TY - JOUR

T1 - Covariant constitutive relations and relativistic inhomogeneous plasmas

AU - Gratus, Jonathan

AU - Tucker, Robin

N1 - © 2011 American Institute of Physics

PY - 2011/4

Y1 - 2011/4

N2 - The notion of a 2-point susceptibility kernel used to describe linear electromagnetic responses of dispersive continuous media in nonrelativistic phenomena is generalized to accommodate the constraints required of a causal formulation in spacetimes with background gravitational fields. In particular the concepts of spatial material inhomogeneity and temporal nonstationarity are formulated within a fully covariant spacetime framework. This framework is illustrated by recasting the Maxwell–Vlasov equations for a collisionless plasma in a form that exposes a 2-point electromagnetic susceptibility kernel in spacetime. This permits the establishment of a perturbative scheme for nonstationary inhomogeneous plasma configurations. Explicit formulae for the perturbed kernel are derived in both the presence and absence of gravitation using the general solution to the relativistic equations of motion of the plasma constituents. In the absence of gravitation this permits an analysis of collisionless damping in terms of a system of integral equations that reduce to standard Landau damping of Langmuir modes when the perturbation refers to a homogeneous stationary plasma configuration. It is concluded that constitutive modeling in terms of a 2-point susceptibility kernel in a covariant spacetime framework offers a natural extension of standard nonrelativistic descriptions of simple media and that its use for describing linear responses of more general dispersive media has wide applicability in relativistic plasma modeling.

AB - The notion of a 2-point susceptibility kernel used to describe linear electromagnetic responses of dispersive continuous media in nonrelativistic phenomena is generalized to accommodate the constraints required of a causal formulation in spacetimes with background gravitational fields. In particular the concepts of spatial material inhomogeneity and temporal nonstationarity are formulated within a fully covariant spacetime framework. This framework is illustrated by recasting the Maxwell–Vlasov equations for a collisionless plasma in a form that exposes a 2-point electromagnetic susceptibility kernel in spacetime. This permits the establishment of a perturbative scheme for nonstationary inhomogeneous plasma configurations. Explicit formulae for the perturbed kernel are derived in both the presence and absence of gravitation using the general solution to the relativistic equations of motion of the plasma constituents. In the absence of gravitation this permits an analysis of collisionless damping in terms of a system of integral equations that reduce to standard Landau damping of Langmuir modes when the perturbation refers to a homogeneous stationary plasma configuration. It is concluded that constitutive modeling in terms of a 2-point susceptibility kernel in a covariant spacetime framework offers a natural extension of standard nonrelativistic descriptions of simple media and that its use for describing linear responses of more general dispersive media has wide applicability in relativistic plasma modeling.

KW - plasma dielectric properties

KW - plasma kinetic theory

KW - plasma Langmuir waves

KW - relativistic plasmas

KW - space-time configurations

KW - Vlasov equation

UR - http://www.scopus.com/inward/record.url?scp=79955407735&partnerID=8YFLogxK

U2 - 10.1063/1.3562929

DO - 10.1063/1.3562929

M3 - Journal article

AN - SCOPUS:79955407735

VL - 52

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 4

M1 - 042901

ER -