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Self-gravitational instability of a fluid cylinder under a transverse varying magnetic field

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Il Nuovo Cimento B (1971-1996)

Summary

The magnetogravitodynamic (MGD) stability of a self-gravitating fluid cylinder under a transverse varying magnetic field is, studied. A general eigenvalue relation is derived, discussed analytically and the results are confirmed numerically. The fluid cylinder is gravitationally unstable to small axisymmetric disturbance and stable to all other disturbances. The longitudinal magnetic field pervades inside the cylinder and has a strong stabilizing influence for all wavelengths. The transverse varying vacuum field has a stabilizing or destabilizing influence according to certain restrictions in different modes of perturbations. The effect of the electromagnetic force on the gravitational instability, examined analytically and numerically, shows that the destabilizing effect of the transverse field is always superior to all other effects. So increasing the magnetic-field strength the unstable domains are quickly increasing for almost all states. In few states the stabilizing influence due to the electromagnetic force can never suppress the gravitational instability, this because the gravitational instability of sufficiently long waves will persist.

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References

  1. Lord Rayleigh:Scientific Papers, Vol. I, II and III (Cambridge, 1902).

  2. Lord Rayleigh:The Theory of Sound, Vol. 1 and 2 (Dover Publ., New York, N.Y., 1945).

    Google Scholar 

  3. S. Chandrasekhar:Hydrodynamic and Hydromagnetic Stability (Dover Publ., New York, N.Y., 1981), chapt. XII.

    Google Scholar 

  4. S. Chandrasekhar andE. Fermi:Astrophys. J.,118, 116 (1953).

    Article  MathSciNet  ADS  Google Scholar 

  5. D. Callebaut andA. E. Radwan:Proceedings of the International Conference on Computing in Plasma Physics (C.P.P.), Garmish, Fed. Rep. of Germany (1986), p. 5.

  6. A. E. Radwan andD. Callebaut:Proc. Belg. Phys. Soc.,21 (1986).

  7. A. E. Radwan:Nuovo Cimento B,105, 1185 (1990).

    Article  ADS  Google Scholar 

  8. A. E. Radwan andS. Elazab:Simon Stevin,61, 219 (1987).

    MathSciNet  Google Scholar 

  9. M. Abramowitz andI. Stegun:Handbook of Mathematical Functions (Dover Publ., New York, N.Y., 1970), p. 376.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Ain-Shams University, Abbassia, Cairo, Egypt

    Ahmed E. Radwan & E. M. Elbashbeshy

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  1. Ahmed E. Radwan
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  2. E. M. Elbashbeshy
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Radwan, A.E., Elbashbeshy, E.M. Self-gravitational instability of a fluid cylinder under a transverse varying magnetic field. Nuov Cim B 106, 1035–1043 (1991). https://doi.org/10.1007/BF02728347

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  • DOI: https://doi.org/10.1007/BF02728347

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