Geodesic
Parametric resonance and energy transfer in dusty plasma
Matematičeskoe modelirovanie, Tome 30 (2018) no. 2, pp. 3-17.

Voir la notice de l'article provenant de la source Math-Net.Ru

Model allowing analytical and numerical studying of dusty plasma system is used to describe dynamics of monolayer of dusty particles. Mechanism of energy transfer between horizontal and vertical particles motion based on parametric resonance is described by an extended Mathieu equation. Resonance regions and growth rates of dust particles energy are obtained. Conditions of resonance occurrence and initial stage of energy transfer are described more precisely based on analysis of derived data. It is shown that a wide spectrum of dust particles oscillations participate in energy transfer. The core harmonics of energy transfer are determined.
Keywords: numerical simulations, parametric resonance, dusty plasma.
Mots-clés : Mathieu equation 
@article{MM_2018_30_2_a0,
     author = {V. P. Semyonov and A. V. Timofeev},
     title = {Parametric resonance and energy transfer in dusty plasma},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--17},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2018_30_2_a0/}
}
TY  - JOUR
AU  - V. P. Semyonov
AU  - A. V. Timofeev
TI  - Parametric resonance and energy transfer in dusty plasma
JO  - Matematičeskoe modelirovanie
PY  - 2018
SP  - 3
EP  - 17
VL  - 30
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2018_30_2_a0/
LA  - ru
ID  - MM_2018_30_2_a0
ER  - 
%0 Journal Article
%A V. P. Semyonov
%A A. V. Timofeev
%T Parametric resonance and energy transfer in dusty plasma
%J Matematičeskoe modelirovanie
%D 2018
%P 3-17
%V 30
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2018_30_2_a0/
%G ru
%F MM_2018_30_2_a0
V. P. Semyonov; A. V. Timofeev. Parametric resonance and energy transfer in dusty plasma. Matematičeskoe modelirovanie, Tome 30 (2018) no. 2, pp. 3-17. http://geodesic.mathdoc.fr/item/MM_2018_30_2_a0/

[1] Vaulina O. S., Petrov O. F., Fortov B. E., et al., Pylevaia plasma: eksperiment i teoriia, Fizmatlit, M., 2009

[2] Fortov V. E., Kharpak A. G., Kharpak S. A., Molotkov V. I., Petrov O. F., “Dusty plasmas”, Physics uspekhi, 47:5 (2004), 447–492 | DOI | DOI | MR

[3] Tsytovich V. N., Morfill G. E., Thomas H. M., Elementary Physics of Complex Plasmas, Springer, Berlin–Heidelberg, 2008, 731 pp.

[4] Schweigert V. A., Schweigert I. V., Melzer A., Homman A., Piel A., “Alignment and instability of dust crystals in plasmas”, Phys. Rev. E, 54:4 (1996), 4155 | DOI

[5] Schweigert I. V., Schweigert V. A., Bedanov V. M., Melzer A., Homann A., Piel A., “Instability and melting of a crystal of microscopic particles in a radio-frequency discharge plasma”, JETP, 87:5 (1998), 905 | DOI

[6] Vaulina O. S., Repin A. Iu., Petrov O. F., Adamovich K. G., “Kinetic temperature and charge of a dust grain in weakly ionized gas-discharge plasmas”, JETP, 102:6 (2006), 986 | DOI

[7] Samarian A. A., James B., Vladimirov S. V., Cramer N. F., “Self-excited vertical oscillations in an rf-discharge dusty plasma”, Phys. Rev. E, 64:2 (2001), 025402 | DOI

[8] Melzer A., Homann A., Piel A., “Experimental investigation of the melting transition of the plasma crystal”, Phys. Rev. E, 53:3 (1996), 2757 | DOI

[9] Nunomura S., Misawa T., Ohno N., Takamura S., “Instability of dust particles in a coulomb crystal due to delayed charging”, Phys. Rev. Lett., 83:6 (1999), 1970 | DOI

[10] Ivanov Y., Melzer A., “Melting dynamics of finite clusters in dusty plasmas”, Phys. Plasmas, 12:7 (2005), 072110 | DOI

[11] Quinn R. A., Goree J., “Experimental investigation of particle heating in a strongly coupled dusty plasma”, Phys. Plasmas, 7:10 (2000), 3904 | DOI

[12] Vaulina O. S., Samarian A. A., James B., Petrov O. F., Fortov V. E., “Analysis of macroparticle charging in the near-electrode layer of a high-frequency capacitive discharge”, JETP, 96:6 (2003), 1037 | DOI

[13] Quinn R. A., Goree J., “Single-particle Langevin model of particle temperature in dusty plasmas”, Phys. Rev. E, 61:3 (2000), 3033 | DOI

[14] Ivlev A. V., Knopka U., Morfill G. E., “Influence of charge variation on particle oscillations in the plasma sheath”, Phys. Rev. E, 62:2 (2000), 2739 | DOI | MR

[15] Norman G. E., Timofeev A. V., “Application of the notion of “temperature” for description of dust particles dynamics in a gas discharge plasma”, Doklady Physics, 57:10 (2012), 378 | DOI

[16] Timofeev A. V., “Time of relaxation in dusty plasma model”, J. Phys.: Conf. Ser., 653:1 (2015), 012137 | DOI

[17] Norman G. E., Timofeev A. V., “Kinetic temperature of dust particle motion in gas-discharge plasma”, Phys. Rev. E, 84:5 (2011), 056401 | DOI

[18] Norman G. E., Stegailov V. V., Timofeev A. V., “Anomalous kinetic energy of a system of dust particles in a gas discharge plasma”, JETP, 113:5 (2011), 887 | DOI

[19] Vaulina O. S., Lisina I. I., Lisin E. A., “Energy exchange in systems of particles with nonreciprocal interaction”, JETP, 121:4 (2015), 717 | DOI

[20] Semyonov V. P., Timofeev A. V., “The parametric resonance features for theory of energy transfer in dusty plasma”, J. Phys.: Conf. Ser., 653:1 (2015), 012138 | DOI

[21] Semyonov V. P., Timofeev A. V., “Resonance regions of extended Mathieu equation”, J. Phys.: Conf. Ser., 681:1 (2016), 012025 | DOI

[22] Couedel L., Nosenko V., Ivlev A. V., Zhdanov S. K., Thomas H. M., Morfill G. E., “Direct observation of mode-coupling instability in two-dimensional plasma crystals”, Phys. Rev. Lett., 104:19 (2010), 195001 | DOI

[23] Yaroshenko V. V., Vladimirov S. V., Morfill G. E., “Vibrations of a pair microparticles suspended in a plasma sheath”, New J. Phys., 8 (2006), 201 | DOI

[24] Ivlev A. V., Zhdanov S. K., Klumov B. A., “Generalized kinetic theory of ensembles with variable charges”, Phys. Plasmas, 12:9 (2005), 092104 | DOI | MR

[25] Momeni M., Kourakis I., Moslehi-Fard M., Shukla P. K., “A Van der Pol-Mathieu equation for the dynamics of dust grain charge in dusty plasmas”, J. Phys. A: Math. Theor., 40:24 (2007), 473 | DOI | MR

[26] Bora M. P., Sarmah D., “Oscillation death in a coupled van der Pol-Mathieu system”, Pramana J. Phys., 81:4 (2013), 677 | DOI

[27] Landau L. D., Lifshitz E. M., Theoretical Physics. Mechanics, Pergamon, London, 1959 | MR

[28] Rabinovich M. I., Trybetskoj D. I., Vvedenie v teoriiukolebanij I voln, Nauka, M., 1984, 217–229

[29] Vasilyak L. M., Fortov V. E., Morfill G. E., Ivlev A. V., Pustylnik M. Y., Polyakov D. N., Thomas H. M., Vetchinin S. P., “Increase of kinetic energy of dusty cluster particles due to parametric instability caused by nanosecond electric pulses”, Contrib. Plasma Phys., 51:6 (2011), 529 | DOI

[30] Schweigert V. A., Schweigert I. V., Nosenko V., Goree J., “Acceleration and orbits of charged particles beneath a monolayer plasma crystal”, Phys. Plasmas, 9:11 (2002), 4465 | DOI

[31] Lisina I. I., Vaulina O. S., Lisin E. A., “Theory of Heating of a Nonreciprocal System of Particles”, IEEE Trans. Plasma Sci., 44:4 (2016), 1 | DOI

[32] Vaulina O. S., Lisina I. I., Lisin E. A., “Kinetic energy in a system of particles with a nonreciprocal interaction”, EPL, 111:5 (2015), 50003 | DOI

[33] Norman G. E., Stegailov V. V., “Stochastic theory of the classical molecular dynamics method”, Math. Models Comp. Simul., 5:4 (2013), 305–333 | DOI | MR