Stability of stagnation via an expanding accretion shock wave

Stagnation of a cold plasma streaming to the center or axis of symmetry via an expanding accretion shock wave is ubiquitous in inertial confinement fusion (ICF) and high-energy-density plasma physics, the examples ranging from plasma flows in x-ray-generating Z pinches [Maron et al., Phys. Rev. Lett...

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Bibliographic Details
Published in:Physics of plasmas 2016-05, Vol.23 (5)
Main Authors: Velikovich, A. L., Murakami, M., Taylor, B. D., Giuliani, J. L., Zalesak, S. T., Iwamoto, Y.
Format: Article
Language:English
Subjects:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
CARTESIAN COORDINATES
COLD PLASMA
Cold plasmas
CYLINDRICAL CONFIGURATION
Deposition
DISTURBANCES
EIGENFUNCTIONS
EIGENVALUES
Eigenvectors
ENERGY DENSITY
GEOMETRY
GRIDS
INERTIAL CONFINEMENT
Inertial confinement fusion
PERTURBATION THEORY
PLASMA DENSITY
Plasma physics
Rarefaction
SHOCK WAVES
SIMULATION
SPHERICAL CONFIGURATION
Spherical coordinates
STABILITY
Stability analysis
STAGNATION
SYMMETRY
THERMONUCLEAR IGNITION
X RADIATION
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Summary:Stagnation of a cold plasma streaming to the center or axis of symmetry via an expanding accretion shock wave is ubiquitous in inertial confinement fusion (ICF) and high-energy-density plasma physics, the examples ranging from plasma flows in x-ray-generating Z pinches [Maron et al., Phys. Rev. Lett. 111, 035001 (2013)] to the experiments in support of the recently suggested concept of impact ignition in ICF [Azechi et al., Phys. Rev. Lett. 102, 235002 (2009); Murakami et al., Nucl. Fusion 54, 054007 (2014)]. Some experimental evidence indicates that stagnation via an expanding shock wave is stable, but its stability has never been studied theoretically. We present such analysis for the stagnation that does not involve a rarefaction wave behind the expanding shock front and is described by the classic ideal-gas Noh solution in spherical and cylindrical geometry. In either case, the stagnated flow has been demonstrated to be stable, initial perturbations exhibiting a power-law, oscillatory or monotonic, decay with time for all the eigenmodes. This conclusion has been supported by our simulations done both on a Cartesian grid and on a curvilinear grid in spherical coordinates. Dispersion equation determining the eigenvalues of the problem and explicit formulas for the eigenfunction profiles corresponding to these eigenvalues are presented, making it possible to use the theory for hydrocode verification in two and three dimensions.
ISSN:1070-664X
1089-7674
DOI:10.1063/1.4948492