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Title: Evolution of Helical Perturbations in a Thin-Shell Model of an Imploding Liner

Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 1070-664X
DOE Contract Number:
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 21; Journal Issue: 11
Country of Publication:
United States

Citation Formats

Ryutov, D D. Evolution of Helical Perturbations in a Thin-Shell Model of an Imploding Liner. United States: N. p., 2014. Web. doi:10.1063/1.4901197.
Ryutov, D D. Evolution of Helical Perturbations in a Thin-Shell Model of an Imploding Liner. United States. doi:10.1063/1.4901197.
Ryutov, D D. Wed . "Evolution of Helical Perturbations in a Thin-Shell Model of an Imploding Liner". United States. doi:10.1063/1.4901197.
title = {Evolution of Helical Perturbations in a Thin-Shell Model of an Imploding Liner},
author = {Ryutov, D D},
abstractNote = {},
doi = {10.1063/1.4901197},
journal = {Physics of Plasmas},
number = 11,
volume = 21,
place = {United States},
year = {Wed Jul 23 00:00:00 EDT 2014},
month = {Wed Jul 23 00:00:00 EDT 2014}
  • A thin-shell model of the liner stability has been revisited and applied to the stability of the helical perturbations. Several stages of the implosion have been identified, starting from a long initial “latent” phase of an almost resting liner, continuing to the second stage of a rapid contraction and significant perturbation growth, and then transitioning to the third stage where perturbations become ballistic and highly non-linear. The stage of stagnation and rebound is beyond the scope of this paper. An importance of vorticity conservation during the late stages is emphasized. Nonlinear evolution of perturbations is followed up to the pointmore » of the formation of cusp structures. Effects of in-surface flows and of their enhancement due to the vorticity conservation are discussed. It is shown that the pre-machined perturbations created only on the outer surface of the liner grow much slower than one could anticipate. The limitations on the thin-shell description are discussed.« less
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  • In some inertial confinement fusion target designs a spherical shell collapses on a void or compresses a small amount of gaseous material. There can be a period during which both the outside (driver) pressure and the inside pressure have a negligible effect on the implosion dynamics, and the motion is essentially ballistic. The changes in the aspect ratio occur mainly because of geometrical convergence. For reasonable parameters the inner surface does not begin to decelerate until shortly before convergence is complete. An approximate description of this ''coasting'' phase has been developed and applied to study the evolution of perturbations onmore » the inner and outer surfaces of the shell in the limit where the fluid is incompressible. The two surfaces are strongly coupled as long as the shell remains thin. When the shell becomes thick compared to the inner radius, the inner and outer surface perturbations decouple. Under these conditions the surface wave action is a good adiabatic invariant, which can be used to estimate the change in the amplitude of a perturbation as a function of the shell inner radius R/sub 1/. Detailed analysis confirms the adiabatic invariance argument and extends the results. The adiabatic invariant may also be applicable in the case of compressible fluids.« less
  • A soluble model of the development of the linear pertubations about a time-varying state of a compressible medium is presented. A Lagrangian description is employed to rederive the equations for the self-similar motion of an ideal fluid and to obtain the linearized equations of motion for pertubations about a general time-varying basic state. The resulting formalism is applied in cylindrical geometry to calculate the growth of flute-like modes associated with a similarity solution modeling the implosion and expansion of a fluid liner. A complete solution is obtained for the perturbed motion. The only modes for which the perturbation amplitudes growmore » faster than the unperturbed liner radius during both implosion and expansion are divergence- and curl-free. Numerical and analytical results are obtained for these and shown to reduce, in the short-wavelength limit, to the Rayleigh--Taylor instability found previously for incompressible time-independent basic states. In addition, a new kind of instability is found: a class of overstable internal modes (sound waves), which are ''pumped up'' in amplitude during implosion, but decay during the expansion phase.« less