For computed tomography (CT) imaging to be considered "real time", one set of tomographic projections are to be acquired in less than 30 ms. Current conventional CT systems are limited to approximately 300 ms because of mechanical and material limitations. To bypass the mechanical limitations of a conventional gantry system, there is an open design challenge to develop a distributed X-ray source that is tightly packed and bright. The work presented here reports a design for a distributed X-ray source based on a rotating cylindrical anode. In particular, this work focuses on designing the electron beam optics for said X-ray source and refining these optics via multi-physics simulation studies. We designed these studies to investigate the electron beam behavior for switching, steering, and focusing. We demonstrated that the high-energy electron beam could be turned off and on via the grid-switching technique, could be steered, and could be dynamically focused for distinct positions along the cylindrical anode. We also report the optimal set of parameters that result in the desired electronic focal spot size (1 mm x 7 mm) and shape at each source position for our system.