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The Modulation of Galactic Cosmic Rays in the Heliosphere: Theory and Models

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Abstract

Almost all theoretical and numerical models for the modulation of cosmic ray in the heliosphere are based on Parker's transport equation which contains all the important basic physical processes. The relative importance of the various mechanisms is however not established and may vary significantly over 22 years. The simultaneous measurements of solar wind parameters, heliospheric magnetic field properties and cosmic rays over a wide range of energies and positions in the heliosphere have brought the realization that modulation is much more complicated than what the original drift models predicted. In the process the sophistication of models based on solving Parker's equation has increased by orders of magnitude. A short review of the global modulation of cosmic rays is given from a theoretical and modelling point of view.

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References

  • Balogh, A.: 1998, Space Sci. Rev., this volume.

  • Bieber, J.W. and Matthaeus, W.H.: 1997, 'Perpendicular diffusion and drift at intermediate cosmic-ray energies', Astrophys. J. in press.

  • Bieber, J.W., Burger, R.A. and Matthaeus, W.H.: 1995, 'The diffusion tensor throughout the heliopshere', Proc. 24th Int. Cosmic Ray Conf. 4, 694-697.

    Google Scholar 

  • Burlaga, L.F., McDonald, F.B., Goldstein, M.L. and Lazarus, A.J.: 1985, 'Cosmic-ray modulation and turbulent interaction regions near 11 AU', J. Geophys. Res. 90, 12,027-12,039.

    Google Scholar 

  • Burlaga, L.F., Ness, N.F and McDonald, F.B.: 1987, 'Large scale fluctuations in B between 13 AU and 22 AU and their effects on cosmic rays, J. Geophys. Res. 92, 13,647-13,652.

    Google Scholar 

  • Burlaga, L.F., McDonald, F.B. and Ness, N.F.: 1993, 'Cosmic ray modulation and the distant heliospheric magnetic field: Voyager 1 and 2 observations from 1986 to 1989, J. Geophys. Res. 98, 1-11.

    Google Scholar 

  • Burger, R.A.: 1990, in S. Grzedzielski and D.E. Page (ed.), 'Physics of the Outer Heliosphere', Proc.1st Cospar Coll., Pergamon Press, Oxford, pp. 179-182.

    Google Scholar 

  • Burger, R.A. and Hattingh, M.: 1995, 'Steady-state drift dominated modulation models for galactic cosmic rays', Astrophys. Space Sci. 230, 375-382.

    Google Scholar 

  • Evenson, P.: 1998, Space Sci. Rev., this volume.

  • Ferrando, P., Raviart, A., Haasbroek, L.J., Potgieter, M.S., Dröge, W., Heber, B., Kunow, H., Müller-Mellin, R., Sierks, H., Wibberenz, G. and Paizis, C.: 1996, 'Latitude variations of ~ 7 MeV and > 300 MeV cosmic ray electron fluxes in the heliosphere: Ulysses COSPIN-KET results and implications', Astro. Astrophys. 316, 528-537.

    Google Scholar 

  • Ferrando, P.: 1997, 'MeV to GeV electrons propagation and modulation: results of the KET telescope onboard Ulysses', Adv. Space Res., in press.

  • Fichtner, H.: 1996, 'Implications for the global structure of the heliosphere', Rev. Modern Astron. 9, 191-220.

    Google Scholar 

  • Fichtner, H., de Bruijn, H. and Sreenivasan, S.R: 1996, 'Logitudinal gradients of the distribution of anomalous cosmic rays in the outer heliopshere', Geophys. Res. Let. 23, 1705-1708.

    Google Scholar 

  • Fisk, L.A.: 1996, 'Motion of the footprints of heliospheric magnetic field lines at the Sun: Implications for recurrent energetic particle events at high heliographic latitudes', J. Geophys. Res. 101, 15,547-15,553.

    Google Scholar 

  • Fisk, L.A. and Schwadron, N.A.: 1995, 'The influence of intermediate-scale variations in the heliospheric field on the transport of galactic cosmic rays', J. Geophys. Res. 100, 7895-7872.

    Google Scholar 

  • Forsyth, R.J., Balogh, A., Smith, E.J., Erdös, G., McComas, D.J.: 1996, 'The underlying Parker spiral structure in the Ulysses magnetic field observations, 1990-1994', J. Geophys. Res. 101, 395-403.

    Google Scholar 

  • Haasbroek L.J. and Potgieter, M.S.: 1995, 'The modulation of cosmic rays in the high latitude heliosphere: a computer simulation', Space Sci. Rev. 72, 385-390.

    Google Scholar 

  • Haasbroek, L.J. and Potgieter, M.S.: 1997, 'Cosmic ray modulation in a non-spherical heliosphere during solar minimum conditions', Adv. Space Res., in press.

  • Haasbroek, L.J., Potgieter, M.S. and le Roux, J.A.: 1995, 'The time-dependent recovery after the large cosmic-ray decrease in 1991', Proc. 24th Int. Cosmic Ray Conf. 4, 710-713.

    Google Scholar 

  • Hattingh, M. and Burger, R.A,: 1995, 'Some properties of a fully three-dimensional drift model for the modulation of galactic cosmic rays', Proc. 24th Int. Cosmic Ray Conf. 4, 337-340.

    Google Scholar 

  • Hattingh, M., Burger, R.A. and Bieber, J.W.: 1995, 'Heliospheric propagation of galactic cosmic rays: quasiliniear theory versus hard-sphere scattering', Proc. 24th Int. Cosmic Ray Conf. 4, 698-701.

    Google Scholar 

  • Hattingh, M, Burger, R.A., Potgieter, M.S. and Haasbroek, L.J.: 1997, 'Cosmic ray latitudinal effects predicted by a three-dimensional drift model', Adv. Space Res., in press.

  • Heber, B., Dröge, W., Ferrando, P., Haasbroek, L.J., Kunow, H., Müller-Mellin, R., Paizis, C., Potgieter, M.S., Raviart, A. and Wibberenz, G.: 1996, Astro. Astrophys. 316, 538-546.

    Google Scholar 

  • Jokipii, J.R.: 1993, 'Particle drifts for a finite scaterring rate', Proc. 23rd Int. Cosmic Ray Conf. 3, 497-500.

    Google Scholar 

  • Jokipii, J.R. and Kóta, J.: 1989, 'The polar heliospheric magnetic field', Geophys. Res. Let. 16, 1-4.

    Google Scholar 

  • Jokipii, J.R., and Giacalone, J.: 1998, Space Sci. Rev., this volume.

  • Jokipii, J.R., Giacalone, J., Jones, F.C. and Kóta, J.: 1995a, 'Numerical simulations and analytic theory of cross-field transport', Proc. 24th Int. Cosmic Ray Conf. 4, 329-332.

    Google Scholar 

  • Jokipii, J.R., Kóta, J., Giacalone, J., Horbury, T.S. and Smith, E.J.: 1995b, 'Interpretation and consequences of large-scale magnetic variances observed at high heliographic latitude', Geophys. Res. Let. 22, 3385-3388.

    Google Scholar 

  • Jokipii, J.R. and Thomas, B.T.: 1981, 'Effects of drift on the transport of cosmic rays IV. Modulation by a wavy interplanetary current sheet', Astrophys. J. 243, 1115-1122.

    Google Scholar 

  • Jokipii, J.R., Levy, E.H. and Hubbard W.B.: 1977, 'Effects of particle drift on cosmic-ray transport. I. General properties, application to solar modulation', Astrophys. J. 213, 861-868.

    Google Scholar 

  • Kóta, J. and Jokipii, J.R.: 1983, 'Effects of drift on the transport of cosmic rays VI. A three-dimesional model including diffusion', Ap.J. 265, 573-581.

    Google Scholar 

  • Kóta, J. and Jokipii, J.R.: 1995, '3-D distribution of cosmic rays in the outer heliosphere', Proc. 24th Int. Cosmic Ray Conf. 4, 680-683.

    Google Scholar 

  • Kóta, J. and Jokipii, J.R.: 1998, Space Sci. Rev., this volume.

  • le Roux, J.A. and Potgieter, M.S.: 1990, 'A time-dependent drift model for the long-term modulation of cosmic rays with special reference to asymmetries with respect to the solar minimum of 1987', Astrophys. J. 361, 275-282.

    Google Scholar 

  • le Roux, J.A. and Potgieter, M.S.: 1992, 'The simulated features of heliopsheric cosmic-ray modulation with a time-dependent drift model. II. On the energy dependence of the onset of new modulation in 1987', Astrophys. J. 390, 661-667.

    Google Scholar 

  • le Roux, J.A. and Potgieter, M.S.: 1995, 'The simulation of complete 11 and 22 year modulation cycles for cosmic rays in the heliopshere using a drift model with global merged interaction regions', Astrophys. J. 442, 847-851.

    Google Scholar 

  • McDonald, F.B.: 1998, Space Sci. Rev., this volume.

  • McDonald, F.B., Lal, N. and McGuire, R.E.: 1993, 'The role of drifts and global merged interaction regions in the long-term modulation of cosmic rays', J. Geophys. Res. 98, 1243-1256.

    Google Scholar 

  • McDonald, F.B., Lal, N., Trainor, J.H., van Hollebeke, M.A.I. and Webber, W.R.: 1981, 'The solar modulation of galactic cosmic rays in the outer heliosphere', Astrophys. J. 249, L71-L75.

    Google Scholar 

  • McDonald, F.B., Ferrando, P., Ravairt, A., Heber, B., Kunow, H., McGuire, R., Müller-Mellin, R., Paizis, C Raviart, A. and Wibberenz, G.: 1997, 'A comparative study of cosmic ray radial and latitudinal gradients in the inner and outer heliosphere', J. Geophys. Res., in press.

  • Parker, E.N.: 1965, 'The passage of energetic charged particles through interplanetary space', Planet. Space Sci. 13, 9-xx.

    Google Scholar 

  • Pauls, H.L. and Zank, G.P.: 1996, 'Interaction of a nonuniform solar wind with the local interstellar medium', J. Geophys. Res. 101, 17,081-17,092.

    Google Scholar 

  • Perko, J.S. and Fisk, L.A.: 1983, 'Solar modulation of galactic cosmic rays. 5. Time-dependent modulation', J. Geophys. Res. 88, 9033-9036.

    Google Scholar 

  • Phillips, J.L., Bame, S.J., Barnes, A., Barraclough, B.L., Feldman, W.C., Goldstein, B.E., Gosling, J.T., Hoogeveen, G.W., McComas, D.J., Neugebauer, M. and Suesss, S.T.: 1995, 'Ulysses solar wind plasma observations from pole to pole', Geophys. Res. Let. 22, 3301-3304.

    Google Scholar 

  • Potgieter, M.S.: 1993, 'Time-dependent cosmic ray modulation: role of drifts and interaction regions', Adv. Space Res. 13, 239-249.

    Google Scholar 

  • Potgieter, M.S.: 1994, in D.A. Leahy, R.B. Hicks and D. Venkatesan (ed.), 'Invited, rapporteur and highlight papers', Proc. 23rd Int. Cosmic Ray Conf., World Scientific, Singapore, pp. 213-242.

    Google Scholar 

  • Potgieter, M.S.: 1995, 'The long-term modulation of galactic cosmic rays in the heliosphere', Adv. Space Res. 16, 191-203.

    Google Scholar 

  • Potgieter, M.S.: 1997, 'The heliospheric modulation of galactic cosmic rays at solar minimum', Adv. Space Res., in press.

  • Potgieter, M.S. and Burger, R.A.: 1990, 'The modulation of cosmic-ray electrons, positrons and helium nuclei as predicted by a drift model with a simulated wavy neutral sheet', Astro. Astrophys. 233, 589-604.

    Google Scholar 

  • Potgieter, M.S. and Haasbroek, L.J.: 1993, 'The simulation of base-line cosmic-ray modulation for the Ulysses trajectory', Proc. 23rd Int. Cosmic Ray Conf. 3, 457-460.

    Google Scholar 

  • Potgieter, M.S., Haasbroek, L.J., Ferrando, P. and Heber, B: 1997, 'The modelling of the latitude dependence of cosmic ray protons and electrons in the inner heliopshere', Adv. Space Res., in press.

  • Potgieter, M.S. and le Roux, J.A.: 1994, 'The long-term heliospheric modulation of galactic cosmic rays according to a time-dependent drift model with merged interaction regions', Astrophys. J. 423, 817-827.

    Google Scholar 

  • Potgieter, M.S., le Roux, J.A. and Burger, R.A.: 1989, 'Interplanetary cosmic rays radial gradients with a steady-state modulation models', J. Geophys. Res. 94, 2323-2332.

    Google Scholar 

  • Potgieter, M.S. and Moraal, H.: 1985, 'A drift model for the modulation of cosmic rays', Astrophys. J. 294, 425-440.

    Google Scholar 

  • Quenby, J.J., Lockwood, J.A. and Webber, W.R.: 1990, Cosmic ray gradient measurements and modulation beyond the inner solar wind termination shock', Astrophys. J. 365, 365-371.

    Google Scholar 

  • Reinecke, J.P.L., Moraal, H., McDonald, F.B.: 1996, 'The cosmic radiation in the heliosphere at successive solar minima 3. Steady-state drift solutions of the transport equation', J. Geophys. Res. 101, 21,581-21,588.

    Google Scholar 

  • Simpson, J.A., Zhang, M., Bame, S.: 1996, 'A solar polar north-south asymmetry for cosmic ray propagation in the heliosphere: the Ulysses pole-to-pole rapid transit”, Astrophys. J. 465, L69-L72.

    Google Scholar 

  • Smith, C.W. and Bieber, J.W.: 1991, 'Solar cycle variation of the interplanetary magnetic field spiral', Astrophys. J. 370, 435-441.

    Google Scholar 

  • Webber, W.R., Potgieter, M.S. and Burger, R.A.: 1990, 'A comparison of predictions of a wavy neutral sheet drift model with cosmic-ray data over a whole modulation cycle: 1976-1987', Astrophys. J. 349, 634-640.

    Google Scholar 

  • Zank, G.P., Matthaeus, W.H. and Smith C.W.: 1996, 'Evolution of turbulent magnetic fluctuation power with heliospheric distance', J. Geophys. Res. 101, 17,093-17,108.

    Google Scholar 

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  1. Space Research Unit, Department of Physics, Potchefstroom University for CHE, 2520, Potchefstroom, South Africa

    M. S. Potgieter

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Potgieter, M.S. The Modulation of Galactic Cosmic Rays in the Heliosphere: Theory and Models. Space Science Reviews 83, 147–158 (1998). https://doi.org/10.1023/A:1005014722123

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