Journal of Plasma Physics

Research Article

Electron interactions and quantum plasma physics

Elizabeth A. Rauschera1

a1 Lawrence Radiation Laboratory, University of California, Livermore, California

Abstract

The ‘quantum electrodynamics’ of the scattering of radiation from a fully ionized, interacting plasma is to be considered.

The plasma particle interaction must properly be treated quantum mechanically when the electron plasma wave phonon energies are comparable to or greater than the mean random electron energies and/or when the phonon momenta are of the order of magnitude or greater than the average electron momenta in the plasma.

In these two circumstances or either one of them, the plasma particle inter action must be treated in a quantum mechanical manner. The ‘solid-state’ plasma recently discussed by D.E.McCumber is an example of a quantum plasma.

Whether a classical or a quantum plasma is considered, the collective properties, as well as the single-particle properties, need to be considered. The collective properties of the plasma become important when it interacts with a radiation field in the case where the electron plasma frequency, ωp, is of the same order of magnitude, or exceeds, the operating radiation frequency ω, i.e. ωp≥ω.

A criterion to distinguish the properties of a plasma as to whether it is classical or quantum mechanical in nature can be defined in terms of three fundamental lengths of the electron gas. These definitions hold for a one-component plasma. They are: the classical length βe2, the Debye screening length S0022377800004013_inline1 and the thermal de Broglie wavelength S0022377800004013_inline2 defined as 1/kT. From these three quantities, we can define two dimensionless parameters. They are the classical parameter S0022377800004013_inline3 and the quantum parameter δ=λ/λD which is a measure of the quantum effects. For a quantum plasma δ>1 and in the classical limit (h = 0),δ=0, Λ<1.

When we take into account the collective behaviour characterized by the plasma oscillations, screening effects are an automatic aspect of the electron plasma gas.

It is hoped that the present review article will provide the background material for general understanding of the field and easy access to the current literature. It is also hoped that the present discussion will establish greater interest in this subject.

As an example of a calculation of plasma properties, a calculation of the generalized dielectric constant for both a low-density plasma in the classical limit and a high-density plasma in the quantum mechanical limit is performed and compared in a suitable manner.

(Received January 22 1968)

(Revised May 31 1968)