## 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] }## 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}

}