This document is Paper 1 of a three part series derived from the unified canonical reference GREMN v25. The v25 mother document contains the complete analytical framework for the Griffiths Rotating Electromagnetic Nozzle including all physics engineering subsystems validation architecture and mission applications. The present paper isolates the physics and MHD theory layer for readers whose primary focus is plasma physics MHD modelling and analytical derivation. Papers 2 and 3 address engineerin