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Kinetic entropy-based measures of distribution function non-Maxwellianity: theory and simulations

Part of: The Many Facets of the Vlasov Equation

Published online by Cambridge University Press:  21 October 2020

Haoming Liang Open the ORCID record for Haoming Liang [Opens in a new window] ,
M. Hasan Barbhuiya Open the ORCID record for M. Hasan Barbhuiya [Opens in a new window] ,
P. A. Cassak Open the ORCID record for P. A. Cassak [Opens in a new window] ,
O. Pezzi Open the ORCID record for O. Pezzi [Opens in a new window] ,
S. Servidio Open the ORCID record for S. Servidio [Opens in a new window] ,
F. Valentini Open the ORCID record for F. Valentini [Opens in a new window]  and
G. P. Zank Open the ORCID record for G. P. Zank [Opens in a new window]
Haoming Liang*
Affiliation:
Center for Space Plasma and Aeronomic Research, University of Alabama in Huntsville, Huntsville, AL35899, USA Department of Physics and Astronomy, West Virginia University, Morgantown, WV26506, USA
M. Hasan Barbhuiya
Affiliation:
Department of Physics and Astronomy, West Virginia University, Morgantown, WV26506, USA
P. A. Cassak
Affiliation:
Department of Physics and Astronomy, West Virginia University, Morgantown, WV26506, USA Center for KINETIC Plasma Physics, West Virginia University, Morgantown, WV26506, USA
O. Pezzi
Affiliation:
Gran Sasso Science Institute, Viale F. Crispi 7, I-67100 L'Aquila, Italy INFN/Laboratori Nazionali del Gran Sasso, I-67100Assergi(AQ), Italy Istituto per la Scienza e Tecnologia dei Plasmi, CNR, Via Amendola 122/D, I-70126Bari, Italy
S. Servidio
Affiliation:
Dipartimento di Fisica, Università della Calabria, I-87036Rende(CS), Italy
F. Valentini
Affiliation:
Dipartimento di Fisica, Università della Calabria, I-87036Rende(CS), Italy
G. P. Zank
Affiliation:
Center for Space Plasma and Aeronomic Research, University of Alabama in Huntsville, Huntsville, AL35899, USA Department of Space Science and Center for Space Plasma and Aeronomic Research, University of Alabama in Huntsville, Huntsville, AL35899, USA
*
†Email address for correspondence: [email protected]
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Abstract

We investigate kinetic entropy-based measures of the non-Maxwellianity of distribution functions in plasmas, i.e. entropy-based measures of the departure of a local distribution function from an associated Maxwellian distribution function with the same density, bulk flow and temperature as the local distribution. First, we consider a form previously employed by Kaufmann & Paterson (J. Geophys. Res., vol. 114, 2009, A00D04), assessing its properties and deriving equivalent forms. To provide a quantitative understanding of it, we derive analytical expressions for three common non-Maxwellian plasma distribution functions. We show that there are undesirable features of this non-Maxwellianity measure including that it can diverge in various physical limits and elucidate the reason for the divergence. We then introduce a new kinetic entropy-based non-Maxwellianity measure based on the velocity-space kinetic entropy density, which has a meaningful physical interpretation and does not diverge. We use collisionless particle-in-cell simulations of two-dimensional anti-parallel magnetic reconnection to assess the kinetic entropy-based non-Maxwellianity measures. We show that regions of non-zero non-Maxwellianity are linked to kinetic processes occurring during magnetic reconnection. We also show the simulated non-Maxwellianity agrees reasonably well with predictions for distributions resembling those calculated analytically. These results can be important for applications, as non-Maxwellianity can be used to identify regions of kinetic-scale physics or increased dissipation in plasmas.

Keywords

space plasma physicsplasma heatingplasma nonlinear phenomena
Type
Research Article
Information
Journal of Plasma Physics , Volume 86 , Issue 5 , October 2020 , 825860502
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Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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