Quaternionic approach on the Dirac-Maxwell, Bernoulli and Navier-Stokes equations for dyonic fluid plasma

TL;DR

This paper develops a quaternionic framework for modeling dyonic plasma, unifying electromagnetic and fluid dynamics equations, and reveals two distinct wave propagation modes in such plasma.

Contribution

It introduces a novel quaternionic formalism for dyonic plasma, combining Dirac-Maxwell, Bernoulli, and Navier-Stokes equations into a unified model.

Findings

Identification of Langmuir-like wave propagation due to electrons

Discovery of t-Hooft-Polyakov-like wave propagation due to magnetic monopoles

Unified quaternionic equations for energy and momentum conservation in dyonic plasma

Abstract

Applying the Hamilton's quaternion algebra, we propose the generalized electromagnetic-fluid dynamics of dyons governed by the combination of the Dirac-Maxwell, Bernoulli and Navier-Stokes equations. The generalized quaternionic hydro-electromagnetic field of dyonic cold plasma consist the electrons and the magnetic monopoles in which there exist dual-mass and dual-charge species in presence of dyons. We construct the conservation of energy and conservation of momentum equations by equating the quaternionic scalar and vector parts for generalized hydro-electromagnetic field of dyonic cold plasma. We propose the quaternionic form of conservation of energy is related to the Bernoulli's like equation while the conservation of momentum is related to Navier-Stokes like equation for dynamics of dyonic plasma fluid. Further, the continuity equation i.e. the conservation of electric and magnetic charges with the dynamics of hydro-electric and hydro-magnetic flow of conducting cold plasma fluid is also analyzed. The quaternionic formalism for dyonic plasma wave emphasizes that there are two types of waves propagation namely the Langmuir like wave propagation due to electrons, and the t-Hooft-Polyakov like wave propagation due to magnetic monopoles.