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Fluid instabifities of a uniformly imploding ablatively driven shell

  • David L. Book (a1) and Ira B. Bernstein (a2)

Abstract

The linear stability of a uniformly imploding shell, modelled as an ideal polytropic fluid, is investigated. Two types of unstable modes are found: incompressible irrotational perturbations localized at the outer surface, ascribable to Rayleigh—Taylor instability, and compressible modes, associated with convective instabiiity. Kidder's result for the Rayleigh—Taylor modes is shown to hold independently of the form of the shell density profile. By means of a variational principle it is shown that the criterion for convective instability is the existence of a region within which d(pp)/dr> 0. Analytic solutions for both spatial and temporal dependence of the perturbations are presented, and the results applied to pellets imploded by the action of a laser or charged-particle beam.

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Abrmowitz, M. & Stegun, I. A. (ed.) 1964 Handbook of Mathematical Functions. U.S. Govt. Printing Office, Washington.
Anisimov, S. A. & Inogamov, N. A. 1974 Soviet Phys. JETP Lett. 20, 74.
Bernstein, I. B. & Book, D. L. 1978 Astrophys. J. 225, 633.
Book, D. L. 1978 Phys. Rev. Lett. 41, 1552.
Book, D. L. 1979 J. Fluid Mech. 95, 779.
Kidder, R. E. 1976 Nucl. Fusion, 16, 3.
Landau, L. D. & Lifeshitz, E. M. 1959 Fluid Mechanics. Addison-Wesley.
Sedov, L. I. 1959 Similarity and Dimensional Methods in Mechanics. Academic.
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Fluid instabifities of a uniformly imploding ablatively driven shell

  • David L. Book (a1) and Ira B. Bernstein (a2)

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