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Numerical study of electrostatic electron cyclotron harmonic waves due to Maxwellian ring velocity distributions
Earth, Planets and Space volume 59, pages 1205–1210 (2007)
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.
Ashour-Abdalla, M. and C. F. Kennel, Multi-harmonic electron cyclotron instabilities, Geophys. Res. Lett., 5, 711–714, 1978a.
Ashour-Abdalla, M. and C. F. Kennel, Nonconvective and convective electron cyclotron harmonic instabilities, J. Geophys. Res., 83, 1531–1543, 1978b.
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.
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.
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.
Convery, P., Ring and nongyrotropic distributions in the Earth’s magnetosphere, Ph.D. Thesis, University of California, Los Angeles, USA, 1997.
Fredricks, R. W., Plasma instability at (n + 1/2)fc and its relationship to some satellite observations, J. Geophys. Res., 76, 5344–5348, 1971.
Harris, E. G., Unstable plasma oscillations in a magnetic field, Phys. Rew. Lett., 2, 34–36, 1959.
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.
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.
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.
Koons, H. C. and J. F. Fennel, Fine structure in electrostatic emission bands between electron gyrofrequency harmonics, J. Geophys. Res., 89, 3015–3018, 1984.
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.
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.
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.
Lee, J. K. and C. K. Birdsall, Velocity space ring-plasma instability, magnetized, Part I: Theory, Phys. Fluids, 22, 1306–1314, 1979.
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.
Muller, D. E., A method for solving algebraic equations using an automatic computer, Math. Tables Aids Comput. (now Math. Comput.), 10, 208–215, 1956.
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.
Rönnmark, K. and P. J. Christiansen, Dayside electron cyclotron harmonic emissions, Nature, 294, 335–338, 1981.
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.
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.
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.
Tataronis, J. A. and F. Crawford, Cyclotron harmonic waves propagation and instabilities: I. Perpendicular propagation, J. Plasma Phys., 4, 231–248, 1970a.
Tataronis, J. A. and F. Crawford, Cyclotron harmonic waves propagation and instabilities: II. Oblique propagation, J. Plasma Phys., 4, 249–264, 1970b.
Umeda, T., Study on nonlinear processes of electron beam instabilities via computer simulations, Ph.D. Thesis, Kyoto University, 2004.
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.
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.
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.
Young, T. S. T., Destabilization and wave-induced evolution of the magnetospheric plasma clouds, J. Geophys. Res., 80, 3995–4003, 1975.
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.
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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
- Electron cyclotron waves
- linear dispersion analysis
- numerical simulation