Role of quaternions in dyonic cold plasma
Loading...
Date
2018-07
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand)
Abstract
In this study, we have made an attempt to formulate the generalized dualmagneto hydrodynamics (MHD) of the dyonic cold plasma in terms of quaternionic formalism. Quaternion is a norm-division algebra over real, which shows four dimensional Euclidean space-time structure. The generalized dual MHD describes the motion of dyons (associated with electrons and magnetic monopoles) in cold plasma fluid. In cold plasma, we consider the temperature of dyons is very less in compared to sun. In other words, the dual MHD theory of cold plasma is an approximation theory, where we neglect the temperature effect. Starting with the quaternionic dual velocities, we have obtained an expression for generalized dyonic field of the cold plasma, namely, the hydro-electric field and the hydro-magnetic field. The hydro-electric field is analogous to the generalized Lamb vector field, while the hydro-magnetic field is analogous to the generalized vorticity vector field for dyonic fluid. The dual Lorentz gauge like conditions, respectively for the hydro-electric and hydro-magnetic field are obtained. Further, we derive a quaternionic expression to the generalized Dirac-Maxwell equations for the dyonic cold plasma which showing a well invariant nature under the duality, Lorentz and CPT transformation. We also discuss the quaternionic unified hydro-electromagnetic wave equation for the dyonic cold plasma. It should be noticed that the hydro-magnetic wave equation shows an analogous to Alfven wave equation which may be generated by magnetic monopoles. Thereafter, we obtain the generalized energy-momentum conservation laws for the hydro-electric and hydro-magnetic field of the dyonic cold plasma. We discuss the Poynting theorem or conservation of energy by comparing the scalar coefficient, while the conservation of momentum is described by comparing vector coefficient of quaternionic formulation. Therefore, these quaternionic expressions, i.e., for the generalized hydro-electromagnetic wave and for the energy-momentum conservation relations are showing an invariant nature under the duality, Lorentz and CPT transformations.
Description
Keywords
null