Wave dispersion derived from the square-root Klein-Gordon-Poisson system

Abstract

Recently, there has been great interest around quantum relativistic models for plasmas. In particular, striking advances have been obtained by means of the Klein-Gordon-Maxwell system, which provides a first-order approach to the relativistic regimes of quantum plasmas. The Klein-Gordon-Maxwell system provides a reliable model as long as the plasma spin dynamics is not a fundamental aspect, to be addressed using more refined (and heavier) models involving the Pauli-Schrödinger or Dirac equations. In this work, a further simplification is considered, tracing back to the early days of relativistic quantum theory. Namely, we revisit the square-root Klein-Gordon-Poisson system, where the positive branch of the relativistic energy-momentum relation is mapped to a quantum wave equation. The associated linear wave propagation is analyzed and compared with the results in the literature. We determine physical parameters where the simultaneous quantum and relativistic effects can be noticeable in weakly coupled electrostatic plasmas. © Cambridge University Press 2013.