I. V. Aleksandrova, E. R. Koresheva, "Advanced fuel layering in line-moving, high-gain direct-drive cryogenic targets," High Power Laser Sci. Eng. 7, 03000e38 (2019)

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- High Power Laser Science and Engineering
- Vol. 7, Issue 3, 03000e38 (2019)
![A high-gain direct-drive target design proposed for a 1.3 MJ KrF laser[7].](/richHtml/hpl/2019/7/3/03000e38/img_1.gif)
Fig. 1. A high-gain direct-drive target design proposed for a 1.3 MJ KrF laser[7].

Fig. 2. The phase state of $\text{D}_{2}$ fuel in the BODNER-Target upon cooling down. (a) PVT-diagram ($T_{\text{S}}$ is the temperature of fuel separation into the liquid and vapor phases). (b) Fuel state in the shell just before the FST layering versus the initial target temperature $T_{\text{in}}$ : (1) gaseous fuel ($T_{\text{in}}>T_{\text{CP}}=38.34$ K), (2) compressed liquid ($36.5~\text{K}\sim T_{\text{S}}, $12.5~\text{atm}
), (3) liquid

Fig. 3. The FST layering method provides rapid symmetrization and freezing of solid ultrafine fuel layers. (a) Schematic of the FST layering module. (b) Target before layering (‘liquid $+$ vapor’ fuel state). (c) Target after FST layering (uniform solid layer). (d) Single-spiral LC (1) in the working assembly. (e) Single-spiral LC (1) shown with magnification. (f) Double-spiral LC.

Fig. 4. The gas pressure in the shell versus the fuel density near the critical point for (a) $\text{D}_{2}$ and (b) D–T.

Fig. 5. Depressurization temperature in the case of the BODNER-Target for $\text{D}_{2}$ , $\text{T}_{2}$ and D–T.

Fig. 6. Dynamical layer symmetrization during FST layering: (a) schematic of the target rolling along the LC; (b) $T_{\text{in}}=21$ K and (c) $T_{\text{in}}=15$ K show the influence of $T_{\text{in}}$ on the layer uniformity. Both targets have the same parameters. But in case (c) during target rolling the liquid $\text{H}_{2}$ begins to spread onto the inner shell surface, and as $T_{\text{in}}=15$ K is close to $T_{\text{TP}}=13.96$ K for $\text{H}_{2}$ , then quick freezing has begun before the achievement of layer uniformity.
![The relative radius of a vapor bubble ($\unicode[STIX]{x1D6FC}$) under the BODNER-Target cooling (filled with $\text{D}_{2}$ up to 1100 atm at room temperature); $\unicode[STIX]{x0394}T_{\text{max}}$ and $\unicode[STIX]{x0394}T_{\text{work}}$ are the maximum and working temperature ranges for uniform layering ($T_{\text{S}}=36.5$ K, $T_{\text{d}}=27.5$ K).](/Images/icon/loading.gif)
Fig. 7. The relative radius of a vapor bubble ($\unicode[STIX]{x1D6FC}$ ) under the BODNER-Target cooling (filled with $\text{D}_{2}$ up to 1100 atm at room temperature); $\unicode[STIX]{x0394}T_{\text{max}}$ and $\unicode[STIX]{x0394}T_{\text{work}}$ are the maximum and working temperature ranges for uniform layering ($T_{\text{S}}=36.5$ K, $T_{\text{d}}=27.5$ K).

Fig. 8. Cooling time of several thin metal overcoats for different target designs ($\varnothing$ – diameter, $W$ – cryogenic layer thickness).
![$\text{H}_{2}$–liquid–vapor interface behavior (meniscus) for $\unicode[STIX]{x1D703}\leqslant 1$ (1, vapor; 2, liquid). In (a), with $\unicode[STIX]{x1D703}=0.69$ (polystyrene shell, $\varnothing =940~\unicode[STIX]{x03BC}\text{m}$, fill pressure $P_{\text{f}}=305$ atm at 300 K), the meniscus varies typically. In (b), with $\unicode[STIX]{x1D703}=0.91$ ($\varnothing =949~\unicode[STIX]{x03BC}\text{m}$, $P_{\text{f}}=445$ atm), near the critical density for $\text{H}_{2}$, the meniscus varies greatly, from strongly concave downwards at $T=14$ K to almost flat at $T=33$ K (a flat meniscus indicates the same material properties on both sides of the meniscus when approaching the critical point).](/Images/icon/loading.gif)
Fig. 9. $\text{H}_{2}$ –liquid–vapor interface behavior (meniscus) for $\unicode[STIX]{x1D703}\leqslant 1$ (1, vapor; 2, liquid). In (a), with $\unicode[STIX]{x1D703}=0.69$ (polystyrene shell, $\varnothing =940~\unicode[STIX]{x03BC}\text{m}$ , fill pressure $P_{\text{f}}=305$ atm at 300 K), the meniscus varies typically. In (b), with $\unicode[STIX]{x1D703}=0.91$ ($\varnothing =949~\unicode[STIX]{x03BC}\text{m}$ , $P_{\text{f}}=445$ atm), near the critical density for $\text{H}_{2}$ , the meniscus varies greatly, from strongly concave downwards at $T=14$ K to almost flat at $T=33$ K (a flat meniscus indicates the same material properties on both sides of the meniscus when approaching the critical point).
![$\text{H}_{2}$–liquid–vapor interface behavior for $\unicode[STIX]{x1D703}>1$ (1, vapor; 2, liquid). (a) $\unicode[STIX]{x1D703}=1.32$ (polystyrene shell, $\varnothing =980~\unicode[STIX]{x03BC}\text{m}$, $P_{\text{f}}=765$ atm); (b) $\unicode[STIX]{x1D703}=1.6$ (superdurable glass shell, $\varnothing =250~\unicode[STIX]{x03BC}\text{m}$, $P_{\text{f}}=1100$ atm).](/Images/icon/loading.gif)
Fig. 10. $\text{H}_{2}$ –liquid–vapor interface behavior for $\unicode[STIX]{x1D703}>1$ (1, vapor; 2, liquid). (a ) $\unicode[STIX]{x1D703}=1.32$ (polystyrene shell, $\varnothing =980~\unicode[STIX]{x03BC}\text{m}$ , $P_{\text{f}}=765$ atm); (b ) $\unicode[STIX]{x1D703}=1.6$ (superdurable glass shell, $\varnothing =250~\unicode[STIX]{x03BC}\text{m}$ , $P_{\text{f}}=1100$ atm).

Fig. 11. A variety of IFE target designs can be balanced by a corresponding choice of the LC design.

Fig. 12. A standard case of LC winding. The difficulty in designing TrCs arises from the need to have smooth target travel along the LC to avoid sudden changes in the acceleration.
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Table 1. Parameters of the BODNER-Target for both $\text{D}_{2}$ and D–T fuel.
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Table 2. Critical parameters (density, pressure, temperature) for the hydrogen isotopes[13].
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Table 3. Pressure and temperature for the hydrogen isotopes at the boiling and triple points[13].
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Table 4. Required tensile strength near the critical point temperature.
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Table 5. The BODNER-Target layering time.
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Table 6. Double-spiral LC (mockup testing results).
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Table 7. Three-fold-spiral LC (mockup testing results).
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Table 8. Combined three-fold-spiral LC.
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Table 9. Existence time of the liquid phase at different temperatures $T_{\text{in}}$ .

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