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Collisionless relaxation of a Lynden-Bell plasma

Published online by Cambridge University Press:  16 September 2022

R.J. Ewart Open the ORCID record for R.J. Ewart [Opens in a new window] ,
A. Brown ,
T. Adkins Open the ORCID record for T. Adkins [Opens in a new window]  and
A.A. Schekochihin Open the ORCID record for A.A. Schekochihin [Opens in a new window]
R.J. Ewart*
Affiliation:
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, UK Balliol College, Oxford OX1 3BJ, UK
A. Brown
Affiliation:
Exeter College, Oxford OX1 3DP, UK
T. Adkins
Affiliation:
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, UK Merton College, Oxford OX1 4JD, UK
A.A. Schekochihin
Affiliation:
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, UK Merton College, Oxford OX1 4JD, UK
*
†Email address for correspondence: robert.ewart@physics.ox.ac.uk
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Abstract

Plasmas whose Coulomb-collision rates are very small may relax on shorter timescales to non-Maxwellian quasi-equilibria, which, nevertheless, have a universal form, with dependence on initial conditions retained only via an infinite set of Casimir invariants enforcing phase-volume conservation. These are distributions derived by Lynden-Bell (Mon. Not. R. Astron. Soc., vol. 136, 1967, p. 101) via a statistical-mechanical entropy-maximisation procedure, assuming perfect mixing of phase-space elements. To show that these equilibria are reached dynamically, one must derive an effective ‘collisionless collision integral’ for which they are fixed points – unique and inevitable provided the integral has an appropriate H-theorem. We describe how such collision integrals are derived and what assumptions are required for them to have a closed form, how to prove the H-theorems for them, and why, for a system carrying sufficiently large electric-fluctuation energy, collisionless relaxation should be fast. It is suggested that collisionless dynamics may favour maximising entropy locally in phase space before converging to global maximum-entropy states. Relaxation due to interspecies interaction is examined, leading, inter alia, to spontaneous transient generation of electron currents. The formalism also allows efficient recovery of ‘true’ collision integrals for both classical and quantum plasmas.

Keywords

astrophysical plasmasplasma dynamicsplasma nonlinear phenomena
Type
Tutorial
Information
Journal of Plasma Physics , Volume 88 , Issue 5 , October 2022 , 925880501
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press

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