Abstract
The elements of dielectric tensor and dispersion relation for obliquely propagating whistler waves with finite \(k_{\perp}<< k_{||}\) in an infinite magnetoplasma are obtained for a kappa distribution in the presence of perpendicular a.c. electric field. Integrals and modified plasma dispersion functions are reduced in power series form. Numerical calculations have been performed to obtain temporal growth rate and real frequencies of the plasma waves for magnetospheric plasma, using linear theory of dispersion relation. The effect and modification introduced by the perpendicular a.c. electric field on the temporal growth rates, real frequencies and resonance condition are discussed for kappa and Maxwellian distributions. Our results and their interpretation are compared with known whistler observations obtained by ground-based techniques and satellite observations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Abraham-Shrauner B., Asbridge J.R., Bame S.J., Feldman W.C., (1979). Proton-driven electromagnetic instabilities in high-speed solar wind streams. J. Geophys. Res. 84:553
Armstrong T.P., Paonessa M.T., Bell II E.V., Krimigis S.M. (1983). Voyager observations of Saturnian ion and electron phase space densities. J. Geophys. Res. 88:8893
Asseo E., Laval G., Pellat R., Welti R., Roux A. (1972). Effect of the plasma inhomogeneity on the nonlinear damping of monocromatic waves. J. Plasma Phys. 8:341
Bell, T.F. and Helliwell, R. A.: 1978, ISEE Trans. Geosci. Elect. GE-16
Bell T.F., James H.G., Inan U.S., Katsufrakis J.P. (1983). The apparent spectral broadening of VLF transmitter signals during transionospheric propagation. J. Geophys. Res. 88:4813–4840
Bell T.F., Ngo H.D. (1990). Electrostatic lower hybrid waves excited by electromagnetic whistler mode waves scattering from planar magnetic-field-aligned density irregularities. J. Geophys. Res. 95:149–172
Budko N.I., Karpman V.I., Pokhotelov O.A. (1971). On nonlinear effects during propagation of monochromatic VLF waves (helicons) in the magnetosphere. JETP. Lett. 14:112
Budko N.I., Karpman V.I., Pokhotelov O.A. (1972). Nonlinear theory of the monochromatic circularly polarized VLF and ULF waves in the magnetosphere. Cosmic Electrodynamics 3:147
Burke W.J., Nelson C. (2000). Maynard, ‘Satellites observations of Electric fields in the inner magnetosphere and their effects in the mid-to-low latitude ionosphere. IEEE Trans. on Plasma Science. 28:1903
Carlson C.R., Helliwell R.A., Inan U.S. (1990). Space time evolution of whistler mode wave growth in the magnetosphere. J. Geophys. Res. 95:15073
Chian A.C.-L., Lopes S.R., Alves M.V. (1994). Nonlinear excitation of Langmuir and Alfven waves by auroral whistler waves in the planetary magnetosphere. Astron. Astrophys. 288:981–984
Fälthammar C.G. (1989). Electric fields in the magnetosphere-The evidence from ISEE, GEOS, and Viking. IEEE transaction on Plasma science 17:174
Hasegawa A. (1975). Plasma Instabilities and Nonlinear Effects. Berlin, Springer-Verlag
Hasegawa A., Mima K., duong-Van M. (1985). Plasma distribution function in a superthermal radiation field, Phys. Rev. Lett. 54:2608
Helliwell R.A. (1965). Whistler and related ionospheric phenomena. Stanford University Press, Stanford California, pp. 288–308
Helliwell R.A., Katsufrakis J.P., Trimpi M.L. (1973). Whistler-induced amplitude perturbation in VLF propagation. J. Geophys. Res. 78:4679
Inan U.S., Bell T.F., Carpenter D.L. (1977). Explorer 45 and IMP6 observations in the magnetosphere of injected waves from the Siple Station VLF transmitter. J. Geophys. Res. 82:1177
Inan U.S., Bell T.F., Helliwell R.A. (1978). Nonlinear pitch angle scattering of energetic electrons by coherent VLF waves in the magnetosphere. J. Geophys. Res. 83:3235–3253
Kennel C.F., Wong H.V. (1967). Resonantly unstable off-angle hydromagnetic waves. J. Plasma Phys. 1:81
Kimura I. (1968). Triggering of VLF magnetospheric noise by low power (∼ ∼100 W) transmitter. J. Geophys. Res. 73:4451
Lalmani M.K.B., Kumar R., Singh R., Gwal A.K. (2000). An explanation of day time discrete VLF emissions observed at Jammu (L=1.17) and determination of magnetospheric parameters. Indian J. Phys. 74B:117
Leubner M.P. (1982). On Jupiter’s whistler emission. J. Geophys. Res. 87:6335
Lindqvist P.A., Marklund G.T. (1990). A statistical study of high-altitude electric field measured on the viking satellite. J. Geophys. Res. 95:5867
Mace R.L. (1998). Whistler instability enhanced by suprathermal electrons within the Earth’s foreshock. J. Geophys. Res. 103:14643
Misra K.D., Pandey R.S. (1995). Generation of Whistler emissions by injection of hot electrons in the presence of a perpendicular a.c. electric field. J. Geophys. Res. 100:19405
Molvig K., Hilfer G., Miller R.H., Myczkowski J. (1988). Self consistent theory of triggered whistler emissions. J. Geophys. Res. 93:5665
Mozer F.S., Torbert R.B., Fahleson U.V., Falthammar C.G., Gonafalone A., Pedersen A., Russel C.T. (1978). Electric field measurements in the solar wind bow shock, magnetosheath, magnetopause and magnetosphere. Space. Sci. Rev. 22:791
Prasad R. (1967). Effect of high frequency spatially uniform external electric field on plasma. Phys. Fluid B 10:2612
Roux A. (1974). Monochromatic waves and inhomogeneity effects. In: McCormac B.M., Reidel D. (eds), magnetospheric physics. Hingham, Mass, pp. 297
Sazhin S.S. (1993). Whistler mode waves in hot plasma. Cambridge University Press, New York
Stix T.H. (1962). The Theory of Plasma Waves. McGraw-Hill, New York
Summers D., Thorne R.M. (1991). The modified plasma dispersion function. Phys. Fluids B 8:1835
Summers D., Xue S., Thorne R.M. (1994). Calculation of the dielectric tensor for a generalized Lorentzian (kappa) distribution function. Phys. Plasma 1:2012
Tanaka Y., Lagoutte D., Hayakawa M., Lefeuvre F., Tajima S. (1987). Spectral broadening of VLF transmitter signals and sidebands structure observed on Aureol-3 satellite at middle latitude. J. Geophys. Res. 92:7551–7559
Tripathi A.K., Misra K.D. (2001). Computer analysis of whistler mode instability in the presence of perpendicular a.c. electric field for Lorentzian (kappa) magnetoplasma. Indian J. of Radio & Space Phys. 30:279
Tripathi A.K., Misra K.D. (2002). Whistler mode instability in a Lorentzian (kappa) magnetoplasma in the presence of perpendicular a.c. electric field and cold plasma injection. Earth, Moon and Planets. 88:131
Vasyliunas V.M. (1968). A Survey of low-energy electrons in the evening sector of the magnetosphere with OGO1 and OGO3. J. Geophys. Res. 73:2839
Vomvoridis J.L., Crystal T.L., Denavit J. (1982). Theory and computer simulations of magnetospheric very low frequency emissions. J. Geophys. Res. 87:1473–1489
Xue S., Thorne R.M., Summers D. (1996). Growth and damping of oblique electromagnetic ion-cyclotron waves in the Earth’s magnetosphere. J. Geophys. Res. 101:15457
Zhang Y., Matsumoto H., Omura Y. (1993). Linear and nonlinear interactions of an electron beam with oblique whistler and electrostatic waves, J. Geophys. Res. 98: 21353
Acknowledgements
The authors gratefully acknowledge the computational help by Shri Girish Chandra of I.E.T., Lucknow, India. This work was supported by a Research Associateship awarded to one of the author (A.K.T.) by the Council of Scientific and Industrial Research, Government of India.
Author information
Authors and Affiliations
Corresponding author
Appendix A
Appendix A
Components of dielectric tensor \(\in_{ij}\)
where
with
where \(J_{n}(\lambda_{1})\) and \(J_{p}(\lambda_{2})\) are the Bessel functions of first kind with the argument of λ1 and λ2 respectively and having the order n and p. \(J'_{n}(\lambda_{1})\) and \(J'_{p}(\lambda_{2})\) are the derivative with respect to λ1 and λ2. ɛ0, e s , m s and N 0s are respectively permittivity of free space, particle charge, mass and number density of species s. \(\omega_{c_{s}}\) and \(\omega_{p_{s}}\) are gyrofrequency and plasma frequency, respectively.
The function \(Z^{*}_{\kappa - 1}\) occurring in (A5), (A7) and (A9) is the modified plasma dispersion function (Summers and Thorne, 1991) which for integral values of κ ≥ 2 may be written as :
In the presence of perpendicular a.c. electric field in the limit λ → 0 the integrals \(S_{1}, S_{2},\ldots, S_{6}\) are reduced to power series form (Summers et al., 1994).
Rights and permissions
About this article
Cite this article
Tripathi, A.K., Singhal, R.P. EFFECT OF PERPENDICULAR A.C. ELECTRIC FIELD ON THE OBLIQUE WHISTLER MODE INSTABILITY IN THE EARTH’S MAGNETOSPHERE. Earth Moon Planet 97, 91–106 (2005). https://doi.org/10.1007/s11038-005-9053-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11038-005-9053-7