# In-Line Target Production for Laser IFE
## 2 Modeling Results  
### FST-Layering Method for Classical High Gain Targets  
Among the reactor-scale targets is a classical high gain target (CHGT-1) with the following parameters [23]: it is a 4-mm diameter CH shell with a 45-\(\upmu\)m thick wall, the cryogenic layer thickness is 200 \(\upmu\)m. For the CHGT-1, in our previous work we calculated the value of \(\uptau_{\text{form}}\) for different initial target temperatures \(T_{\text{in}}\)[6] (Table 1). Another example of a classical high gain target (CHGT-2) was proposed in Reference [24]. The target consists of four parts: a gold-coated CH shell, a D-T filled CH foam ablator, a layer of pure solid D-T fuel, and a D-T vapor cavity. We use this CHGT-2 to examine issues affecting the possibility of its fabrication by the FST layering method taking into account that it has a very thin CH shell (1 \(\upmu\)m) compared with CHGT-1 (45 \(\upmu\)m). The CHGT-2 specifications are given in Table 2, where D\({}_{\text{i}}\) and D\({}_{0}\) are the inner and the outer diameters of each layer, and \(\Delta_{l}\) and \(\rho_{l}\) are the layer thickness and density, respectively. A thin CH layer has a gold overcoat (0.03 \(\upmu\)m) to withstand the thermal chamber environment. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**CHGT-1 Design**} & \multicolumn{2}{c}{\(\uptau_{\text{form}}\)} \\ \cline{2-4}  & \multicolumn{1}{c}{**T\({}_{\text{in}}\) = 37 K**} & \multicolumn{1}{c}{**T\({}_{\text{in}}\) = 27 K**} \\ \hline
1 & CH shell without overcoat & 227.5 c & 149.0 c \\ \hline
2 & Gold-coated CH shell & 13.65 c & 8.94 c \\ \hline \hline \end{tabular}
\end{table} 
Table 1: FST layering time for classical high gain target (CHGT-1). Figure 1: Free-standing target (FST)-layering setup. In (**a**): general view; in (**b**): FST-layering module (LM)—target transport is injection between the basic units: shell container (SC)—layering channel (LC)—test chamber (TC)); in (**c**): (vapor (1) – liquid (2)) interface behavior in 1-mm CH -shell (P = 765 atm of H2 at 300 K); in (**d**): LC as a part of the insert into the cryostat. The program on CHGT-2 modeling includes the computation of the FST layering time and the LC specifications, such as: number of spirals, inclination angle of the spiral, total length of the spiral, the spiral diameter, and number of turns. The obtained results will allow one to calculate the baseline parameters necessary at designing of the FST-LM as a means of high-gain direct-drive target production. For a better understanding of the time-integral performance (TIP) criterion under the FST-LM operation, we emphasize that the LC must have a well-defined geometry to satisfy the condition:  
\[\text{Target is formed in the LC if }\tau_{\text{form}}\leq\tau_{\text{res}}, \tag{1}\]  
where \(\tau_{\text{form}}\) is the layering time, and \(\tau_{\text{res}}\) is the time of target residence in the LC. Since a liquid sagged fuel is the initial state before the FST layering (Figure 1c), then for dynamical fuel symmetrization in a batch of rolling targets the time of liquid phase existence, \(\tau_{\text{liquid}}\), is a key parameter and must be sufficient for layer symmetrization. This depends on the temperature \(T_{\text{in}}\) of the target entry into the LC and on the temperature distribution along the LC, i.e., the temperature profiling procedure can play an important role for successful FST layering. Generally, one can view the target motion in the following rolling conditions:  
* Target slides on the LC surface (no rotation: sliding and only sliding or pure S&S-mode);
* Target combines rolling with sliding (rolling with sliding or mixed R&S-mode);
* Target rolls on the LC surface without sliding (rolling and only rolling or pure R&R-mode). A key problem of our investigations is that it is necessary to realize only the R&R-mode to avoid the outer shell roughening and to achieve the fuel layer uniformity.