Effect of cold electron beam for Whistler mode waves have been studied for relativistic and non- relativistic subtracted bi-Maxwellian distribution and in the presence of perpendicular AC electric field to magnetic field by using the method of characteristic solutions and kinetic approach. The detailed derivation and calculations has been done for dispersion relation and growth rate for magnetosphere of Uranus. Parametric analysis has been done by changing plasma parameters: thermal velocity, ac frequency, temperature anisotropy etc. The effect of AC frequency on the Doppler shifting frequency and comparative study of relativistic and non- relativistic effect on growth rate are analyzed. The new results using subtracted bi-Maxwellian distribution function are found and discussed in relation to bi-Maxwellian distribution function. It is seen that the effective parameters for the generation of Whistler mode wave are not only the temperature anisotropy but also the relativistic factor, AC field frequency, amplitude of subtracted distribution and width of the loss-cone distribution function which has been discussed in result and discussion section.
2. Kurth, W. S., "Voyager plasma wave observations near the outer planets," Adv. Space Res., Vol. 11, 59-68, 1991.
3. Tripathi, A. K. and R. P. Singhal, "Whistler mode instability in magnetosphere of Uranus and Neptune," Planet Space Sci., Vol. 56, 310-319, 2007.
4. Sazhin, S. S. and N. M. Temme, "Marginal stability of parallel whistler mode wave (Asymptotic Analysis)," Ann. Geophysicae, Vol. 9, 304, 1991.
5. Pandey, R. P., S. M. D. Karim, and K. M. Singh, "Effect of cold plasma injection on whistler mode instability triggered by perpendicular AC electric field at Uranus," Earth, Moon and Planets, Vol. 91, 195-207, 2002.
6. Singh, D., S. Singh, and R. P. Singh, "Thermal effects on parallel resonance energy of whistler mode wave," Pramana --- J. Phys., Vol. 66, 467-472, 2006.
7. Bret, A., M.-C. Firpo, and C. Deutsch, "Electromagnetic instabilities for relativistic beam-plasma interaction in whole k space: Nonrelativistic beam and temperature effects," Physical Review E, Vol. 72, 016403-016403.14, 2005.
8. Bret, A., M.-C. Firpo, and C. Deutsch, "Collective electromagnetic modes for beam-plasma interaction in the whole k space," Physical Review E, Vol. 70, 046401, 2004.
9. Pandey, R. S., R. P. Pandey, K. M. Singh, and N. M. Mishra, "Cold plasma injection on VLF wave mode for relativistic magnetoplasma with AC electric field," Progress In Electromagnetic Research C, Vol. 2, 217-232, 2008.
10. Zhang, Y. L., H. Matsumoto, and Y. Omura, "Linear and nonlinear interactions of an electron beam with oblique whistler and electrostatic waves in the magnetosphere," J. Geophys. Res., Vol. 98, 21353, 1993.
11. Devine, P. E., S. C. Chapman, and J. W. Eastwood, "One-and two-dimensional simulations of whistler mode waves in an anisotropic plasma," J. Geophys. Res., Vol. 100, 17189-17203, 1995.
12. Ahirwar, G., P. Varma, and M. S. Tiwari, "Electromagnetic ion-cyclotron instability in the presence of a parallel electric field with general loss-cone distribution function --- Particle aspect analysis," Ann. Geophysicae, Vol. 24, 1919-1930, 2006.
13. Mozer, F. S., R. B. Torbert, U. V. Fahleson, C. Falthammar, A. Gonafalone, A. Pedersen, and C. T. Russel, "Electric field measurements in the solar wind bow shock, magnetosheath, magnetopause and magnetosphere," Space Sci. Rev., Vol. 22, 791, 1978.
14. Wygant, J. R., M. Bensadoun, and F. S. Mozer, "Electric field measurements at sub critical, oblique bow shock crossings," J. Geophys. Res., Vol. 92, 11109, 1987.
15. Lindquist, P. A. and F. S. Mozer, "The average tangential electric field at the noon magnetopause," J. Geophys. Res., Vol. 95, 17137, 1990.
16. Misra, K. D. and R. S. Pandey, "Generation of whistler emissions by injection of hot electrons in the presence of perpendicular AC electric field," J. Geophys. Res., Vol. 100, 19405, 1995.
17. Misra, , K. D. and B. D. Singh, "On the modification of whistler electric field by cold plasma injection," J. Geophys. Res., Vol. 85, 5138, 1980.
18. Pandey, R. S. and D. K. Singh, "Whistler mode instability with AC electric field for relativistic subtracted bi-maxwellian magnetoplasma," Archives of Applied Sci. Res., Vol. 3, No. 5, 350-361, 2011.
19. andey, R. S. and D. K. Singh, "Study of electromagnetic ion cyclotron instability in magneto-plasma," Progress In Electromagnetic Research M, Vol. 14, 147-161, 2010.