Abstract
An analytical solution to the nonlinear set of equations describing the electron dynamics and electric field structure in the vicinity of the critical density in a nonuniform plasma is constructed using the renormalization group approach with allowance for relativistic effects of electron motion. It is demonstrated that the obtained solution describes two regimes of plasma oscillations in the vicinity of the plasma resonance— stationary and nonstationary. For the stationary regime, the spatiotemporal and spectral characteristics of the resonantly enhanced electric field are investigated in detail and the effect of the relativistic nonlinearity on the spatial localization of the energy of the plasma relativistic field is considered. The applicability limits of the obtained solution, which are determined by the conditions of plasma wave breaking in the vicinity of the resonance, are established and analyzed in detail for typical laser and plasma parameters. The applicability limits of the earlier developed nonrelativistic theories are refined.
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References
N. G. Denisov, Sov. Phys. Sov. Phys. JETP 4, 544 (1957).
B. N. Gershman, V. L. Ginzburg, and N. G. Denisov, Usp. Fiz. Nauk 61, 561 (1957).
A. D. Piliya, Sov. Phys. Tech. Phys. 11, 609 (1966).
T. A. Davydova, Sov. J. Plasma Phys. 7, 507 (1981).
D. W. Forslund, J. M. Kindel, K. Lee, E. L. Lindman, and R. L. Morse, Phys. Rev. A 11, 679 (1975).
G. J. Pert, Plasma Phys. 20, 175 (1978).
N. S. Erokhin, V. K. Zakharov, and S. S. Moiseev, Sov. Phys. JETP 29, 101 (1969).
A. B. Vladimirskii and V. P. Silin, Sov. J. Plasma Phys. 6, 196 (1980).
N. S. Erochin, S. S. Moiseev, and V. V. Mukhin, Nucl. Fusion 14, 333 (1974).
N. P. Trotsenko, Candidate’s Dissertation in Physics and Mathematics (Moscow, 1983).
J. Albritton and P. Koch, Phys. Fluids 18, 1136 (1975).
S. V. Bulanov, L. M. Kovrizhnykh, and A. S. Sakharov, Sov. Phys. JETP 45, 949 (1977).
A. Y. Lee, Y. Nishida, N. C. Lundmann, S. P. Obenschain, B. Gu, and M. Rhodes, Phys. Rev. Lett. 48, 319 (1982).
V. F. Kovalev and V. V. Pustovalov, Teor. Mat. Fiz. 81, 69 (1989).
S. V. Bulanov, N. M. Naumova, and F. Pegoraro, Phys. Plasmas 1, 745 (1994).
S. V. Bulanov, T. Zh. Esirkepov, M. Kando, A. S. Pirozhkov, and N. N. Rozanov, Phys. Usp. 56, 429 (2013).
A. I. Akhiezer and G. Ya. Lyubarskii, Dokl. Akad. Nauk SSSR 80, 193 (1951).
J. M. Dawson, Phys. Rev. 113, 383 (1959).
T. P. Coffey, Phys. Fluids 14, 1402 (1971).
V. F. Kovalev and D. V. Shirkov, Phys. Usp. 51, 815 (2008).
M. B. Isichenko and V. V. Yan’kov, JETP Lett. 37, 351 (1983).
M. B. Isichenko and V. V. Yan’kov, Zh. Eksp. Teor. Fiz. 87, 1914 (1984) [Sov. Phys. JETP 60, 1101 (1984)].
J. F. Drake, Y. C. Lee, K. Nishikawa, and N. L. Tsintsadze, Phys. Rev. Lett. 36, 196 (1976).
W.-J. Ding, Z.-M. Sheng, J. Zhang, and M. Y. Yu, Phys. Plasmas 16, 042315 (2009).
S. V. Milyutin, A. A. Frolov, and E. V. Chizhonkov, Vychisl. Metody Program. 14, 295 (2013).
A. A. Frolov and E. V. Chizhonkov, Vychisl. Metody Program. 15, 537 (2014).
S. V. Bulanov and L. M. Kovrizhnykh, Sov. J. Plasma Phys. 2, 58 (1976).
S. K. Rajouria, K. K. Magesh Kumar, and V. K. Tripathi, Phys. Plasmas 20, 083112 (2013).
A. M. Zhuravskii, Handbook of Elliptic Functions (Izd. Akad. Nauk SSSR, Moscow, 1941) [in Russian].
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series (Nauka, Moscow, 1981; Gordon & Breach, New York, 1986), Vol. 1.
P. Appel’, Theoretical Mechanics (Fizmatlit, Moscow, 1960), Vol. 1 [in Russian].
A. A. Kharkevich, Fundamentals of Radio Engineering (Fizmatlit, Moscow, 2007) [in Russian].
V. L. Ginzburg, The Propagation of Electromagnetic Waves in Plasmas (Nauka, Moscow, 1967; Pergamon, Oxford, 1970).
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Original Russian Text © I.I. Metelskii, V.F. Kovalev, V.Yu. Bychenkov, 2017, published in Fizika Plazmy, 2017, Vol. 43, No. 2, pp. 169–186.
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Metelskii, I.I., Kovalev, V.F. & Bychenkov, V.Y. Nonlinear relativistic plasma resonance: Renormalization group approach. Plasma Phys. Rep. 43, 175–190 (2017). https://doi.org/10.1134/S1063780X1702009X
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DOI: https://doi.org/10.1134/S1063780X1702009X