Abstract
A self consistent formulation of the Jeans instability of a dusty plasma with proper inclusion of charge dynamics is described. It is shown that charge fluctuations significantly affect the Jeans as well as the Buneman mode. For plasma particles (electrons and ions) in local thermal equilibrium, the Jeans lengthλ J is given byλ J≈λ g F(R, ε, β/η), whereλ g is the Debye length of the charged grains,R is the square of the ratio of the Jeans to the plasma frequency of the grains,ε is the square of the ratio of the Debye length of the grains and the plasma particles andβ/η is the ratio of the attachment to the decay frequency of the electronic charges to the grain surface. The functional form ofF is given in the text. Numerical investigation of the Jeans-Buneman mode for a two and three component plasma shows that the Jeans mode dominates atkλ D≪1 (wherek is the wave number andλ D is the Debye length of plasma particles), whereas atkλ D≫1 only the Buneman mode operates. Charge fluctuations reduce the area of overlap of the two modes. Furthermore, in the absence of gravity, there exists a new, charge fluctuation induced unstable mode in a streaming dusty plasma. Astrophysical applications of the results are discussed.
Similar content being viewed by others
References
E R Wollman,Astrophys. J. 392, 80 (1992)
V B Il’in and N V Voschennikov,Astron. Rep. 37, 362 (1993)
B G Anandrao, S R Pottasch and D B Vaidya,Astron. Astrophys. 273, 570 (1993)
H Netzer,Active Galactic Nuclei, Saas-Fee Advanced course 20, Lecture Note 1990, Swiss Society for Astrophysics and Astronomy edited by T J-L Courvoisier and M Mayor (Springer-Verlag, Berlin)
C K Goertz,Rev. Geophys. 27, 271 (1989)
O Havnes,Astron. Astrophys. 193, 309 (1988)
M Horyani and C K Goertz,Astrophys. J. 361, 155 (1989)
U de Angelis,Phys. Scr. 45, 465 (1992)
T W Hartquist, O Havnes and G E Morfill,Fund. Cosmic Plasma 15, 167 (1992)
D A Mendis and M Rosenberg,Ann. Rev. Astron. Astrophys. 32, 419 (1994)
F Verheest,Space Sci. Rev. (1996) (in press)
R K Varma, P K Shukla and V Krishan,Phys. Rev. E50, 1422 (1994)
M R Jana, P K Kaw and A Sen,Phys. Rev. E48, 3930 (1994)
J R Bhatt and B P Pandey,Phys. Rev. E50, 3980 (1994)
S V Vladmirov,Phys. Plasmas 1, 2762 (1994);Phys. Rev. E50, 1422 (1994)
F Verheest,Planet. Space Sci. 42, 883 (1994)
R V Reddy, G S Lakhina, F Verheest and P Meuris,Planet Space Sci. 44, 129 (1996)
C B Dwivedi and B P Pandey,Phys. Plasmas 2, 4134 (1995)
F Verheest and P Meuris,Phys. Lett. A198, 228 (1995)
B P Pandey and C B Dwivedi,Pramana — J. Phys. 45, 255 (1995)
A S Eddington,Internal Constitution of the Stars (Cambridge University Press, Cambridge, England, 1926)
T Mukai,Evolution of interstellar dust and related topics in Proceedinge of the International School of Physica “Enrico Fermi”, Course CI, Verenna, 1986 edited by A Bonetti, J M Greenberg and S Aiellu (North Holland, Amsterdam, 1989) p. 357
S Barbash and R Lundin,IEEE Trans. Plasma Sci. 22, 173 (1994)
J Binney and S Tremaine,Galactic Dynamics (Princeton University Press, Princeton, NJ, 1988)
H Alfven and A D Mendis,Adv. Space Res. 3, 95 (1983)
G Gisler, Q R Ahmad and E R Wollman,IEEE Trans. Plasma Sci. 20, 922 (1992)
B P Pandey, K Avinash and C B Dwivedi,Phys. Rev. E49, 5599 (1994)
R Chhajalani and A Parihar,Astrophys. J. 422, 746 (1994)
K Avinash and P K Shukla,Phys. Lett. A189, 470 (1994)
B P Pandey and C B Dwivedi,J. Plasma Phys. 55, 395 (1996)
L Mohanta, B J Saikia, B P Pandey and S Bujarbarua,J. Plasma Phys. 55, 401 (1996)
L Spitzer,Physical Processes in the Interstellar Medium (John Wiley, New York, 1978)
B T Draine and E E Salpeter,Astrophys. J. 15, 77 (1979)
E C Whipple, T G Northrop and D A Mendis,J. Geophys. Res. 90, 7405 (1985)
V E Golant, A P Zhilinsky and I E Shakharov,Fundamentals of Plasma Physics (John Wiley, New York, 1980)
F Melandso, T Aslaksen and O Havnes,J. Geophys. Res. 98, 13315 (1993)
B G Elmgreen,Astrophys. J. 232, 729 (1979)
T Umebayashi and T Nakano,Publ. Astron. Soc. Jpn. 32, 405 (1980)
H L F Houpis and D A Mendis,The Moon and Planets 29, 39 (1983)
O Buneman,Phys. Rev. 115, 503 (1959)
J Frank, A R King and D J Raine,Accretion power in astrophysics (Cambridge University Press, Cambridge, 1985)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Pandey, B.P., Lakhina, G.S. Jeans-Buneman instability in a dusty plasma. Pramana - J Phys 50, 191–204 (1998). https://doi.org/10.1007/BF02847529
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02847529