TO THE QUESTION OF CHOOSING THE MODEL OF WEAK INTERPLANETARY SCINTILLATIONS OF COSMIC SOURCES RADIOEMISSION IN RANGE FROM 8 TO 80 MHZ - Кuhai, N. V.; Kalinichenko, N. N. (Видавничий дім «Академперіодика», 2019)
PACS number: 96.50.shPurpose: An overview of the models of electromagnetic wave propagation in random media for the possibility of using them to describe the weak interplanetary scintillations of radio emission of cosmic sources in the range from 8 to80 MHz, as well as estimation of the applicability conditions of the models for this case and comparison of the scintillation spectra calculated on the basis of different models.Design/methodology/approach: literature review, analysis, mathematical calculations.Findings: On the basis of scientific publications, the problem of propagation of radio emission of cosmic sources with frequency in the range from 8 to 80 MHz in the interplanetary plasma in the weak scattering regime (large elongations) is considered. The stages of solving the problem are shown, when by taking into account some certain constraints a gradual transition from the Maxwell equations to the simpler parabolic equation is carried out. The main approximate methods of solving the parabolic equation (the Rytov method, path integral technique, the phase screen model) are considered. An estimation of the conditions for the applicability of the parabolic equation itself and theabove-mentioned methods for finding approximate solutions is made. The evaluation showed that both the parabolic equation and the above-mentioned methods for finding its approximate solutions can be used in the case of the problem of propagation of radio emission of cosmic sources with frequency in the range from 8 to 80 MHz in the interplanetary plasma in the weak scattering regime. For each method, expression for the scintillation spectrum taken from literary sources is given. By calculation it is shown that in the weak scattering regime, the Rytov method, path integral technique and the phase screen model give close scintillation spectra. A small change in the parameters of the interplanetary plasma can fit each model spectrum with the experimental one, but such variations of the model spectrum will be of the order of the error of obtaining the experimental spectrum, which, in the normal statistics of interplanetary scintillation observations in the range from 8 to 80 MHz, is 10 to 20 %.Conclusions: Three methods: the Rytov method, path integral technique, the phase screen method (with caution) can be applied to simulate the weak interplanetary scintillations of cosmic sources radio emission in the range from 8 to 80 MHz.Key words: propagation, radio emission, interplanetary scintillations, weak scattering regime, the Rytov method, path integral technique, phase screen model Manuscript submitted 01.04.2019Radio phys. radio astron. 2019, 24(2): 117-128REFERENCES1. HEWISH, A., SCOTT, P. F.and WILLS, D., 1964. Interplanetary scintillations of small diameter radio sources. Nature. vol. 203, is. 4951, pp. 1214–1217. DOI: https://doi.org/10.1038/2031214a02. RICKETT, B. J., COLES, W. A. and BOURGOIS, G., 1984. Slow scintillations in the interstellar medium. Astron. Astrophys. vol. 134, is. 2, pp. 390–395.3. COLES, W. A. and KAUFMAN, J. J., 1977. Angular size of the Crab pulsar at 74 MHz. Mon. Not. R. Astron. Soc. vol. 181, is. 1, pp. 57P–59P. DOI: https://doi.org/10.1093/mnras/181.1.57P4. LEE, L. C. and JOKIPII, J. R., 1975. Strong scintillations in astrophysics. II. A theory of temporal broadening of pulses. Astrophys. J. vol. 201, pp. 532–543. DOI:https://doi.org/10.1086/1539165. FALKOVICH, I. S., KONOVALENKO, A .A., KALINICHENKO, N. N., OLYAK, M. R., GRIDIN, A. A., BUBNOV, I. N., LECACHEUX, A. and RUCKER, H. O., 2006. Variations of parameters of solar wind stream structure outside 1 AU in 2003-2004. Radio Phys. Radio Astron. vol. 11, no. 1, pp. 31–41. (in Russian).6. FALKOVICH, I. S., KONOVALENKO, A. A., KALINICHENKO, N. N., OLYAK, M. R., GRIDIN, A. A., BUBNOV, I. N., BRAZHENKO, A. I., LECACHEUX, A. and RUCKER, H. O., 2007. First results of the dispersion analysis of the interplanetary scintillations at decameter wavelengths. Radio Phys. Radio Astron. vol. 12, no. 4, pp. 350–356. (in Russian).7. KALINICHENKO, N. N., 2009. A search for compact radio sources in supernova remnants using the interplanetary scintillation technique. Astrophys. Space Sci. vol. 319, is. 2, pp. 131–138. DOI: https://doi.org/10.1007/s10509-008-9960-y8. KONOVALENKO, A., SODIN, L., ZAKHARENKO, V., ZARKA, P., ULYANOV, O., SIDORCHUK, M., STEPKIN, S., TOKARSKY, P., MELNIK, V., KALINICHENKO, N., STANISLAVSKY, A., KOLIADIN, V., SHEPELEV, V., DOROVSKYY, V., RYABOV, V.,  KOVAL, A., BUBNOV, I., YERIN, S., GRIDIN, A., KULISHENKO, V., REZNICHENKO, A., BORTSOV, V., LISACHENKO, V., REZNIK, A., KVASOV, G., MUKHA, D., LITVINENKO, G., KHRISTENKO, A., SHEVCHENKO, V. V., SHEVCHENKO, V. A., BELOV, A., RUDAVIN, E., VASYLIEVA, I., MIROSHNICHENKO, A., VASILENKO, N., OLYAK, M., MYLOSTNA, K., SKORYK, A., SHEVTSOVA, A., PLAKHOV, M., KRAVTSOV, I., VOLVACH, Y., LYTVINENKO, O., SHEVCHUK, N., ZHOUK, I., BOVKUN, V., ANTONOV, A., VAVRIV, D., VINOGRADOV, V., KOZHIN, R., KRAVTSOV, A., BULAKH, E., KUZIN, A., VASILYEV, A., BRAZHENKO, A., VASHCHISHIN, R., PYLAEV, O., KOSHOVYY, V., LOZINSKY, A., IVANTYSHIN, O., RUCKER, H. O., PANCHENKO, M., FISCHER, G.,  ECACHEUX, A., DENIS, L., COFFRE, A., GRIEß-MEIER, J.-M., TAGGER, M., GIRARD, J., CHARRIER, D., BRIAND, C. and MANN, G., 2016. The modern radio astronomy network in Ukraine: UTR-2, URAN and GURT. Exp. Astron. vol. 42, is. 1, pp. 11–48. DOI: https://doi.org/10.1007/s10686-016-9498-x9. ZHOUCK, N. I., 1980. Analysis of the angular structure of cosmic sources by the scintillation method. Review. Izv. Vyssh. Uchebn. Zaved. Radiofiz. vol. 23, no. 8, pp. 893–918. (in Russian).10. BOVKOON, V. P. and ZHOUCK, I. N., 1981. Scintillations of cosmic radio sources in the decameter waveband. Astrophys. Space Sci. vol. 79, is. 1, pp. 165–180. DOI: https://doi.org/10.1007/BF0065591411. OLYAK, M. R., 2002. On the application of statistical radiophysics methods for the analysis of decameter in-terplanetary scintillations. Vestnik Kharkovskogo Natsionalnogo Universiteta. no. 570, is. 2, pp. 210–211. (in Russian).12. OLYAK, M. R., 2004. On the methods of analysis of decameter radio source scintillations on interplanetary plasma. Kinematika i fizika Nebesnykh Tel. vol. 20, no. 5, pp. 416–421. (in Russian).13. OLYAK, M. R., 2005. On the peculiarities of the analysis-of-variance method application in the decameter wavelength study of solar wind. Radio Phys. Radio Astron. vol. 10, no. 4, pp. 385–391. (in Russian).14. KALINICHENKO, N. N., KONOVALENKO, A. A., BRAZHENKO, A. I. and SOLOV’EV, V. V., 2013. 2011 February 15 CME in the interplanetary medium by observations of radio source scintillations at the decameter wavelengths. Radio Phys. Radio Astron. vol. 18, no. 4, pp. 301–308. (in Russian).15. SCHWENN, R and MARSCH, E., 1990. Physics of the Inner Heliosphere. 1. Large-Scale Phenomena. Berlin, Heidelberg: Springer-Verlag. DOI: https://doi.org/10.1007/978-3-642-75361-916. RYTOV, S. M., KRAVTSOV, YU. A. and TATARSKII, V. I., 1978. Introduction to statistical radiophysics. Part ІІ. Random fields. Moscow, Russia: Nauka Publ. (in Russian).17. TATARSKII, V.I., 1967. Propagation of waves in a turbulent atmosphere. Moskow: Nauka (in Russian).18. RYTOV, S. M., 1937. On the diffraction of light by ultrasonic waves. Izv. Akad. Nauk SSSR. no. 2, pp. 223–259. (in Russian).19. OBUKHOV, A. M., 1953. On the effect of weak atmospheric inhomogeneities on the propagation of sound and light. Izv. Akad. Nauk SSSR. Ser. Geofiz. no. 2, pp. 155–165. (in Russian).20. FEYNMAN, R. P. and HIBBS, A. R., 1965. Quantum Mechanics and Path Integrals. New York: McGraw-Hill Companies, Inc.21. DASHEN, R., 1979. Path Integrals for Waves in Random Media. J. Math. Phys. vol. 20, is. 5, pp. 894–920. DOI: https://doi.org/10.1063/1.52413822. FREHLICH, R. G., 1987. Space-time fourth moment of waves propagating in random media. Radio Sci. vol. 22, is. 4, pp. 481–490. DOI: https://doi.org/10.1029/RS022i004p0048123. KUKUSHKIN, A. and OLYAK, M., 1994. Propagation effects in the radio interferometry of polarized radiation: I. Spatial Fourier components of the Stokes parameters. Waves Random Media. vol. 4, is. 1, pp. 59–70. DOI: https://doi.org/10.1088/0959-7174/4/1/007KUKUSHKIN, A. and OLYAK, 1994. M., Propagation effects in the radio interferometry of polarized radiation: II. Fluctuations of polarized radiation in a random magnetoplasma. Waves Random Media. vol. 4, is. 1, pp. 71–81. DOI: https://doi.org/10.1088/0959-7174/4/1/00824. CRONIN, W. M., 1970. The analysis of radio scattering and space-probe observations of small-scale structure in the interplanetary medium. Astrophys. J. vol. 161, pp. 755–763. DOI: https://doi.org/10.1086/15057625. SALPETER, E. E., 1967. Interplanetary scintillations. I. Theory. Astrophys. J. vol. 147, pp. 433–448. DOI: 7https://doi.org/10.1086/14902726. LEONTOVICH, М. A. and Fok, V. A., 1946. Solution of the problem of propagation of electromagnetic waves along the Earth’s surface by the method of a parabolic equations. Zh. Eksp. Teor. Fiz. vol. 16, pp. 557–573. (in Russian).27. BRAUDE, S. YA., GALANIN, V. V., INUTIN, G. A., MEGN, A. V., MORI, X., RASHKOVSKII, S. L., SINITSIN, V. G. and SHARYKIN, N. K., 1995. The turbulent structure of the solar wind from observations in the decameter radio wavelength range. Astron. Zh. vol. 72, no. 5, pp. 761–766. (in Russian).28. MANOHARAN, P. K., KOJIMA, M., GOPALSWAMY, N., KONDO, T. and SMITH, Z., 2000. Radial evolution and turbulence characteristics of a coronal mass ejection. Astrophys. J. vol. 530, no. 2. P. 1061–1070. DOI: https://doi.org/10.1086/30837829. SHISHOV, V. I., 2007. Review of theory of interplanetary and interstellar scintillation. Astron. Astrophys. Trans. vol. 26, is. 6, pp. 415–427. DOI: https://doi.org/10.1080/1055679070160021830. COHEN, M. H., 1969. High-resolution observations of radio sources. Ann. Rev. Astron. Astrophys. vol. 7, is. 1, pp. 619–664. DOI: https://doi.org/10.1146/annurev.aa.07.090169.00315531. SHISHOV, V. I. and SHISHOVA, T. D., 1978. The influence of the source sizes on the interplanetary scintillation spectra. Theory. Astron. Zh. vol. 55, no. 2, pp. 411–418. (in Russian).32. SHISHOV, V. I. and SHISHOVA, T. D., 1979. The influence of the source size on the spectra of interplanetary scintillations. Observations. Astron. Zh. vol. 56, no. 3, pp. 613–622. (in Russian).33. RYTOV, S. M., 1976. Introduction to statistical radiophysics. Vol. І. Random processes. Moskow, Russia: Nauka Publ. (in Russian).34. GOCHELASHVILI, K. S. and SHISHOV, V. I., 1981. Waves in Randomly Inhomogeneous Media. In: N. D. USTINOV, ed. Results of science and technology. Radiophysics. Physical Principles of Electronics. Acoustics. Vol. 1. Moscow, Russia: VINITI Publ. (in Russian).35. KALINICHENKO, N. N., FALKOVICH, I. S., KONOVALENKO, A. A. and BRAZHENKO, A. I., 2013. Separation of interplanetary and ionospheric scintillations of cosmic sources at decameter wavelengths. Radio Phys. Radio Astron. vol. 18, no. 3, pp. 210–219. (in Russian).