Momentum, angular momentum, and spin of waves in an isotropic collisionless plasma

TL;DR

This paper investigates the momentum, angular momentum, and spin of linear waves in an isotropic collisionless plasma, revealing their properties and implications for plasma wave phenomena through both macroscopic and microscopic theoretical approaches.

Contribution

It introduces a detailed analysis of the canonical and kinetic momentum and spin densities of plasma waves, highlighting their similarities to fluid waves and electromagnetic fields, and explores their physical implications.

Findings

Canonical momentum and spin densities of Langmuir waves resemble those of sound waves.

Electromagnetic wave densities can be expressed in dual-symmetric forms involving electric and magnetic fields.

Derived properties have implications for plasma transport phenomena like Stokes drift and inverse Faraday effect.

Abstract

We examine the momentum and angular momentum (including spin) properties of linear waves, both longitudinal (Langmuir) and transverse (electromagnetic), in an isotropic nonrelativistic collisionless electron plasma. We focus on conserved quantities associated with the translational and rotational invariance of the wave fields with respect to the homogeneous medium; these are sometimes called pseudo-momenta. There are two types of the momentum and angular momentum densities: (i) the kinetic ones associated with the energy flux density and the symmetrized (Belinfante) energy-momentum tensor and (ii) the canonical ones associated with the conserved Noether currents and canonical energy-momentum tensor. We find that the canonical momentum and spin densities of Langmuir waves are similar to those of sound waves in fluids or gases; they are expressed via the electron velocity field. In turn, the momentum and spin densities of electromagnetic waves can be written either in the forms known for free-space electromagnetic fields, involving only the electric field, or in the dual-symmetric forms involving both electric and magnetic fields, as well as the effective permittivity of plasma. We derive these properties both within the phenomenological macroscopic approach and microscopic Lagrangian field theory for the coupled electromagnetic fields and electrons. Finally, we explore implications of the canonical momentum and spin densities in transport and electrodynamic phenomena: the Stokes drift, the wave-induced magnetization (inverse Faraday effect), etc.