The beam transport system is an essential part of any accelerator.  This research investigates how a charged particle beam extracted from a plasma source behaves as it passes through a virtual beam transport system consisting of a series of C-bending magnets. This is done by analyzing the equations of motion of charged particles through this system. In addition, the study investigates the effect of the free drift space regions between these magnets and studies the behavior of charged particles beam passing through the suggested system for both horizontal and vertical planes using a computer program designed for this purpose. The results indicate many focusing regions along the beam path (beam envelop) for both the horizontal and vertical planes. The presence of free drift regions between the magnets strongly affects the beam envelop for both horizontal and vertical planes.