This book consists of three major components: gas kinetic studies of vacuum chamber facility effects on the background flows; theoretical studies on collision-less free plume flow out of different exits. These analytical solutions are validated with numerical methods; and simulations of plasma and neutral plume flows from a cluster of Electric Propulsion (EP) Hall thrusters into low pressure background with the direct simulation Monte Carlo (DSMC) and Particle-In-Cell (PIC) methods. The last part adopts two electron models are used, the Boltzmann relation and a detailed electron model. A a general finite element solver working on unstructured mesh is developed to solve the generalized Possion's equation for the electron properties. This is a practical engineering book which contains several pieces of seminal work which inspires researchers from both academia and industry, including communities of rarefied gas dynamics; vacuum sciences and industry; aerospace and space engineering, such as propulsion and electric propulsion, spacecrafts and rockets.