C. A. de Azevedo

The completely conservative difference schemes for the nonlinear Landau—Fokker—Planck equation

Conservativity and complete conservativity of finite difference schemes are considered in connection with the nonlinear kinetic Landau-Fokker-Planck equation. The characteristic feature of this equation is the presence of several conservation laws. Finite difference schemes, preserving density and energy are constructed for the equation in one- and two-dimensional velocity spaces. Some general methods of constructing such schemes are formulated. The constructed difference schemes allow us to carry out the numerical solution of the relaxation problem in a large time interval without error accumulation. An illustrative example is given.

Alfvén wave forces, affecting the tokamak edge plasma in the presence of impurities or dust

Dust particles appear on the edge of tokamak plasmas as a result of disruptions and plasma interactions with divertor plates, limiters, or blankets, as well as of pellet injections. It is shown that the presence of the dust impurities can lead to an effective decrease of the slow Alfven wave absorption in the region. These waves are used for heating, current drive, and control of the low-to-high (L–H) confinement transition. Radio-frequency forces can also be strongly changed in the presence of dust particles.

Coronal loop heating by Alfvén waves

The excitation and dissipation of global and surface Alfvén waves and their conversion into kinetic Alfvén waves have been analyzed for solar coronal loops using a cylindrical model of a magnetized plasma. Also the optimal conditions for coronal loop heating regimes with density of dissipated power ≈103 erg cm−3 s−1 by the new scheme named combined Alfvén wave resonance are found. Combined Alfvén wave heating regime appears when the global Alfvén wave is immersed into the Alfvén continuum with the condition of not-so-sharp distribution of axial current.

Alfvén waves and rotation of collisional plasmas in tokamaks

The effect of radio frequency fields on a plasma rotation in the edge (collisional) region of slightly rippled tokamaks is considered. The expressions for poloidal and toroidal velocities and for quasistationary radial electric fields are obtained as a function of absorbed rf power. The estimations of these quantities for the Phaedrus‐T tokamak [N. Hershkovitz et al., 15th International Atomic Energy Agency Conference on Plasma Physics and Controlled Fusion, Seville, 1994 (International Atomic Energy Agency, Vienna, in press)] are also presented. It is shown that Alfven waves can strongly modify the rotation velocities and radial electric fields in collisional regions of tokamak plasmas.

Hydrodynamic description of Alfvén and fast wave current drive in weakly collisional plasmas of magnetic traps

In this paper, general aspects of the Alfven and fast wave nonresonant and resonant current‐drive problem are considered both for collisional and weakly collisional plasmas. The magnetohydrodynamic approach is used for all collisional regimes and Landau damping is taken into account in the weakly collisional plasma case. Averaged in time and over magnetic surface, the general form of current‐drive forces are derived, including the viscosity and collision frequency perturbation terms. As an example, a weakly collisional plasma cylinder case is discussed and some disagreements on this problem between different authors results are eliminated.

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.

Plasma rotation in toroidal devices with circular cross-sections

The plasma rotation is theoretically investigated in toroidal devices. The dependence of magnetic axis curvature and torsion on the longitudinal coordinate and magnetic field ripples are taken into account. The calculations are carried out within the large aspect ratio and circular magnetic surfaces approximation. General equations for the relaxation of poloidal and toroidal velocities are obtained. The analysis of these equations is completed for the strongly collisional regime (the Pfirsch–Schluter regime). It is shown that, as a result of the relaxation due to the ion parallel viscosity, there is an equilibrium with the ion toroidal velocity equal to zero. The general expression for the ion poloidal velocity in the Pfirsch–Schluter regime is obtained. As in the tokamak case, this velocity is proportional to the ion temperature gradient. It does not depend on the plasma density gradient and on the radial electric field. The problems considered in the paper are of interest, specifically for toroidal devi...

Non-inductive current driven by Alfvén waves in solar coronal loops

It has been shown that Alfvén waves can drive non-inductive current in solar coronal loops via collisional or collisionless damping. Assuming that all the coronal-loop density of dissipated wave power (W= 10−3 erg cm−3 s−1), which is necessary to keep the plasma hot, is due to Alfvén wave electron heating, we have estimated the axial current density driven by Alfvén waves to be 〈jz〉 ≈ 103–105 statA cm−2. This current can indeed support the quasi-stationary equilibrium and stability of coronal loops and create the poloidal magnetic field up to Bθ≈1−5 G.

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.

Coronal loop heating by discrete Alfvén waves

We have modeled the solar coronal loop heating by discrete Alfven waves. Discrete Alfven waves (DAW) are a new class of Alfven waves which can be describe by the two fluid model with finite ion cyclotron frequency or the MHD model with plasma current along the magnetic field line as shown by Appert, Vaclavik and Villar (1984). We have modeled the coronal loop as a semi-toroidal plasma. We have shown that the absorptions of the discrete Alfven wave by the plasma through the viscosity can account for at least 20% of the necessary coronal power density of 10–9 erg cm -3 s -1.