Analytical properties of linear electrostatic waves in twocomponent quantum and classical plasmas
Abstract
We examine the properties of linear electrostatic waves in unmagnetised quantum and classical plasmas consisting of one or two populations of electrons with analytically tractable distribution functions in the presence of a stationary neutralising ion background. Beginning with the kinetic quantum plasma longitudinal susceptibility, we assess the effects due to increasing complexity of the background distribution function. Firstly, we analyse dispersion and Landau damping in onecomponent plasmas and consider distribution functions with a variety of analytical properties: the Dirac delta function, the Cauchy profile with two complex firstorder poles, the squared Cauchy profile with two secondorder poles and the inversequartic profile with four firstorder poles; we also briefly discuss the nonmeromorphic totally and arbitrarily degenerate FermiDirac distribution. In order to study electrostatic instabilities, we then turn to plasmas with two populations of electrons streaming relative to each other in two cases: a symmetric case of two counterstreaming identical populations and a bumpontail case with a primary population and a deltafunction beam. We obtain the corresponding linear kinetic dispersion relations and evaluate the properties of instabilities when the electron distribution functions are of the delta function, Cauchy, squared Cauchy or inversequartic types. In agreement with other studies, we find that in general quantum effects reduce the range of wavelengths for unstable modes at long wavelengths. We also find a second window of instability at shorter wavelengths and elucidate its nature as being due to quantum recoil. We note the possible implications for studies of laboratory and astrophysical quantum plasmas.
 Publication:

Journal of Plasma Physics
 Pub Date:
 August 2018
 DOI:
 10.1017/S0022377818000843
 arXiv:
 arXiv:1807.01458
 Bibcode:
 2018JPlPh..84d9008R
 Keywords:

 plasma instabilities;
 plasma waves;
 quantum plasma;
 Physics  Plasma Physics
 EPrint:
 44 pages, 22 figures, 2 tables