In this paper hydrodynamic and kinetic approaches to model low pressure capacitively coupled radio-frequency discharges are discussed. In particular approaches and results for power modulated discharges in a mixture of silane and hydrogen and for discharges containing a considerable amount of dust particles will be presented.

The parameters of self-consistent dusty sheaths are investigated using computer simulations of the temporal evolution of one-dimensional slab plasma with two-temperature electrons and dust particles. The evolution is caused by collection of electrons and ions by an electrode (wall) and also by dust particles, which are initially injected into the plasma around the electrode (wall). A peculiarity of the sheaths is a nonmonotonic spatial distribution of the electric potential that causes protection of the electrode (wall) from fast ions. The degree of protection depends on the temperature and density ratios of both electron components.

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Dynamics of dust particles in a divertor plasma is simulated using numerical solutions of dust momentum and charging equations in an electrostatic sheath and an ionizing presheath, where an electrostatic force and a drag force due to absorption of plasma ions are taken into account. Spatial distributions of plasma parameters in a divertor are obtained with particle simulations including ionization by electron-impact. We found that the critical dust radius exists. Dust particles with a larger radius than this critical one are incapable to come off a divertor plate because the ion drag force is stronger compared to the electrostatic force. Control of the plate potential can suppress the dust motion from the plate. The radii of heavy dust particles are classified with respect to equilibrium positions. Considering dust particles started at the plate with radii smaller than the critical one, two types of dust motion were found. Dust particles with the first type of motion come back to the plate before approaching their equilibrium positions. The second type of motion is presented by smaller dust particles which oscillate around their equilibrium positions.

The expansion of a bounded plasma with dust particles is investigated by means of computer modelling, taking into account the dynamics of the dust particle charge as well as the Coulomb collisions of electrons and ions with dust particles. The PIC method is used for the computer modelling. The collection of electrons and ions by dust particles is described in a way similar to orbit-limited probe theory. Coulomb interactions are described in the framework of stochastic differential equations. It is shown that the mean distribution functions of electrons and ions are influenced by the dust particles during plasma expansion. The evolution of the ion distribution function leads to a strong deviation from equilibrium. Dust particles also influence the temporal behaviour of the plasma parameters.