A new approach has been developed for the kinetic description of the screening of the charge of macroparticles and the determination of the distribution of the effective potential in a nonequilibrium...

An asymptotic theory for the screening of the electric field of a dust particle or a spherical probe in a plasma with an external steady and/or internal (proportional to the electron density) gas...

Screening and charging of a grain in a weakly ionized plasma background are studied within the drift-diffusion approximation. The computations evidence that the account of grain charging results in a distinct qualitative change in the screened field as compared to the thermodynamically equilibrium case of a grain with a constant charge. The stationary grain charge as well as the field within the sheath around the grain are shown to be almost independent of the type of boundary conditions (for relatively low ionization rates and small grain sizes), whereas the asymptotical behavior of the effective field is rather sensitive to them.

The problem of random motion of charged particles in an external magnetic field is studied under the assumption that the Langevin sources produce anisotropic diffusion in velocity space and the friction force is dependent on the direction of particle motion. It is shown that in the case under consideration, the kinetic equation describing particle transitions in phase space is reduced to the equation with a Fokker-Planck collision term in the general form (nonisotropic friction coefficient and nonzero off-diagonal elements of the diffusion tensor in the velocity space). The solution of such an equation has been obtained and the explicit form of the transition probability is found. Using the obtained transition probability, the mean-square particle displacements in configuration and velocity space were calculated and compared with the results of numerical simulations, showing good agreement. The obtained results are used to generalize the theory of large-scale fluctuations in plasmas to the case of anisotropic diffusion across an external magnetic field. Such diffusion is expected to be observed in the case of an anisotropic $k$ spectrum of fluctuations generating random particle motion (for example, in the case of drift-wave turbulence).

Within the kinetic approach the velocity and the charge distributions of grains in stationary dusty plasmas are calculated and the relations between the effective temperatures of such distributions and plasma parameters are established. It is found that the effective temperature which determines the velocity grain distribution could be anomalously large due to the action of accelerating ionic bombarding force. The possibility to apply the results obtained to the explanation of the increasing grain temperature in the course of Coulomb-crystal melting by reduction of the gas pressure is discussed.