Rayleigh-Taylor stability for a shock wave-density discontinuity interaction
Shells in inertial fusion targets are typically accelerated and decelerated by two or three shocks followed by continuous acceleration. The analytic solution for perturbation growth of a shock wave striking a density discontinuity in an inviscid fluid is investigated. The Laplace transform of the solution results in a functional equation, which has a simple solution for weak shock waves. The solution for strong shock waves may be given by a power series. It is assumed that the equation of state is given by a gamma law. The four independent parameters of the solution are the gamma values on each side of the material interface, the density ratio at the interface, and the shock strength. The asymptotic behavior (for large distances and times) of the perturbation velocity is given. For strong shocks the decay of the perturbation away from the interface is much weaker than the exponential decay of an incompressible fluid. The asymptotic value is given by a constant term and a number of slowly decaying discreet frequencies. The number of frequencies is roughly proportional to the logarithm of the density discontinuity divided by that of the shock strength. The asymptotic velocity at the interface is tabulated for representative values of the independent parameters. For weak shocks the solution is compared with results for an incompressible fluid. The range of density ratios with possible zero asymptotic velocities is given.
- Research Organization:
- Los Alamos National Lab., NM (USA)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 6314938
- Report Number(s):
- LA-UR-81-2263; CONF-810576-3; ON: DE81028707
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
700208* -- Fusion Power Plant Technology-- Inertial Confinement Technology
ANALYTICAL SOLUTION
CONFINEMENT
IMPLOSIONS
INERTIAL CONFINEMENT
INSTABILITY
INTEGRAL TRANSFORMATIONS
LAPLACE TRANSFORMATION
LASER IMPLOSIONS
LASER TARGETS
PLASMA CONFINEMENT
RAYLEIGH-TAYLOR INSTABILITY
SHELLS
SHOCK WAVES
TARGETS
TRANSFORMATIONS