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Analytical properties of linear electrostatic waves in two-component quantum and classical plasmas

Published online by Cambridge University Press:  22 August 2018

Shane Rightley Open the ORCID record for Shane Rightley [Opens in a new window]  and
Dmitri Uzdensky
Shane Rightley*
Affiliation:
Center for Integrated Plasma Physics, Department of Physics, University of Colorado, Boulder, CO 80309-0390, USA Department of Physics and Astronomy, University of Iowa, Iowa City, IA 52242, USA
Dmitri Uzdensky
Affiliation:
Center for Integrated Plasma Physics, Department of Physics, University of Colorado, Boulder, CO 80309-0390, USA
*
†Email address for correspondence: [email protected]
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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 one-component plasmas and consider distribution functions with a variety of analytical properties: the Dirac delta function, the Cauchy profile with two complex first-order poles, the squared Cauchy profile with two second-order poles and the inverse-quartic profile with four first-order poles; we also briefly discuss the non-meromorphic totally and arbitrarily degenerate Fermi–Dirac 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 counter-streaming identical populations and a bump-on-tail case with a primary population and a delta-function 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 inverse-quartic 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.

Keywords

plasma instabilitiesplasma wavesquantum plasma
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 4 , August 2018 , 905840408
Copyright
© Cambridge University Press 2018 

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