Parametric excitation of Alfvén waves by gravitational radiation

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 62, Issue 6, 2000, Pages 8493-8500

  Servin, M ^a   Brodin, G ^a   Bradley, M ^a   Marklund, M ^b  

^a UMEÅ UNIVERSITY   (Sweden)

^b CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRIC EXCITATION; ELECTROMAGNETIC FIELD EFFECTS; MAGNETOHYDRODYNAMICS; MATHEMATICAL TECHNIQUES; MAXWELL EQUATIONS; WAVE PLASMA INTERACTIONS;

ALFVEN WAVES; GRAVITATIONAL RADIATION;

PLASMA WAVES;

EID: 0034514447     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.62.8493     Document Type: Article

References (33)

1. Yu. G. Ignat’ev, Phys. Lett. A 230, 171 (1997).
2. V. I. Denisov, Zh. Éksp. Teor. Fiz. 74, 401 (1978) [Sov. Phys. JETP 42, 209 (1978)].
3. M. Demiański, Relativistic Astrophysics (Pergamon Press, New York, 1985), pp. 256–257.
4. M. Marklund, G. Brodin, and P. K. S. Dunsby, Astrophys. J. 536, 875 (2000).
5. U. N. Gerlach, Phys. Rev. D 62, 101501 (2000).
6. M. Marklund, P. K. S. Dunsby, and G. Brodin, Phys. Rev. D (to be published).
7. G. A. Lupanov, Zh. Éksp. Teor. Fiz. 52, 118 (1967) [Sov. Phys. JETP 25, 76 (1967)].
8. V. B. Braginskiĭ, L. P. Grishchuk, A. G. Doroshkevich, Ya. B. Zel’dovich, I. D. Novikov, and M. V. Sazhin, Zh. Éksp. Teor. Fiz. 65, 1729 (1973) [Sov. Phys. JETP 38, 865 (1974)].
9. L. P. Grishchuk and M. V. Sazhin, Zh. Éksp. Teor. Fiz. 68, 1569 (1975) [Sov. Phys. JETP 41, 787 (1976)].
10. A. B. Balakin and Yu. G. Ignat’ev, Phys. Lett. A 96, 10 (1983).
11. Yu. G. Ignat’ev, Zh. Éksp. Teor. Fiz. 81, 3 (1981) [Sov. Phys. JETP 54, 1 (1981)].
12. G. Brodin and M. Marklund, Phys. Rev. Lett. 82, 3012 (1999).
13. J. T. Mendonça, P. K. Shukla, and R. Bingham, Phys. Lett. A 250, 144 (1998).
14. R. Bingham , Phys. Scr. T75, 61 (1998).
15. F. I. Cooperstock, Ann. Phys. (N.Y.) 47, 173 (1968).
16. Ya. B. Zeldovich, Zh. Éksp. Teor. Fiz. 65, 1311 (1973) [Sov. Phys. JETP 38, 652 (1974)].
17. L. P. Grishchuk and A. G. Polnarev, in General Relativity and Gravitation, edited by A. Held (Plenum Press, New York, 1980), Vol. 2.
18. A. M. Anile, J. K. Hunter, and B. Truong, J. Math. Phys. 40, 4474 (1999).
19. A. Greco and L. Seta, J. Class. Ouantum Grav. 15, 3655 (1998).
20. We could also have started from previous general relativistic MHD equations, see e.g., A. M. Anile, Relativistic Fluids and Magneto-fluids (Cambridge University Press, Cambridge, 1989), but the present derivation has a value as a guide for future generalizations to the case of general relativistic two-fluid equations.
21. Naturally the condition (Formula presented) cannot hold in arbitrary reference frames. We assume it to be true in the rest frame of the fluid, but due the condition of nonrelativistic fluid velocities it also holds in all frames of relevance.
22. J. Weiland and H. Wilhelmsson, Coherent Nonlinear Interaction of Waves in Plasmas (Pergamon Press, New York, 1977).
23. This is an additional restriction as compared to the general case, since the choice of gravitational polarization (i.e., letting (Formula presented) makes the x- and y-axis nonequivalent.
24. In order to check the algebra we have verified that identical coupling coefficients (Formula presented) and (Formula presented) follows from a tetrad formalism.
25. We assume that terms that are both nonlinear and proportional to the small dissipation parameter is negligible.
26. Generally it is not entirely unproblematic to make energy conservation arguments in general relativity. However, as will be clear from the last section, energy conservation using the standard expression for the gravitational wave energy can be applied to our case.
27. Using (Formula presented) and estimating (Formula presented) and (Formula presented) as given by Eqs. (31) and (32), applying the dispersion relations and the frequency matching conditions, we get (Formula presented) also for nonparallel propagation and independently of the ratio (Formula presented)
28. The possible particle densities in the example of considerations have a very wide range. For example (Formula presented) for low-density unperturbed interstellar matter. The value (Formula presented) chosen by us somewhat arbitrarily, is of the some order of magnitude as the density in the solar corona. Much larger number densities, as found in accretion disks, are also possible.
29. G. Brodin and J. Lundberg, J. Plasma Phys. 46, 299 (1991).
30. Note that the even in standard plasma problems, the quantum picture should not be taken too literally, since the process is indeed nonlinear, and the interaction of single wave quantas thus is negligible.
31. J. Larsson, Phys. Scr. 58, 97 (1998).
32. G. Brodin and L. Stenflo, J. Plasma Phys. 39, 277 (1988).
33. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon Press, Oxford, 1975).