Covariant Constitutive Relations, Landau Damping and Non-Stationary Inhomogeneous Plasmas

Abstract

Abstract-Models of covariant linear electromagnetic constitutive relations are formulated that have wide applicability to the computation of susceptibility tensors for dispersive and inhomogeneous media. A perturbative framework is used to derive a linear constitutive relation for a globally neutral plasma enabling one to describe in this context a generalized Landau damping mechanism for non-stationary inhomogeneous plasma states.

Derivations of Relativistic Force Transformation Equations

“…Comparing the first Equation (2) and Equation (17), it follows that for the Lorentz force the corresponding scalar χ vanishes identically. Then, supposing that the Lorentz force is the only force acting on a charged particle in the electromagnetic field, Equation (20) implies that m is constant, consistent with Planck's assumption tacitly made in [3]. As another example, consider a three-force f = −(g/γ u )∇Φ, where a Lorentz scalar g plays the same role as does charge in electromagnetism, and Φ = Φ(r, t) is a Lorentz scalar field; f represents the relativistic force arising in the scalar meson theory of the nucleus [10,[12][13][14].…”

“…(In the calculation, equations γ u = γ u γ V (1 − V u x /c 2 ) [2] and dΦ/dt = ∂Φ/∂t + (∇Φ) · u are used.) Then Equations (14) and (20) imply that the mass of a particle which moves in the field Φ is given by…”

“…Since relativistic force transformation equations are closely related with a variety of basic concepts, we believe that the present paper could be helpful for teaching special relativity and relativistic electrodynamics. Despite ramified applications of relativistic electrodynamics (cf, e.g., [16][17][18][19][20]), it seems that some of its basic concepts still need clarification.…”

On the Fundamental Equations of Electromagnetism in Finslerian Spacetimes

“…We will adopt the language of differential forms (see [8,[26][27][28]), which provides elegant, concise equations and is tightly related to variational calculus.…”

Covariant constitutive relations and relativistic inhomogeneous plasmas

“…However even within a spacetime covariant formulation there remains great freedom in how to accommodate electromagnetic responses that depend on material dispersion induced by spatial correlations or temporal delays of electromagnetic interactions 1 . The incorporation of such effects in a theoretical description often relies on a detailed structural model of the medium particularly if it is inhomogeneous or external gravitational gradients are relevant.…”