TITLE:
Shock Fronts in Non-Polar Electro-Conducting Media
AUTHORS:
Michael Grinfeld, Pavel Grinfeld
KEYWORDS:
Electric Current in Conductors, Boundary Value Problems, Exact Solution, Ray-Equations
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.4,
April
7,
2022
ABSTRACT: We analyze the propagation of electromagnetic fronts in unbounded electric conductors. Our model is based on the Maxwell model of electromagnetism, which includes the displacement current and Ohm’s law in its simplest forms. The shock-like electromagnetic front is a propagating surface, across which the electric and magnetic fields, as well as their higher temporal and spatial derivatives, experience finite jumps. The shock-like fronts are essentially different as compared with the weak fronts; in particular, the bulk Maxwell equations are essentially insufficient for the analysis of the shock-like fronts, and they should be amended we the physical jump conditions. We choose these additional conditions by using conditions similar to those suggested by Heaviside. We derive the basic shock intensity relationships implied by this model.