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Analytical stress modeling of high-energy laser windows: Application to fusion-cast calcium fluoride windows
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10.1063/1.2007874
/content/aip/journal/jap/98/4/10.1063/1.2007874
http://aip.metastore.ingenta.com/content/aip/journal/jap/98/4/10.1063/1.2007874

Figures

Image of FIG. 1.
FIG. 1.

Beam profile factor for the far-field focal intensity and the window hoop stress as a function of the beam truncation parameter.

Image of FIG. 2.
FIG. 2.

Gaussian beam profiles for truncation parameters ranging from 0.3 to 3.0. The case illustrates the profile of an optimally truncated beam of total power and peak intensity. The and shapes refer to a beam passing through an -diameter window.

Image of FIG. 3.
FIG. 3.

Failure probability of an -diameter window made of fusion-cast and subjected to a uniform biaxial stress. The Weibull statistical parameters are as derived in the Appendix. Note that surface treatment does not alter the failure probability.

Image of FIG. 4.
FIG. 4.

Schematic description of the window geometry.

Image of FIG. 5.
FIG. 5.

Predicted pressure-induced planar stresses acting in a freely-supported cylindrical window made of fusion-cast , measuring in diameter and in thickness, subjected to a uniform load of .

Image of FIG. 6.
FIG. 6.

Beam-induced thickness-averaged stress dependence on the radial coordinate and the truncation parameter for Gaussian axisymmetric temperature distributions. (a) Nondimensional radial stress; (b) nondimensional azimuthal stress. Note that the radial stress remains compressive throughout the parameter space, whereas the azimuthal stress turns tensile for and reaches peak values at some distance off the edge if .

Image of FIG. 7.
FIG. 7.

Predicted thickness-averaged planar stress acting in a window made of fusion-cast , in diameter and in thickness, exposed to an optimally truncated Gaussian chemical-laser beam for durations of 1, 3, and .

Image of FIG. 8.
FIG. 8.

Axial temperature profile of an AR-coated laser window as a function of the nondimensional time parameter . Note that the “zero” axial position identifies the middle plane. The profiles are identical on both sides of this plane.

Image of FIG. 9.
FIG. 9.

On-axis, temperature-gradient-induced stress enhancement as a function of the axial position for beam-exposure times of 1, 3, and . The calculation applies to an AR-coated window made of fusion-cast , thick, exposed to a Gaussian chemical laser beam of peak intensity. Note that, as expected, the thickness-averaged stress enhancement is equal to zero.

Image of FIG. 10.
FIG. 10.

Temperature-gradient-induced stress enhancement as a function of radial position and exposure time, for the two surfaces and the middle plane of a model window as in Fig. 9, on assuming a truncation parameter .

Image of FIG. 11.
FIG. 11.

Combined pressure- and beam-induced planar stresses as a function of the normalized radial distance. The figure depicts the situation on the front (high-pressure) side, the middle plane, and the back (low-pressure) side of a model window made of fusion-cast (diameter: ; thickness: ) subjected to a pressure differential and exposed to an optimally truncated chemical laser beam. (a) Laser run time: ; (b) laser run time: ; (c) laser run time: .

Image of FIG. 12.
FIG. 12.

Combined peak stresses in a model window made of fusion-cast , in diameter and in thickness, exposed to optimally truncated Gaussian chemical laser beams for durations of . The symbol refers to the peak irradiance level. (a) Peak tensile stress at the backface edge; (b) peak compressive stress at the frontface center.

Image of FIG. 13.
FIG. 13.

Predicted on-axis temperature rise experienced by a model window made of fusion-cast , in diameter and in thickness, exposed to an optimally truncated Gaussian chemical laser beam for durations up to .

Image of FIG. 14.
FIG. 14.

Figure of merit for stress of the six laser-window material candidates identified in Table III. Note that, for comparative purposes, the of was set equal to 1.

Image of FIG. 15.
FIG. 15.

Uniaxial fracture-strength Weibull plot for fusion-cast ; the “as-received” and “FCP-treated” data points reflect fracture-strength test results recorded in Refs. 17 and 18, respectively.

Tables

Generic image for table
Table I.

List of symbols (see also Table II).

Generic image for table
Table II.

Key properties of fusion-cast at room temperature.

Generic image for table
Table III.

Relevant room-temperature properties and figure of merit for stress, , of key laser-window material candidates.

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/content/aip/journal/jap/98/4/10.1063/1.2007874
2005-08-18
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Analytical stress modeling of high-energy laser windows: Application to fusion-cast calcium fluoride windows
http://aip.metastore.ingenta.com/content/aip/journal/jap/98/4/10.1063/1.2007874
10.1063/1.2007874
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