This work describes computer simulations of the behaviour of plasmas similar to those observed in the near Earth environment The work can be split into three main threads Firstly we have developed a set of algorithms to allow the implementation of particle type simulation models on parallel computer architectures ranging from small workstation clusters to massively parallel supercomputers These algorithms allow large simulations with many particles to be performed We address the problems of e cient use of available computational resources and the scaling of algorithms as computers get larger Secondly we use a parallel implementation of a two dimensional hybrid simulation code with periodic boundaries to explore the evolution of ion beam distributions similar to those observed upstream of the Earth s bow shock We follow the evolution of the resonant instabilities of these cool tenuous proton beams both isotropic and anisotropic in temperature into the non linear regime We examine the waves generated their e ects on the ion distribution function the phenomenon of gyrophase bunching and describe the life cycles of two dimensional magnetic features including oblique propagating shocklets We suggest that such two dimensional structures may play a role in the saturation of beam instabilities Coherence lengths of the waves are calculated We see some evidence of anisotropy driven mirror waves late on in these simulations Thirdly we explore the nature of parametric instabilities in two dimensions We examine the role of parametric or wave wave instabilities in the late evolution of beam instability generated waves We nd little evidence of any parametric instability in this case The two dimensional evolution of a wave known to be unstable to one dimensional parametric instability is described We nd that in this case the instability develops in a manner similar to that found in one dimensional simulations although with some angular broadening in wavevector space There is some evidence of anisotropy driven instabilities later in the simulation