Dusty plasma systems are common in all aspects of plasma physics, from space, to
our Earth's atmosphere, to low temperature discharges and fusion devices. In this
work the basic plasma dust interactions are studied, with the main focus being on
RF discharges and tokamak plasmas. One very important physical characteristic of
a dust grain immersed in a plasma environment, which plays a central role in the
study of its dynamical behaviour, is its charge. It determines the ion and electron
fluxes on the dust and through that, one can calculate the forces exerted on the solid
particle and the energy fluxes onto it. In this work an overview of the basic charging
theory used in dusty plasma, the Orbital Motion Limited (OML) approach, will be
presented, and its implications will be studied in the context of RF discharges and
tokamak plasmas. In the case of RF discharges, modifications of the OML approach
will be explored for the accommodation of time varying phenomena. This will have
two directions. The first, concerning the presence of time varying electric fields in a
uniform plasma background and the second, the presence of different forms of time
dependent current carrying electron distributions. In the tokamak case, the work
is focused on the modelling of the dynamical behaviour of dust particles in a tokamak
plasma environment. An improved version of the existing Dust in TOKamakS
(DTOKS) code has been developed. Results for the Mega Amp Spherical Tokamak
(MAST) and ITER are presented, as well as an assessment of the importance of the
various aspects of the physical model from the plasma background, the dust grain
charge, the forces on the particle and the dust heating model. Furthermore, the first
basic comparison between DTOKS and the DUST Transport (DUSTT) code, the
only other similar code available at the moment, is being presented.