We obtain an approximate analytical solution for the initial problem of quasi-linear relaxation of the synchrotron instability in a cold plasma for the case of a quasi-isotropic monoenergetic initial distribution of relativistic electrons and low initial radiation energy density. The key parameters of the analytical solution coincide with the results of the numerical calculation with 20% accuracy.
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M.Wang, A.K.Ganguly, and J. L.Hirshfield, Phys. Rev. Lett., 87, No. 15, 158301 (2001).
U. Arp, G.T.Fraser, A.R.Hight Walker, et al., Phys. Rev. Spec. Top. Accel. Beams, 4, No. 5, 054401 (2001).
J. M. Byrd, W.P. Leemans, A. Loftsdottir, et al., Phys. Rev. Lett., 89, No. 22, 224801 (2002).
J. L. Hirshfield and G. S.Park, Int. J. Infrared and Millimeter Waves, 12, No. 3, 275 (1991).
G. Stupakov and S.Heifets, Phys. Rev. Spec. Top. Accel. Beams, 5, No. 5, 054402 (2002).
J. S.Nodvick and D. S. Saxon, Phys. Rev., 96, 180 (1954).
M.Venturini, R.Warnock, R. Ruth, and J. A. Ellison, Phys. Rev. Spec. Top. Accel. Beams, 8, No. 1, 014202 (2005).
V. V. Zheleznyakov, Radiation in Astrophysical Plasmas, Kluwer Academic Publishers, Dordrecht (1996).
M. Spada, M. Salvati, and F.Pacini, Astrophys. J ., 511, 136 (1999).
D. B. Melrose, Publ. Astron. Soc. Australia, 19, 34 (2002).
Y. Lyubarsky, Astrophys. J ., 652, 1297 (2006).
S. D. Hyman, T. J.W. Lazio, N.E.Kassim, et al., Nature, 434, 50 (2005).
G.Bekefi, J. L.Hirshfield, and S. C.Brown, Phys. Rev., 122, No. 4, 1037 (1961).
J.P. Wild, S.F. Smerd, and A. A.Weiss, Ann. Rev. Astron. Astrophys., 1, 291 (1963).
V. V. Zheleznyakov, Zh. Éksp. Teor. Fiz ., 51, No. 2, 570 (1966).
R.McCray, Science, 154, No. 3754, 1320 (1966).
V. V. Zheleznyakov and E.V. Suvorov Sov. Phys. JETP, 27, 335 (1968).
Ya. L.Bogomolov, V. L.Bratman, and N. S. Ginzburg, Sov. J. Plasma Phys., 13, No. 11, 810 (1987).
V. V. Zheleznyakov and S.A.Koryagin, Radiophys. Quantum Electron., 49, No. 11, 872 (2006).
V. V. Zheleznyakov and S.A.Koryagin, Radiophys. Quantum Electron., 49, No. 12, 968 (2006).
A.R.Crusius-Wätzel, Astrophys. J ., 368, No. 2, 390 (1991).
R. M.Corless, G. H. Gonnet, D. E. G. Hare, et al., Adv. Comp. Math., 5, 329 (1996).
M.Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, National Bureau of Standards, Washington (1970).
A.P. Prudnikov, Yu.A.Brychkov, and O. I.Marichev, Integrals and Series, Vol. 2: Special Functions, Gordon and Breach, New York (1986).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 52, Nos. 5–6, pp. 455–464, May–June 2009.
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Koryagin, S.A. Approximate analytical solution for quasi-linear equations of synchrotron instability. Radiophys Quantum El 52, 413 (2009). https://doi.org/10.1007/s11141-009-9146-7
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DOI: https://doi.org/10.1007/s11141-009-9146-7