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Based on the general expression for spectral-angular distribution of the radiation emitted by a charged particle moving in exterior medium, the essential role of stationary phase points in Čerenkov effect is investigated. And the stationary phase method of calculating spectral-angular distribution of Čerenkov radiation from a charged particle moving in curved path is proposed. By the stationary phase method, the asymptotic form of spectral-angular distribution of synchrotron-Čerenkov radiation is calculated, and the result indicates that the spectrum of synchrotron-Čerenkov radiation near critical angle c is quite different from that near the plane of particle's orbit.
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Keywords:
- Čerenkov effect /
- stationary phase point /
- stationary phase method /
- synchrotron-Čerenkov radiation
[1] Čerenkov P A 1934 Dold. Akad. Nauk USSR 2 451
[2] Frank I M, Tamm I E 1937 Dold. Akad. Nauk USSR 14 107
[3] Schwinger J, Tsai W Y 1976 Ann. Phys. 96 303
[4] Erber T, White D, Tsai W Y, Latal H G 1976 Ann. Phys. 102 405
[5] Rynne T M, Baumgartner G B, Erber T 1978 J. Appl. Phys. 49 2233
[6] Patro D N 1982 Phys. Rev. Lett. 49 1083
[7] Bonin K D, McDonald K T, Russell D P, Flanz J B 1986 Phys. Rev. Lett. 57 2264
[8] McDonald K T 2004 Science 303 310
[9] Konstantinovich A V, Konstantinovich I A 2008 Astropart. Phys. 30 142
[10] Saharian A A, Kotanjyan A S 2009 J. Phys. Math. Theory 42 135402
[11] Šoln J 1999 Astron. Nachr. 320 141
[12] Bender C M, Orszag S A 1999 Advanced Mathematical Methods for Scientists and Engineers (Berlin: Springer) pp276-279
[13] Jackson J D 1998 Classical Electrodynamics (3rd Ed.) (New York: Wiley) p638
[14] Lyutikov M, Machabeli G, Blandford R 1999 Astron. J. 512 804
[15] de Vries K D, van den Berg A M, Scholten O, Werner K 2011 Phys. Rev. Lett. 107 061101
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[1] Čerenkov P A 1934 Dold. Akad. Nauk USSR 2 451
[2] Frank I M, Tamm I E 1937 Dold. Akad. Nauk USSR 14 107
[3] Schwinger J, Tsai W Y 1976 Ann. Phys. 96 303
[4] Erber T, White D, Tsai W Y, Latal H G 1976 Ann. Phys. 102 405
[5] Rynne T M, Baumgartner G B, Erber T 1978 J. Appl. Phys. 49 2233
[6] Patro D N 1982 Phys. Rev. Lett. 49 1083
[7] Bonin K D, McDonald K T, Russell D P, Flanz J B 1986 Phys. Rev. Lett. 57 2264
[8] McDonald K T 2004 Science 303 310
[9] Konstantinovich A V, Konstantinovich I A 2008 Astropart. Phys. 30 142
[10] Saharian A A, Kotanjyan A S 2009 J. Phys. Math. Theory 42 135402
[11] Šoln J 1999 Astron. Nachr. 320 141
[12] Bender C M, Orszag S A 1999 Advanced Mathematical Methods for Scientists and Engineers (Berlin: Springer) pp276-279
[13] Jackson J D 1998 Classical Electrodynamics (3rd Ed.) (New York: Wiley) p638
[14] Lyutikov M, Machabeli G, Blandford R 1999 Astron. J. 512 804
[15] de Vries K D, van den Berg A M, Scholten O, Werner K 2011 Phys. Rev. Lett. 107 061101
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