Abstract
The stability properties of the collisionless plasma and encounterless stellar gas described by the Vlasov equations are studied. The introduction of the ‘multiple Water Bag’ model allows, for one-dimensional plane geometry, a treatment of the general case and removes some of the difficulties connected with the formulation of the energy variation. From this last result it can be deduced that both plasma and stellar systems steady state described by a monotonically decreasing distribution F(ε) are stable. The demonstration is extended to the spherically symmetric case for self-gravitating gas. Next the constraint of a monotonically decreasing F(ε) is relaxed and it is supposed that the instability appears through the point ω = 0. This is known to be true for some type of plasma instabilities (two streams) but is a simple working hypothesis in the gravitational case. For this marginal mode the N ‘bags’ equations degenerate into a single wave equation and the stability of the system is given by the sign of the eigenvalues of a Schroedinger type operator. A simple physical picture is obtained for the plasma case where the quantitity ∫(dF/dε) dV (the square of the local maximum wavenumber of instability) is introduced. A virtual variation of this quantity indicates if the initial steady state was stable or unstable.
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References
Antonov, V. A.: 1961, Soy. Astron.-AJ 4, 859.
Doremus, J. P., Feix, M. R., and Baumann, G.: 1971, Phys. Rev. Letters 26, 725.
Hohl, F.: 1969, Phys. Fluids 12, 230.
Hohl, F. and Feix, M. R.: 1967, Astrophys. J. 147, 1164.
Hohl, F. and Feix, M. R.: 1968, Astrophys. J. 151, 783.
Kulsrud, R. M. and Mark, J. W. K.: 1970, Astrophys. J. 160, 471.
Lynden Bell, D.: 1969, Monthly Notices Roy. Astron. Soc. 144, 189.
Lynden Bell, D. and Sanitt, N.: 1969, Monthly Notices Roy. Astron. Soc. 143, 167.
Penrose, O.: 1960, Phys. Fluids 3, 258.
Santini, F.: 1969, Plasma Phys. 12, 230.
Whittaker, E. T. and Watson, G. N.: 1966, A Course of Modern Analysis, Cambridge University Press.
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© 1972 D. Reidel Publishing Company, Dordrecht, Holland
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Feix, M.R., Doremus, J.P., Baumann, G. (1972). Stability Properties for Encounterless Self-Gravitational Stellar Gas and Plasma. In: Lecar, M. (eds) Gravitational N-Body Problem. Astrophysics and Space Science Library, vol 31. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2870-7_35
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DOI: https://doi.org/10.1007/978-94-010-2870-7_35
Publisher Name: Springer, Dordrecht
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