Stability of stagnation via an expanding accretion shock wave

Journal Article · Sun May 15 00:00:00 EDT 2016 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4948492· OSTI ID:22600194

Velikovich, A. L.; Giuliani, J. L. ^[1]; Murakami, M. ^[2]; Taylor, B. D. ^[3]; Zalesak, S. T. ^[4]; Iwamoto, Y. ^[5]

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1. Plasma Physics Division, Naval Research Laboratory, Washington, DC 20375 (United States)
2. Institute of Laser Engineering, Osaka University, Osaka 565-0871 (Japan)
3. Laboratory for Computational Physics and Fluid Dynamics, Naval Research Laboratory, Washington, DC 20375 (United States)
4. Berkeley Research Associates, Beltsville, Maryland 20705 (United States)
5. Ehime University, Matsuyama, Ehime Pref. 790-8577 (Japan)

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.

• OSTI ID: 22600194
• Journal Information: Physics of Plasmas, Vol. 23, Issue 5; Other Information: (c) 2016 U.S. Government; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
CARTESIAN COORDINATES
COLD PLASMA
CYLINDRICAL CONFIGURATION
DISTURBANCES
EIGENFUNCTIONS
EIGENVALUES
ENERGY DENSITY
GEOMETRY
GRIDS
INERTIAL CONFINEMENT
PERTURBATION THEORY
PLASMA DENSITY
SHOCK WAVES
SIMULATION
SPHERICAL CONFIGURATION
STABILITY
STAGNATION
SYMMETRY
THERMONUCLEAR IGNITION
X RADIATION