treated than the original drift-kinetic equation. The corresponding 2D balance equations in toroidal coordinates are averaged over the magnetic surfaces with appropriate weighting factors, leading to the usual 1D balance equations describing the netto fluxes in radial direction. In this derivation the role of parallel
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Citation Formats
Claassen, H A, and Gerhauser, H.
Impurity transport at the plasma edge: the transition from 2D to 1D models in axisymmetric toroidal systems and the role of poloidal source distributions.
Germany: N. p.,
1992.
Web.
Claassen, H A, & Gerhauser, H.
Impurity transport at the plasma edge: the transition from 2D to 1D models in axisymmetric toroidal systems and the role of poloidal source distributions.
Germany.
Claassen, H A, and Gerhauser, H.
1992.
"Impurity transport at the plasma edge: the transition from 2D to 1D models in axisymmetric toroidal systems and the role of poloidal source distributions."
Germany.
@misc{etde_10130928,
title = {Impurity transport at the plasma edge: the transition from 2D to 1D models in axisymmetric toroidal systems and the role of poloidal source distributions}
author = {Claassen, H A, and Gerhauser, H}
abstractNote = {Under due consideration of anomalous transport phenomena resulting from electromagnetics field fluctuations a 2D drift-kinetic equation for impurity ions is formulated in toroidal coordinates assuming the usual model for the helical magnetic field in axisymmetric tokamak configurations. A general solution for T,,{ne} Tperpendicular to (different kinetic temperatures for longitudinal and cross-field thermal motion) can be constructed in the form of a series expansion in Hermite polynomials with respect to {nu},, and in laguerre polynomials with respect to v perpendicular to, which in the limit T,, = T perpendicular to is equivalent to a gyro-averaged version of Grad`s expansion in tensorial Hermite polynomials. The lowest order approximations with respect to the Laguerre polynomials lead to kinetic equations for the reduced guiding-centre distribution functions 2{pi}{sub 0} {integral} d{nu}{sub perpendicular} {sub to}{theta}{sub perpendicular} {sub to} (1, {nu}{sup 2}{sub perpendicular} {sub to}) {chi}, {theta}`,, ({nu}{sub perpendicular} {sub to}), which in the presence of anomalous transport can be more easily treated than the original drift-kinetic equation. The corresponding 2D balance equations in toroidal coordinates are averaged over the magnetic surfaces with appropriate weighting factors, leading to the usual 1D balance equations describing the netto fluxes in radial direction. In this derivation the role of parallel shear flows in the presence of anomalous viscosity and the effect of poloidally dependent source functions on the netto cross-field fluxes become apparent. It is shown as an example that a source concentration around the ALT-II limiter of TEXTOR yields an outward netto convection of impurity ions under normal operating conditions concerning the current and magnetic field direction. (orig.).}
place = {Germany}
year = {1992}
month = {Jan}
}
title = {Impurity transport at the plasma edge: the transition from 2D to 1D models in axisymmetric toroidal systems and the role of poloidal source distributions}
author = {Claassen, H A, and Gerhauser, H}
abstractNote = {Under due consideration of anomalous transport phenomena resulting from electromagnetics field fluctuations a 2D drift-kinetic equation for impurity ions is formulated in toroidal coordinates assuming the usual model for the helical magnetic field in axisymmetric tokamak configurations. A general solution for T,,{ne} Tperpendicular to (different kinetic temperatures for longitudinal and cross-field thermal motion) can be constructed in the form of a series expansion in Hermite polynomials with respect to {nu},, and in laguerre polynomials with respect to v perpendicular to, which in the limit T,, = T perpendicular to is equivalent to a gyro-averaged version of Grad`s expansion in tensorial Hermite polynomials. The lowest order approximations with respect to the Laguerre polynomials lead to kinetic equations for the reduced guiding-centre distribution functions 2{pi}{sub 0} {integral} d{nu}{sub perpendicular} {sub to}{theta}{sub perpendicular} {sub to} (1, {nu}{sup 2}{sub perpendicular} {sub to}) {chi}, {theta}`,, ({nu}{sub perpendicular} {sub to}), which in the presence of anomalous transport can be more easily treated than the original drift-kinetic equation. The corresponding 2D balance equations in toroidal coordinates are averaged over the magnetic surfaces with appropriate weighting factors, leading to the usual 1D balance equations describing the netto fluxes in radial direction. In this derivation the role of parallel shear flows in the presence of anomalous viscosity and the effect of poloidally dependent source functions on the netto cross-field fluxes become apparent. It is shown as an example that a source concentration around the ALT-II limiter of TEXTOR yields an outward netto convection of impurity ions under normal operating conditions concerning the current and magnetic field direction. (orig.).}
place = {Germany}
year = {1992}
month = {Jan}
}