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Numerical study of electrostatic electron cyclotron harmonic waves due to Maxwellian ring velocity distributions

Abstract

Excitation of electrostatic electron cyclotron harmonic (ECH) waves is studied by performing linear dispersion analysis and particle-in-cell computer simulation. The ECH wave emissions can be excited by a positive slope in a velocity distribution function perpendicular to the ambient magnetic field, such as that due to a loss cone or ring velocity distribution. However, there exists no analytic expression for integration of Maxwellian ring velocity distribution functions. Here we present a method to solve the linear dispersion relations of Maxwellian ring velocity distribution functions with numerical integration. The obtained dispersion relations are confirmed by particle-in-cell simulation.

References

  • Ashour-Abdalla, M. and C. F. Kennel, Multi-harmonic electron cyclotron instabilities, Geophys. Res. Lett., 5, 711–714, 1978a.

    Article  Google Scholar 

  • Ashour-Abdalla, M. and C. F. Kennel, Nonconvective and convective electron cyclotron harmonic instabilities, J. Geophys. Res., 83, 1531–1543, 1978b.

    Article  Google Scholar 

  • Ashour-Abdalla, M., G. Chanteur, and R. Pellat, A contribution to the theory of the electrostatic half-harmonic electron gyrofrequency waves in the magnetosphere, J. Geophys. Res., 80, 2775–2782, 1975.

    Article  Google Scholar 

  • Ashour-Abdalla, M., C. F. Kennel, and W. Livesey, A parametric study of electron multiharmonic instabilities in the magnetosphere, J. Geophys. Res., 84, 6540–6546, 1979.

    Article  Google Scholar 

  • Ashour-Abdalla, M., J.-N. Leboeuf, J. M. Dawson, and C. F. Kennel, A simulation study of cold electron heating by loss cone instabilities, Geophys. Res. Lett., 7, 889–892, 1980.

    Article  Google Scholar 

  • Convery, P., Ring and nongyrotropic distributions in the Earth’s magnetosphere, Ph.D. Thesis, University of California, Los Angeles, USA, 1997.

    Google Scholar 

  • Fredricks, R. W., Plasma instability at (n + 1/2)fc and its relationship to some satellite observations, J. Geophys. Res., 76, 5344–5348, 1971.

    Article  Google Scholar 

  • Harris, E. G., Unstable plasma oscillations in a magnetic field, Phys. Rew. Lett., 2, 34–36, 1959.

    Article  Google Scholar 

  • Horne, R. B., P. J. Christiansen, M. P. Gough, K. Rönnmark, J. F. E. Johnson, J. Sojka, and G. L. Wrenn, Amplitude variations of electron cyclotron harmonic waves, Nature, 294, 338–340, 1981.

    Article  Google Scholar 

  • Horne, R. B., P. J. Christiansen, and M. P. Gough, Weak electrostatic waves near the upper hybrid frequency: A comparison between theory and experiment, J. Geophys. Res., 92, 3243–3259, 1987.

    Article  Google Scholar 

  • Kennel, C. F., F. L. Scarf, R. W. Fredricks, J. H. Mcghee, and F. V. Coroniti, VLF electric field observations in the inner magnetosphere, J. Geophys. Res., 75, 6136–6152, 1970.

    Article  Google Scholar 

  • Koons, H. C. and J. F. Fennel, Fine structure in electrostatic emission bands between electron gyrofrequency harmonics, J. Geophys. Res., 89, 3015–3018, 1984.

    Article  Google Scholar 

  • Kurth, W. S., M. Ashour-Abdalla, L. A. Frank, C. F. Kennel, D. A. Gurnett, D. D. Sentman, and B. G. Burek, A comparison of intense electrostatic waves near fUHR with linear instability theory, Geophys. Res. Lett., 6, 487–490, 1979a.

    Article  Google Scholar 

  • Kurth, W. S., J. D. Craven, L. A. Frank, and D. A. Gurnett, Intense electrostatic waves near the upper hybrid resonance frequency, J. Geophys. Res., 84, 4145–4164, 1979b.

    Article  Google Scholar 

  • Kurth, W. S., L. A. Frank, D. A. Gurnett, B. G. Burek, and M. Ashour-Abdalla, Observations of a free-energy source for intense electrostatic waves, Geophys. Res. Lett., 7, 293–296, 1980.

    Article  Google Scholar 

  • Lee, J. K. and C. K. Birdsall, Velocity space ring-plasma instability, magnetized, Part I: Theory, Phys. Fluids, 22, 1306–1314, 1979.

    Article  Google Scholar 

  • Matsumoto, H. and H. Usui, Intense bursts of electron cyclotron harmonic waves near the dayside magnetopause observed by GEOTAIL, Geophys. Res. Lett., 24, 49–52, 1997.

    Article  Google Scholar 

  • Muller, D. E., A method for solving algebraic equations using an automatic computer, Math. Tables Aids Comput. (now Math. Comput.), 10, 208–215, 1956.

    Article  Google Scholar 

  • Nakamura, T. K. and M. Hoshino, One-over-polynomial approximation for linear kinetic dispersion and its application to relativistic cyclotron resonance, Phys. Plasmas, 5, 3547–3551, 1998.

    Article  Google Scholar 

  • Rönnmark, K. and P. J. Christiansen, Dayside electron cyclotron harmonic emissions, Nature, 294, 335–338, 1981.

    Article  Google Scholar 

  • Rönnmark, K., H. Borg, P. J. Christensen, M. P. Gough, and D. Jones, Banded electron cyclotron harmonic instability: A first comparison of theory and experiment, Space Sci. Rev., 22, 401–417, 1978.

    Article  Google Scholar 

  • Shinbori, A., T. Ono, M. Iizima, A. Kumamoto, S. Shirai, A. Hanaoka, K. Okamoto, M. Ohashi, and H. Oya, Electrostatic electron cyclotron harmonic waves observed by the Akebono satellite near the equatorial region of the plasmasphere, Earth Planets Space, 59, 613–629, 2007.

    Article  Google Scholar 

  • Sotnikov, V. I., D. Schriver, M. Ashour-Abdalla, J. Ernstmeyer, and N. Myers, Excitation of electron acoustic waves by a gyrating electron beam, J. Geophys. Res., 100, 19,765–19,772, 1995.

    Article  Google Scholar 

  • Tataronis, J. A. and F. Crawford, Cyclotron harmonic waves propagation and instabilities: I. Perpendicular propagation, J. Plasma Phys., 4, 231–248, 1970a.

    Article  Google Scholar 

  • Tataronis, J. A. and F. Crawford, Cyclotron harmonic waves propagation and instabilities: II. Oblique propagation, J. Plasma Phys., 4, 249–264, 1970b.

    Article  Google Scholar 

  • Umeda, T., Study on nonlinear processes of electron beam instabilities via computer simulations, Ph.D. Thesis, Kyoto University, 2004.

    Google Scholar 

  • Umeda, T., M. Ashour-Abdalla, D. Schriver, R. L. Richard, and F. V. Coroniti, Particle-in-cell simulation of Maxwellian ring velocity distribution J. Geophys. Res., 112, A04212, doi:10.1029/2006JA012124, 2007.

  • Usui, H., J. Koizumi, and H. Matsumoto, Statistical study of electron cyclotron harmonic waves observed in the dayside magnetosphere, Adv. Space Res., 20, 857–860, 1997.

    Article  Google Scholar 

  • Usui, H., H. Matsumoto, T. Mukai, and Y. Saito, Geotail observation of electron cyclotron harmonic waves near the dayside magnetopause, Adv. Space Res., 24, 99–102, 1999a.

    Article  Google Scholar 

  • Usui, H., W. R. Paterson, H. Matsumoto, L. A. Frank, M. Nakamura, H. Matsui, T. Yamamoto, O. Nishimura, and J. Koizumi, Geotail electron observations in association with intense bursts of electron cyclotron harmonic waves in the dayside magnetosphere, J. Geophys. Res., 104, 4477–4484, 1999b.

    Article  Google Scholar 

  • Young, T. S. T., Destabilization and wave-induced evolution of the magnetospheric plasma clouds, J. Geophys. Res., 80, 3995–4003, 1975.

    Article  Google Scholar 

  • Young, T. S. T., J. D. Callen, and J. E. McCune, High-frequency electrostatic waves in the magnetosphere, J. Geophys. Res., 78, 1082–1099, 1973.

    Article  Google Scholar 

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Correspondence to Takayuki Umeda.

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Umeda, T. Numerical study of electrostatic electron cyclotron harmonic waves due to Maxwellian ring velocity distributions. Earth Planet Sp 59, 1205–1210 (2007). https://doi.org/10.1186/BF03352068

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  • DOI: https://doi.org/10.1186/BF03352068

Key words

  • Electron cyclotron waves
  • linear dispersion analysis
  • numerical simulation