Asymptotic Scaling Laws for Imploding Thin Fluid Shells

Basko, M.M.; Meyer-ter-Vehn, Jürgen

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Asymptotic Scaling Laws for Imploding Thin Fluid Shells

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Basko, M.M.
Max Planck Society;

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Meyer-ter-Vehn, Jürgen
Laboratory for Attosecond Physics, Max Planck Institute of Quantum Optics, Max Planck Society;
Laser Plasma Physics, Max Planck Institute of Quantum Optics, Max Planck Society;

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Basko, M., & Meyer-ter-Vehn, J. (2002). Asymptotic Scaling Laws for Imploding Thin Fluid Shells. Physical Review Letters, 88(24): 244502. Retrieved from http://link.aps.org/abstract/PRL/v88/e244502.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-C207-E

Abstract

Scaling laws governing implosions of thin shells in converging flows are established by analyzing the implosion trajectories in the A, M≫ parametric plane, where A is the in-flight aspect ratio, and M is the implosion Mach number. Three asymptotic branches, corresponding to three implosion phases, are identified for each trajectory in the limit of A, M≫1. It is shown that there exists a critical value γ_cr = 1 + 2/ν (ν= 1, 2 for, respectively, cylindrical and spherical flows) of the adiabatic index gamma, which separates two qualitatively different patterns of the density buildup in the last phase of implosion. The scaling of the stagnation density ρ_s and pressure P_s with the peak value M₀ of the Mach number is obtained. ©2002 The American Physical Society