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The radial diffusion of trapped particles induced by fluctuating magnetospheric fields

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Abstract

Small fluctuations in magnetospheric electric and magnetic fields lead to random changes in the radial positions of trapped particles. The characteristics of this radial diffusion are described theoretically in terms of the statistical properties of the field fluctuations, in particular the power spectra of the various spatial components. A large body of trapped particle data demonstrates that diffusion with the predicted properties actually takes place. These data include the average radial and energy distributions and the time variations in particle fluxes. This radial diffusion has a major influence on the structure of the radiation belts; and since the net flow of particles is inward at most positions of the magnetosphere, the process acts as a strong source of trapped particles. Further experiments are needed to establish the importance of this mechanism relative to magnetic storm effects and to collective instabilities.

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References

  • Birmingham, T. J., Northrop, T. G., and Fälthammar, C.-G.: 1967, ‘Charged Particle Diffusion by Violation of the Third Adiabatic Invariant’, Phys. Fluids 10, 2389.

    Article  ADS  Google Scholar 

  • Birmingham, T. J.: 1969, ‘Convection Electric Fields and the Diffusion of Trapped Magnetospheric Radiation’, J. Geophys. Res. 74, 2169.

    ADS  Google Scholar 

  • Blake, J. B. and Paulikas, G. A.: 1970, ‘Measurement of Trapped α-Particles: 2≤L≤4.5’, in Particles and Fields in the Magnetosphere (ed. by B. M. McCormac), D. Reidel Publ. Co., Dordrecht- Holland, p. 380.

    Google Scholar 

  • Brown, W. L.: 1966, ‘Observations of the Transient Behavior of Electrons in the Artificial Radiation Belts’, in Radiation Trapped in the Earth's Magnetic Field (ed. by B. M. McCormac), D. Reidel Publ. Co., Dordrecht-Holland, p. 610.

    Google Scholar 

  • Chang, D. B., Pearlstein, L. D., and Rosenbluth, M. N.: 1965, ‘On the Interchange Stability of the Van Allen Belt’, J. Geophys. Res. 70, 3085.

    MathSciNet  ADS  Google Scholar 

  • Cladis, J. B., Davidson, G. T., Francis, W. E., Newkirk, L. L., Tepley, L. R., Walt, M., and Wentworth, R. C.: 1965, ‘Search for Possible Loss Processes for Geomagnetically Trapped Particles’, Defense Atomic Support Agency Report 1713, Washington, D.C.

  • Cornwall, J. M.: 1970, ‘Mutually Interacting Instabilities in the Magnetosphere’, in Particles and Fields in the Earth's Magnetosphere (ed. by B. M. McCormac), D. Reidel Publ. Co., Dordrecht-Holland, p. 266.

    Google Scholar 

  • Cornwall, J. M.: 1971, ‘Transport and Loss Processes for Magnetospheric Helium’, J. Geophys. Res. 76, 264.

    ADS  Google Scholar 

  • Craven, J. D.: 1966, ‘Temporal Variations of Electron Intensities at low Altitudes in the Outer Radiation Zone as Observed with Satellite Injun 3’, J. Geophys. Res. 71, 5643.

    ADS  Google Scholar 

  • Davis, L. and Chang, D. B.: 1962, ‘On the Effect of Geomagnetic Fluctuations on Trapped Particles’, J. Geophys. Res. 67, 2169.

    MATH  ADS  Google Scholar 

  • DeForest, S. E.: 1970, ‘Long Term Variations in High-Energy Geomagnetically Trapped Particles’, Thesis, University of California, La Jolla, California, UCSD-SP-70–2.

    Google Scholar 

  • Dungey, J. W.: 1965, ‘Effects of Electromagnetic Perturbations on Particles Trapped in the Radiation Belt’, Space Sci. Rev. 4, 199.

    Article  ADS  Google Scholar 

  • Fälthammar, C.-G.: 1965, ‘Effects of Time Dependent Electric Fields on Geomagnetically Trapped Radiation’, J. Geophys. Res. 70, 2503.

    MathSciNet  ADS  Google Scholar 

  • Fälthammar, C.-G.: 1966, ‘On the Transport of Trapped Particles in the Outer Magnetosphere’, J. Geophys. Res. 71, 1487.

    ADS  Google Scholar 

  • Fälthammar, C.-G.: 1968, ‘Radial Diffusion by Violation of the Third Adiabatic Invariant’, in Earth's Particles and Fields (ed. by B. M. McCormac), Reinhold, New York, p. 157.

    Google Scholar 

  • Fälthammar, C.-G.: 1971, ‘Diffusion and Acceleration in the Earth's Radiation Belts’, Proc. Intern. Symp. Solar-Terrestrial Phys., Leningrad, U.S.S.R., May 11–16, 1970 (to be published).

  • Fälthammar, C.-G. and Walt, M.: 1969, ‘Radial Motion Resulting from Pitch-Angle Scattering of Trapped Electrons in the Distorted Geomagnetic Field’, J. Geophys. Res. 74, 4184.

    ADS  Google Scholar 

  • Farley, T.A.: 1969a, ‘Radial Diffusion of Electrons at Low L-Values’, J. Geophys. Res. 74, 377.

    ADS  Google Scholar 

  • Farley, T. A.: 1969b, ‘Radial Diffusion of Starfish Electrons’, J. Geophys. Res. 74, 3591.

    ADS  Google Scholar 

  • Farley, T. A., Tomassian, A. D., and Walt, M.: 1970, ‘Source of High Energy Protons in the Van Allen Radiation Belt’, Phys. Rev. Letters 25, 47.

    Article  ADS  Google Scholar 

  • Frank, L. A.: 1965, ‘Inward Radial Diffusion of Electrons Greater than 1.6 MeV in the Outer Radiation Zone’, J. Geophys. Res. 70, 3533.

    ADS  Google Scholar 

  • Frank, L. A., Van Allen, J. A., and Hills, H. K.: 1964, ‘A Study of Charged Particles in the Earth's Outer Radiation Zone with Explorer 14’, J. Geophys. Res. 69, 2171.

    ADS  Google Scholar 

  • Gold, T.: 1959, ‘Origin of the Radiation near the Earth Discovered by Means of Satellites’, Nature 183, 355.

    Article  ADS  Google Scholar 

  • Haerendel, G.: 1968, ‘Diffusion Theory of Trapped Particles and the Observed Proton Distribution’, Earth's Particles and Fields (ed. by B. M. McCormac), Reinhold, New York, p. 171.

    Google Scholar 

  • Haerendel, G.: 1970, ‘On the Balance Between Radial and Pitch Angle Diffusion’, in Particles and Fields in the Magnetosphere (ed. by B. M. McCormac), D. Reidel Publ. Co., Dordrecht-Holland, p. 416.

    Google Scholar 

  • Imhof, W. L.: 1968, ‘Electron Precipitation in the Radiation Belts’, J. Geophys. Res. 73, 4167.

    ADS  Google Scholar 

  • Kavanagh, L. D.: 1968, ‘An Empirical Evaluation of Radial Diffusion Coefficients for Electrons of 50–100 keV from L = 4 to L = 7’, J. Geophys. Res. 73, 2959.

    ADS  Google Scholar 

  • Kavanagh, L. D.: 1969, ‘Radial Diffusion of Trapped Electrons in a Magnetosphere with Oscillating Electric Field’, Trans. Am. Geophys. Union, Vol. 50, No. 4, 292, and private communication.

    Google Scholar 

  • Kellogg, P. J.: 1959, ‘Van Allen Radiation of Solar Origin’, Nature 183, 1295.

    Article  ADS  Google Scholar 

  • Kennel, C. F. and Petschek, H. E.: 1966, ‘Limit on Stably Trapped Particle Fluxes’, J. Geophys. Res. 71, 1.

    ADS  Google Scholar 

  • Krimigis, S. M.: 1970, ‘Alpha Particles Trapped in the Earth's Magnetic Field’, in Particles and Fields in the Magnetosphere (ed. by B. M. McCormac), D. Reidel Publ. Co., Dordrecht-Holland, p. 364.

    Google Scholar 

  • Lanzerotti, L. J., Maclennan, C. G., and Schulz, M.: 1970, ‘Radial Diffusion of Outer-Zone Electrons; An Empirical Approach to Third-Invariant Violation’, J. Geophys. Res. 75, 5351.

    ADS  Google Scholar 

  • MacDonald, W. M. and Walt, M.: 1961, ‘Distribution Function of Magnetically Confined Electrons in a Scattering Atmosphere’, Ann. Phys. 15, 44.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Manson, D. J., Fennell, J. F., George, J. A., Hickeson, J. L., Maldonado, G. V. and Weber, A. H.: 1969, Defense Atomic Support Agency Report No. 2309, Washington, D.C.

  • McDiarmid, I. B. and Burrows, J. R.: 1967, ‘Dependence of the Position of the Outer Radiation Zone Intensity Maxima on Electron Energy and Magnetic Activity’, Can. J. Phys. 45, 2873.

    ADS  Google Scholar 

  • Mead, G. D.: 1964, ‘Deformation of the Geomagnetic Field by the Solar Wind’, J. Geophys. Res. 69, 1181.

    MATH  ADS  Google Scholar 

  • Nakada, M. P., Dungey, J. W., and Hess, W. N.: 1965, ‘Theoretical Studies of Protons in the Outer Radiation Belts’, J. Geophys. Res. 70, 3529.

    ADS  Google Scholar 

  • Nakada, M. P. and Mead, G. D.: 1965, ‘Diffusion of Protons in the Outer Radiation Belt’, J. Geophys. Res. 70, 4777.

    ADS  Google Scholar 

  • Newkirk, L. L. and Walt, M.: 1968a, ‘Radial Diffusion Coefficient for Electrons at Low L-Values’, J. Geophys. Res. 73, 1013.

    ADS  Google Scholar 

  • Newkirk, L. L. and Walt, M.: 1968b, ‘Radial Diffusion Coefficient for Electrons at 1.76<L<5’, J. Geophys. Res. 73, 7231.

    ADS  Google Scholar 

  • Northrop, T. G. and Teller, E.; 1960, ‘Stability of the Adiabatic Motion of Charged Particles in the Earth's Field’, Phys. Rev. 117, 215.

    Article  MathSciNet  ADS  Google Scholar 

  • Parker, E. N.: 1960, ‘Geomagnetic Fluctuations and the Form of the Outer Zone of the Van Allen Radiation Belt’, J. Geophys. Res. 65, 3117.

    ADS  Google Scholar 

  • Pfitzer, K. A. and Winckler, J. R.: 1968, ‘Experimental Observation of a Large Addition to the Electron Inner Radiation Belt After a Solar Flare Event’, J. Geophys. Res. 73, 5792.

    ADS  Google Scholar 

  • Pizzella, G. and Frank, L. A.: 1971, ‘Energy Spectrums for Proton (200 eV ≤E≤1 MeV) Intensities in the Outer Radiation Zone’, J. Geophys. Res. 76, 88.

    ADS  Google Scholar 

  • Roederer, J. G.: 1968, ‘Shell Splitting and Radial Diffusion of Geomagnetically Trapped Particles’, in Earth's Particles and Fields (ed. by B. M. McCormac), Reinhold Book Corporation, New York, p. 193.

    Google Scholar 

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

    Google Scholar 

  • Roederer, J. G. and Schulz, M.: 1969, ‘Effect of Shell Splitting on Radial Diffusion in the Magnetosphere’, J. Geophys. Res. 74, 4117.

    ADS  Google Scholar 

  • Russell, C. T. and Thorne, R. M.: 1970, ‘On the Structure of the Inner Magnetosphere’, Cosmic Electrodyn, 1, 67.

    Google Scholar 

  • Schulz, M. and Eviatar, A.: 1969, ‘Diffusion of Equatorial Particles in the Outer Radiation Zone’, J. Geophys. Res. 74, 2182.

    ADS  Google Scholar 

  • Söraas, F.: 1969, ‘Comparison of Post-Storm Nonadiabatic Recovery of Trapped Protons with Radial Diffusion’, GSFC Report X-612-69-241, Greenbelt, Md.

  • Thede, A. L.: 1969, ‘OV3-4 Dose Rate and Proton Spectral Measurements’, Air Force Weapons Laboratory Report No. AFWL-TR-68-128. Albuquerque, New Mexico, (unpublished).

  • Theodoridis, G. C., Paolini, F. R., and Frankenthal, S.: 1969, ‘Acceleration of Trapped Electrons and Protons Through Bimodal Diffusion in the Earth's Radiation Belts’, J. Geophys. Res. 74, 1238.

    ADS  Google Scholar 

  • Tverskoy, B. A.: 1964, ‘Dynamics of the Radiation Belts of the Earth2’, Geomagnetizm Aeronomiya, 4, 351.

    Google Scholar 

  • Tverskoy, B. A.: 1965, ‘Transport and Acceleration of Charged Particles in the Earth's Magnetosphere’, Geomagnetizm i Aeronomiya 5, 617.

    Google Scholar 

  • Van Allen, J. A., McIlwain, C. E., and Ludwig, G. H.: 1959, ‘Satellite Observations of Electrons Artificially Injected into the Geomagnetic Field’, J. Geophys. Res. 64, 877.

    ADS  Google Scholar 

  • Van Allen, J. A., Randall, B. A., and Krimigis, S. M.: 1970, ‘Energetic Carbon, Nitrogen and Oxygen Nuclei in the Earth's Outer Radiation Zone’, J. Geophys. Res. 75, 6085.

    Article  ADS  Google Scholar 

  • Vernov, S. N., Kuznetsov, S. N., Logachev, Yw. I., Lopatina, P. B., Sosnovets, E. N., and Stolpovsky, V. G.: 1968, ‘Radial Diffusion of 100 keV Electrons in the Outer Radiation Belt’, Geomagnetizm i Aeronomiya 8, 401.

    Google Scholar 

  • Vette, J. I., Lucero, A. B., and Wright, J. A.: 1966, Models of the Trapped Radiation Environment II, Inner and Outer Zone Electrons, NASA SP-3024, Washington, D.C.

  • Walt, M.: 1964, ‘The Effects of Atmospheric Collisions on Geomagnetically Trapped Electrons’, J. Geophys. Res. 69, 3947.

    ADS  Google Scholar 

  • Walt, M.: 1970, ‘Radial Diffusion of Trapped Particles’, in Particles and Fields in the Magnetosphere (ed. by B. M. McCormac), D. Reidel Publ. Co., Dordrecht-Holland, p. 410.

    Google Scholar 

  • Walt, M. and Newkirk, L. L.: 1971, ‘Comments on the Paper ‘Radial Diffusion of Outer-zone Electrons: An Empirical Approach to Third-Invariant Violation’ by L. J. Lanzerotti, C. G. Maclennan and M. Schulz’, J. Geophys. Res. (to be published).

  • Williams, D. J.: 1970, ‘Sources, Losses and Transport of Magnetospherically Trapped Particles’, ESSA Technical Report ERL 180-SDL 16, Superintendent of Documents, U.S. Government Printing Office, Washington, D.C..

    Google Scholar 

  • Williams, D. J., Arens, J. F., and Lanzerotti, L. J.: 1968, ‘Observations of Trapped Electrons at Low and High Altitudes’, J. Geophys. Res. 73, 5673.

    ADS  Google Scholar 

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Walt, M. The radial diffusion of trapped particles induced by fluctuating magnetospheric fields. Space Sci Rev 12, 446–485 (1971). https://doi.org/10.1007/BF00171975

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  • DOI: https://doi.org/10.1007/BF00171975

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