volume | PIER Journals

Abstract

The modulational instability of a lower hybrid wave is investigated in a dusty plasma slab by developing a non-local theory of this four wave parametric interaction process. The immersed dust grains modify the dispersion relation and growth rate expression of low frequency unstable mode. A numerical analysis shows that the frequencies and growth rate of unstable mode is higher in dusty plasma than that in without dust grains. The growth rate of the unstable mode is proportional to pump amplitude and has strong dependence on pump frequency.

1. Wolf, N. S., R. Majeski, H. Lashinky, V. K. Tripathi, and C. S. Liu, "Stabilization of the current-driven electrostatic ion-cyclotron instability by lower-hybrid waves," Phys. Rev. Lett., Vol. 45, No. 10, 799-802, 1980.
doi:10.1103/PhysRevLett.45.799 Google Scholar

2. Liu, C. S., V. S. Chan, D. K. Bhandari, and R. W. Harvey, "Theory of run away-current sustainment by lower-hybrid waves," Phys. Rev. Lett., Vol. 48, No. 21, 1479-1482, 1982.
doi:10.1103/PhysRevLett.48.1479 Google Scholar

3. Liu, C. S., V. K. Tripathi, V. S. Chan, and V. Stefan, "Density threshold for parametric instability of lower-hybrid waves in tokamaks," Phys. Fluids, Vol. 27, No. 7, 1709-1717, 1984.
doi:10.1063/1.864826 Google Scholar

4. Akimoto, K., "Parametric instabilities of Langmuir waves in weak/moderate magnetic fields," Phys. Fluids, Vol. 1, No. 10, 1998-2009, 1989.
doi:10.1063/1.859063 Google Scholar

5. Stenflo, L., "Resonant three-wave interactions in plasmas," Phys. Scr., Vol. 15, No. T50, 15-20, 1994.
doi:10.1088/0031-8949/1994/T50/002 Google Scholar

6. Sharma, R. P., K. Ramamurthy, and M. Y. Yu, "Parametric excitation of electron acoustic waves," Phys. Fluids, Vol. 27, No. 2, 399-401, 1984.
doi:10.1063/1.864633 Google Scholar

7. Saleem, H. and G. Murtaza, "Nonlinear excitation of electron-acoustic waves," Phys. Plasmas, Vol. 36, No. 2, 295-299, 1986.
doi:10.1017/S0022377800011764 Google Scholar

8. Tripathi, V. K., C. S. Liu, and C. Grebogi, "Parametric decay of lower hybrid waves in a plasma: Effect of ion nonlinearity," Phys. Fluids, Vol. 22, No. 2, 301-309, 1979.
doi:10.1063/1.862581 Google Scholar

9. Liu, C. S. and V. K. Tripathi, "Parametric instabilities in a magnetized plasma," Phys. Reports, Vol. 130, No. 3, 143-216, 1986.
doi:10.1016/0370-1573(86)90108-0 Google Scholar

10. Jain, V. K. and P. J. Christiansen, "Excitation of multiple-cyclotron harmonic waves in a thin beam-plasma system," Phys. Lett. A, Vol. 82, No. 3, 127-130, 1981.
doi:10.1016/0375-9601(81)90929-4 Google Scholar

11. Jain, V. K. and P. J. Christiansen, "Excitation of electron-cyclotron harmonic wave instabilities in a thin beam-plasma system," Plasma Phys. and Controlled Fusion, Vol. 26, No. 4, 613-616, 1984.
doi:10.1088/0741-3335/26/4/003 Google Scholar

12. Praburam, G. and A. K. Sharma, "Second-harmonic excitation of a Gould-Trivelpiece mode in a beam-plasma system," J. Plasma Phys., Vol. 48, No. 1, 3-12, 1992.
doi:10.1017/S0022377800016330 Google Scholar

13. Kruer, W. L., The Physics of Laser Plasma Interactions, Addision-Wesley, 1987.

14. Das, K. P. and S. Sihi, "Modulational instability of two transverse waves in a cold plasma," J. Plasma Phys., Vol. 21, No. 1, 183-191, 1979.
doi:10.1017/S0022377800021747 Google Scholar

15. Whipple, E. C., T. G. Northdrop, and D. A. Mendis, "The electrostatics of a dusty plasma," J. Geophys. Res., Vol. 90, No. A8, 7405-7413, 1985.
doi:10.1029/JA090iA08p07405 Google Scholar

16. Jana, M. R., A. Sen, and P. K. Kaw, "Collective effects due to charge-fluctuation dynamics in a dusty plasma," Phys. Rev. E, Vol. 48, No. 5, 3930-3933, 1993.
doi:10.1103/PhysRevE.48.3930 Google Scholar

17. Chow, V. W. and M. Rosenberg, "Electrostatic ion cyclotron instability in dusty plasma," Planetary and Space Science, Vol. 43, No. 5, 613-618, 1995.
doi:10.1016/0032-0633(94)00134-D Google Scholar

18. Chow, V. W. and M. Rosenberg, "A note on the electrostatic ion cyclotron instability in dusty plasmas - Comparison with experiment," Planetary and Space Science, Vol. 44, No. 5, 465-467, 1996.
doi:10.1016/0032-0633(95)00137-9 Google Scholar

19. Barkan, A., N. D'Angelo, and R. L. Merlino, "Laboratory experiments on electrostatics ion cyclotron waves in a dusty plasma," Planetary and Space Science, Vol. 43, No. 7, 905-908, 1995.
doi:10.1016/0032-0633(94)00226-H Google Scholar

20. D'Angelo, N., "Low-frequency electrostatic waves in dusty plasmas," Planetary and Space Science, Vol. 38, No. 9, 1143-1146, 1990.
doi:10.1016/0032-0633(90)90022-I Google Scholar

21. Merlino, R. L., A. Barkan, C. Thompson, and N. D'Angelo, "Laboratory studies of waves and instabilities in dusty plasmas," Phys. Plasmas, Vol. 5, No. 5, 1607-1614, 1998.
doi:10.1063/1.872828 Google Scholar

22. Song, B., D. Suszcynsky, N. D'Angelo, and R. L. Merlino, "Electrostatic ion-cyclotron waves in a plasma with negative ions," Phys. Fluids B1, Vol. 1, No. 12, 2316-2318, 1989.
doi:10.1063/1.859049 Google Scholar

23. Sharma, S. C. and M. P. Srivastava, "Ion beam driven ion-cyclotron waves in a plasma cylinder with negative ions," Phys. Plasmas, Vol. 8, No. 3, 679-686, 2001.
doi:10.1063/1.1336533 Google Scholar

24. Sharma, S. C. and A. Gahlot, "Ion beam driven ion-acoustic waves in a plasma cylinder with negative ions," Phys. Plasmas, Vol. 15, No. 7, 0737051-0737056, 2008.
doi:10.1063/1.2949708 Google Scholar

25. Sharma, S. C. and A. Gahlot, "Excitation of upper-hybrid waves by a gyrating relativistic electron beam in a magnetized dusty plasma cylinder," Phys. Plasmas, Vol. 16, No. 12, 1237081-1237085, 2009.
doi:10.1063/1.3280024 Google Scholar

26. Chow, V. W. and M. Rosenberg, "Electrostatic ion cyclotron instabilities in negative ion plasmas," Phys. Plasmas, Vol. 3, No. 4, 1202-1211, 1996.
doi:10.1063/1.871744 Google Scholar

27. Suszcynsky, D. M., N. D'Angelo, and R. L. Merlino, "An experimental study of electrostatic ion cyclotron waves in a two-ion component plasma," J. Geophys. Res., Vol. 94, No. A7, 8966-8972, 1989.
doi:10.1029/JA094iA07p08966 Google Scholar

28. Ma, J.-X. and M. Y. Yu, "Self-consistent theory of ion acoustic waves in a dusty plasma," Phys. Plasmas, Vol. 1, No. 11, 3520-3522, 1994.
doi:10.1063/1.870887 Google Scholar

29. Vladimirov, S. V., K. N. Ostrikov, and M. Y. Yu, "Ion-acoustic waves in a dust-contaminated plasma," Phys. Rev. E, Vol. 60, No. 3, 3257-3261, 1999.
doi:10.1103/PhysRevE.60.3257 Google Scholar

30. Ostrikov, K. N., S. Kumar, and H. Sugai, "Charging and trapping of macroparticles in near-electrode regions of fluorocarbon plasmas with negative ions," Phys. Plasmas, Vol. 8, No. 7, 3490-3497, 2001.
doi:10.1063/1.1375149 Google Scholar

31. Vladimirov, S. V., K. Ostrikov, M. Y. Yu, and G. E. Morfill, "Ion-acoustic waves in a complex plasma with negative ions," Phys. Rev. E, Vol. 67, No. 3, 036406-036416, 2003.
doi:10.1103/PhysRevE.67.036406 Google Scholar

32. Rosenberg, M., E. Thomas, Jr., and R. L. Merlino, "A note on dust wave excitation in a plasma with warm dust - Comparison with experiment," Phys. Plasmas, Vol. 15, No. 7, 0737011-0737015, 2008.
doi:10.1063/1.2943218 Google Scholar

33. Barnes, M. S., J. H. Keller, J. C. Forster, J. A. O'Neill, and D. Keith Coultas, "Transport of dust particles in glow-discharge plasmas," Phys. Rev. Lett., Vol. 68, No. 3, 313-316, 1992.
doi:10.1103/PhysRevLett.68.313 Google Scholar

34. Ostrikov, K. N., M. Y. Yu, S. V. Vladimirov, and O. Ishihara, "On the realization of the current-driven dust ion-acoustic instability," Phys. Plasmas, Vol. 6, No. 3, 737-740, 1999.
doi:10.1063/1.873310 Google Scholar

35. Ostrikov, K. N., S. V. Vladimirov, M. Y. Yu, and G. E. Morfill, "Low-frequency dispersion properties of plasmas with varible-charge impurities," Phys. Plasmas, Vol. 7, No. 2, 461-465, 2000.
doi:10.1063/1.873831 Google Scholar

36. Sharma, S. C. and A. Gahlot, "The effect of dust charge fluctuation on lower-hybrid suppression of drift waves in a magnetized plasma cylinder," Phys. Plasmas, Vol. 17, No. 2, 0237021-0237027, 2010.
doi:10.1063/1.3298737 Google Scholar

37. Sharma, S. C. and A. Gahlot, "The effect of dust charge fluctuation on collisional drift waves in a magnetized plasma cylinder," Phys. Plasmas, Vol. 17, No. 2, 0237021-0237027, 2010.
doi:10.1063/1.3298737 Google Scholar

38. Ma, J. X. and P. K. Shukla, "Compact dispersion relation for parametric instabilities of electromagnetic waves in dusty plasmas," Phys. Plasmas, Vol. 2, No. 5, 1506-1509, 1995.
doi:10.1063/1.871366 Google Scholar

39. Shukla, P. K. and S. V. Vladimirov, "Stimulated scattering of electromagnetic waves in collisional dusty plasmas," Phys. Plasmas, Vol. 2, No. 8, 3179-3183, 1995.
doi:10.1063/1.871450 Google Scholar

40. Vladimirov, S. V., "Propagation of waves in dusty plasmas with variable charges on dust particles," Phys. Plasmas, Vol. 1, No. 5, 2762-2767, 1994.
doi:10.1063/1.870511 Google Scholar

41. Annou, R. and V. K. Tripathi, "Stimulated scattering of a whistler wave off ion-cyclotron and ion-acoustic modes in a dusty plasma," Phys. Plasmas, Vol. 5, No. 1, 60-62, 1998.
doi:10.1063/1.872675 Google Scholar

42. Bingham, R. and C. N. Lashmore-Davies, "On the nonlinear development of the Langmuit modulational instability," Phys. Plasmas, Vol. 21, No. 1, 51-69, 1979.
doi:10.1017/S0022377800021644 Google Scholar

43. Murtaza, G. and M. Salahuddin, "Modulational instability of ion acoustic waves in a magnetized plasma," Phys. Plasmas, Vol. 24, No. 1, 451-596, 1982.
doi:10.1088/0032-1028/24/5/001 Google Scholar

44. Konar, S., V. K. Jain, and V. K. Tripathi, "Modulational instability of a lower hybrid wave in a plasma slab," J. Appl. Phys., Vol. 65, No. 10, 3798-3801, 1989.
doi:10.1063/1.343392 Google Scholar

45. Varma, R. K., P. K. Shukla, and V. Krishan, "Electrostatic oscillation in the presence of grain-charge perturbations in dusty plasmas," Phys. Rev. E, Vol. 47, No. 5, 3612-3616, 1993.
doi:10.1103/PhysRevE.47.3612 Google Scholar

Dr. Ajay Gahlot