First observations on wall plasma expansion and x-ray flux in foam hohlraum at 100 kJ laser facility

A gold hohlraum is usually filled with helium to prevent it from filling with ablated gold, which could then block the propagation of laser beams into the hohlraum.^1,2 The gas fill density has been identified as a key parameter controlling both the energy coupling efficiency and symmetry.^3,4 It has been shown that a lower gas-filled (0.03 mg/cm³) hohlraum has superior performance: laser–plasma interaction is minimal, and the laser-to-hohlraum coupling remains above 97%.⁵ Fortunately, the use of higher-density carbon (HDC) ablators has reduced the implosion time to 7–8 ns. This has also reduced the amount of wall blow-in plasma filling the hohlraum, synergistically with the use of a lower hohlraum gas fill.^6–8 Furthermore, by increasing the diameter of the HDC capsule and controlling the implosion shape symmetry using cross-beam energy transfer (CBET),⁹ a gain greater than 1 has been achieved in which 2.05 MJ of 351 nm laser light has produced 3.1 MJ of total fusion yield at the National Ignition Facility (NIF).¹⁰ 

However, achieving high gain using HDC ablators faces some challenges. In particular, the high pressure of the first shock limits the highest achievable areal density ρR.¹¹ A long-pulse, low-adiabat drive in a low-gas-fill hohlraum using CH ablators may be a competitive approach.^12–14 Meanwhile, higher laser energy is conducive to producing even higher energy yields, but is limited by concerns regarding damage to the optics. Therefore, it is crucial to achieve further reductions in the hohlraum low-mode drive asymmetry^15,16 caused by hohlraum wall blowoff and thus by altered laser beam absorption regions, as well as further increases in hohlraum energy coupling efficiency to create greater soft X-ray drive.

Planar target experiments and simulations have shown that low-density high-Z foam material has unique advantages when applied to hohlraums.^17–19 This approach yields higher radiation temperatures,²⁰ owing to reduced X-ray energy loss in the hohlraum wall,^21–23 and results in less plasma blowoff.²⁴ Experiments have been carried out to demonstrate that a hohlraum with low-density Ta₂O₅ produces higher radiation temperatures than one with high-density Ta₂O₅.²⁵ Experiments involving hohlraums lined with Ta₂O₅ aerogel have demonstrated an improvement in capsule performance.²⁶ However, hohlraums are usually made of gold or gold-lined depleted uranium to increase the X-ray emission, and there have been no investigations of wall plasma motion in hohlraums with low-density foam walls. Therefore, it is necessary to study the performance of hohlraums with low-density gold foam walls.

Here, we show for the first time that the use of gold foam at ∼0.8 g/cm³ density leads to significantly better hohlraum performance. The middle of the hohlraum was irradiated by 16 laser beams, each of 2.5 kJ and with a 3 ns square pulse and forming a circle of laser spots on the wall. The expanding plasma emission, the backscatter fraction of the incident laser, and the hohlraum radiation temperature at several typical angles were measured. The results show that the expanding plasma from the wall moves more slowly in a foam hohlraum. Meanwhile, the hohlraum radiation temperatures are higher in a foam hohlraum, except at the angle of 0°, which is attributed to the reduced expansion of plasma in a foam hohlraum. A two-dimensional (2D) radiation hydrodynamics simulation was performed with the Icefire code. The simulation results are consistent with the experimental results. The use of a foam wall can reduce the wall plasma expansion when the laser ablates the wall, and this reduction is conducive to laser injection, enables better control of symmetry, and increases the hohlraum radiation temperature.

The experiments were carried out on the 100 kJ SG-III laser facility.^27,28 The middle of the hohlraum was irradiated through the bottom by 16 laser beams at a wavelength of 0.35 μm, forming a circle of laser spots on the wall. Each beam was of 2.5 kJ and with a 3 ns square pulse. As shown in Fig. 1, the laser spots were initially located in the middle of the hohlraum, with neighboring spots overlapping to form a closed loop. The hohlraums were fabricated from gold foam of density about 0.8 g/cm³ with a 1 mm-thick wall or from solid gold of density 19.3 g/cm³ with a 25 μm-thick wall. Both hohlraums were 2.8 mm in inner diameter and 2.08 mm in length, with laser entrance holes (LEHs) 2.8 mm in diameter, and were filled with 0.15 atm C₅H₁₂ gas.

The hohlraum radiation temperature T_r(t) was measured by broadband X-ray spectrometry with flat-response X-ray diodes (FXRDs)^29,30 through the up LEH at angles of 16°, 42°, and 64° and through the down LEH at angles of 20° and 0°. X-ray emission images from the expanding plasma were viewed using an X-ray framing camera (XFC)³¹ vertically through the upper LEH. A 4 × 4 array of 20 μm-diameter pinholes was used at the front of the camera to create 16 separate images with 2× magnification. The pinholes were covered with 2 μm zinc to image the emissivity for the 0.8–1.2 keV photon energy range. The backscatter fractions of the incident laser due to stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS) were measured with a full aperture backscatter station (FABS) and a near backscatter station (NBS). Thus, there were a total of four stations.

When the laser interacts with the inner wall of the hohlraum, a hot low-density plasma is created and expands toward the central axis of the hohlraum. Emission images of expanding plasmas recorded by XFC are shown in Figs. 2(a) and 2(b). Figure 2(a) shows emission images between 1 and 2.4 ns from the foam hohlraum, and Fig. 2(b) shows those from the solid hohlraum. It is found that the emission front in the foam hohlraum moves more slowly than that in the solid hohlraum. At 2.4 ns, the emission front is located near the center of the solid gold hohlraum. By circling the emission front of every available image, we obtained the average value of the radius at which the emission front is located. Figure 2(e) shows the radius of the emission front between 0.8 and 1.2 keV from the experiments. Before 1.8 ns, the emission front moves linearly, the movement velocity in the solid hohlraum (black circles) is about 730 μm/ns, while that in the foam hohlraum (red triangles) is about 570 μm/ns, about 20% lower. At 1.8 ns, the difference between the emission fronts in the two hohlraums is 150 μm.

Furthermore, four stations measured the backscattered energy of four of the laser beams (the total energy of these four beams was about 10 kJ). The SRS energies of the foam and solid hohlraums were measured as 14.6 and 10.7 J, respectively. The SBS energies in the foam and solid hohlraums were measured as 64.6 and 139.8 J, respectively. The backscattered fraction due to SRS was about 1.5‰ in the foam hohlraum and 1.1‰ in the solid hohlraum, and that due to SBS was about 0.65% in the foam hohlraum and 1.40% in the solid hohlraum. The SRS is lower than the SBS in both the solid and foam hohlraums at this low gas fill. The SBS in the foam hohlraum is about half of that in the solid hohlraum, which is further evidence that the expanding plasma density is lower in the foam hohlraum.

Figure 3(a) shows the angular distributions of hohlraum radiation temperatures measured by the FXRDs at 3 ns: the temperature is plotted vs the angle Θ of the FXRD viewing direction with respect to the hohlraum axis. It can be seen that the temperatures of the foam hohlraum are distinctly larger than those of the solid hohlraum at Θ = 42° and 64°, slightly larger at Θ = 16° and 20°, and distinctly smaller at Θ = 0°. The variations of temperature with time are shown in Figs. 3(b) and 3(c) at angles Θ = 0° and 64°, respectively. In the cases of smaller angles Θ, most of the detected X rays come from expanding plasma. A lower temperature means less wall plasma expanding in the foam hohlraum, which is consistent with the XFC results. When the angle Θ is larger, such as 64°, most of the detected X rays come from the wall, and are absorbed by the expanding plasma, and so the temperature decreases in the solid hohlraum are caused by a greater amount of expanding plasma.

Numerical simulations were carried out with the 2D radiation hydrodynamics code Icefire in an (r, z) geometry. Icefire includes plasma hydrodynamics, multigroup radiation transport, flux-limited thermal conduction, and 3D laser-ray tracing. The equation of state (EOS) database was taken from the SESAME library, the opacity data were computed using the SNOP code,³² and the electron thermal conduction flux limiter was set as 0.1. Rotational symmetric conditions were used.

Figures 2(c) and 2(d) display the X-ray emission at 0.8–1.2 keV through the upper LEH according to the 2D simulation. The electron temperature and density of the expanding plasma are simulated in the r–z plane, and there is a rotationally symmetric distribution in the hohlraum. The X-ray emission images in Figs. 2(c) and 2(d) were obtained from the hohlraum plasma emission transport along the z axis. The emission front moves less to the center in the foam hohlraum [Fig. 2(c)] than in the solid hohlraum [Fig. 2(d)], consistent with the experimental images. Figure 2(e) shows the variations of the positions of the emission front with time in the two hohlraums according to both experiments and simulations. The simulated mean velocity of the emission front between 1 and 1.8 ns is ∼610 μm/ns in the solid hohlraum and ∼580 μm/ns in the foam hohlraum. At 1.8 ns, the simulated difference between the emission fronts in the two hohlraums is ∼53 μm, which is less than the experimental result. At 2.4 ns, the simulated emission positions are similar to the experimental results in the solid hohlraum, but are less than the experimental results in the foam hohlraum. However, the simulated trend of expanding plasma motion slowing down in the foam hohlraum is consistent with the experiment.

Figure 4 shows the radial distributions (at z = 1040 μm) of electron density and temperature at t = 1, 1.5, 1.8, and 2.4 ns for the solid hohlraum (solid lines) and the foam hohlraum (dashed lines). When the gold wall is ablated by the lasers, electrons are heated and in a non-local thermal equilibrium state, and N-band (Au ∼ 1 keV) and M-band (Au ∼ 3 keV) photons are emitted. The radial electron distribution depends on the radiation ablative wave, laser ablative wave, and pressure balance with filling gas. A double-rarefaction model can be used to describe the approximate density profiles after the radiation ablation front.²⁴ One rarefaction propagates in the thermal conduction zone caused by the temperature jump at the radiation ablation front (rarefactionI), and the other rarefaction (rarefactionII) propagates in the underdense corona caused by the temperature jump at the critical surface. It should be noted that the X-ray emission recorded by the XFC is emitted from the plasma expanding from the wall.

According to Eq. (1), the ablated electron density in the foam hohlraum is lower in the thermal conduction zone (rarefactionI), which is the same as in the simulation results. This leads to a deeper position of the critical density ρ_c at which the rarefaction II front in the corona is located. This distance is 43, 55, 69, and 85 μm at t = 1, 1.5, 1.8, and 2.4 ns, respectively. The density distribution influenced by rarefaction II is similar to the initial density ρ_c, and only the rarefaction front exhibits a discrepancy. It should be noted that the density is larger at the margin of the expanding plasma, and the density increases with increasing time. This is caused by the shock from the LEH membrane. Even so, the bubble interface moves about 50 μm less in the foam hohlraum than in the solid hohlraum. Therefore, the plasma density in the foam hohlraum is lower at the same radial position.

Meanwhile, the electron temperature of the expanding plasma in the foam hohlraum is at most 7% higher than that in the solid hohlraum. The X-ray emission intensity in the corona is proportional to $Tene2$⁠.³³ The electron density has a greater influence on the emission intensity. Figure 5 displays the simulated radial spatial distribution of X-ray emission between 0.8 and 1.2 keV from the upper LEHs in the solid and foam hohlraums. At a given time, the emission intensity in the foam hohlraum is lower than that in the solid hohlraum, and the emission front in the foam hohlraum moves less, which consistent with the results measured by the XFC in Fig. 2.

The hohlraum radiation temperature at an angle of 0° measured by the FXRDs through the down LEH can also be derived from the expanding plasma emission. In Fig. 3(b), the temperature in the foam hohlraum is about 7% lower than that in the solid hohlraum. The experimental results from the FXRDs provide supporting evidence that the low-density foam hohlraum has less wall plasma expansion at all times.

In summary, the first foam hohlraum experiment has been accomplished on a 100 kJ laser facility. The emission front was viewed by an XFC through the upper LEH. The results show that the emission front moves about 20% more slowly in a foam hohlraum with 0.8 g/cm³ wall density than in a solid hohlraum. Also, the reduced filling of the hohlraum by wall plasma leads to less SBS in a foam hohlraum—about half of that in a solid hohlraum, according to backscatter measurements. Moreover, the measured radiation temperatures in a foam hohlraum at most angles (16°, 20°, 42°, and 64°) are higher because of less absorption by expanding plasma, except for an angle of 0°, which is lower because of reduced expanding plasma emission. Simulation results using the Icefire code are consistent with experimental results. When the laser ablates the wall, the expanding plasma density in a foam hohlraum is lower than that in a solid hohlraum, which can be explained theoretically by the double-rarefaction model. Thus, the X-ray emission by expanding plasma is less in a foam hohlraum, and the emission front moves more slowly.

The use of a longer pulse and lower adiabat drive in a low-gas-fill hohlraum is one of the approaches currently favored for obtaining a higher fusion yield. Therefore, in this context, to control low-mode implosion asymmetry, it is important to prevent wall blowoff. The use of a hohlraum with a low-density gold foam wall is beneficial to restrain expansion of the wall plasma and increase the radiation temperature. However, the enhancement of hohlraum radiation temperature by lower wall loss is restricted at a wall density of 0.8 g/cm³. A still lower wall density is needed for further improvements in hohlraum radiation temperature. In addition, the use of a foam wall could be combined with other measures to improve hohlraum performance, such as He-gas filling and the use of a six-cylinder-port hohlraum.¹³ 

This work is performed with support from the National Natural Science Foundation of China (Grant Nos. 11775204 and 12105269) and the Presidential Foundation of the China Academy of Engineering Physics (Grant No. YZJJLX2018011).

The authors have no conflicts to disclose.

Lu Zhang: Investigation (equal); Writing – original draft (equal). Zhiwei Lin: Writing – review & editing (equal). Longfei Jing: Data curation (equal); Software (equal). Jianhua Zheng: Data curation (equal). Qiangqiang Wang: Data curation (equal). Sanwei Li: Conceptualization (equal); Data curation (equal). Zhurong Cao: Data curation (equal). Yunsong Dong: Investigation (equal). Bo Deng: Data curation (equal). Liling Li: Data curation (equal). Hang Li: Data curation (equal). Yulong Li: Data curation (equal). Huabing Du: Data curation (equal). Xiayu Zhan: Data curation (equal). Xibin Xu: Data curation (equal). Gao Niu: Data curation (equal). Wei Zhou: Data curation (equal). Longyu Kuang: Investigation (equal); Software (equal); Writing – review & editing (equal). Dong Yang: Conceptualization (equal); Investigation (equal). Jiamin Yang: Conceptualization (equal); Investigation (equal). Zongqing Zhao: Conceptualization (equal). Yongkun Ding: Conceptualization (equal); Investigation (equal); Writing – review & editing (equal). Weiyan Zhang: Conceptualization (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.