Instability of a planar expansion wave
- Plasma Physics Division, Naval Research Laboratory, Washington, DC 20375 (United States)
- Science Applications International Corporation, McLean, Virginia 22150, USA and NRCN, P.O. Box 9001, Beer Sheva (Israel)
- E.T.S.I. Industriales, Universidad de Castilla-La Mancha, 13071 Cuidad Real (Spain)
An expansion wave is produced when an incident shock wave interacts with a surface separating a fluid from a vacuum. Such an interaction starts the feedout process that transfers perturbations from the rippled inner (rear) to the outer (front) surface of a target in inertial confinement fusion. Being essentially a standing sonic wave superimposed on a centered expansion wave, a rippled expansion wave in an ideal gas, like a rippled shock wave, typically produces decaying oscillations of all fluid variables. Its behavior, however, is different at large and small values of the adiabatic exponent {gamma}. At {gamma}>3, the mass modulation amplitude {delta}m in a rippled expansion wave exhibits a power-law growth with time {proportional_to}t{sup {beta}}, where {beta}=({gamma}-3)/({gamma}-1). This is the only example of a hydrodynamic instability whose law of growth, dependent on the equation of state, is expressed in a closed analytical form. The growth is shown to be driven by a physical mechanism similar to that of a classical Richtmyer-Meshkov instability. In the opposite extreme {gamma}-1<<1, {delta}m exhibits oscillatory growth, approximately linear with time, until it reaches its peak value {approx}({gamma}-1){sup -1/2}, and then starts to decrease. The mechanism driving the growth is the same as that of Vishniac's instability of a blast wave in a gas with low {gamma}. Exact analytical expressions for the growth rates are derived for both cases and favorably compared to hydrodynamic simulation results.
- OSTI ID:
- 20709769
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 72, Issue 4; Other Information: DOI: 10.1103/PhysRevE.72.046306; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-651X
- Country of Publication:
- United States
- Language:
- English
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