Abstract
Very low frequency electromagnetic waves in the magnetosphere of Saturn are the focus of the present study. Hot injected beam effect on these waves like whistler mode waves for relativistic and non-relativistic subtracted bi-Maxwellian distribution function have been studied in the presence of perpendicular A.C electric field. By using the method of characteristics solutions and kinetic approach, expression for dispersion relation and growth rate has been derived via detailed calculations and derivations. By changing parameters of plasma like: ac frequency, thermal anisotropy, number density, parametric analysis has been done. The influence of AC frequency on Doppler shift is analyzed, and the comparative study of the effects of oblique and parallel propagating waves on the growth rate has been done. Some different results were found using the subtracted bi-Maxwellian distribution function discussed with the results of bi-Maxwellian distribution function. It can be seen that the effective parameters for generating whistler mode waves are not only temperature anisotropy, but also relativistic factor, alternating field frequency, subtracted distribution amplitude and the width of the loss cone distribution function, which have been discussed in the results and discussion section.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Allcock, G.M.: A study of the audio-frequency radio phenomenon known as “dawn chorus”. Aust. J. Phys. 10, 286 (1957)
Anderson, R.R., Maeda, K.: VLF emissions associated with enhanced magnetospheric electrons. J. Geophys. Res. 82, 135–146 (1977). https://doi.org/10.1029/JA082i001p00135
Andriopoulou, M., Roussos, E., Krupp, N., Paranicas, C., Thomsen, M., Krimigis, S., Dougherty, M.K., Glassmeier, K.-H.: Spatial and temporal dependence of the convective electric field in Saturn’s inner magnetosphere. Icarus 229, 57–70 (2014)
Bortnik, J., Thorne, R.M.: The dual role of ELF/VLF chorus waves in the acceleration and precipitation of radiation belt electrons. J. Atmos. Sol.-Terr. Phys. 69, 378–386 (2007). https://doi.org/10.1016/j.jastp.2006.05.030
Breneman, A., Kletzing, C.A., Chum, J., Santolik, O., Gurnett, D.A., Pickett, J.S.: Multispacecraft observations of chorus dispersion and source location. J. Geophys. Res. 112, A05221 (2007). https://doi.org/10.1029/2006JA012058
Burtis, W.J., Helliwell, R.A.: Banded chorus—a new type of VLF radiation observed in the magnetosphere by OGO 1 and OGO 3. J. Geophys. Res. 74, 3002–3010 (1969). https://doi.org/10.1029/JA074i011p03002
Burton, R.K.: Critical electron pitch angle anisotropy necessary for chorus generation. J. Geophys. Res. 81, 4779–4781 (1976). https://doi.org/10.1029/JA081i025p04779
Burton, R., Holzer, R.E.: The origin and propagation of chorus in the outer magnetosphere. J. Geophys. Res. 79, 1014–1023 (1974). https://doi.org/10.1029/JA079i007p01014
Chum, J., Santolik, O., Breneman, A.W., Kletzing, C.A., Gurnett, D.A., Pickett, J.S.: Chorus source properties that produce time shifts and frequency range differences observed on different spacecraft. J. Geophys. Res. 112, A06206 (2007). https://doi.org/10.1029/2006JA012061
Cornilleau-Wehrlin, N., Gendrin, R., Lefeuvre, F., Parrot, M., Grard, R., Jones, D., Bahnsen, A., Ungstrup, E., Gibbons, W.: VLF electromagnetic waves observed onboard GEOS-1. Space Sci. Rev. 22, 371–382 (1978)
Curtis, S.A.: A theory for chorus generation by energetic electrons during substorms. J. Geophys. Res. 83, 3841–3848 (1978). https://doi.org/10.1029/JA083iA08p03841
Dunckel, N., Helliwell, R.A.: Whistler mode emissions on the OGO-1 satellite. J. Geophys. Res. 74, 6371–6385 (1969). https://doi.org/10.1029/JA074i026p06371
Goldstein, B.E., Tsurutani, B.T.: Wave normal directions of chorus near the equatorial source region. J. Geophys. Res. 89, 2789–2810 (1984). https://doi.org/10.1029/JA089iA05p02789
Gurnett, D.A., O’Brien, B.J.: High-latitude geophysical studies with satellite Injun 3: 5. Very-low-frequency electromagnetic radiation. J. Geophys. Res. 69, 65–89 (1964). https://doi.org/10.1029/JZ069i001p00065
Gurnett, D.A., Kurth, W.S., Scarf, F.L.: Plasma waves near Saturn: initial results from Voyager 1. Science 212, 235–239 (1981). https://doi.org/10.1126/science.212.4491.235
Hayakawa, M., Yamanaka, Y., Parrot, M., Lefeuvre, F.: The wave normals of magnetospheric chorus emissions observed on board GEOS 2. J. Geophys. Res. 89, 2811–2821 (1984). https://doi.org/10.1029/JA089iA05p02811
Hayakawa, M., Hattori, K., Shimakura, S., Parrot, M., Lefeuvre, F.: Direction finding of chorus emissions in the outer magnetosphere and their generation and propagation. Planet. Space Sci. 38, 135–143 (1990). https://doi.org/10.1016/0032-0633(90)90012-F
Helliwell, R.A.: Low-frequency waves in the magnetosphere. Rev. Geophys. 7, 281–303 (1969). https://doi.org/10.1029/RG007i001p00281
Horne, R.B., Glauert, S.A., Thorne, R.M.: Resonant diffusion of radiation belt electrons by whistler-mode chorus. Geophys. Res. Lett. 30(9), 1493 (2003). https://doi.org/10.1029/2003GL016963
Horne, R.B., Thorne, R.M., Glauert, S.A., Albert, J.M., Meredith, N.P., Anderson, R.R.: Timescale for radiation belt electron acceleration by whistler mode chorus waves. J. Geophys. Res. 110, A03225 (2005). https://doi.org/10.1029/2004JA010811
Hospodarsky, G.B., Averkamp, T.F., Kurth, W.S., Gurnett, D.A., Dougherty, M., Inan, U., Wood, T.: Wave normal and Poynting vector calculations using the Cassini radio and plasma wave instrument. J. Geophys. Res. 106, 30,253–30,269 (2001). https://doi.org/10.1029/2001JA900114
Inan, U.S., Chiu, Y.T., Davidson, G.T.: Whistler-mode chorus and morningside aurorae. Geophys. Res. Lett. 19, 653–656 (1992). https://doi.org/10.1029/92GL00402
Inan, U.S., Platino, M., Bell, T.F., Gurnett, D.A., Pickett, J.S.: Cluster measurements of rapidly moving sources of ELF/VLF chorus. J. Geophys. Res. 109, A05214 (2004). https://doi.org/10.1029/2003JA010289
Isenberg, P.A., Koons, H.C., Fennell, J.F.: Simultaneous observations of energetic electrons and dawnside chorus in geosynchronous orbit. J. Geophys. Res. 87, 1495–1503 (1982). https://doi.org/10.1029/JA087iA03p01495
Katoh, Y., Omura, Y.: Relativistic particle acceleration in the process of whistler-mode chorus wave generation. Geophys. Res. Lett. 34, L13102 (2007). https://doi.org/10.1029/2007GL029758
Kennel, C.F., Petschek, H.E.: Limit on stably trapped particle fluxes. J. Geophys. Res. 71, 1–28 (1966)
Kurth, W.S., Gurnett, D.A.: Plasma waves in planetary magnetospheres. J. Geophys. Res. 96, 18,977–18,991 (1991)
Kurth, W.S., Gurnett, D.A., Scarf, F.L.: A search for Saturn electrostatic discharges in the Voyager plasma wave data. Icarus 53, 255–261 (1983)
Lauben, D.S., Inan, U.S., Bell, T.F., Kirchner, D.L., Hospodarsky, G.B., Pickett, J.S.: VLF chorus emissions observed by polar during the January 10, 1997, magnetic cloud. Geophys. Res. Lett. 25, 2995–2998 (1998). https://doi.org/10.1029/98GL01425
Lauben, D.S., Inan, U.S., Bell, T.F., Gurnett, D.A.: Source characteristics of ELF/VLF chorus. J. Geophys. Res. 107(A12), 1429 (2002). https://doi.org/10.1029/2000JA003019
LeDocq, M.J., Gurnett, D.A., Hospodarsky, G.B.: Chorus source location from VLF Poynting flux measurements with the Polar spacecraft. Geophys. Res. Lett. 25, 4063–4066 (1998). https://doi.org/10.1029/1998GL900071
Maclennan, C.G., Lanzerotti, L.J., Krimigis, S.M.: Low-energy particles at the bow shock, magnetopause, and outer magnetosphere of Saturn. J. Geophys. Res. 88, 8817 (1983)
Maurice, S., Sittler, E.C., Cooper, J.F., Mauk, B.H., Blanc, M., Selesnick, R.S.: Comprehensive analysis of electron observations at Saturn: Voyager 1 and 2. J. Geophys. Res. 101, 15,211–15,232 (1996)
Meredith, N.P., Horne, R.B., Anderson, R.R.: Substorm dependence of chorus amplitides: implications for the acceleration of electrons to relativistic energies. J. Geophys. Res. 106, 13,165–13,178 (2001). https://doi.org/10.1029/2000JA900156
Moncuquet, M., Lecacheux, A., Meyer-Vernet, N., Cecconi, B., Kurth, W.S.: Quasi thermal noise spectroscopy in the inner magnetosphere of Saturn with Cassini/RPWS: electron temperatures and density. Geophys. Res. Lett. 32, L20S02 (2005). https://doi.org/10.1029/2005GL022508
Nagano, I., Yagitani, S., Kojima, H., Matsumoto, H.: Analysis of wave normal and Poynting vectors of chorus emissions observed by Geotail. J. Geomagn. Geoelectr. 48, 299–307 (1996)
Omura, Y., Summers, D.: Dynamics of high-energy electrons interacting with whistler mode chorus emissions in the magnetosphere. J. Geophys. Res. 111, A09222 (2006). https://doi.org/10.1029/2006JA011600
Omura, Y., Katoh, Y., Summers, D.: Theryand simulation of the generation of whistler-mode chorus. J. Geophys. Res. 113, A04223 (2008). https://doi.org/10.1029/2007JA012622
Pandey, R.S., Kaur, R.: Generation of low frequency electromagnetic wave by injection of cold electron for relativistic and non-relativistic subtracted bi-Maxwellian distribution with perpendicular AC electric field for magnetosphere of Uranus. Prog. Electromagn. Res. B 45, 337–352 (2012)
Pandey, R.S., Singh, D.K.: Whistler mode instability with AC electric field for relativistic subtracted bi-Maxwellian magneto-plasma. Arch. Appl. Sci. Res. 3(5), 350–361 (2011)
Parrot, M., Santolik, O., Cornilleau-Wehrlin, N., Maksimovic, M., Harvey, C.C.: Source location of chorus emissions observed by Cluster. Ann. Geophys. 21, 473–480 (2003)
Persoon, A.M., Gurnett, D.A., Kurth, W.S., Hospodarsky, G.B., Groene, J.B., Canu, P., Dougherty, M.K.: Equatorial electron density measurements in Saturn’s inner magnetosphere. Geophys. Res. Lett. 32, L23105 (2005). https://doi.org/10.1029/2005GL024294
Persoon, A.M., Gurnett, D.A., Kurth, W.S., Groene, J.B.: A simple scale height model of the electron density in Saturn’s plasma disk. Geophys. Res. Lett. 33, L18106 (2006). https://doi.org/10.1029/2006GL027090
Richardson, J.D., Sittler, E.C. Jr.: A plasma density model for Saturn based on Voyager observations. J. Geophys. Res. 95, 12019–12031 (1990)
Santolik, O., Gurnett, D.A., Pickett, J.S., Parrot, M., Cornilleau- Wehrlin, N.: Spatio-temporal structure of storm-time chorus. J. Geophys. Res. 108(A7), 1278 (2003). https://doi.org/10.1029/2002JA009791
Santolik, O., Gurnett, D.A., Pickett, J.S., Parrot, M., Cornilleau-Wehrlin, N.: A microscopic and nanoscopic view of storm-time chorus on 31 March 2001. Geophys. Res. Lett. 31, L02801 (2004). https://doi.org/10.1029/2003GL018757
Santolik, O., Gurnett, D.A., Pickett, J.S., Parrot, M., Cornilleau-Wehrlin, N.: Central position of the source region of storm-time chorus. Planet. Space Sci. 53, 299–305 (2005). https://doi.org/10.1016/j.pss.2004.09.056
Sazhin, S.S., Hayakawa, M.: Magnetospheric chorus emissions: a review. Planet. Space Sci. 40, 681–697 (1992). https://doi.org/10.1016/0032-0633(92)90009-D
Scarf, F.L., Gurnett, D.A., Kurth, W.S., Poynter, R.L.: Voyager 2 plasma wave observations at Saturn. Science 215, 587–594 (1982). https://doi.org/10.1126/science.215.4532.587
Scarf, F.L., Gurnett, D.A., Kurth, W.S., Poynter, R.L.: Voyager plasma wave measurements at Saturn. J. Geophys. Res. 88, 8971–8984 (1983). https://doi.org/10.1029/JA088iA11p08971
Scarf, F.L., Frank, L.A., Gurnett, D.A., Lanzerotti, L.J., Lazarus, A., Sittler, E.C. Jr.: Measurements of plasma, plasma waves and suprathermal charged particles in Saturn’s inner magnetosphere. In: Gehrels, T. (ed.) Saturn, pp. 318–353. Univ. of Ariz. Press, Tucson (1984)
Sittler, E.C. Jr., Ogilvie, K.W., Scudder, J.D.: Survey of low energy plasma electrons in Saturn’s magnetosphere: Voyager 1 and 2. J. Geophys. Res. 88, 8847–8870 (1983)
Sittler, E.C. Jr., et al.: Preliminary results on Saturn’s inner plasmasphere as observed by Cassini: comparison with Voyager. Geophys. Res. Lett. 32, L14S07 (2005). https://doi.org/10.1029/2005GL022653
Sittler, E.C. Jr., et al.: Cassini observations of Saturn’s inner plasmasphere: Saturn orbit insertion results. Planet. Space Sci. 54, 1197–1210 (2006)
Sittler, E.C. Jr., Andre, N., Blanc, M., Burger, M., Johnson, R.E., Coates, A., Rymer, A., Reisenfeld, D., Thomsen, M.F., Persoon, A., Dougherty, M., Smith, H.T., Baragiola, R.A., Hartle, R.E., Chornay, D., Shappirio, M.D., Simpson, D., McComas, D.J., Young, D.T.: Ion and neutral sources and sinks within Saturns inner magnetosphere: Cassini results. Planet. Space Sci. 56, 3–18 (2008)
Storey, L.R.O.: An investigation of whistling atmospherics. Philos. Trans. R. Soc. Lond. Ser. A 246, 113–141 (1953). https://doi.org/10.1098/rsta.1953.0011
Summers, D., Ni, B., Meredith, N.P.: Timescales for radiation belt electron acceleration and loss due to resonant wave-particle interactions: 1. Theory. J. Geophys. Res. 112, A04206 (2007). https://doi.org/10.1029/2006JA011801
Tsurutani, B.T., Smith, E.J.: Postmidnight chorus: a substorm phenomenon. J. Geophys. Res. 79, 118–127 (1974). https://doi.org/10.1029/JA079i001p00118
Tsurutani, B.T., Smith, E.J.: Two types of magnetospheric ELF chorus and their substorm dependence. J. Geophys. Res. 82, 5112–5128 (1977). https://doi.org/10.1029/JA082i032p05112
Tsurutani, B.T., Smith, E.J., West, H.I. Jr., Buck, R.M.: Chorus, energetic electrons and magnetospheric substorms. In: Palmadesso, P.J., Papadopoulos, K. (eds.) Wave Instabilities in Space Plasma, pp. 55–62. Reidel, Dordrecht (1979)
Wahlund, J.E., Bostrom, R., Gustafsson, G., Gurnett, D.A., Kurth, W.S., Averkamp, T., Hospodarsky, G.B., Persoon, A.M., Canu, P., Pedersen, A., Desch, M.D., Eriksson, A.I., Gill, R., Morooka, M.W., Andre, M.: The inner magnetosphere of Saturn: Cassini RPWS cold plasma results from the first encounter. Geophys. Res. Lett. 32, L20S09 (2005). https://doi.org/10.1029/2005GL022699
Young, D.T., et al.: Composition and dynamics of plasma in Saturn’s magnetosphere. Science 307, 1262–1266 (2005)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Shukla, K.N., Singh, D. & Pandey, R.S. Study of relativistic beam of electron on whistler mode waves for subtracted distribution in Saturnian magnetosphere. Astrophys Space Sci 364, 124 (2019). https://doi.org/10.1007/s10509-019-3618-9
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10509-019-3618-9