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 $+$ vapor ($18.73~\text{K}=T_{\text{TP}}, $P<12.5$  atm).

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.

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).

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).

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.

Table 1. Parameters of the BODNER-Target for both $\text{D}_{2}$ and D–T fuel.

Table 2. Critical parameters (density, pressure, temperature) for the hydrogen isotopes^[13].

Table 3. Pressure and temperature for the hydrogen isotopes at the boiling and triple points^[13].

Table 4. Required tensile strength near the critical point temperature.

Table 5. The BODNER-Target layering time.

Table 6. Double-spiral LC (mockup testing results).

Table 7. Three-fold-spiral LC (mockup testing results).

Table 8. Combined three-fold-spiral LC.

Table 9. Existence time of the liquid phase at different temperatures $T_{\text{in}}$.