Geodesic
Dispersion relation in the kinetic model of collisionless plasma
Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 3, pp. 442-454 Cet article a éte moissonné depuis la source Math-Net.Ru

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For the Vlasov equation with a self-consistent field, a connection is established between the dispersion relation and the Schur algebraic complement of the generator of the corresponding dynamical system. An estimate of the instability index is obtained in terms of the Hankel transform of the background distribution of electrons, the sign of which is determined using the saddle point method.
Keywords: Vlasov equation with self-consistent field, Schur algebraic complement, instability index, saddle point method.
Mots-clés : dispersion relation 
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S. A. Stepin; A. G. Tarasov. Dispersion relation in the kinetic model of collisionless plasma. Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 3, pp. 442-454. http://geodesic.mathdoc.fr/item/TMF_2022_210_3_a8/

[1] A. A. Vlasov, “O vibratsionnykh svoistvakh elektronnogo gaza”, ZhETF, 8:3 (1938), 291–318; УФН, 93:3 (1967), 444–470 ; | DOI | DOI

[2] N. Kroll, A. Traivelpis, Osnovy fiziki plazmy, Mir, M., 1975

[3] A. A. Galeev, R. Sudan (red.), Osnovy fiziki plazmy, v. 1, Energoatomizdat, M., 1983

[4] V. V. Vedenyapin, Kineticheskie uravneniya Boltsmana i Vlasova, Fizmatlit, M., 2001

[5] V. V. Kozlov, “Obobschennoe kineticheskoe uravnenie Vlasova”, UMN, 63:4(382) (2008), 93–130 | DOI | DOI | MR | Zbl

[6] V. V. Vedenyapin, “Granichnye zadachi dlya statsionarnogo uravneniya Vlasova”, Dokl. AN SSSR, 290:4 (1986), 777–780 | MR | Zbl

[7] V. V. Vedenyapin, M. A. Negmatov, “O vyvode i klassifikatsii uravnenii tipa Vlasova i magnitnoi gidrodinamiki. Tozhdestvo Lagranzha, forma Godunova i kriticheskaya massa”, SMFN, 47 (2013), 5–17 | DOI

[8] V. E. Golant, A. P. Zhilinskii, I. E. Sakharov, Osnovy fiziki plazmy, Atomizdat, M., 1977

[9] A. A. Arsenev, Lektsii o kineticheskikh uravneniyakh, Nauka, M., 1992

[10] A. B. Mikhailovskii, Teoriya plazmennykh neustoichivostei, Atomizdat, M., 1970

[11] D. G. Lominadze, Cyclotron Waves in Plasma, Pergamon Press, New York, 1981

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

[13] A. I. Akhiezer (red.), Elektrodinamika plazmy, Nauka, M., 1974

[14] T. Stiks, Teoriya plazmennykh voln, Atomizdat, M., 1965 | MR

[15] I. B. Bernstein, J. M. Greene, M. D. Kruskal, “Exact nonlinear plasma oscillations”, Phys. Rev., 108:3 (1957), 546–551 | DOI | MR

[16] S. I. Pokhozhaev, “O statsionarnykh resheniyakh uravnenii Vlasova–Puassona”, Differ. uravneniya, 46:4 (2010), 527–534 | DOI

[17] V. V. Vedenyapin, M. A. Negmatov, N. N. Fimin, “Uravneniya tipa Vlasova i Liuvillya, ikh mikroskopicheskie, energeticheskie i gidrodinamicheskie sledstviya”, Izv. RAN. Cer. matem., 81:3 (2017), 45–82 | DOI | DOI | MR

[18] L. D. Landau, “O kolebaniyakh elektronnoi plazmy”, ZhETF, 16:7 (1946), 574–586; Собрание трудов, т. 2, Наука, М., 1969, 7–25 | MR

[19] V. P. Maslov, M. V. Fedoryuk, “Lineinaya teoriya zatukhaniya Landau”, Matem. sb., 127(169):4(8) (1985), 445–475 | DOI | MR | Zbl

[20] C. Mouhot, C. Villani, “On Landau damping”, Acta Math., 207:1 (2011), 29–201 | DOI | MR

[21] O. Penrose, “Electrostatic instabilities of a uniform non-Maxwellian plasma”, Phys. Fluids, 3:2 (1960), 258–264 | DOI

[22] A. Gurvits, R. Kurant, Teoriya funktsii, Nauka, M., 1968 | MR | Zbl

[23] M. V. Fedoryuk, Asimptotika: integraly i ryady, Nauka, M., 1987 | MR

[24] S. A. Stepin, A. G. Tarasov, “Stationary-phase method for Hankel transform of order zero”, Russ. J. Math. Phys., 26:4 (2019), 501–516 | DOI | MR

[25] A. V. Latyshev, A. A. Yushkanov, “Prodolnaya elektricheskaya provodimost v kvantovoi plazme s peremennoi chastotoi stolknovenii v ramkakh podkhoda Mermina”, TMF, 178:1 (2014), 147–160 | DOI | DOI | MR | Zbl