Geodesic
Study of small perturbations of a stationary state in a model of upper hybrid plasma oscillations
Teoretičeskaâ i matematičeskaâ fizika, Tome 211 (2022) no. 2, pp. 319-332 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We show that a constant external magnetic field, generally speaking, is not able to prevent breaking (loss of smoothness) of relativistic plasma oscillations, even if these are arbitrarily small perturbations of the zero steady state. This result sharply differs from the nonrelativistic case, where the breaking of oscillations can be suppressed at any initial deviations by increasing the magnetic field strength. Nevertheless, even in the relativistic case, there are subclasses of solutions corresponding to solutions that are globally smooth in time.
Keywords: quasilinear hyperbolic system, oscillation breaking, external magnetic field.
Mots-clés : plasma oscillations, small perturbations 
@article{TMF_2022_211_2_a10,
     author = {O. S. Rozanova},
     title = {Study of small perturbations of a~stationary state in a~model of upper hybrid plasma oscillations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {319--332},
     year = {2022},
     volume = {211},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2022_211_2_a10/}
}
TY  - JOUR
AU  - O. S. Rozanova
TI  - Study of small perturbations of a stationary state in a model of upper hybrid plasma oscillations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2022
SP  - 319
EP  - 332
VL  - 211
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2022_211_2_a10/
LA  - ru
ID  - TMF_2022_211_2_a10
ER  - 
%0 Journal Article
%A O. S. Rozanova
%T Study of small perturbations of a stationary state in a model of upper hybrid plasma oscillations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2022
%P 319-332
%V 211
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2022_211_2_a10/
%G ru
%F TMF_2022_211_2_a10
O. S. Rozanova. Study of small perturbations of a stationary state in a model of upper hybrid plasma oscillations. Teoretičeskaâ i matematičeskaâ fizika, Tome 211 (2022) no. 2, pp. 319-332. http://geodesic.mathdoc.fr/item/TMF_2022_211_2_a10/

[1] A. F. Aleksandrov, L. S. Bogdankevich, A. A. Rukhadze, Osnovy elektrodinamiki plazmy, Vysshaya shkola, M., 1988 | MR

[2] V. L. Ginzburg, A. A. Rukhadze, Volny v magnitoaktivnoi plazme, Nauka, M., 1975

[3] V. P. Silin, A. A. Rukhadze, Elektromagnitnye svoistva plazmy i plazmopodobnykh sred, URSS, M., 2018

[4] E. V. Chizhonkov, Matematicheskie aspekty modelirovaniya kolebanii i kilvaternykh voln v plazme, Fizmatlit, M., 2018 | Zbl

[5] R. C. Davidson, Methods in Nonlinear Plasma Theory, Acad. Press, New York, 1972

[6] B. L. Rozhdestvenskii, N. N. Yanenko, Sistemy kvazilineinykh uravnenii i ikh prilozheniya k gazovoi dinamike, Nauka, M., 1978 | MR

[7] I. Bakholdin, A. Il'ichev, A. Zharkov, “Steady magnetoacoustic waves and decay of solitonic structures in a finite-beta plasma”, J. Plasma Phys., 67:1 (2002), 1–26 | DOI

[8] E. Esarey, C. B. Schroeder, W. P. Leemans, “Physics of laser-driven plasma-based electron accelerators”, Rev. Modern Phys., 81:3 (2009), 1229–1285 | DOI

[9] R. W. C. Davidson, P. P. J. M. Schram, “Nonlinear oscillations in a cold plasma”, Nucl. Fusion, 8:3 (1968), 183–195 | DOI

[10] M. Karmakar, C. Maity, N. Chakrabarti, “Wave-breaking amplitudes of relativistic upper-hybrid oscillations in a cold magnetized plasma”, Phys. Plasmas, 23:6 (2016), 064503 | DOI

[11] C. Maity, Lagrangian fluid technique to study nonlinear plasma dynamics, PhD Thesis, Saha Institute of Nuclear Physics, Kolkata, India, 2013

[12] C. Maity, N. Chakrabarti, S. Sengupta, “Breaking of upper hybrid oscillations in the presence of an inhomogeneous magnetic field magnetized plasma”, Phys. Rev. E, 86:1 (2012), 016408, 6 pp. | DOI

[13] C. Maity, A. Sarkar, P. K. Shukla, N. Chakrabarti, “Wave-breaking phenomena in a relativistic magnetized plasma”, Phys. Rev. Lett., 110:21 (2013), 215002, 5 pp. | DOI

[14] P. S. Verma, J. K. Soni, S. Segupta, P. K. Kaw, “Nonlinear oscillations in a cold dissipative plasma”, Phys. Plasmas, 17:4 (2010), 044503, 4 pp. | DOI

[15] C. M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, Springer, Berlin, Heidelberg, 2016 | DOI | MR

[16] O. S. Rozanova, E. V. Chizhonkov, The influence of an external magnetic field on cold plasma oscillations, arXiv: 2109.08680

[17] O. S. Rozanova, E. V. Chizhonkov, “On the conditions for the breaking of oscillations in a cold plasma”, Z. Angew. Math. Phys., 72:1 (2021), 13, 15 pp. | DOI | MR

[18] G. Beitmen, A. Eirdeii, Vysshie transtsendentnye funktsii, v. 3, Ellipticheskie i avtomorfnye funktsii. Funktsii Lame i Mate, Nauka, M., 1967 | MR | MR | Zbl