Skip to main content
Log in

Quantitative models of the magnetospheric magnetic field: Methods and results

A review

  • Published:
Space Science Reviews Aims and scope Submit manuscript

Abstract

The paper reviews various approaches to the problem of evaluation and numerical representation of the magnetic field distributions produced within the magnetosphere by the main electric current systems including internal Earth's sources, the magnetopause surface current, the tail plasma sheet, the large-scale systems of Birkeland current, the currents due to radiation belt particles, and the partial ring current circuit. Some basic physical principles as well as mathematical background for development of magnetospheric magnetic field models are discussed.

A special emphasis is placed on empirical modeling based on datasets created from large bodies of spacecraft measurements. A review of model results on the average magnetospheric configurations and their dependence on the geomagnetic disturbance level and the state of interplanetary medium is given. Possibilities and perspectives for elaborating the ‘instantaneous’ models capable of evaluating a current distribution of magnetic field and force line configuration based on a synoptic monitoring the intensity of the main magnetospheric electric current systems are also discussed. Some areas of practical use of magnetospheric models are reviewed in short. Magnetospheric plasma and energetic particle measurements are considered in the context of their use as an independent tool for testing and correcting the magnetic field models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Akasofu, S.-I.: 1981, Space Sci. Rev. 28, 121.

    Google Scholar 

  • Akasofu, S.-I. and Chapman, S.: 1961, J. Geophys. Res. 66, 1321.

    Google Scholar 

  • Akasofu, S.-I. and Chapman, S.: 1972, Solar-Terrestrial Physics, Clarendon Press, Oxford.

    Google Scholar 

  • Alekseev, I. I. and Shabansky, V. P.: 1972, Planetary Space Sci. 20, 117.

    Google Scholar 

  • Alekseev, I. I., Kirillov, A. A., and Chuikova, T. A.: 1975, Geomagnetizm i Aeronomiya 15, 508 (in Russian).

    Google Scholar 

  • Alekseev, I. I.: 1978, Geomagnetizm i Aeronomiya 18, 656 (in Russian).

    Google Scholar 

  • Alfvén, H. and Fälthammar, C.-G.: 1963, Cosmical Electrodynamics, Fundamental Principles, 2nd ed., Clarendon Press, Oxford.

    Google Scholar 

  • Allen, J. H., Abston, C. C., Papitashvili, V. O., Kharin, E. P., and Papitashvili, N. E.: 1982, International Catalog of Geomagnetic Data, Rept. UAG-86, NOAA, Boulder.

    Google Scholar 

  • Antonova, A. E. and Shabansky, V. P.: 1968, Geomagnetizm i Aeronomiya 8, 891.

    Google Scholar 

  • Backus, G.: 1986, Rev. Geophys. 24, 75.

    Google Scholar 

  • Baker, D. N., Fritz, T. A., McPherron, R. L., Fairfield, D. H., Kamide, Y., and Baumjohann, W.: 1985, J. Geophys. Res. 90, 1205.

    Google Scholar 

  • Barish, F. D. and Roederer, J. G.: 1969, Preprint, University of Denver.

  • Barish, F. D. and Wiley, R. E.: 1970, J. Geophys. Res. 75, 6342.

    Google Scholar 

  • Barraclough, D. R.: 1987, Phys. Earth Planet. Interiors 48, 279.

    Google Scholar 

  • Barraclough, D. R., Harwood, G. M., Leaton, B. R., and Malin, S. R. C.: 1975, Geophys. J. Roy. Astron. Soc. 43, 645.

    Google Scholar 

  • Basu, S. and Rowlands, G.: 1986, Planetary Space Sci. 34, 631.

    Google Scholar 

  • Beard, D. B.: 1979, J. Geophys. Res. 84, 2118.

    Google Scholar 

  • Beard, D. B. and Jenkins, E. B.: 1962, J. Geophys. Res. 67, 3361.

    Google Scholar 

  • Beard, D. B., Hirschi, D., and Propp, K.: 1982, J. Geophys. Res. 87, 2533.

    Google Scholar 

  • Behannon, K. W.: 1968, J. Geophys. Res. 73, 907.

    Google Scholar 

  • Behannon, K. W.: 1970, J. Geophys. Res. 75, 743.

    Google Scholar 

  • Birn, J.: 1987, J. Geophys. Res. 92, 11101.

    Google Scholar 

  • Birn, J., Sommer, K., and Schindler, K.: 1977, J. Geophys. Res. 82, 147.

    Google Scholar 

  • Burch, J. L.: 1972, J. Geophys. Res. 77, 6696.

    Google Scholar 

  • Bythrow, P. F. and Potemra, T. A.: 1983, Geophys. Res. Letters 32, 573.

    Google Scholar 

  • Caan, M. N., McPherron, R. L., and Russell, C. T.: 1973, J. Geophys. Res. 78, 8087.

    Google Scholar 

  • Cahill, L. J.: 1966, J. Geophys. Res. 71, 4505.

    Google Scholar 

  • Cain, J. C., Hendricks, S. J., Langel, R. A., and Hudson, W. V.: 1967, J. Geomagn. Geoelectr. 19, 335.

    Google Scholar 

  • Chapman, S. and Ferraro, V. C. A.: 1931, J. Geophys. Res. 36, 77.

    Google Scholar 

  • Choe, J. Y. and Beard, D. B.: 1974, Planetary Space Sci. 22, 609.

    Google Scholar 

  • Choe, J. Y., Beard, D. B., and Sullivan, E. C.: 1973, Planetary Space Sci. 21, 485.

    Google Scholar 

  • Coleman, P. J. and McPherron, R. L.: 1976, in K. Knott and B. Battrick (eds.), The Scientific Satellite Program during the International Magnetospheric Study, D. Reidel Publ. Co., Dordrecht, Holland, pp. 345–365.

    Google Scholar 

  • Cowley, S. W. H.: 1973, Radio Sci. 8, 903.

    Google Scholar 

  • Cowley, S. W. H.: 1981, Planetary Space Sci. 29, 79.

    Google Scholar 

  • Cramer, H.: 1957, Mathematical Methods of Statistics, Princeton Univ. Press, Princeton.

    Google Scholar 

  • Crooker, N. U. and Siscoe, G. L.: 1981, J. Geophys. Res. 86, 11201.

    Google Scholar 

  • Crooker, N. U., Berchem, J., and Russell, C. T.: 1987, J. Geophys. Res. 92, 13467.

    Google Scholar 

  • Dandouras, J.: 1988, J. Geophys. Res. 93, 7345.

    Google Scholar 

  • Erickson, G. M.: 1984, in E. W. Hones (ed.), Magnetic Reconnection, Geophys. Monograph Ser., Vol. 30, AGU, Washington, D.C., pp. 296–302.

    Google Scholar 

  • Erickson, G. M. and Wolf, R. A.: 1980, Geophys. Res. Letters 7, 897.

    Google Scholar 

  • Fairfield, D. H.: 1971, J. Geophys. Res. 76, 6700.

    Google Scholar 

  • Fairfield, D. H. and Mead, G. D.: 1975, J. Geophys. Res. 80, 535.

    Google Scholar 

  • Fairfield, D. H.: 1980, J. Geophys. Res. 85, 775.

    Google Scholar 

  • Fairfield, D. H.: 1986, J. Geophys. Res. 91, 4238.

    Google Scholar 

  • Fairfield, D. H., Acuña, M. H., Zanetti, L. J., and Potemra, T. A.: 1987, J. Geophys. Res. 92, 7432.

    Google Scholar 

  • Frank, L. A.: 1967, J. Geophys. Res. 72, 3753.

    Google Scholar 

  • Fuchs, K. and Voigt, G.-H.: 1979, in W. P. Olson (ed.), Quantitative Modeling of Magnetospheric Processes, Geophys. Monograph Ser., Vol. 21, AGU, Washington, D.C., pp. 86–95.

    Google Scholar 

  • Gauss, C. F.: 1839, Allgemeine Theorie des Erdmagnetismus. Resultate, 1839, Werke, V.B., pp. 119–175, Nachtrag, pp. 175–180.

    Google Scholar 

  • Goltzman, F. M.: 1971, Statistical Interpretation Models, Nauka, Moscow (in Russian).

    Google Scholar 

  • Goltzman, F. M.: 1982, Physical Experiment and Statistical Inferences, Leningrad Univ. Press, Leningrad (in Russian).

    Google Scholar 

  • Gosling, J. T., McComas, D. J., Thomsen, M. F., Bame, S. J., and Russell, C. T.: 1986, J. Geophys. Res. 91, 7093.

    Google Scholar 

  • Gray, P. C. and Lee, L. C.: 1982, J. Geophys. Res. 87, 7445.

    Google Scholar 

  • Gustafsson, G.: 1970, Arkiv Geofysik 5, 595.

    Google Scholar 

  • Hakura, Y.: 1965, Rep. Ionosphere Space Res. Japan 19, 121.

    Google Scholar 

  • Halderson, D. W., Beard, D. B., and Choe, J. Y.: 1975, Planetary Space Sci. 23, 887.

    Google Scholar 

  • Harel, M., Wolf, R. A., Spiro, R. W., Reiff, P. H., and Chen, C.-K.: 1981, J. Geophys. Res. 86, 2242.

    Google Scholar 

  • Hedgecock, P. C. and Thomas, B. T.: 1975, Geophys. J. Roy. Astron. Soc. 41, 391.

    Google Scholar 

  • Hedgecock, P. C. and Thomas, B. T.: 1979, Imperial College preprint, London.

  • Heelis, R. A. and Hanson, W. B.: 1980, J. Geophys. Res. 85, 1995.

    Google Scholar 

  • Hilmer, R. V. and Voigt, G.-H.: 1987, J. Geophys. Res. 92, 8660.

    Google Scholar 

  • Hoffman, R. A. and Bracken, P. A.: 1965, J. Geophys. Res. 70, 3541.

    Google Scholar 

  • Hoffman, R. A. and Bracken, P. A.: 1967, J. Geophys. Res. 72, 6039.

    Google Scholar 

  • Hoffman, R. A. and Cahill, L. J.: 1968, J. Geophys. Res. 73, 6711.

    Google Scholar 

  • Iijima, T. and Potemra, T. A.: 1976, J. Geophys. Res. 81, 2165.

    Google Scholar 

  • Iijima, T. and Potemra, T. A., and Zanetti, L. J.: 1989, J. Geophys. Res. (in press).

  • Imhof, W. L.: 1988, J. Geophys. Res. 93, 9743.

    Google Scholar 

  • Imhof, W. L., Reagan, J. B., and Gaines, E. E.: 1977, J. Geophys. Res. 82, 5215.

    Google Scholar 

  • Isaev, S. I. and Pudovkin, M. I.: 1972, Polar Aurora and Processes in the Earth's Magnetosphere, Nauka, Leningrad (in Russian).

    Google Scholar 

  • Izhovkina, N. I.: 1979, Geomagnetizm i Aeronomiya 19, 1125 (in Russian).

    Google Scholar 

  • Kamide, Y. and Fukushima, N.: 1971, Rept. Ionosphere Space Res. Japan 25, 125.

    Google Scholar 

  • Kaufmann, R. L.: 1987, J. Geophys. Res. 92, 7471.

    Google Scholar 

  • Kendall, P. C., Chapman, S., Akasofu, S.-I., and Swartztrauber, P. N.: 1966, Geophys. J. Roy. Astron. Soc. 11, 349.

    Google Scholar 

  • King, J. H.: 1977, Interplanetary Medium Data Book, NSSDS, Greenbelt.

    Google Scholar 

  • Kivelson, M. G. and Spence, H. E.: 1989, Geophys. Res. Letters (in press).

  • Korn, G. A. and Korn, T. M.: 1961, Mathematical Handbook for Scientists and Engineers, Ch. 6, McGraw-Hill Book Co. Inc., New York.

    Google Scholar 

  • Kosik, J.-C.: 1978, Space Sci. Rev. 22, 481.

    Google Scholar 

  • Kosik, J.-C.: 1984, Planetary Space Sci. 32, 965.

    Google Scholar 

  • Kropotkin, A. P.: 1977, Geomagnetizm i Aeronomiya 17, 259 (in Russian).

    Google Scholar 

  • Langel, R. A.: 1974, Goddard Space Flight Center Report, X-645-73-225.

  • Langel, R. A. and Sweeney, R. E.: 1971, J. Geophys. Res. 76, 4420.

    Google Scholar 

  • Lin, R. P. and Barfield, J. N.: 1984, Planetary Space Sci. 32, 1283.

    Google Scholar 

  • Lui, A. T. Y.: 1983, in Magnetospheric Currents, Geophys. Monograph, Vol. 28, AGU, Washington, D.C., pp. 158–170.

    Google Scholar 

  • Lui, A. T. Y., McEntire, R. W., and Krimigis, S. M.: 1987, J. Geophys. Res. 92, 7459.

    Google Scholar 

  • Lyons, L. R. and Williams, D. J.: 1984, in Quantitative Aspects of Magnetospheric Physics, D. Reidel Publ. Co., Dordrecht, Holland.

    Google Scholar 

  • Marquardt, D. W.: 1963, J. Soc. Ind. Appl. Math. 11, 431.

    Google Scholar 

  • McComas, D. J., Russell, C. T., Elphic, R. C., and Bame, S. J.: 1986, J. Geophys. Res. 91, 4287.

    Google Scholar 

  • McIlwain, C. E.: 1974, in B. M. McCormac (ed.), Magnetospheric Physics, D. Reidel Publ. Co., Dordrecht, Holland, p. 143.

    Google Scholar 

  • Mead, G. D.: 1964, J. Geophys. Res. 69, 1181.

    Google Scholar 

  • Mead, G. D. and Beard, D. B.: 1964, J. Geophys. Res. 69, 1169.

    Google Scholar 

  • Mead, G. D. and Fairfield, D. H.: 1975, J. Geophys. Res. 80, 523.

    Google Scholar 

  • Meng, C.-I.: 1982, Geophys. Res. Letters 9, 60.

    Google Scholar 

  • Midgley, J. E.: 1964, J. Geophys. Res. 69, 1197.

    Google Scholar 

  • Midgley, J. E. and Davis, L., Jr.: 1962, J. Geophys. Res. 67, 499.

    Google Scholar 

  • Midgley, J. E. and Davis, L., Jr.: 1963, J. Geophys. Res. 68, 5111

    Google Scholar 

  • Mihalov, J. D., Colburn, D. S., Currie, R. G., and Sonett, C. P.: 1968, J. Geophys. Res. 73, 943.

    Google Scholar 

  • Morfill, G.: 1975, Space Sci. Rev. 17, 391.

    Google Scholar 

  • Morfill, G. and Scholer, M.: 1973, Space Sci. Rev.15, 267.

    Google Scholar 

  • Nagai, T.: 1987, J. Geophys. Res. 92, 11215.

    Google Scholar 

  • Newell, P. T. and Meng, C.-I.: 1989, J. Geophys. Res. 94, 6949.

    Google Scholar 

  • Ogino, T., Walker, R. J., Ashour-Abdalla, M., and Dawson, M.: 1986, J. Geophys. Res. 91, 10029.

    Google Scholar 

  • Ohtani, S., Kokubun, S., Elphic, R. C., and C. T. Russell: 1988, J. Geophys. Res. 93, 9709.

    Google Scholar 

  • Olson, W. P.: 1969, J. Geophys. Res. 74, 5642.

    Google Scholar 

  • Olson, W. P. and Pfitzer, K. A.: 1974, J. Geophys. Res. 79, 3739.

    Google Scholar 

  • Olson, W. P. and Pfitzer, K. A.: 1977, McDonnell Douglas Astronautics Co. preprint.

  • Olson, W. P. and Pfitzer, K. A.: 1982, J. Geophys. Res. 87, 5943.

    Google Scholar 

  • Ono, T.: 1987, Mem. Nat. Inst. Polar Res. Japan, Spec. Issue 48, 46.

    Google Scholar 

  • Parker, E. N.: 1957, Phys. Rev. 107, 924.

    Google Scholar 

  • Peddie, N. W.: 1982, J. Geomagn. Geoelectr. 34, 309.

    Google Scholar 

  • Pellinen, R. J. and Heikkila, W. J.: 1984, Space Sci. Rev. 37, 1.

    Google Scholar 

  • Pilipp, W. G. and Morfill, G.: 1978, J. Geophys. Res. 83, 5670.

    Google Scholar 

  • Popielawska, B., Szalinska-Piechota, E., and Tsyganenko, N. A.: 1985, Planetary Space Sci. 33, 1433.

    Google Scholar 

  • Pudovkin, M. I. and Semenov, V. S.: 1985, Space Sci. Rev. 41, 1.

    Google Scholar 

  • Pudovkin, M. I., Barsukov, V. M., and Tsyganenko, N. A.: 1971, Physical Institute, Leningrad University preprint.

  • Pudovkin, M. I., Tsyganenko, N. A., and Usmanov, A. V.: 1986, Geomagnetizm i Aeronomiya 26, 946 (in Russian).

    Google Scholar 

  • Pugachev, V. S.: 1962, Theory of Random Functions and Its Applications to Problems of Automatic Operation, Nauka, Moscow (in Russian).

    Google Scholar 

  • Roederer, J. G.: 1969, Rev. Geophys. 1, 77.

    Google Scholar 

  • Roederer, J. G.: 1970, Dynamics of Geomagnetically Trapped Radiation, Springer-Verlag, Heidelberg.

    Google Scholar 

  • Roederer, J. G.: 1977, Space Sci. Rev. 21, 23.

    Google Scholar 

  • Roelof, E. C.: 1987, Geophys. Res. Letters 14, 652.

    Google Scholar 

  • Rostoker, G., Savoie, D., and Phan, T. D.: 1988, J. Geophys. Res. 93, 8633.

    Google Scholar 

  • Russell, C. T. and Brody, K. I.: 1967, J. Geophys. Res. 72, 6104.

    Google Scholar 

  • Sato, T. and Iijima, T.: 1979, Space Sci. Rev. 24, 347.

    Google Scholar 

  • Schieid, M. A.: 1969, J. Geophys. Res. 74, 1275.

    Google Scholar 

  • Schindler, K.: 1974, Space Sci. Rev. 17, 589.

    Google Scholar 

  • Schindler, K.: 1979, Space Sci. Rev. 23, 365.

    Google Scholar 

  • Schindler, K. and Birn, J.: 1986, Space Sci. Rev. 44, 307.

    Google Scholar 

  • Scholer, M.: 1975, Space Sci. Rev. 17, 3.

    Google Scholar 

  • Schulz, M.: 1980, J. Geomag. Geoelectr. 32, 507.

    Google Scholar 

  • Schulz, M. and McNab, M. C.: 1987, Geophys. Res. Letters 14, 182.

    Google Scholar 

  • Sckopke, N.: 1972, Cosmic Electrodyn. 3, 330.

    Google Scholar 

  • Sergeev, V. A.: 1987, Geomagnetizm i Aeronomiya 27, 612 (in Russian).

    Google Scholar 

  • Sergeev, V. A. and Malkov, M. V.: 1988, Geomagnetizm i Aeronomiya 28, 649 (in Russian).

    Google Scholar 

  • Sergeev, V. A. and Lennartsson, W.: 1988, Planetary Space Sci. 36, 353.

    Google Scholar 

  • Sergeev, V. A. and Tsyganenko, N. A.: 1980, The Earth's Magnetosphere, Nauka, Moscow (in Russian).

    Google Scholar 

  • Sergeev, V. A. and Tsyganenko, N. A.: 1982, Planetary Space Sci. 30, 999.

    Google Scholar 

  • Sergeev, V. A., Sazhina, E. M., Tsyganenko, N. A., Lundblad, J. Å., and Søraas, F.: 1983, Planetary Space Sci. 31, 1147.

    Google Scholar 

  • Sibeck, D. G., Siscoe, G. L., Slavin, J. A., Smith, E. J., Tsurutani, B. T., and Lepping, R. P.: 1985, J. Geophys. Res. 90, 4011.

    Google Scholar 

  • Sibeck, D. G., McEntire, R. W., Lui, A. T. Y., Lopez, R. E., and Krimigis, S. M.: 1987, J. Geophys. Res. 92, 13485.

    Google Scholar 

  • Siscoe, G. L.: 1966, Planetary Space Sci. 14, 947.

    Google Scholar 

  • Sozou, C. and Windle, D. W.: 1969a, Planetary Space Sci. 17, 375.

    Google Scholar 

  • Sozou, C. and Windle, D. W.: 1969b, Planetary Space Sci. 17, 999.

    Google Scholar 

  • Sozou, C. and Windle, D. W.: 1970, Planetary Space Sci. 18, 699.

    Google Scholar 

  • Speiser, T. W. and Ness, N. F.: 1967, J. Geophys. Res. 72, 131.

    Google Scholar 

  • Spence, H. E., Kivelson, M. G., and Walker, R. J.: 1987, Geophys. Res. Letters 14, 872.

    Google Scholar 

  • Stern, D. P.: 1976, Rev. Geophys. Space Phys. 14, 199.

    Google Scholar 

  • Stern, D. P.: 1983, Rev. Geophys. Space Phys. 21, 125.

    Google Scholar 

  • Stern, D. P.: 1985, J. Geophys. Res. 90, 10851.

    Google Scholar 

  • Stern, D. P.: 1987a, J. Geophys. Res. 92, 4437.

    Google Scholar 

  • Stern, D. P.: 1987b, Rev. Geophys. 25, 523.

    Google Scholar 

  • Stern, D. P. and Alexeev, I. I.: 1988, Rev. Geophys. 26, 782.

    Google Scholar 

  • Stiles, G. S., Hones, E. W., Jr., Bame, S. J., and Asbridge, J. R.: 1978, J. Geophys. Res. 83, 3166.

    Google Scholar 

  • Sugiura, M.: 1972, J. Geophys. Res. 77, 6093.

    Google Scholar 

  • Sugiura, M. and Poros, D. J.: 1973, Planetary Space Sci. 21, 1763.

    Google Scholar 

  • Taylor, H. E. and Hastie, R. J.: 1971, Cosmic Electrodyn. 2, 211.

    Google Scholar 

  • Taylor, H. E. and Hones, E. W.: 1965, J. Geophys. Res. 70, 3605.

    Google Scholar 

  • Troschichev, O. A.: 1982, Space Sci. Rev. 32, 275.

    Google Scholar 

  • Tsyganenko, N. A.: 1975a, Kosm. Issled. 13, 215 (in Russian).

    Google Scholar 

  • Tsyganenko, N. A. 1975b, Geomagnetizm i Aeronomiya 15, 487 (in Russian).

    Google Scholar 

  • Tsyganenko, N. A.: 1976, Ann. Geophys. 32, 1.

    Google Scholar 

  • Tsyganenko, N. A.: 1979, Subroutines and Tables for the Geomagnetic Field Computations, WDC-B2, Moscow.

  • Tsyganenko, N. A.: 1981, Ann. Geophys. 37, 381.

    Google Scholar 

  • Tsyganenko, N. A.: 1982a, Planetary Space Sci. 30, 1007.

    Google Scholar 

  • Tsyganenko, N. A.: 1982b, Planetary Space Sci. 30, 433.

    Google Scholar 

  • Tsyganenko, N. A.: 1987a, Planetary Space Sci. 35, 1347.

    Google Scholar 

  • Tsyganenko, N. A.: 1987b, Geomagnetizm i Aeronomiya 27, 987 (in Russian).

    Google Scholar 

  • Tsyganenko, N. A.: 1988, Geomagnetizm i Aeronomiya 28, 389 (in Russian).

    Google Scholar 

  • Tsyganenko, N. A.: 1989a, Planetary Space Sci. 37, 5.

    Google Scholar 

  • Tsyganenko, N. A.: 1989b, Planetary Space Sci. 37, 183.

    Google Scholar 

  • Tsyganenko, N. A.: 1989c, Planetary Space Sci. 37, 1037.

    Google Scholar 

  • Tsyganenko, N. A. and Usmanov, A. V.: 1982, Planetary Space Sci. 30, 985.

    Google Scholar 

  • Tsyganenko, N. A. and Usmanov, A. V.: 1984, Planetary Space Sci. 32, 97.

    Google Scholar 

  • Tsyganenko, N. A., Usmanov, A. V., Papitashvili, V. O., Papitashvili, N. E., and Popov, V. A.: 1987, in V. A. Nechitailenko (ed.), Software for Computations of the Geomagnetic Field and Related Coordinate Systems, Soviet Geophysical Committee, Acad. of Sci. USSR, Moscow.

    Google Scholar 

  • Usmanov, A. V.: 1984, ‘Quantitative Modeling of the Magnetosphere Based on Spacecraft Data’, Cand. Sci. Dissertation, Leningrad State University.

  • Usmanov, A. V. and Tsyganenko, N. A.: 1984, Geomagnetizm i Aeronomiya 24, 968 (in Russian).

    Google Scholar 

  • Voigt, G.-H.: 1972, Z. Geophys. 38, 319.

    Google Scholar 

  • Voigt, G.-H.: 1981, Planetary Space Sci. 29, 1.

    Google Scholar 

  • Voigt, G.-H.: 1984, J. Geophys. Res. 89, 2169.

    Google Scholar 

  • Voigt, G.-H.: 1986, in Y. Kamide and J. A. Slavin (eds.), Solar Wind — Magnetosphere Coupling, Terra Scientific Publ. Co., Tokyo, pp. 233–273.

    Google Scholar 

  • Voigt, G.-H. and Hilmer, R. V.: 1987, in A. T. Y. Lui (ed.), Magnetotail Physics, The Johns Hopkins University Press, Baltimore, pp. 91–97.

    Google Scholar 

  • Voigt, G.-H. and Wolf, R. A.: 1985, J. Geophys. Res. 90, 4046.

    Google Scholar 

  • Wagner, J. S., Kan, J. R., and Akasofu, S.-I.: 1979, J. Geophys. Res. 84, 891.

    Google Scholar 

  • Walker, R. J.: 1976, Rev. Geophys. Space Phys. 14, 411.

    Google Scholar 

  • Walker, R. J.: 1979, in W. P. Olson (ed.), Quantitative Modeling of Magnetospheric Processes, Geophys. Monogr. Ser., Vol. 21, AGU, Washington, D.C., pp. 9–34.

    Google Scholar 

  • Walker, R. J.: 1983, Rev. Geophys. 21, 495.

    Google Scholar 

  • Walker, R. J. and Southwood, D. J.: 1982, J. Geophys. Res. 87, 7460.

    Google Scholar 

  • West, H. I., Buck, R. M., and Kivelson, M. G.: 1978a, J. Geophys. Res. 83, 3805.

    Google Scholar 

  • West, H. I., Buck, R. M., and Kivelson, M. G.: 1978b, J. Geophys. Res. 83, 3819.

    Google Scholar 

  • Williams, D. J.: 1987, Rev. Geophys. 25, 570.

    Google Scholar 

  • Williams, D. J. and Mead, G. D.: 1965, J. Geophys. Res. 70, 3017.

    Google Scholar 

  • Willis, D. M. and Pratt, R. J.: 1972, J. Atmospheric Terrest. Phys. 34, 1955.

    Google Scholar 

  • Wright, A. N.: 1985, Planetary Space Sci. 33, 847.

    Google Scholar 

  • Yamamoto, T. and Tamao, T.: 1978, Planetary Space Sci. 26, 1185.

    Google Scholar 

  • Zaitseva, S. A. and Pudovkin, M. I.: 1976, Planetary Space Sci. 24, 518.

    Google Scholar 

  • Zanetti, L. J., Baumjohann, W., and Potemra, T. A.: 1983, J. Geophys. Res. 88, 4875.

    Google Scholar 

  • Zmuda, A. J. and Armstrong, J. C.: 1974, J. Geophys. Res. 79, 4611.

    Google Scholar 

  • Zmuda, A. J., Martin, J. H., and Heuring, F. T.: 1966, J. Geophys. Res. 71, 5033.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tsyganenko, N.A. Quantitative models of the magnetospheric magnetic field: Methods and results. Space Sci Rev 54, 75–186 (1990). https://doi.org/10.1007/BF00168021

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00168021

Keywords

Navigation