Advanced fuel layering in line-moving, high-gain direct-drive cryogenic targets 
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Lebedev Physical Institute, Russian Academy of Sciences, Moscow 119991, Russia
Figures & Tables
Fig. 1. A high-gain direct-drive target design proposed for a 1.3 MJ KrF laser[7].
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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 $+$ vapor ($18.73~\text{K}=T_{\text{TP}}, $P<12.5$ atm).
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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.
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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.
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Fig. 5. Depressurization temperature in the case of the BODNER-Target for $\text{D}_{2}$, $\text{T}_{2}$ and D–T.
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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.
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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).
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Fig. 8. Cooling time of several thin metal overcoats for different target designs ($\varnothing$ – diameter, $W$ – cryogenic layer thickness).
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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).
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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).
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Fig. 11. A variety of IFE target designs can be balanced by a corresponding choice of the LC design.
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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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Table1. Parameters of the BODNER-Target for both $\text{D}_{2}$ and D–T fuel.
| Parameters | values | D–T values |
|---|
| Target mass | ${\sim}$3.5 mg | ${\sim}$4.4 mg | | Shell mass | $160.5~\unicode[STIX]{x03BC}\text{g}$ | $160.5~\unicode[STIX]{x03BC}\text{g}$ | | – compact polymer | $51.2~\unicode[STIX]{x03BC}\text{g}$ | $51.2~\unicode[STIX]{x03BC}\text{g}$ | | – porous polymer | $109.3~\unicode[STIX]{x03BC}\text{g}$ | $109.3~\unicode[STIX]{x03BC}\text{g}$ | | Fuel mass | 3.3 mg | 4.2 mg | | – in-porous fuel | 2.1 mg | 2.7 mg | | – pure solid fuel | 1.2 mg | 1.5 mg | | – vapor fuel | $6.3~\unicode[STIX]{x03BC}\text{g}$ | $4.24~\unicode[STIX]{x03BC}\text{g}$ | | Fill density, $\unicode[STIX]{x1D70C}_{\text{f}}$ | ${\sim}107~\text{mg}/\text{cm}^{3}$ | ${\sim}136~\text{mg}/\text{cm}^{3}$ | | Fill pressure, $P_{\text{f}}$ | ${\sim}$1100 atm | ${\sim}$1100 atm |
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Table2. Critical parameters (density, pressure, temperature) for the hydrogen isotopes[13].
| Hydrogen isotopes | | | | D–T |
|---|
| $\unicode[STIX]{x1D70C}_{\text{CP}}$, $\text{mg}/\text{cm}^{3}$ | 30.10 | 69.80 | 108.97 | 87.10 | | $P_{\text{CP}}$, atm | 12.98 | 16.43 | 18.26 | 17.50 | | $T_{\text{CP}}$, K | 33.19 | 38.34 | 40.44 | 39.42 |
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Table3. Pressure and temperature for the hydrogen isotopes at the boiling and triple points[13].
| Hydrogen isotopes | | | | D–T |
|---|
| $T_{\text{BP}}$, K | 20.39 | 23.66 | 25.04 | 24.38 | | $P_{\text{BP}}$, atm | 1.0 | 1.0 | 1.0 | 1.0 | | $T_{\text{TP}}$, K | 13.96 | 18.73 | 20.62 | 19.79 | | $P_{\text{TP}}$, atm | 0.07 | 0.17 | 0.21 | 0.19 |
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Table4. Required tensile strength near the critical point temperature.
| Target | Pressure | Tensile strength |
|---|
| temperature | $\text{D}_{2}$ | D–T | $\text{D}_{2}$ | D–T |
|---|
| 45.00 K | 47.68 atm | 44.94 atm | ${\sim}$4654 MPa | ${\sim}$4368 MPa | | 40.00 K | 28.96 atm | 25.89 atm | ${\sim}$2826 MPa | ${\sim}$2527 MPa | | 38.34 K ($\text{D}_{2}$) | 22.74 atm | – | ${\sim}$2219 MPa | – | | 39.42 K (D–T) | – | 23.99 atm | – | ${\sim}$2341 MPa |
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Table5. The BODNER-Target layering time.
| $\text{D}_{2}$ fuel |
|---|
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|---|
| Layering time | $\unicode[STIX]{x1D70F}_{\text{Liquid}}$ | $\unicode[STIX]{x1D70F}_{\text{Solid}}$ | $\unicode[STIX]{x1D70F}_{\text{Cool}}$ | $\unicode[STIX]{x1D70F}_{\text{Form}}$ ($\unicode[STIX]{x1D712}_{\text{g}}$) | $\unicode[STIX]{x1D70F}_{\text{Form}}$ ($\unicode[STIX]{x1D712}_{\text{eff}}$) |
|---|
| Stage 1 | | | | | | | (a) $T_{\text{in}}=T_{\text{S}}\sim 35.0$ K | 17.48 s | – | – | (a) 22.45 s | less than | | (b) $T_{\text{in}}=T_{\text{d}}=27.5$ K | 7.08 s | | | (b) 12.05 s | 0.5 s | | Stage 2 | | | | | | | $T_{\text{TP}}=18.71$ K | – | 4.97 s | – | | | | | D–T fuel | | | Layering time | $\unicode[STIX]{x1D70F}_{\text{Liquid}}$ | $\unicode[STIX]{x1D70F}_{\text{Solid}}$ | $\unicode[STIX]{x1D70F}_{\text{Cool}}$ | $\unicode[STIX]{x1D70F}_{\text{Form}}$ ($\unicode[STIX]{x1D712}_{\text{g}}$) | $\unicode[STIX]{x1D70F}_{\text{Form}}$ ($\unicode[STIX]{x1D712}_{\text{eff}}$) | | | Stage 1 | | | | | | | (a) $T_{\text{in}}=T_{\text{S}}\sim 37.5$ K | 22.14 s | – | – | (a) 28.52 s | less than | | (b) $T_{\text{in}}=T_{\text{d}}=28.0$ K | 7.87 s | | | (b) 14.25 s | 0.5 s | | Stage 2 | | | | | | | $T_{\text{TP}}=19.79$ K | – | 5.23 s | – | | | | Stage 3 | | | | | | | $T_{\text{Cool}}=18.3$ K | – | – | 1.15 s | | |
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Table6. Double-spiral LC (mockup testing results).
| Specifications | Values | Specifications | Values |
|---|
| Spiral number | $n=2$ | Total number of turns | $\unicode[STIX]{x1D714}=44$ | | Spiral diameter | $\text{OD}=42$ mm | Tube diameter | $\text{ID}=4.4$ mm, $\text{OD}=6$ mm | | Spiral height | $H=450$ mm | Length of each spiral | $L_{n}=2261$ mm | | Spiral angle | $\unicode[STIX]{x1D6FC}=11.5^{\circ }$ | Residence time (PS shell)a | $\unicode[STIX]{x1D70F}_{\text{Res}}=23.5$ s ($\unicode[STIX]{x1D70F}_{\text{Form}}=22.45$ s for $\text{D}_{2}$) |
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Table7. Three-fold-spiral LC (mockup testing results).
| Specifications #1 | Values | Specifications #1 | Values |
|---|
| Spiral number | $n=3$ | Total number of turns | $\unicode[STIX]{x1D714}=77$ | | Spiral diameter | $\text{OD}=42$ mm | Tube diameter | $\text{ID}=4.4$ mm, $\text{OD}=6$ mm | | Spiral height | $H=880$ mm | Length of each spiral | $L_{n}=3066$ mm | | Spiral angle | $\unicode[STIX]{x1D6FC}=16.7^{\circ }$ | Residence time (CH shell)a | $\unicode[STIX]{x1D70F}_{\text{Res}}>35$ s ($\unicode[STIX]{x1D70F}_{\text{Form}}=28.52$ s for D–T) |
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Table8. Combined three-fold-spiral LC.
| Specifications #2 | Values |
|---|
| Radius of Spiral 4 | 21 mm | | Length of Spiral 4 | 2.070 m | | Total length of Spiral 3 $+$ Spiral 4 | 5.136 m | | Angle of Spiral 4 | $\unicode[STIX]{x1D6FC}=3^{\circ }$ | | Height of Spiral 4 | 10.8 cm |
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Table9. Existence time of the liquid phase at different temperatures $T_{\text{in}}$.
| Experiment | Calculation |
|---|
| # | | LC | | | |
|---|
| 1 | 21 K | Cylinder | 8 s | 7.22 s | 2.97 s | | 2 | 15 K | Cylinder | 8 s | 5.13 s | 0.97 s |
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I. V. Aleksandrova, E. R. Koresheva. Advanced fuel layering in line-moving, high-gain direct-drive cryogenic targets[J]. High Power Laser Science and Engineering, 2019, 7(3): 03000e38.
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