• High Power Laser Science and Engineering
  • Vol. 7, Issue 3, 03000e38 (2019)
I. V. Aleksandrova and E. R. Koresheva
Author Affiliations
  • Lebedev Physical Institute, Russian Academy of Sciences, Moscow 119991, Russia
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    DOI: 10.1017/hpl.2019.23 Cite this Article Set citation alerts
    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 Copy Citation Text show less

    Abstract

    In inertial fusion energy (IFE) research, a number of technological issues have focused on the ability to inexpensively fabricate large quantities of free-standing targets (FSTs) by developing a specialized layering module with repeatable operation. Of central importance for the progress towards plasma generation with intense thermonuclear reactions is the fuel structure, which must be isotropic to ensure that fusion will take place. In this report, the results of modeling the FST layering time, $\unicode[STIX]{x1D70F}_{\text{Form}}$, are presented for targets which are shells of ${\sim}4~\text{mm}$ in diameter with a wall made from compact and porous polymers. The layer thickness is ${\sim}200~\unicode[STIX]{x03BC}\text{m}$ for pure solid fuel and ${\sim}250~\unicode[STIX]{x03BC}\text{m}$ for in-porous solid fuel. Computation shows $\unicode[STIX]{x1D70F}_{\text{Form}}<23$ s for $\text{D}_{2}$ fuel and $\unicode[STIX]{x1D70F}_{\text{Form}}<30$ s for D–T fuel. This is an excellent result in terms of minimizing the tritium inventory, producing IFE targets in massive numbers (${\sim}$1 million each day) and obtaining the fuel as isotropic ultrafine layers. It is shown experimentally that such small layering time can be realized by the FST layering method in line-moving, high-gain direct-drive cryogenic targets using $n$-fold-spiral layering channels at $n=2,3$.
    $$\begin{eqnarray}\displaystyle \unicode[STIX]{x1D6FC}(\unicode[STIX]{x1D703},T)=\sqrt[3]{\frac{\unicode[STIX]{x1D70C}_{\text{c}}(T)-\unicode[STIX]{x1D703}\unicode[STIX]{x1D70C}_{\text{CP}}}{\unicode[STIX]{x1D70C}_{\text{c}}(T)-\unicode[STIX]{x1D70C}_{\text{v}}(T)}}. & & \displaystyle\end{eqnarray}$$(1)

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    $$\begin{eqnarray}\unicode[STIX]{x1D70F}_{\text{Form}}<\unicode[STIX]{x1D70F}_{\text{Res}},\end{eqnarray}$$(2)

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    $$\begin{eqnarray}P_{\text{st}}=2\unicode[STIX]{x1D70E}_{\text{st}}\unicode[STIX]{x1D6FF},\end{eqnarray}$$(3)

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    $$\begin{eqnarray}P=\frac{R_{\text{G}}T}{\unicode[STIX]{x1D707}/\unicode[STIX]{x1D70C}-b}-\frac{a\unicode[STIX]{x1D70C}^{2}}{\unicode[STIX]{x1D707}^{2}},\end{eqnarray}$$(4)

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    $$\begin{eqnarray}P(\unicode[STIX]{x1D70C}_{\text{f}},T_{\text{d}})< P_{\text{st}},\end{eqnarray}$$(5)

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    $$\begin{eqnarray}\displaystyle \unicode[STIX]{x1D70F}_{\text{Sym}}\sim \unicode[STIX]{x1D70F}_{\text{Liquid}}. & & \displaystyle\end{eqnarray}$$(6)

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    $$\begin{eqnarray}\displaystyle \begin{array}{@{}c@{}}\text{D}_{2}:~18.73~\text{K}=T_{\text{TP}}< T_{\text{in}}< T_{\text{d}}=27.5~\text{K},\\ \text{and}\\ \text{D}{-}\text{T}:~19.79~\text{K}=T_{\text{TP}}< T_{\text{in}}< T_{\text{d}}=28.0~\text{K},\end{array} & & \displaystyle\end{eqnarray}$$(7)

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    $$\begin{eqnarray}\text{D}_{2}:~1.47<\unicode[STIX]{x1D703}_{\text{D2}}=1.54<1.61\quad (\unicode[STIX]{x0394}T=35{-}20~\text{K}).\end{eqnarray}$$(8)

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    $$\begin{eqnarray}\unicode[STIX]{x1D712}_{\text{g}}=S_{\text{ca}}/S_{\text{sh}}=\sqrt{\frac{3G}{4\unicode[STIX]{x1D70B}r_{0}^{2}\unicode[STIX]{x1D6FF}E}},\end{eqnarray}$$(9)

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    $$\begin{eqnarray}\unicode[STIX]{x1D6FE}=\frac{1}{(1-r_{0}/R_{\text{tube}})^{1/3}}.\end{eqnarray}$$(10)

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    $$\begin{eqnarray}\unicode[STIX]{x1D70F}_{\text{Form}}=\unicode[STIX]{x1D70F}_{\text{Liquid}}+\unicode[STIX]{x1D70F}_{\text{Solid}}+\unicode[STIX]{x1D70F}_{\text{Cool}}.\end{eqnarray}$$(11)

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    $$\begin{eqnarray}\displaystyle & & \displaystyle N(T_{1/2})=N_{0}/2,\quad N_{0}\exp (-\unicode[STIX]{x1D706}T_{1/2})=N_{0}/2\quad \text{and}\quad \nonumber\\ \displaystyle & & \displaystyle \exp (-\unicode[STIX]{x1D706}T_{1/2})=1/2,\nonumber\end{eqnarray}$$(12)

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    $$\begin{eqnarray}N=N_{0}\exp (-t\ln 2/T_{1/2}).\end{eqnarray}$$(13)

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    $$\begin{eqnarray}P_{\unicode[STIX]{x1D6FD}}=\frac{N_{0}\ln 2}{T_{1/2}}\langle E_{\text{decay}}\rangle ,\end{eqnarray}$$(14)

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    $$\begin{eqnarray}\unicode[STIX]{x1D6EF}=P_{\unicode[STIX]{x1D6FD}}/Q_{\text{out}}=0.0125.\end{eqnarray}$$(15)

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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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