F. M. Nekrasov

The parallel permittivity of magnetized toroidal plasmas with elliptic magnetic surfaces

The asymptotic solution of the Vlasov equation under the drift approximation, for an axially symmetric toroidal plasma configuration with an elliptic cross section of magnetic surfaces, is presented. The analytical expressions for the parallel component of the dielectric permittivity tensor are obtained. These expressions are used for theoretical analyses of the trapped and untrapped electron influence on the collisionless wave dissipation. The evaluated dielectric tensor components can be used for computer calculations of the radio frequency field structure and the collisionless dissipated power related to trapped and untrapped electrons in tokamak plasmas.

Dielectric permeability of a mirror-trapped plasma

Analytical expressions for the wave permeability tensor are derived for a two-dimensional plasma model of a straight axisymmetric mirror trap. The dielectric tensor components are found through a solution of the Vlasov equation, using the theory of Jacobian elliptic functions. The bounce-resonance effect of trapped particles on wave dissipation is analysed. It is shown that collisionless wave dissipation in the plasma with a mirror-trap configuration of a magnetic field can differ essentially from Landau damping in a plasma with straight uniform magnetic field lines. This dielectric tensor can be used in numerical calculations of Alfven and ion cyclotron heating of mirror-trap plasmas.

Effect of background plasma nonlinearities on dissipation processes in plasmas

Abstract The Coulomb collision effect on the bounce-resonance dissipation is considered for toroidal magnetized plasmas. The solution of the Vlasov equation with a simplified Fokker-Planck collision operator is presented. The parallel components of the dielectric tensor are obtained. A collisionless limit of wave dissipation is found.

Radiofrequency parallel permittivity of magnetized plasmas in low aspect ratio tokamaks

The solution of the Vlasov equation is presented for axially symmetric low aspect ratio tokamak plasmas having magnetic surfaces with a circular cross section. The analytical expression for the parallel component of the dielectric permittivity tensor of trapped and untrapped particles is obtained. This expression is used for theoretical analyses of the low aspect ratio effect on the bounce-resonance wave dissipation. The evaluated dielectric tensor components can be used for computer calculations of the radio frequency (RF) field structure and the RF dissipated power in the low aspect ratio tokamak plasmas.

Current drive by Alfvén waves in elongated cross-section tokamak

The general approach to the Alfven wave current drive problem in tokamaks with elongated transverse cross-sections was considered in this paper. Model approximations are used to describe circulating and trapped particle dynamics. This approach gives the accuracy of some percents. The expressions for the time-averaged longitudinal current and the radio-frequency currents have been obtained. They are supposed to be useful for a further analytical and computational solution of this problem. As an example, kinetic Alfven waves are considered in this paper.

The perpendicular permittivity of magnetized toroidal plasmas with elliptic magnetic surfaces

The Vlasov equation for charged particles is analyzed in an axially symmetric toroidal plasma configuration with an elliptic cross section of magnetic surfaces. The asymptotic solution of the Vlasov equation is found. The analytical expressions for the perpendicular component of the dielectric permittivity tensor are obtained. These expressions are used for theoretical analyses of the trapped and untrapped ion influence on the collisionless cyclotron wave dissipation. The evaluated dielectric tensor components can be used for computer calculations of the radio frequency field structure and the collisionless dissipated power related to trapped and untrapped ions in tokamak plasmas. It is shown that ion cyclotron resonance dissipation in tokamaks depends on toroidicity and ellipticity parameters and does not depend on plasma temperature.

The Coulomb scattering effect on trapped particles bounce-resonance dissipation in magnetized toroidal plasmas

The solution of the Vlasov equation with a simplified Fokker–Planck collision operator is presented for axially symmetric tokamak plasmas with a circular cross section of magnetic surfaces. The analytical expression for the parallel component of the dielectric permittivity tensor of trapped particles is obtained. This expression is used for theoretical analyses of the collision effect on the bounce-resonance wave dissipation. Conditions for a collisionless description of radio-frequency (rf) oscillations are found. This dielectric tensor components can be used for computer calculations of the rf field structure and the rf dissipated power related to trapped electrons in tokamak plasmas.

The weak collision effect on bounce-resonance dissipation in magnetized toroidal plasmas

The asymptotic solution of the Vlasov equation under the drift approximation with a simplified Fokker-Planck collision operator (Boltzmann equation) is presented for an axially symmetric toroidal plasma configuration with a circular cross section of magnetic surfaces. Analytical expressions for the parallel component of the dielectric permittivity tensor are obtained. These expressions are used for theoretical analyses of the collision effect on the bounce-resonance wave dissipation. Conditions of a collisionless description of radio-frequency (rf) oscillations are found. The evaluated dielectric tensor components can be used for computer calculations of the rf field structure and the collisionless dissipated power related to trapped and untrapped electrons in tokamak plasmas.