A Unified Force Density Framework for Plasma Confinement: Integrating Navier-Stokes with Local Interaction Field Equilibrium (LIFE)

Achieving stable magnetic confinement in nuclear fusion plasmas remains a profound theoretical and engineering challenge. Fundamentally, plasma confinement is a problem of macroscopic force density equilibrium. However, standard Magnetohydrodynamic (MHD) models treat mechanical fluid dynamics and electrodynamics as coupled but distinct systems, often relying on fragmented approximations that struggle to predict complex plasma instabilities.

This paper introduces a unified theoretical framework that seamlessly integrates the mechanical fluid dynamics of the Navier-Stokes equations (governing mechanical pressure and fluid velocity) with the Local Interaction Field Equilibrium (LIFE) theory. By strictly expressing all physical interactions—including mechanical pressure, radiation pressure, electromagnetic field tensors, inertia, and gravitational coupling—in identical dimensions of force density (N/m³), we derive a single, continuous equilibrium field equation.

This exact dimensional consistency eliminates the mathematical boundaries between the material plasma (Deuterium infusion) and the energetic confinement fields (microwave heating and magnetic containment). The resulting unified N/m³ equation provides a novel, rigorous analytical foundation for understanding high-energy plasma dynamics, offering new predictive pathways for mitigating instabilities in Tokamak and stellarator confinement systems.