Smolyakov, Andrei2015-08-262015-08-262015-082015-08-25August 201http://hdl.handle.net/10388/ETD-2015-08-2150In many natural and laboratory conditions, plasmas are often in the non-equilibrium state due to presence of stationary flows, when one particle species (or a special group, such as group of high energy particles, i.e., beam) is moving with respect to the other plasma components. Such situations are common for a number of different plasma applications such as diagnostics with emissive plasma probes, plasma electronics devices and electric propulsion devices. The presence of plasmas flows often leads to the instabilities in such systems and subsequent development of large amplitude perturbations. The goal of this work is to develop physical insights and numerical tools for studies of ion sound instabilities driven by the ion flow in a system of a finite length. The ion sound waves are modified by the presence of ion beam resulting in negative and positive energy modes. The instability develops due to coupling of negative and positive energy modes mediated by reflections from the boundary. It is shown that the wave dispersion due to deviation from quasi-neutrality is crucial for the stability. In finite length system, the dispersion is characterized by the length of the system measured in units of the Debye length. The instability is studied analytically and the results are compared with direct initial value numerical simulations. The numerical tools to simulate these systems are developed based on Godunov and multiple shooting methods. The initial value simulations show the time dependent evolution from which the growth rates were determined for different parameters of the system. The results of the simulations were benchmarked against the analytical results in some limiting cases. In the pursuit of simulation efficiency, the parallelization of the code was investigated for two basic types of parallel systems: shared and distributed memory. The OpenMP and MPI library were used correspondingly.engplasma wavesplasma instabilitiesplasma flowstext