The following report describes a new propulsion concept based on self-guiding of combined light and particle beam and explores the physics, technology and design principles needed to implement such a system for an interstellar fly-by mission to Proxima b. While the relevant self-focusing mechanism has been considered in an optical context, this is the first application to space propulsion known to the authors.The purpose of the present study is to provide a broad overview of the pertinent physics and design principles, credibly assess propulsion capabilities, and lay a comprehensive foundation for further, more targeted investigations of critical system elements and processes. Starting from basic principles, this report describes the equations of motion and physical phenomena needed to establish the feasibility of self-guiding and furthermore analyze the production and sustainment of the self-guided beam. Compared with laser or particle beam propulsion alone, the self-guided beam concept introduces a plethora of light-matter interactions and additional complexities, imposing certain constraints on the geometric and physical characteristics of the beam sources. In particular, we have the identified the particle beam as a crucial element of the proposed concept. System constraints are quantitatively analyzed and then explored by developing and applying a mission design process to a Proxima b flyby mission as well as a nearer-term mission to the solar gravitational lens point.