Solar-Terrestrial Physics Solar-Terrestrial Physics Solar-Terrestrial Physics 2500-0535 19709 10.12737/stp-34201704 Results of current research Results of current research Results of current research Sky-distribution of intensity of synchrotron radio emission of relativistic electrons trapped in Earth’s magnetic field Sky-distribution of intensity of synchrotron radio emission of relativistic electrons trapped in Earth’s magnetic field Клименко Владимир Васильевич Klimenko Vladimir Vasilyevich klimenko@appl.sci-nnov.ru

кандидат физико-математических наук;

candidate of physical and mathematical sciences;

 Институт прикладной физики РАН Нижний Новгород Россия Institute of Applied Physics RAS Nyzhny Novgorod Russian Federation 3 4 32 43 https://zh-szf.ru/en/nauka/article/19709/view

This paper presents the calculations of synchrotron radio emission intensity from Van Allen belts with Gaussian space distribution of electron density across L-shells of a dipole magnetic field, and with Maxwell’s relativistic electron energy distribution. The results of these calculations come to a good agreement with measurements of the synchrotron emission intensity of the artificial radiation belt’s electrons during the Starfish nuclear test. We have obtained two-dimensional distributions of radio brightness in azimuth — zenith angle coordinates for an observer on Earth’s surface. The westside and eastside intensity maxima exceed several times the maximum level of emission in the meridian plane. We have also constructed two-dimensional distributions of the radio emission intensity in decibels related to the background galactic radio noise level. Isotropic fluxes of relativistic electrons (E~1 MeV) should be more than 107 cm–2s–1 for the synchrotron emission intensity in the meridian plane to exceed the cosmic noise level by 0.1 dB (riometer sensitivity threshold).

This paper presents the calculations of synchrotron radio emission intensity from Van Allen belts with Gaussian space distribution of electron density across L-shells of a dipole magnetic field, and with Maxwell’s relativistic electron energy distribution. The results of these calculations come to a good agreement with measurements of the synchrotron emission intensity of the artificial radiation belt’s electrons during the Starfish nuclear test. We have obtained two-dimensional distributions of radio brightness in azimuth — zenith angle coordinates for an observer on Earth’s surface. The westside and eastside intensity maxima exceed several times the maximum level of emission in the meridian plane. We have also constructed two-dimensional distributions of the radio emission intensity in decibels related to the background galactic radio noise level. Isotropic fluxes of relativistic electrons (E ~ 1 MeV) should be more than 107 cm–2s–1 for the synchrotron emission intensity in the meridian plane to exceed the cosmic noise level by 0.1 dB (riometer sensitivity threshold).

 synchrotron radio emission relativistic electrons radiation belt dipole magnetic field synchrotron radio emission relativistic electrons radiation belt dipole magnetic field

Allen C.W. Astrofizicheskie velichiny [Astrophysical quantities]. Moscow: Mir Publ., 1977. 448 p. (In Russian). English edition: Allen C.W. Astrophysical quantities. University of London. The Athlon Press. 1973. 448 p. Allen C.W. Astrofizicheskie velichiny [Astrophysical quantities]. Moscow: Mir Publ., 1977. 448 p. (In Russian). English edition: Allen C.W. Astrophysical quantities. University of London. The Athlon Press. 1973. 448 p. Astronomicheskii kalendar. Postoyannaya chast. [Astronomical Calendar. Basic Part]. Moscow: Nauka Publ., 1981. 704 p. (In Russian) Astronomicheskii kalendar. Postoyannaya chast. [Astronomical Calendar. Basic Part]. Moscow: Nauka Publ., 1981. 704 p. (In Russian) Borovsky J.E., Cayton T.E., Denton M.H., Belian R.D., Christensen R.A., Ingraham J.C. The proton and electron radiation belts at geosynchronous orbit: Statistics and behavior during high-speed stream-driven storms. J. Geophys. Res.: Space Phys. 2016, vol. 121, pp. 5449-5488. Borovsky J.E., Cayton T.E., Denton M.H., Belian R.D., Christensen R.A., Ingraham J.C. The proton and electron radiation belts at geosynchronous orbit: Statistics and behavior during high-speed stream-driven storms. J. Geophys. Res.: Space Phys. 2016, vol. 121, pp. 5449-5488. Chivers H.J.A., Wells H.W. Observations of unusual radiofrequency noise emission and absorption at 80 Mc/s. J. Atmosph. Terr. Phys. 1959, vol. 17, pp. 13-19. Chivers H.J.A., Wells H.W. Observations of unusual radiofrequency noise emission and absorption at 80 Mc/s. J. Atmosph. Terr. Phys. 1959, vol. 17, pp. 13-19. Detrick D.L., Rosenberg T.J. A phased-array radiowave imager for studies of cosmic noise absorption. Radio Sci. 1990, vol. 25, no. 4, pp. 325-338. Detrick D.L., Rosenberg T.J. A phased-array radiowave imager for studies of cosmic noise absorption. Radio Sci. 1990, vol. 25, no. 4, pp. 325-338. Driatskii V.M. Priroda anomalnogo pogloshcheniya kosmicheskogo radioizlucheniya v nizhnei ionosfere vysokikh shirot [The Nature of Anomalous Cosmic Radio Noise Absorption in the Lower Ionosphere of High Latitudes]. Leningrad: Gydrometeoizdat Publ., 1974. 224 p. (In Russian). Driatskii V.M. Priroda anomalnogo pogloshcheniya kosmicheskogo radioizlucheniya v nizhnei ionosfere vysokikh shirot [The Nature of Anomalous Cosmic Radio Noise Absorption in the Lower Ionosphere of High Latitudes]. Leningrad: Gydrometeoizdat Publ., 1974. 224 p. (In Russian). Dyce R.B., Horowitz S. Measurements of synchrotron radiation at central Pacific sites. J. Geophys. Res. 1963, vol. 68, no. 3, pp. 713-721. DOI: 10.1029/JZ068i003p00713. Dyce R.B., Horowitz S. Measurements of synchrotron radiation at central Pacific sites. J. Geophys. Res. 1963, vol. 68, no. 3, pp. 713-721. DOI: 10.1029/JZ068i003p00713. Dyce R.B., Nakada M.R. On the possibility of detecting synchrotron radiation from electrons in the Van Allen belts. J. Geophys. Res. 1959, vol. 64, no. 9, pp. 1163-1168. Dyce R.B., Nakada M.R. On the possibility of detecting synchrotron radiation from electrons in the Van Allen belts. J. Geophys. Res. 1959, vol. 64, no. 9, pp. 1163-1168. Egan R.D., Peterson A.M. Auroral noise at HF. J. Geophys. Res. 1960, vol. 65, no. 11, p. 3830. Egan R.D., Peterson A.M. Auroral noise at HF. J. Geophys. Res. 1960, vol. 65, no. 11, p. 3830. Ellyett C.D. Radio noise of auroral origin. J. Atmosph. Terr. Phys. 1969, vol. 31, pp. 671-682. Ellyett C.D. Radio noise of auroral origin. J. Atmosph. Terr. Phys. 1969, vol. 31, pp. 671-682. Friedel R.H.W., Reeves G.D., Obara T. Relativistic electron dynamics in the inner magnetosphere - A review. J. Atmos. Solar-Terr. Phys. 2002, vol. 64, no. 1, pp. 57-72. Friedel R.H.W., Reeves G.D., Obara T. Relativistic electron dynamics in the inner magnetosphere - A review. J. Atmos. Solar-Terr. Phys. 2002, vol. 64, no. 1, pp. 57-72. Eriksen G., Harang L. Radio noise from the ionosphere on 225 MHz during a great ionosphere disturbance. Phys. Norveg. 1969, vol. 4, no. 1, pp. 1-4. Eriksen G., Harang L. Radio noise from the ionosphere on 225 MHz during a great ionosphere disturbance. Phys. Norveg. 1969, vol. 4, no. 1, pp. 1-4. Ginzburg V.L., Syrovatsky S.I. Cosmic synchrotron radiation. Uspehi fizicheskikh nauk [Physics-Uspekhi (Adv. Phys. Sci.)] 1965, vol. 87, no. 1, pp. 65-111. (In Russian). Ginzburg V.L., Syrovatsky S.I. Cosmic synchrotron radiation. Uspehi fizicheskikh nauk [Physics-Uspekhi (Adv. Phys. Sci.)] 1965, vol. 87, no. 1, pp. 65-111. (In Russian). Hess W.N. The artificial radiation belt made on July 9, 1962. J. Geophys. Res. 1963, vol. 68, no. 3, pp. 667-683. DOI: 10.1029/JZ068i003p00667. Hess W.N. The artificial radiation belt made on July 9, 1962. J. Geophys. Res. 1963, vol. 68, no. 3, pp. 667-683. DOI: 10.1029/JZ068i003p00667. Korchak A.A. On the synchrotron radiation of charged particles in the dipole magnetic field. I. Astronomicheskii Zhurnal [Astronomy Reports]. 1963, vol. 40, pp. 994-1006. (In Russian). Korchak A.A. On the synchrotron radiation of charged particles in the dipole magnetic field. I. Astronomicheskii Zhurnal [Astronomy Reports]. 1963, vol. 40, pp. 994-1006. (In Russian). Kraus J.D. Radioastronomiya [Radio Astronomy]. Moscow: Sovetskoe Radio Publ., 1973. 456 p. (In Russian). English edition: Kraus J.D. Radio Astronomy. McGraw-Hill Book Company. New York, St. Louis, San Francisco, Toronto, London, Sydney, 1966. Kraus J.D. Radioastronomiya [Radio Astronomy]. Moscow: Sovetskoe Radio Publ., 1973. 456 p. (In Russian). English edition: Kraus J.D. Radio Astronomy. McGraw-Hill Book Company. New York, St. Louis, San Francisco, Toronto, London, Sydney, 1966. Little C.G., Leinbach H. Some measurements of high-latitude ionospheric absorption using extraterrestrial radio waves. Proc. IRE. 1958, vol. 46, no. 1, pp. 334-348. Little C.G., Leinbach H. Some measurements of high-latitude ionospheric absorption using extraterrestrial radio waves. Proc. IRE. 1958, vol. 46, no. 1, pp. 334-348. Ochs G.R., Farley Jr. D.T., Bowles K.L., Bandyopadhay P. Observations of synchrotron radio noise at the magnetic equator following the high-altitude nuclear explosion of July 9, 1962. J. Geophys. Res. 1963, vol. 68, no. 3, pp. 701-711. DOI: 10.1029/JZ068i003p00701. Ochs G.R., Farley Jr. D.T., Bowles K.L., Bandyopadhay P. Observations of synchrotron radio noise at the magnetic equator following the high-altitude nuclear explosion of July 9, 1962. J. Geophys. Res. 1963, vol. 68, no. 3, pp. 701-711. DOI: 10.1029/JZ068i003p00701. Owens H.D., Frank L.A. Electron omnidirectional intensity contours in the Earth`s outer radiation zone at the magnetic equator. J. Geophys. Res. 1968, vol. 73, no. 1, pp. 199-208. DOI: 10.1029/JA073i001p00199. Owens H.D., Frank L.A. Electron omnidirectional intensity contours in the Earth`s outer radiation zone at the magnetic equator. J. Geophys. Res. 1968, vol. 73, no. 1, pp. 199-208. DOI: 10.1029/JA073i001p00199. Pakholchik A.G. Radioastrofizika [Radio Astrophysics]. Moscow: Mir Publ., 1973. 252 p. (In Russian). English Edition: Pacholczyk A.G. Radio Astrophysics. W.H. Freeman & Company. San Fracisco, 1970. Pakholchik A.G. Radioastrofizika [Radio Astrophysics]. Moscow: Mir Publ., 1973. 252 p. (In Russian). English Edition: Pacholczyk A.G. Radio Astrophysics. W.H. Freeman & Company. San Fracisco, 1970. Peterson A.M., Hower G.L. Synchrotron radiation from high-energy electrons. J. Geophys. Res. 1963, vol. 68, no. 3, pp. 723-734. DOI: 10.1029/JZ068i003p00713. Peterson A.M., Hower G.L. Synchrotron radiation from high-energy electrons. J. Geophys. Res. 1963, vol. 68, no. 3, pp. 723-734. DOI: 10.1029/JZ068i003p00713. Potapov A.S. Relativistic electrons of the outer radiation belt and methods of their forecast (review). Solar-Terr. Phys. 2017, vol. 3, no. 1, pp. 57-72. Potapov A.S. Relativistic electrons of the outer radiation belt and methods of their forecast (review). Solar-Terr. Phys. 2017, vol. 3, no. 1, pp. 57-72. Romanova N.V. et al. Statistical correlation of the rate of failures on synchronous satellites with fluxes of energetic electrons and protons. Cosmic Res. 2005, vol. 43, no. 3, pp. 179-185. Romanova N.V. et al. Statistical correlation of the rate of failures on synchronous satellites with fluxes of energetic electrons and protons. Cosmic Res. 2005, vol. 43, no. 3, pp. 179-185. Savenko I.A., Senchuro I.N., Shavrin P.I. On maximal electron fluxes with E>1 MeV energy in the Earth’s outer radiation belt on 1958-1971. Kosmicheskiye issledovaniya [Cosmic Res.]. 1979, vol. 17, no. 1, pp. 141-145. (In Russian). Savenko I.A., Senchuro I.N., Shavrin P.I. On maximal electron fluxes with E>1 MeV energy in the Earth’s outer radiation belt on 1958-1971. Kosmicheskiye issledovaniya [Cosmic Res.]. 1979, vol. 17, no. 1, pp. 141-145. (In Russian). Thorne R.M., Andreoli L.J. Polyarnaya verkhnyaya atmosfera [Polar Upper Atmosphere]. Moscow: Mir Publ., 1983, pp. 367-379. (In Russian). English Edition: Thorne R.M., Andreoli L.J. Mechanism of the relativistic electron intensive precipitation. Exploration of the Polar Upper Atmosphere. Proc. of the NATO Adv. Study Inst. held at Lillehammer, Norway, May 5-16, 1980. Eds. C.S. Deer, J.A. Holtet. D. Reidel. Publ. Comp. Dordrecht - Boston - London, 1980. Thorne R.M., Andreoli L.J. Polyarnaya verkhnyaya atmosfera [Polar Upper Atmosphere]. Moscow: Mir Publ., 1983, pp. 367-379. (In Russian). English Edition: Thorne R.M., Andreoli L.J. Mechanism of the relativistic electron intensive precipitation. Exploration of the Polar Upper Atmosphere. Proc. of the NATO Adv. Study Inst. held at Lillehammer, Norway, May 5-16, 1980. Eds. C.S. Deer, J.A. Holtet. D. Reidel. Publ. Comp. Dordrecht - Boston - London, 1980. Trubnikov B.A. Radiation of plasma in magnetic field. Doklady Akademii nauk [Doklady Physics]. 1958, vol. 118, no. 5, pp. 913-916. (In Russian). Trubnikov B.A. Radiation of plasma in magnetic field. Doklady Akademii nauk [Doklady Physics]. 1958, vol. 118, no. 5, pp. 913-916. (In Russian). Van Allen J.A., Frank L.A., O’Brien B.J. Satellite observations of the artificial radiation belt of July 1962. J. Geophys. Res. 1963, vol. 68, no. 3, pp. 619-627. DOI: 10.1029/ JZ068i003p00619. Van Allen J.A., Frank L.A., O’Brien B.J. Satellite observations of the artificial radiation belt of July 1962. J. Geophys. Res. 1963, vol. 68, no. 3, pp. 619-627. DOI: 10.1029/ JZ068i003p00619. Vernov S.N., Gorchakov E.V., Kuznetsov S.N. et al. The particle fluxes in the outer magnetic field. Fizika magnitosfery [Magnetospheric Phys.]. Eds. D.J. Williams, G.D. Mead. Moscow: Mir Publ., 1972, pp. 318-344. (In Russian). Vernov S.N., Gorchakov E.V., Kuznetsov S.N. et al. The particle fluxes in the outer magnetic field. Fizika magnitosfery [Magnetospheric Phys.]. Eds. D.J. Williams, G.D. Mead. Moscow: Mir Publ., 1972, pp. 318-344. (In Russian). Vesecky J.F., Peterson A.M. Radio frequency synchrotron radiation from the Van Allen belts. J. Geophys. Res. 1967, vol. 72, no. 5, pp. 1647-1650. Vesecky J.F., Peterson A.M. Radio frequency synchrotron radiation from the Van Allen belts. J. Geophys. Res. 1967, vol. 72, no. 5, pp. 1647-1650. Yetes K.W., Wielebinski R. Observational results of radio sky spectrum. Astrophys. J. 1967, vol. 149, pp. 439-440. Yetes K.W., Wielebinski R. Observational results of radio sky spectrum. Astrophys. J. 1967, vol. 149, pp. 439-440.