The aim of this thesis is to study coherent plasma effects and collective plasma processes in pulsar environments. Pulsars are one of the most enigmatic objects in the universe. Formed in supernova explosions, pulsars are rapidly rotating neutron stars identified by their periodically pulsed electromagnetic emission. The source of the radiation is believed to be associated with the electron-positron (pair) plasma populating the pulsar magnetosphere. The theory of pulsar radiation is still in its infancy and there is lack of understanding about the energetic processes involved. The initial aim of this thesis is to study a possible emission mechanism in which electrostatic oscillations are coupled to propagating electromagnetic waves by a magnetic field inhomogeneity, thus creating a source of radiation in the pulsar magnetosphere. The full nonlinear equations in cylindrical geometry for a streaming cold pair plasma are solved numerically, together with Maxwell s equations, using a Finite-Difference Time Domain method. Electrostatic oscillations are induced in a streaming plasma in the presence of a non-uniform magnetic field, and the resulting electromagnetic waves are modelled self-consistently. Also presented is the linear perturbation analysis of these model equations perturbed from a dynamical equilibrium in order to probe the fundamental modes present in the system. These simulations successfully exhibit the coupling mechanism and the nonlinear interaction between electromagnetic waves and independent plasma oscillations, confirming the importance of coherent plasma effects and collective plasma processes in the pulsar magnetosphere. The observed electromagnetic signature is characterised by the nature of the emission mechanism and possibly by the menagerie of dust it encounters as it propagates through the surrounding supernova remnant. Supernova remnants are composed of multi-species electron-ion dusty plasmas. Conventional modelling of dust growth in this environment is based upon coagulation and nucleation of gas phase material. The second aim of this thesis is to study a possible spheroidal dust growth mechanism via plasma deposition. Dust grains immersed in a plasma acquire a net negative charge forming a plasma sheath. Ions are accelerated from the bulk plasma into the sheath and are deposited on the surface of the grain altering its shape and size. Grains with an elliptical geometry have a non-radial electric field and further anisotropic growth occurs if the deposited ions are non-inertial. In reality the extent of such growth depends upon the initial kinetic energy of the ions and the magnitude of the electric field in the sheath. Laplace s equation for the electric field for a range grain eccentricities is numerically solved using a bespoke finite difference method, the dynamics of the ions in the sheath are solved, showing how elliptical growth is related to the initial eccentricity and size of the seed relative to the sheath length.