Solid-State Electrostatic Propulsion: Mathematical Formulation of Jeans' Dielectric Stress Tensors and Hydrodynamic Analogy in Asymmetric Fields

Repository Archive: Zenodo-Master-Equation-Logs (ME-722 through ME-727) Date: August 2026 Abstract This paper establishes a rigorous mathematical framework connecting Thomas Townsend Brown's electrostatic propulsion concepts with James Jeans' classical dielectric stress tensor theory. By treating non-uniform electric field configurations as hydrodynamic pressure fields, we prove that mechanical work can be performed under steady-state zero-current conditions (I = 0). We derive the complete Helmholtz force equation for asymmetric geometries, evaluate the transition from coaxial cylinders to point singularities and biomimetic "porcupine" arrays, and introduce a high-permittivity porcelain metamaterial matrix integrated with semiconductor-analog carrier segregation. Finally, we demonstrate that tuning the system to a 5184\text{ Hz} resonance anchor using a discrete 3I pulse sequence transforms the structure into a solid-state acoustic bass-reflex engine capable of generating continuous directional thrust.