Nonlinear dynamics of kinetic fluctuations and quasi-linear relaxation in plasma

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dc.citation.epage434
dc.citation.issue2
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage421
dc.contributor.affiliationІнститут теоретичної фізики ім. О. І. АхІєзера ННЦ Харківський фізико-технічний інститут
dc.contributor.affiliationНаціональний університет «Львівська політехніка»
dc.contributor.affiliationAkhiezer Institute for Theoretical Physics, NSC Kharkiv Institute of Physics and Technology
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.authorСлюсаренко, Ю. В.
dc.contributor.authorРижа, І. А.
dc.contributor.authorКірдін, А. І.
dc.contributor.authorSlyusarenko, Yu. V.
dc.contributor.authorRyzha, I. A.
dc.contributor.authorKirdin, A. I.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-04T10:28:08Z
dc.date.created2023-02-28
dc.date.issued2023-02-28
dc.description.abstractЗапропоновано наближення парних кореляцій для розв’язку рівнянь кінетичної теорії довгохвильових (або крупномасштабних) флуктуацій у газоподібних середовищах. Базовими є загальні нелінійні рівняння теорії крупномасштабних флуктуацій на кінетичному етапі еволюції системи, виведені із перших принципів статистичної механіки. Показано, що виходячи з рівнянь кінетики довгохвильових флуктуацій у разі слабкої взаємодії між частинками, у наближенні парних флуктуацій можна відтворити основні результати квазілінійної теорії плазми. Тим самим відомій квазілінійній теорії плазми надається першопринципове обґрунтування.
dc.description.abstractWe propose an approximation of pair correlations for solving the equations of the kinetic theory of long-wave (or large-scale) fluctuations in gaseous media. The basic ones are the general nonlinear equations of the large-scale fluctuations theory at the kinetic stage of system evolution, derived from the first principles of statistical mechanics. We show that based on the equations of the long-wave fluctuations kinetics in the case of weak nteraction between particles, in the approximation of pair fluctuations it is possible to reproduce the main results of the quasi-linear theory of plasma. Thus, the well-known quasi-linear theory of plasma is provided with a first-principle justification.
dc.format.extent421-434
dc.format.pages14
dc.identifier.citationSlyusarenko Yu. V. Nonlinear dynamics of kinetic fluctuations and quasi-linear relaxation in plasma / Yu. V. Slyusarenko, I. A. Ryzha, A. I. Kirdin // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 2. — P. 421–434.
dc.identifier.citationenSlyusarenko Yu. V. Nonlinear dynamics of kinetic fluctuations and quasi-linear relaxation in plasma / Yu. V. Slyusarenko, I. A. Ryzha, A. I. Kirdin // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 2. — P. 421–434.
dc.identifier.doi10.23939/mmc2023.02.421
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/63404
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 2 (10), 2023
dc.relation.ispartofMathematical Modeling and Computing, 2 (10), 2023
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dc.relation.references[7] Zubarev D. N., Morozov V. G. Statistical mechanics of nonlinear hydrodynamic fluctuations. Physica A. 120 (3), 411–467 (1983).
dc.relation.references[8] Peletminsky S., Slusarenko Y. On theory of long wave nonequilibrium fluctuations. Physica A. 210 (1–2), 165–204 (1994).
dc.relation.references[9] Peletminsky S., Slusarenko Y., Sokolovsky A. Kinetics and hydrodynamics of long-wave fluctuations under external random force. Physica A. 326 (3–4), 412–429 (2003).
dc.relation.references[10] Sliusarenko O. Yu., Slyusarenko Yu. V. Reduced description method in the kinetic theory of Brownian motion with active fluctuations. Journal of Physics A: Mathematical and Theoretical. 52, 445001 (2019).
dc.relation.references[11] Nikolayenko S. O., Slyusarenko Yu. V. Theory of macroscopic fluctuations in systems of particles, interacting with hydrodynamic and gaslike media. Journal of Mathematical Physics. 51 (11), 113301 (2010).
dc.relation.references[12] Silin V. P. Introduction to the kinetic theory of gases. Moscow, Science (1971), (in Russian).
dc.relation.references[13] Ecker G. Theory of Fully Ionized Plasmas. Academic Press, New York and London (1972).
dc.relation.references[14] Slyusarenko Yu. V., Sliusarenko O. Yu. Kinetic theory of weakly ionized dilute gas of hydrogen-like atoms of the first principles of quantum statistics and dispersion laws of eigenwaves. Journal of Mathematical Physics. 58 (11), 113302 (2017).
dc.relation.references[15] Vedenov A. A. Quasi-linear plasma theory (theory of a weakly turbulent plasma). Journal of Nuclear Energy. Part C, Plasma Physics, Accelerators, Thermonuclear Research. 5 (3), 169 (1963).
dc.relation.references[16] Akhiezer A. I., Akhiezer I. A., Polovin R. V., Sitenko A. G., Stepanov K. N. Plasma Electrodynamics. Volume 1: Linear Theory. Volume 68 in International Series of Monographs in Natural Philosophy. Pergamon Press, Oxford, New York (1975).
dc.relation.references[17] Akhiezer A. I., Akhiezer I. A., Polovin R. V., Sitenko A. G., Stepanov K. N. Plasma Electrodynamics. Volume 2: Non-Linear Theory and Fluctuations. Volume 69 in International Series of Monographs in Natural Philosophy. Pergamon Press, Oxford, New York (1975).
dc.relation.references[18] Besse N., Elskens Y., Escande D., Bertrand P. Validity of quasilinear theory: refutations and new numerical confirmation. Plasma Physics and Controlled Fusion. 53 (2), 025012 (2011).
dc.relation.references[19] Ledenev V. G., Starygin A. P. Quasilinear relaxation of a low-density electron beam in a plasma. Plasma Physics Reports. 29, 300–306 (2003).
dc.relation.references[20] Hellinger P., Tr´avn´ıˇcek P. M. On the quasi-linear diffusion in collisionless plasmas (to say nothing about Landau damping). Physics of Plasmas. 19 (6), 062307 (2012).
dc.relation.references[21] Jeong S. Y., Verscharen D., Wicks R. T., Fazakerley A. N. A Quasi-linear Diffusion Model for Resonant Wave-Particle Instability in Homogeneous Plasma. The Astrophysical Journal. 902 (2), 128 (2020).
dc.relation.references[22] Brizard A. J., Chan A. A. Hamiltonian formulations of quasilinear theory for magnetized plasmas. Frontiers in Astronomy and Space Sciences. 9, 1010133 (2022).
dc.relation.referencesen[1] Akhiezer A. I., Peletminskii S. V. Methods of Statistical Physics. Pergamon, Oxford (1981).
dc.relation.referencesen[2] Bogolyubov N. Problems of Dynamical Theory in Statistical Physics. Providence College, Providence, RI (1959).
dc.relation.referencesen[3] Huang K. Statistical Mechanics. John Wiley & Sons, Inc., New York – London (1963).
dc.relation.referencesen[4] Alder B. J., Wainwright T. E. Decay of Velocity Autocorrelation Functions. Physical Review A. 1 (1), 18–21 (1970).
dc.relation.referencesen[5] Dorfman J. R., Cohen E. G. D. Velocity Correlation Function in Two and Three Dimensions. Physical Review Letters. 25 (18), 1257–1260 (1970).
dc.relation.referencesen[6] Ernst M. H., Hauge E. N., van Leewen J. M. Asymptotic Time Behaviour of Correlation Functions. Physical Review Letters. 25, 1254–1256 (1970).
dc.relation.referencesen[7] Zubarev D. N., Morozov V. G. Statistical mechanics of nonlinear hydrodynamic fluctuations. Physica A. 120 (3), 411–467 (1983).
dc.relation.referencesen[8] Peletminsky S., Slusarenko Y. On theory of long wave nonequilibrium fluctuations. Physica A. 210 (1–2), 165–204 (1994).
dc.relation.referencesen[9] Peletminsky S., Slusarenko Y., Sokolovsky A. Kinetics and hydrodynamics of long-wave fluctuations under external random force. Physica A. 326 (3–4), 412–429 (2003).
dc.relation.referencesen[10] Sliusarenko O. Yu., Slyusarenko Yu. V. Reduced description method in the kinetic theory of Brownian motion with active fluctuations. Journal of Physics A: Mathematical and Theoretical. 52, 445001 (2019).
dc.relation.referencesen[11] Nikolayenko S. O., Slyusarenko Yu. V. Theory of macroscopic fluctuations in systems of particles, interacting with hydrodynamic and gaslike media. Journal of Mathematical Physics. 51 (11), 113301 (2010).
dc.relation.referencesen[12] Silin V. P. Introduction to the kinetic theory of gases. Moscow, Science (1971), (in Russian).
dc.relation.referencesen[13] Ecker G. Theory of Fully Ionized Plasmas. Academic Press, New York and London (1972).
dc.relation.referencesen[14] Slyusarenko Yu. V., Sliusarenko O. Yu. Kinetic theory of weakly ionized dilute gas of hydrogen-like atoms of the first principles of quantum statistics and dispersion laws of eigenwaves. Journal of Mathematical Physics. 58 (11), 113302 (2017).
dc.relation.referencesen[15] Vedenov A. A. Quasi-linear plasma theory (theory of a weakly turbulent plasma). Journal of Nuclear Energy. Part C, Plasma Physics, Accelerators, Thermonuclear Research. 5 (3), 169 (1963).
dc.relation.referencesen[16] Akhiezer A. I., Akhiezer I. A., Polovin R. V., Sitenko A. G., Stepanov K. N. Plasma Electrodynamics. Volume 1: Linear Theory. Volume 68 in International Series of Monographs in Natural Philosophy. Pergamon Press, Oxford, New York (1975).
dc.relation.referencesen[17] Akhiezer A. I., Akhiezer I. A., Polovin R. V., Sitenko A. G., Stepanov K. N. Plasma Electrodynamics. Volume 2: Non-Linear Theory and Fluctuations. Volume 69 in International Series of Monographs in Natural Philosophy. Pergamon Press, Oxford, New York (1975).
dc.relation.referencesen[18] Besse N., Elskens Y., Escande D., Bertrand P. Validity of quasilinear theory: refutations and new numerical confirmation. Plasma Physics and Controlled Fusion. 53 (2), 025012 (2011).
dc.relation.referencesen[19] Ledenev V. G., Starygin A. P. Quasilinear relaxation of a low-density electron beam in a plasma. Plasma Physics Reports. 29, 300–306 (2003).
dc.relation.referencesen[20] Hellinger P., Tr´avn´ıˇcek P. M. On the quasi-linear diffusion in collisionless plasmas (to say nothing about Landau damping). Physics of Plasmas. 19 (6), 062307 (2012).
dc.relation.referencesen[21] Jeong S. Y., Verscharen D., Wicks R. T., Fazakerley A. N. A Quasi-linear Diffusion Model for Resonant Wave-Particle Instability in Homogeneous Plasma. The Astrophysical Journal. 902 (2), 128 (2020).
dc.relation.referencesen[22] Brizard A. J., Chan A. A. Hamiltonian formulations of quasilinear theory for magnetized plasmas. Frontiers in Astronomy and Space Sciences. 9, 1010133 (2022).
dc.rights.holder© Національний університет “Львівська політехніка”, 2023
dc.subjectфункція розподілу
dc.subjectкореляційні функції
dc.subjectдовгохвильові флуктуації
dc.subjectкінетична теорія флуктуацій
dc.subjectрівняння нелінійної динаміки
dc.subjectнаближення парних кореляцій
dc.subjectквазілінійна релаксація в плазмі
dc.subjectdistribution function
dc.subjectcorrelation functions
dc.subjectlong-wave fluctuations
dc.subjectkinetic theory of fluctuations
dc.subjectnonlinear dynamic equations
dc.subjectapproximation of pair correlations
dc.subjectquasi-linear relaxation in plasma
dc.titleNonlinear dynamics of kinetic fluctuations and quasi-linear relaxation in plasma
dc.title.alternativeНелінійна динаміка кінетичних флуктуацій та квазілінійна релаксація в плазмі
dc.typeArticle

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Mathematical Modeling And Computing. – 2023. – Vol. 10, No. 2