Extended Field Interactions in Poisson’s Equation Revision

Abstract

This investigation introduces a new variational approach to refining Poisson’s equation, enabling the inclusion of a broader spectrum of physical phenomena, particularly in the emerging fields of spintronics and the analysis of resonant structures. The innovative formulation extends the traditional capabilities of Poisson’s equation, offering a nonlocal extension to classical theories of gravitation and opening new directions for energy conversion and enhanced communication technologies. By introducing a novel geometric structure, ω˜, into the equation, a deeper understanding of electrostatic potentials is achieved, and the intricate dynamics of the gravitational potential in systems characterized by radial vorticity fluctuations are illuminated. Furthermore, the research elucidates the generation of longitudinal electromagnetic waves and resonant phenomena within dusty plasma media, thereby contributing to the methodological advances in the study of nonequilibrium systems. These theoretical advances have the potential to transform the understanding of complex physical systems and open up opportunities for significant technological achievements across a range of scientific sectors.