Abstract
Kinetic theory is used to develop equations describing dynamics of small-amplitude electromagnetic perturbations in toroidal axisymmetric plasmas. The closed Vlasov-Maxwell equations are first solved for a hot stationary plasma using the expansion in the small parameter {epsilon}{sub e}={rho}/L, where {rho} is the Larmor radius and L a characteristic length scale of the stationary state. The ordering and additional assumptions are specified so as to obtain the well-known Grad-Shafranov equation. The dielectric tensor of such a plasma is then derived. The Vlasov equation for the perturbed distribution function is solved by the expansion in the small parameters {epsilon}{sub e} and {epsilon}{sub p}={rho}/{lambda}, where {lambda} is a characteristic wavelength of the perturbing electromagnetic field. The solution is obtained up to the first order in {epsilon}{sub e} and the second order in {epsilon}{sub p}. By integrating the resulting distribution function over velocity space, an explicit expression for the tensor is derived in the form of a two-dimensional partial differential operator. The operator is shown to possess the proper symmetry corresponding to the energy conservation law. (author) 6 refs.
Brunner, S;
Vaclavik, J
[1]
- Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP)
Citation Formats
Brunner, S, and Vaclavik, J.
Dielectric tensor operator of hot plasmas in toroidal axisymmetric systems.
Switzerland: N. p.,
1992.
Web.
Brunner, S, & Vaclavik, J.
Dielectric tensor operator of hot plasmas in toroidal axisymmetric systems.
Switzerland.
Brunner, S, and Vaclavik, J.
1992.
"Dielectric tensor operator of hot plasmas in toroidal axisymmetric systems."
Switzerland.
@misc{etde_10119875,
title = {Dielectric tensor operator of hot plasmas in toroidal axisymmetric systems}
author = {Brunner, S, and Vaclavik, J}
abstractNote = {Kinetic theory is used to develop equations describing dynamics of small-amplitude electromagnetic perturbations in toroidal axisymmetric plasmas. The closed Vlasov-Maxwell equations are first solved for a hot stationary plasma using the expansion in the small parameter {epsilon}{sub e}={rho}/L, where {rho} is the Larmor radius and L a characteristic length scale of the stationary state. The ordering and additional assumptions are specified so as to obtain the well-known Grad-Shafranov equation. The dielectric tensor of such a plasma is then derived. The Vlasov equation for the perturbed distribution function is solved by the expansion in the small parameters {epsilon}{sub e} and {epsilon}{sub p}={rho}/{lambda}, where {lambda} is a characteristic wavelength of the perturbing electromagnetic field. The solution is obtained up to the first order in {epsilon}{sub e} and the second order in {epsilon}{sub p}. By integrating the resulting distribution function over velocity space, an explicit expression for the tensor is derived in the form of a two-dimensional partial differential operator. The operator is shown to possess the proper symmetry corresponding to the energy conservation law. (author) 6 refs.}
place = {Switzerland}
year = {1992}
month = {Aug}
}
title = {Dielectric tensor operator of hot plasmas in toroidal axisymmetric systems}
author = {Brunner, S, and Vaclavik, J}
abstractNote = {Kinetic theory is used to develop equations describing dynamics of small-amplitude electromagnetic perturbations in toroidal axisymmetric plasmas. The closed Vlasov-Maxwell equations are first solved for a hot stationary plasma using the expansion in the small parameter {epsilon}{sub e}={rho}/L, where {rho} is the Larmor radius and L a characteristic length scale of the stationary state. The ordering and additional assumptions are specified so as to obtain the well-known Grad-Shafranov equation. The dielectric tensor of such a plasma is then derived. The Vlasov equation for the perturbed distribution function is solved by the expansion in the small parameters {epsilon}{sub e} and {epsilon}{sub p}={rho}/{lambda}, where {lambda} is a characteristic wavelength of the perturbing electromagnetic field. The solution is obtained up to the first order in {epsilon}{sub e} and the second order in {epsilon}{sub p}. By integrating the resulting distribution function over velocity space, an explicit expression for the tensor is derived in the form of a two-dimensional partial differential operator. The operator is shown to possess the proper symmetry corresponding to the energy conservation law. (author) 6 refs.}
place = {Switzerland}
year = {1992}
month = {Aug}
}