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  • 1
    Electronic Resource
    Electronic Resource
    Spline qualocation methods for boundary integral equations (1992)
    Springer
    Numerische Mathematik 62 (1992), S. 295-295 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396230
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  • 2
    Electronic Resource
    Electronic Resource
    Spline qualocation methods for boundary integral equations (1990)
    Springer
    Numerische Mathematik 58 (1990), S. 537-567 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) 65R20 ; CR. G.1.9
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper further develops the qualocation method for the solution of integral equations on smooth closed curves. Qualocation is a (Petrov-)Galerkin method in which the outer integrals are performed numerically by special quadrature rules. Here we allow the use of splines as trial and test functions, and prove stability and convergence results for certain qualocation rules when the underlying (Petrov-)Galerkin method is stable. In the common case of a first kind equation with the logarithmic kernel, a typical qualocation method employs piecewise-linear splines, and performs the outer integrals using just two points per interval. This method, with appropriate choice of the quadrature points and weights, has orderO(h 5) convergence in a suitable negative norm. Numerical experiments suggest that these rates of convergence are maintained for integral equations on open intervals when graded meshes are used to cope with unbounded solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385639
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  • 3
    Electronic Resource
    Electronic Resource
    Midpoint collocation for Cauchy singular integral equations (1992)
    Springer
    Numerische Mathematik 62 (1992), S. 483-509 
    Details
    ISSN: 0945-3245
    Keywords: 65R20 ; 45L10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A Cauchy singular integral equation on a smooth closed curve may be solved numerically using continuous piecewise linear functions and collocation at the midpoints of the underlying grid. Even if the grid is non-uniform, suboptimal rates of convergence are proved using a discrete maximum principle for a modified form of the collocation equations. The same techniques prove negative norm estimates when midpoint collocation is used to determine piecewise constant approximations to the solution of first kind equations with the logarithmic potential.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396240
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  • 4
    Electronic Resource
    Electronic Resource
    Scaling and optimization of the radiation temperature in dynamic hohlraums (2001)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 8 (2001), S. 1673-1691 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A quasianalytic model of the dynamic hohlraum is presented. Results of the model are compared to both experiments and full numerical simulations with good agreement. The computational simplicity of the model allows one to find the behavior of the hohlraum radiation temperature as a function of the various parameters of the system and thus find optimum parameters as a function of the driving current. The model is used to investigate the benefits of ablative standoff and quasispherical Z pinches. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1360213
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  • 5
    Electronic Resource
    Electronic Resource
    Obtaining absolute spatial flux measurements with a time-resolved pinhole camera (1999)
    [S.l.] : American Institute of Physics (AIP)
    Review of Scientific Instruments 70 (1999), S. 2012-2015 
    Details
    ISSN: 1089-7623
    Source: AIP Digital Archive
    Topics: Physics , Electrical Engineering, Measurement and Control Technology
    Notes: A technique is described to determine the spatial x-ray flux emitted from a hohlraum wall and subsequently transmitted through a diagnostic hole. This technique uses x-ray diodes, bolometers, and a time-resolved pinhole camera to determine the spatial flux of x rays emitted through a hohlraum's diagnostic hole. The primary motivation for this analysis was the relatively long duration, nearly 100 ns, of the x-ray drive present in z-pinch driven hohlraums. This radiation causes plasma to ablate from the hohlraum walls surrounding the diagnostic hole and results in a partial obscuration that reduces the effective area over which diagnostics view the radiation. The effective change in area leads to an underestimation of the wall temperature when nonimaging diagnostics such as x-ray diodes and bolometers are used to determine power and later to infer a wall temperature. An analysis similar to the one described below is then necessary to understand the radiation environment present in x-ray driven hohlraums when these diagnostics are used and hole closure is important. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1149703
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  • 6
    Electronic Resource
    Electronic Resource
    High-temperature dynamic hohlraums on the pulsed power driver Z : The 40th annual meeting of the division of plasma physics of the american physical society (1999)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 6 (1999), S. 2023-2029 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In the concept of the dynamic hohlraum an imploding Z pinch is optically thick to its own radiation. Radiation may be trapped inside the pinch to give a radiation temperature inside the pinch greater than that outside the pinch. The radiation is typically produced by colliding an outer Z-pinch liner onto an inner liner. The collision generates a strongly radiating shock, and the radiation is trapped by the outer liner. As the implosion continues after the collision, the radiation temperature may continue to increase due to ongoing PdV (pressure times change in volume) work done by the implosion. In principal, the radiation temperature may increase to the point at which the outer liner burns through, becomes optically thin, and no longer traps the radiation. One application of the dynamic hohlraum is to drive an ICF (inertial confinement fusion) pellet with the trapped radiation field. Members of the dynamic hohlraum team at Sandia National Labs have used the pulsed power driver Z (20 MA, 100 ns) to create a dynamic hohlraum with temperature linearly ramping from 100 to 180 eV over 5 ns. On this shot zp214 a nested tungsten wire array of 4 and 2 cm diam with masses of 2 and 1 mg imploded onto a 2.5 mg plastic annulus at 5 mm diam. The current return can on this shot was slotted. It is likely the radiation temperature may be increased to over 200 eV by stabilizing the pinch with a solid current return can. A current return can with nine slots imprints nine filaments onto the imploding pinch. This degrades the optical trapping and the quality of the liner collision. A 1.6 mm diam capsule situated inside this dynamic hohlraum of zp214 would see 15 kJ of radiation impinging on its surface before the pinch itself collapses to a 1.6 mm diam. Dynamic hohlraum shots including pellets were scheduled to take place on Z in September of 1998. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.873457
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  • 7
    Electronic Resource
    Electronic Resource
    Optimization of power density by decreasing the length of tungsten wire array Z pinches (1998)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 5 (1998), S. 2605-2608 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Reducing the length of 30 mm diam tungsten wire arrays on the 20 MA Z pulsed power accelerator [R. B. Spielman, S. F. Breeze, C. Deeney et al., Proceedings of the 11th International Conference on Particle Beams, Prague, Czech Republic, edited by K. Junwirth and J. Ullschmied (Czech Academy of Sciences, Prague, 1996), p. 150] from 2 to 0.75 cm has shown that the radiated powers are energies that remain constant at 170±30 TW and 1600±150 kJ. The length-independent nature of the power and energy results in the radiated power per unit length increasing from 85±10 to 240±30 TW/cm. These high-power densities should result in approximately a 20% increase in radiation temperatures produced by a Z-pinch-driven vacuum or internal hohlarums. Two-dimensional radiation magnetohydrodynamic calculations indicate that the constant radiated energies with varying pinch lengths is consistent with the energy input being due to the work done by the Lorentz forces during the radial collapse, resulting in kinetic energy and during the on-axis pinch phase, resulting in pdV or compressional heating. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.872947
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  • 8
    Electronic Resource
    Electronic Resource
    Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ : The 39th annual meeting of division of plasma physics of APS (1998)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 5 (1998), S. 2105-2111 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Here Z, a 60 TW/5 MJ electrical accelerator located at Sandia National Laboratories, has been used to implode tungsten wire-array Z pinches. These arrays consisted of large numbers of tungsten wires (120–300) with wire diameters of 7.5 to 15 μm placed in a symmetric cylindrical array. The experiments used array diameters ranging from 1.75 to 4 cm and lengths from 1 to 2 cm. A 2 cm long, 4 cm diam tungsten array consisting of 240, 7.5 μm diam wires (4.1 mg mass) achieved an x-ray power of ∼200 TW and an x-ray energy of nearly 2 MJ. Spectral data suggest an optically thick, Planckian-like radiator below 1000 eV. One surprising experimental result was the observation that the total radiated x-ray energies and x-ray powers were nearly independent of pinch length. These data are compared with two-dimensional radiation magnetohydrodynamic code calculations. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.872881
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  • 9
    Electronic Resource
    Electronic Resource
    Inertial confinement fusion ablator physics experiments on Saturn and Nova : The 38th annual meeting of the Division of Plasma Physics (DPP) of the American Physical Society (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 4 (1997), S. 1818-1824 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The Saturn pulsed power accelerator [R. B. Spielman et al., in Proceedings of the 2nd International Conference on Dense Z-pinches, Laguna Beach, CA, 1989, edited by N. R. Pereira, J. Davis, and N. Rostoker (American Institute of Physics, New York, 1989), p. 3] at Sandia National Laboratories (SNL) and the Nova laser [J. T. Hunt and D. R. Speck, Opt. Eng. 28, 461 (1989)] at Lawrence Livermore National Laboratory (LLNL) have been used to explore techniques for studying the behavior of ablator material in x-ray radiation environments comparable in magnitude, spectrum, and duration to those that would be experienced in National Ignition Facility (NIF) hohlraums [J. D. Lindl, Phys. Plasmas 2, 3933 (1995)]. The large x-ray outputs available from the Saturn pulsed-power-driven z pinch have enabled us to drive hohlraums of full NIF ignition scale size at radiation temperatures and time scales comparable to those required for the low-power foot pulse of an ignition capsule. The high-intensity drives available in the Nova laser have allowed us to study capsule ablator physics in smaller-scale hohlraums at radiation temperatures and time scales relevant to the peak power pulse for an ignition capsule. Taken together, these experiments have pointed the way to possible techniques for testing radiation-hydrodynamics code predictions of radiation flow, opacity, equation of state, and ablator shock velocity over the range of radiation environments that will be encountered in a NIF hohlraum. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.872295
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  • 10
    Electronic Resource
    Electronic Resource
    Characterization of diagnostic hole-closure in Z-pinch driven hohlraums (2000)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 7 (2000), S. 681-688 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In this article we investigate the partial closure of diagnostic holes in Z-pinch driven hohlraums. These hohlraums differ from current laser-driven hohlraums in a number of ways such as their larger size, greater x-ray drive energy, and lower temperature. Although the diameter of the diagnostic holes on these Z-pinch driven hohlraums can be much greater than their laser-driven counterparts, 4 mm in diameter or larger, radiation impinges on the wall material surrounding the hole for the duration of the Z pinch, nearly 100 ns. This incident radiation causes plasma to ablate from the hohlraum walls surrounding the diagnostic hole and partially obscure this diagnostic hole. This partial obscuration reduces the effective area over which diagnostics view the hohlraum's radiation. This reduction in area can lead to an underestimation of the wall temperature when nonimaging diagnostics such as x-ray diodes and bolometers are used to determine power and later to infer a wall temperature. In this article we describe the techniques used to characterize the hole-closure in these hohlraums and present the experimental measurements of this process. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.873852
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