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Radiation-Dominated Implosion with Flat Target

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Inertial confinement fusion is a promising option to provide massive, clean, and affordable energy for humanity in the future. The present status of research and development is hindered by hydrodynamic instabilities occurring at the intense compression of the target fuel by energetic laser beams. A recent proposal by Csernai et al. [1] combines advances in two fields: detonations in relativistic fluid dynamics and radiative energy deposition by plasmonic nanoshells. To avoid instabilities, the initial compression of the target pellet can be eliminated or decreased. Rapid volume ignition can be achieved by a final and more energetic short laser pulse, which should be as short as the penetration time of the light across the target. In the present study, we discuss a flat fuel target irradiated from both sides simultaneously. Here we propose ignition with smaller compression, by largely increased energy, and entropy increase. Instead of external indirect heating and huge energy loss, we aim for maximized internal heating in the target with the help of recent advances in nanotechnology. The reflectivity of the target can be made negligible, and the absorptivity can be increased by one or two orders of magnitude using plasmonic nanoshells embedded into the target fuel. Thus, we achieve higher ignition energy and radiation-dominated dynamics. Here in most of the interior, we will reach the ignition energy simultaneously based on the results of relativistic fluid dynamics. This reduces development of instabilities, which up to now prevented the complete ignition of the fuel.

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  1. Due to the flat target geometry and the light pulse strength degradation, the irradiation of the central domains is about three times weaker than in the previously demonstrated spherical configuration [1].

  2. For comparison, the 3D NIF experiments use a linear size compression of 30 and a density increase of almost 1000.


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Enlightening discussions with Larissa Bravina, I. Földes and G. Pokol, P. Rácz, K. Taradiy, and S. Varró are gratefully acknowledged. Horst Stöcker acknowledges the Judah M. Eisenberg Professor Laureatus chair at Fachbereich Physik of Goethe Universität at Frankfurt.


This work is supported in part by the Institute of Advance Studies, Köszeg, Hungary, the Research Council of Norway, grant no. 255253, the National Research, Development and Innovation Office (NKFIH) projects “Optimized nanoplasmonics” (K116362), the “Ultrafast physical processes in atoms, molecules, nanostructures and biological systems” (EFOP-3.6.2-16-2017-00005), and the Frankfurt Institute for Advanced Studies.

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Correspondence to L. P. Csernai.

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Based on the results of NIF [14] (case B), the necessary ignition energy of the DT target is Q/m = 207.7 kJ/mg. Then, assuming that laser pulse energy Q0 = 100 J, we can ignite a DT target of mass m = 0.481 μg. The density of DT ice is ρ = 0.225 g/cm3, which leads to a target volume of V = 2.14 × 10–3 mm3. For a minimal target surface, the diameter and height of the DT target cylinder becomes 2R = h = 0.14 mm, and its cross section is A = 0.0153 mm2.

The critical energy density for ignition is ε = ρQ/m = 46.47 MJ/cm3 (kJ/mm3), while the required pulse duration is tpulse = h/cDT = 0.526 ps. During this time interval, we should deposit the total pulse energy Q0 to the whole target, which leads to an initial energy flux at the flat surface of the target u0 = ε/tpulse = εcDT/h = 88.8 kJc/mm4. Therefore, we get U0 = Au0 = 1.359 kJc/mm2.

Taking into account that in the beam direction the light front propagates with the speed of light (in the target material), we get the deposited energy

$$\int {u(x,t){{d}^{3}}xdt} = \int {Au(x,t)\delta (x - ct)} dxdt,$$

and we can introduce the linear deposited surface energy density, Au(x, t), inside the target as

$$D(x)dx = \int\limits_{{{t}_{0}}} {Au(x,t)\delta (x - ct)} dtdx$$

along a light beam starting at t0. From the incoming surface energy density Q(x) a part, αK(x), is deposited in the target material:

$$D(x)dx = {{\alpha }_{K}}(x)Q(x)dx,$$

and the remaining lesser part continues to propagate along the light beam as described in Sect. 4.


According to our calculations, for constant absorptivity αK, only inhomogeneous heating of the target is possible. This is shown in Fig. 6.

Fig. 6.
figure 6

(Color online) Same as Fig. 3, but without nanoshells. The integrated energy up to a given time in the space–time across the depth, h, of the flat target. The color strip indicates the energy density in units of the critical energy density (Tc). The contour line T = 1 indicates points where the phase transition or the ignition in the target is reached. This contour line, compared to the one in Fig. 3, is never constant in time, indicating no simultaneous whole volume transition or ignition. The time-like (causally unconnected) part of the transition takes place only in the central ~15% of the target volume. The two straight lines indicate the light cones originating at the outside edges of the target, and show the end of the irradiation pulses.

In our numerical calculations with nanoshells implanted in the target to increase central absorption (see Figs. 2 and 3), we used the distribution

$${{\alpha }_{{{\text{ns}}}}}(s) = \alpha _{{{\text{ns}}}}^{C} + {{\alpha }_{{{\text{ns}}}}}(0)\exp\left[ {4\frac{{{{{\left( {{s \mathord{\left/ {\vphantom {s {100}}} \right. \kern-0em} {100}}} \right)}}^{2}}}}{{\left( {{s \mathord{\left/ {\vphantom {s {100}}} \right. \kern-0em} {100}} - 1} \right)\left( {{s \mathord{\left/ {\vphantom {s {100}}} \right. \kern-0em} {100}} + 1} \right)}}} \right].$$

One can see that αns(s) is maximal at the center of the target, s = 0. Here the length scale, s, is chosen so that s = 100 corresponds to x = h/2 = 0.0555 mm. The edge absorptivity of the fuel is αk0 = 1.0 cm–1. The constant contribution of the nanoshells is \(\alpha _{{{\text{ns}}}}^{C}{\kern 1pt} \) = 9.10 cm–1, and the additional implantation at the center reaches αns(0) = 20.2 cm–1. Thus, in the center the total absorptivity is \({{\alpha }_{{k0}}}{\kern 1pt} + \alpha _{{{\text{ns}}}}^{C}{\kern 1pt} + {{\alpha }_{{{\text{ns}}}}}(0)\) = 30.3 cm–1. For this absorptivity parameters, we need a modest density of nanospheres embedded into the target fuel. In the center ρns(0) = 2.48 × 1010 cm–3, while at the outside edges less: \(\rho _{{{\text{ns}}}}^{E}{\kern 1pt} \) = 8.05 × 109 cm–3. In the center of the target material, the nanoshells will occupy only 2.9 × 10–4% of the volume.

With these absorption parameters, only 0.25% of the energy of the incoming laser pulse reaches the opposite side of the target. Thus, the expectation is an energy balance with a possible minimum of loss.

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Csernai, L.P., Csete, M., Mishustin, I.N. et al. Radiation-Dominated Implosion with Flat Target. Phys. Wave Phen. 28, 187–199 (2020).

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