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.