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Numerical simulation of resonant scattering of energetic electrons in the outer radiation belt


Resonant diffusion processes of high energy electrons are studied numerically by using an original simulation scheme where cold electrons are treated as a fluid and hot electrons are treated as particles including fully relativistic effects. The present simulation scheme enables us to investigate the resonant scattering process in the inner magnetosphere, which has been difficult to study by using the PIC code. We investigated the variation of the distribution of electrons through the resonant diffusion process by comparing the present numerical experiment and the quasi-linear theory under the same condition of the interaction between whistler-mode waves and high energy electrons. The difference between their results suggests the importance of the verification of the theory under the realistic plasma condition corresponding to the observed parameters in the outer radiation belt.


  • Albert, J. M., Analysis of quasi-linear diffusion coefficients, J. Geophys. Res., 104, 2429–2441, 1999.

    Article  Google Scholar 

  • Albert, J. M., Gyroresonant interactions of radiation belt particles with a monochromatic electromagnetic wave, J. Geophys. Res., 105, 21191–21209, 2000.

    Article  Google Scholar 

  • Baker, D. N., J. B. Blake, L. B. Callis, J. R. Cummings, D. Hovestadt, S. Kanekal, B. Klecker, R. A. Mewaldt, and R. D. Zwickl, Relativistic electron acceleration and decay time scales in the inner and outer radiation belts: SAMPEX, Geophys. Res. Lett., 21, 409–412, 1994.

    Article  Google Scholar 

  • Birdsall, C. K. and A. B. Langdon, Plasma Physics via Computer Simulation, McGraw-Hill, 1985.

    Google Scholar 

  • Blake, J. B., W. A. Kolasinski, R. W. Fillius, and E. G. Mullen, Injection of electrons and protons with energies of tens of MeV into L<3 on 24 March 1991, Geophys. Res. Lett., 19, 821–824, 1992.

    Article  Google Scholar 

  • Brautigam, D. H. and J. M. Albert, Radial diffusion analysis of outer radiation belt electrons during the October 9, 1990, magnetic storm, J. Geophys. Res., 105, 291–309, 2000.

    Article  Google Scholar 

  • Horne, R. B., S. A. Glauert, and R. M. Thorne, Resonant diffusion of radiation belt electrons by whistler-mode chorus, Geophys. Res. Lett., 30, 1493–1496, 2003.

    Article  Google Scholar 

  • Kozyra, J. U., C. E. Rasmussen, R. H. Miller, and E. Villalon, Interaction of ring current and radiation belt protons with ducted plasmaspheric hiss 2. Time evolution of the distribution function, J. Geophys. Res., 100, 21911–21919, 1995.

    Article  Google Scholar 

  • Lyons, L. R., Pitch angle and energy diffusion coefficients from resonant interactions with ion-cyclotron and whistler waves, J. Plasma Phys., 12, 417–432, 1974.

    Article  Google Scholar 

  • Lyons, L. R. and R. M. Thorne, Equilibrium structure of radiation belt electrons, J. Geophys. Res., 78, 13,2142–2149, 1973.

    Google Scholar 

  • Meredith, N. P., R. B. Horne, D. Summers, R. M. Thorne, R. H. A. Iles, D. Heyndreickx, and R. R. Anderson, Evidence for acceleration of outer zone electrons to relativistic energies by whistler mode chorus, Ann. Geophys., 20, 967–979, 2002.

    Article  Google Scholar 

  • Miyoshi, Y., A. Morioka, T. Obara, H. Misawa, T. Nagai, and Y. Kasahara, Rebuilding process of the outer radiation belt during the 3 November 1993 magnetic storm: NOAA and EXOS-D observations, J. Geophys. Res., 108, 1004–1018, 2003.

    Article  Google Scholar 

  • Obara, T., T. Nagatsuma, M. Den, Y. Miyoshi, and A. Morioka, Mainphase creation of “seed” electrons in the outer radiation belt, Earth Planets Space, 52, 41–47, 2000.

    Article  Google Scholar 

  • Omura, Y and H. Matsumoto, Computer simulations of basic process of coherent whistler wave-particle interactions in the magnetosphere, J. Geophys. Res., 87, 4435–4444, 1982.

    Article  Google Scholar 

  • Omura, Y. and H. Matsumoto, KEMPO1: Technical guide to one-dimensional electromagnetic particle code, in Computer Space Plasma Physics: Simulation Techniques and Softwares, edited by H. Matsumoto and Y Omura, Terra Scientific Pub., Tokyo, 1985.

    Google Scholar 

  • Rathmann, C. E., J. L. Vomvoridis, and J. Denavit, Long-time-scale simulation of resonant particle effects in Langmuir and whistler waves, J. Computational Phys., 26, 408–442, 1978.

    Article  Google Scholar 

  • Roth, I., M. Temerin, and M. K. Hudson, Resonant enhancement of relativistic electron fluxes during geomagnetically active periods, Ann. Geophys., 17, 631–638, 1999.

    Article  Google Scholar 

  • Selesnick, R. S. and J. B. Blake, On the source location of radiation belt relativistic electrons, J. Geophys. Res., 105, 2607–2624, 2000.

    Article  Google Scholar 

  • Summers, D. and C. Y Ma, A model for generating relativistic electrons in the Earth’s inner magnetosphere based on gyroresonant wave-particle interactions, J. Geophys. Res., 105, 2625–2639, 2000.

    Article  Google Scholar 

  • Taguchi, T., J. Thomas, M. Antonsen, C. S. Liu, and K. Mima, Structure formation and tearing of an MeV cylindrical electron beam in a laser-produced plasma, Phys. Rev. Lett., 86, 5055–5058, 2001.

    Article  Google Scholar 

  • Vampola, A. L. and A. Korth, Electron drift echoes in the inner magnetosphere, Geophys. Res. Lett., 19, 625–628, 1992.

    Article  Google Scholar 

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Correspondence to Yuto Katoh.

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Katoh, Y., Ono, T. & Iizima, M. Numerical simulation of resonant scattering of energetic electrons in the outer radiation belt. Earth Planet Sp 57, 117–124 (2005).

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Key words

  • Radiation belt
  • numerical experiment
  • quasi-linear diffusion
  • relativistic electrons