Hostname: page-component-cb9f654ff-d5ftd Total loading time: 0 Render date: 2025-08-26T17:47:35.609Z Has data issue: false hasContentIssue false
  • English
  • Français

Hydrodynamic and kinetic representation of the microscopic classic dynamics at the transition on the macroscopic scale

Published online by Cambridge University Press:  02 February 2024

Pavel A. Andreev Open the ORCID record for Pavel A. Andreev [Opens in a new window]
Pavel A. Andreev*
Affiliation:
Department of General Physics, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russian Federation
*
†Email address for correspondence: andreevpa@physics.msu.ru
Get access Rights & Permissions [Opens in a new window]

Abstract

An open problem of the derivation of the relativistic Vlasov equation for systems of charged particles moving with velocities up to the speed of light and creating the electromagnetic field in accordance with the full set of the Maxwell equations is considered. Moreover, the method of derivation is illustrated on the non-relativistic kinetic model. Independent derivation of the relativistic hydrodynamics is also demonstrated. The key role of these derivations of the hydrodynamic and kinetic equations includes the explicit operator of averaging on the physically infinitesimal volume suggested by L.S. Kuzmenkov.

Keywords

hydrodynamicsmicroscopic modelkinetic theorymean-field approximationrelativistic plasmasplasma dynamics

Information

Type
Research Article
Information
Journal of Plasma Physics , Volume 90 , Issue 1 , February 2024 , 905900108
Check for updates
Copyright
Copyright © The Author(s), 2024. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Akhiezer, I.A. 1975 Plasma Electrodynamics. Pergamon Press.Google Scholar
Aleksandrov, A.F., Bogdankevich, L.S. & Rukhadze, A.A. 1984 Principles of Plasma Electrodynamics. Springer-Verlag.CrossRefGoogle Scholar
Andreev, P.A. 2022 a On the structure of relativistic hydrodynamics for hot plasmas. Phys. Scr. 97, 085602.CrossRefGoogle Scholar
Andreev, P.A. 2022 b Relativistic hydrodynamic model with the average reverse gamma factor evolution for the degenerate plasmas: high-density ion-acoustic solitons. Phys. Plasmas 29, 062109.CrossRefGoogle Scholar
Andreev, P.A. 2022 c Spin-electron-acoustic waves and solitons in high-density degenerate relativistic plasmas. Phys. Plasmas 29, 122102.CrossRefGoogle Scholar
Andreev, P.A. 2023 a Waves propagating parallel to the magnetic field in relativistically hot plasmas: a hydrodynamic models. Contrib. Plasma Phys. 63, e202200191.CrossRefGoogle Scholar
Andreev, P.A. 2023 b Microscopic model for relativistic hydrodynamics of ideal plasmas. Eur. Phys. J. D 77, 145.CrossRefGoogle Scholar
Andreev, P.A. 2023 c Nonlinear coupling of electromagnetic and spin-electron-acoustic waves in spin-polarized degenerate relativistic astrophysical plasma. Phys. Plasmas 30, 072110.CrossRefGoogle Scholar
Andreev, P.A., Kuz'menkov, L.S. & Trukhanova, M.I. 2011 Quantum hydrodynamics approach to the formation of waves in polarized two-dimensional systems of charged and neutral particles. Phys. Rev. B 84, 245401.CrossRefGoogle Scholar
Asenjo, F.A., Munoz, V., Valdivia, J.A. & Mahajan, S.M. 2011 A hydrodynamical model for relativistic spin quantum plasmas. Phys. Plasmas 18, 012107.CrossRefGoogle Scholar
Asenjo, F.A., Zamanian, J., Marklund, M., Brodin, G. & Johansson, P. 2012 Semi-relativistic effects in spin-1/2 quantum plasmas. New J. Phys. 14, 073042.CrossRefGoogle Scholar
Bret, A. & Haas, F. 2011 Quantum kinetic theory of the filamentation instability. Phys. Plasmas 18, 072108.CrossRefGoogle Scholar
Chen, L., Li, X., Pickl, P. & Yin, Q. 2020 Combined mean field limit and nonrelativistic limit of Vlasov–Maxwell particle system to Vlasov–Poisson system. J. Math. Phys. 61, 061903.CrossRefGoogle Scholar
Comisso, L. & Asenjo, F.A. 2014 Thermal-inertial effects on magnetic reconnection in relativistic pair plasmas. Phys. Rev. Lett. 113, 045001.CrossRefGoogle ScholarPubMed
Dobrushin, R.L. 1979 Vlasov equations. Funkts. Anal. Pril. 13 (2), 48.Google Scholar
Drofa, M.A. & Kuz'menkov, L.S. 1996 Continual approach to multiparticle systems with long-range interaction. Hierarchy of macroscopic fields and physical consequences. Theor. Math. Phys. 108, 849.CrossRefGoogle Scholar
Elskens, Y., Escande, D.F. & Doveil, F. 2014 Vlasov equation and N-body dynamics. How central is particle dynamics to our understanding of plasmas? Eur. Phys. J. D 68, 218.CrossRefGoogle Scholar
Elskens, Y. & Kiessling, M.K.-H. 2020 Microscopic foundations of kinetic plasma theory: the relativistic Vlasov–Maxwell equations and their radiation-reaction-corrected generalization. J. Stat. Phys. 180, 749.CrossRefGoogle Scholar
Escande, D.F., Benisti, D., Elskens, Y., Zarzoso, D. & Doveil, F. 2018 Basic microscopic plasma physics from N-body mechanics. Rev. Mod. Plasma Phys. 2, 9.CrossRefGoogle Scholar
Escande, D.F., Doveil, F. & Elskens, Y. 2016 N-body description of Debye shielding and Landau damping. Plasma Phys. Control. Fusion 58, 014040.CrossRefGoogle Scholar
Golse, F. 2012 The mean-field limit for a regularized Vlasov–Maxwell dynamics. Commun. Math. Phys. 310, 789.CrossRefGoogle Scholar
Golse, F. 2022 Mean-Field Limits In Statistical Dynamics. Lecture Notes. Available at: https://hal-polytechnique.archives-ouvertes.fr/hal-03514290v1/document, arXiv:2201.02005.Google Scholar
Grass, P. 2021 Microscopic derivation of Vlasov equations with singular potentials. arXiv:2105.06509.Google Scholar
Hakim, R. 2011 Introduction to Relativistic Statistical Mechanics Classical and Quantum. World Scientific Publishing Co. Pte. Ltd.CrossRefGoogle Scholar
Hakim, R., Mornas, L., Peter, P. & Sivak, H.D. 1992 Relaxation time approximation for relativistic dense matter. Phys. Rev. D 46, 4603.CrossRefGoogle ScholarPubMed
Hakim, R. & Sivak, H. 1982 Covariant Wigner function approach to the relativistic quantum electron gas in a strong magnetic field. Ann. Phys. 139, 230.CrossRefGoogle Scholar
Hauray, M. & Jabin, P.-E. 2007 N-particles approximation of the Vlasov equations with singular potential. Arch. Rat. Mech. Anal. 183, 489.CrossRefGoogle Scholar
Hazeltine, R.D. & Mahajan, S.M. 2002 Fluid description of relativistic, magnetized plasma. Astrophys. J. 567, 1262.CrossRefGoogle Scholar
Ivanov, A.Y., Andreev, P.A. & Kuz'menkov, L.S. 2014 Balance equations in semi-relativistic quantum hydrodynamics. Intl J. Mod. Phys. B 28, 1450132.CrossRefGoogle Scholar
Ivanov, A.Y., Andreev, P.A. & Kuz'menkov, L.S. 2015 Langmuir waves in semi-relativistic spinless quantum plasmas. Prog. Theor. Exp. Phys. 2015, 063I02.CrossRefGoogle Scholar
Jabin, P.-E. 2014 A review of the mean field limits for Vlasov equations. Kinet. Rel. Models 7, 661.CrossRefGoogle Scholar
Kiessling, M.K.-H. 2014 The microscopic foundations of Vlasov theory for Jellium-Like Newtonian N-body systems. J. Stat. Phys. 155, 1299.CrossRefGoogle Scholar
Klimontovich, Y.L. 1967 The Statistical Theory Non-Equilibrium Processes in a Plasma. Pergamon Press.Google Scholar
Klimontovich, Y.L. 1986 Statistical Physics. Harwood.Google Scholar
Kuz'menkov, L.S. 1991 Field form of dynamics and statistics of systems of particles with electromagnetic interaction. Theor. Math. Phys. 86, 159.CrossRefGoogle Scholar
Kuz'menkov, L.S. 2015 Theoretical Physics: Classical Mechanics. Nauka [in Russian].Google Scholar
Kuz'menkov, L.S. & Andreev, P.A. 2012 Microscopic classic hydrodynamic and methods of averaging. Presented in PIERS Proceedings, p. 158, August 19–23, Moscow.Google Scholar
Landau, L. & Lifshitz, E.M. 1980 Statistical Physics, Part II. Pergamon.Google Scholar
Lazarovici, D. & Pickl, P. 2017 A mean field limit for the Vlasov–Poisson system. Arch. Rat. Mech. Anal. 225, 1201.CrossRefGoogle Scholar
Li, Q., Hwang, E.H. & Sarma, S.D. 2011 Collective modes of monolayer, bilayer, and multilayer fermionic dipolar liquid. Phys. Rev. B 82, 235126.CrossRefGoogle Scholar
Mahajan, S.M. & Hazeltine, R.D. 2002 Fluid description of a magnetized plasma. Phys. Plasmas 9, 1882.CrossRefGoogle Scholar
Mahajan, S.M. & Yoshida, Z. 2011 Relativistic generation of vortex and magnetic field. Phys. Plasmas 18, 055701.CrossRefGoogle Scholar
Melrose, D.B. (Ed.) 2008 Quantum Plasmadynamics. Volume 735 of Lecture Notes in Physics. Springer Verlag.CrossRefGoogle Scholar
Melrose, D.B. & Weise, J.I. 2009 Response of a relativistic quantum magnetized electron gas. J. Phys. A 42, H5502.CrossRefGoogle Scholar
Melrose, D.B. & Weise, J.I. 2012 Spin-dependent relativistic quantum magnetized electron gas. J. Phys. A 45, 5501.CrossRefGoogle Scholar
Mendonca, J.T. 2011 Wave kinetics of relativistic quantum plasmas. Phys. Plasmas 18, 062101.CrossRefGoogle Scholar
Orlov, Y.N. & Pavlotsky, I.P. 1989 The equations of weakly-relativistic inviscid hydrodynamics. Matem. Mod. 1, 31.Google Scholar
Pavlotskii, I.P. 1973 An example of weak relativistic kinetic equation taking account of the interaction delay. Dokl. Akad. Nauk USSR 213, 812.Google Scholar
Rohrlich, F. 1990 Classical Charged Particles. Addison Wesley.Google Scholar
Romatschke, P. 2010 New developments in relativistic viscous hydrodynamics. Intl J. Mod. Phys. E 19, 1.CrossRefGoogle Scholar
Ruiz, D.E. & Dodin, I.Y. 2015 First-principle variational formulation of polarization effects in geometrical optics. Phys. Rev. A 92, 043805.CrossRefGoogle Scholar
Serfaty, S. 2020 Mean field limit for coulomb-type flows. Duke Math. J. 169, 2887.CrossRefGoogle Scholar
Shatashvili, N.L., Javakhishvili, J.I. & Kaya, H. 1997 Nonlinear wave dynamics in two-temperature electron-positron-ion plasma. Astrophys. Space Sci. 250, 109.CrossRefGoogle Scholar
Shatashvili, N.L., Mahajan, S.M. & Berezhiani, V.I. 2020 Nonlinear coupling of electromagnetic and electron acoustic waves in multi-species degenerate astrophysical plasma. Phys. Plasmas 27, 012903.CrossRefGoogle Scholar
Shatashvili, N.L. & Rao, N.N. 1999 Localized nonlinear structures of intense electromagnetic waves in two-electrontemperature electron–positron–ion plasmas. Phys. Plasmas 6, 66.CrossRefGoogle Scholar
Spohn, H. 1991 Large Scale Dynamics of Interacting Particles. Springer.CrossRefGoogle Scholar
Spohn, H. 2004 Dynamics of Charged Particles and their Radiation Fields. Cambridge University Press.CrossRefGoogle Scholar
Vlasov, A.A. 1938 J. Expl Theor. Phys. 8, 291; Vlasov, A.A. 1968 The vibrational properties of an electron gas. Sov. Phys. Uspekhi 10, 721.Google Scholar
Weinberg, S. 1972 Gravitation and Cosmology. John Wiley and Sons, Inc.Google Scholar
Zaslavskii, G.M. 1966 An asymptotic method for studying nonequilibrium systems. J. Appl. Mech. Tech. Phys. 7 (2), 33.CrossRefGoogle Scholar
Zhu, J. & Ji, P. 2012 Dispersion relation and Landau damping of waves in high-energy density plasmas. Plasma Phys. Control. Fusion 54, 065004.CrossRefGoogle Scholar