Determination of laser entrance hole size for ignition-scale octahedral spherical hohlraums

Yao-Hua Chen; Zhichao Li; Hui Cao; Kaiqiang Pan; Sanwei Li; Xufei Xie; Bo Deng; Qiangqiang Wang; Zhurong Cao; Lifei Hou; Xingsen Che; Pin Yang; Yingjie Li; Xiaoan He; Tao Xu; Yonggang Liu; Yulong Li; Xiangming Liu; Haijun Zhang; Wei Zhang; Baibin Jiang; Jun Xie; Wei Zhou; Xiaoxia Huang; Wen Yi Huo; Guoli Ren; Kai Li; Xudeng Hang; Shu Li; Chuanlei Zhai; Jie Liu; Shiyang Zou; Yongkun Ding; Ke Lan

doi:10.1063/5.0102447

Abstract

A recently proposed octahedral spherical hohlraum with six laser entrance holes (LEHs) is an attractive concept for an upgraded laser facility aiming at a predictable and reproducible fusion gain with a simple target design. However, with the laser energies available at present, LEH size can be a critical issue. Owing to the uncertainties in simulation results, the LEH size should be determined on the basis of experimental evidence. However, determination of LEH size of an ignition target at a small-scale laser facility poses difficulties. In this paper, we propose to use the prepulse of an ignition pulse to determine the LEH size for ignition-scale hohlraums via LEH closure behavior, and we present convincing evidence from multiple diagnostics at the SGIII facility with ignition-scale hohlraum, laser prepulse, and laser beam size. The LEH closure observed in our experiment is in agreement with data from the National Ignition Facility. The total LEH area of the octahedral hohlraum is found to be very close to that of a cylindrical hohlraum, thus successfully demonstrating the feasibility of the octahedral hohlraum in terms of laser energy, which is crucially important for sizing an ignition-scale octahedrally configured laser system. This work provides a novel way to determine the LEH size of an ignition target at a small-scale laser facility, and it can be applied to other hohlraum configurations for the indirect drive approach.

I. INTRODUCTION

Achieving ignition is the major step on the path to controlled nuclear fusion energy, which has been a quest of scientists worldwide for more than a half a century.1–3 Recently, the marvelous 1.37 MJ nuclear yield4–7 of the National Ignition Facility (NIF)8–10 is a clue that access to high fusion yields via indirect drive inertial confinement fusion may be attainable in the future. However, there are still major obstacles at the NIF to obtaining a predictable and reproducible fusion gain, such as irradiation asymmetry,11–13 laser plasma instabilities (LPIs),14–16 and hydrodynamic instabilities,2,17,18 all of which are strongly connected with the hohlraum configuration and laser arrangement. The recently proposed octahedral spherical hohlraum19–22 (hereinafter referred to simply as the octahedral hohlraum) with a single laser injection angle of 55° is an attractive concept for achieving a stable fusion gain at an upgraded facility23 and can provide a high-symmetry drive on the capsule without any symmetry tuning. Experimental campaigns started in 2014 at the SG laser facility,24 addressing the key issues regarding the design,25–28 energetics,29–31 and proof-of-concept32 of the octahedral hohlraum. This novel approach has attracted broad interest in the fusion community.33–39

In contrast to cylindrical hohlraums with their two laser entrance holes (LEHs),2,40–43 an octahedral hohlraum has six LEHs, and so LEH size can be a critical issue, given the laser energies that are available at present. As an example, we consider an Au octahedral hohlraum for the CH Rev5 ignition capsule44 of the NIF, which can produce a clean one-dimensional (1D) yield 17.5 MJ according to Ref. 44. We calculate below the required laser energy and asymmetry of an octahedral hohlraum for this capsule. The absorbed laser energy E_aL of the hohlraum can be calculated using the energy balance2,45,46 $\begin{align} η_{L X} E_{a L} & = E_{wall} + E_{cap} + E_{loss} \\ = σ τ T_{r}^{4} [(1 - α_{W}) A_{W} + (1 - α_{C}) A_{C} + A_{LEH}] . \end{align}$ (1)Here, η_LX is the laser-to-x-ray conversion efficiency, E_wall and E_cap are the energies absorbed by the hohlraum wall and the capsule, and E_loss is the radiation loss via LEHs. σ is the Stefan–Boltzmann constant, τ is the effective laser pulse width, T_r is the radiation temperature, α_W is the wall albedo, α_C is the capsule albedo, A_W is the hohlraum wall area, A_C is the capsule surface area, and A_LEH is the total LEH area. From 2D simulations using the 2D multigroup radiation transfer hydrodynamic code LARED-Integration,47,48η_LX ∼ 87% for an Au wall under an ignition pulse. From Ref. 44, we have a capsule diameter Φ_C = 2.216 mm and E_cap = 165 kJ, which gives α_C = 0.594 under a 300 eV ignition pulse. We take the nominal laser energy from Ref. 44 as E_aL and the nominal peak laser power as the absorbed laser power P_aL. From E_aL = 1.35 MJ and P_aL = 415 TW, we have τ = 3.25 ns. From the energy balance in Eq. (1), we find that for a 300 eV ignition pulse in the cylindrical hohlraum of Ref. 44 under such a laser, we have α_W = 0.91. Taking η_aL as the laser absorption efficiency of the hohlraum, we obtain the required input laser energy as E_L = E_aL/η_aL. We take the unabsorbed light to be 10% for the octahedral hohlraum,27 i.e., η_aL = 90%. With these parameters, we can use the energy balance to calculate the required laser energy for the CH Rev5 capsule inside an octahedral hohlraum of diameter Φ_H with LEH diameter Φ_LEH. The result is $E_{L} (M J) = 0.956 + 0.144 {[Φ_{LEH} (m m)]}^{2}$ for Φ_H/Φ_C = 4, and $E_{L} (M J) = 1.376 + 0.144 {[Φ_{LEH} (m m)]}^{2}$ for Φ_H/Φ_C = 5.

To calculate the radiation asymmetry on the capsule, we expand the radiation flux on capsule surface as $\sum_{l = 0}^{\infty} \sum_{m = - l}^{l} a_{l m} Y_{l m} (θ, ϕ)$ , where Y_lm(θ, ϕ) is the spherical harmonic of polar mode l and azimuthal mode m, and a_lm is the spherical harmonic decomposition. We define C_l0 = a_l0/a₀₀ and C_lm = a_lm/a₀₀ for m > 0, and calculate C_lm with our 3D view factor code VF3D20 by taking the relative fluxes of the laser spot, hohlraum wall, and LEH as 2:1:0.

In Tables I and II, we present C_lm, ϵ_rms, E_aL, E_L, and the radiation loss from LEHs for the CH Rev5 capsule inside octahedral hohlraums with Φ_H/Φ_C = 4 and 5, respectively, at Φ_LEH = 1.6–3.6 mm. Here, ϵ_rms is the overall %rms including all modes.3 We take the initial radii of the hohlraum and capsule in the calculation. It can be seen that Y_2m and Y_lm are absent for all odd l, because they are naturally zero in the octahedral geometry. For Φ_H/Φ_C = 4, Y₄₀ dominates the asymmetry and increases with increasing Φ_LEH, with Y₄₀ < 1% at Φ_LEH ≤ 3.6 mm. For Φ_H/Φ_C = 5, termed the golden radius ratio in Ref. 20, the asymmetry is dominated by Y₈₀, with Y₈₀ < 3.4 × 10⁻⁴ for all Φ_LEH. Thus, the asymmetry in all cases easily meets the ignition criterion of 1%.2 However, E_aL is sensitive to Φ_LEH, because the six LEHs of larger size can lead to a remarkably high radiation energy loss. From Tables I and II, it can be seen that changing the LEH size makes a significant difference to the laser energy required. The calculations show that the energy requirement exceeds the present laser energy of 2 MJ at the NIF for Φ_LEH > 2.7 mm at Φ_H = 8.864 mm, and for Φ_LEH > 2.1 mm at Φ_H = 11.08 mm. Obviously, the upper limit of LEH size is restricted by the available laser energy. It seems that a smaller LEH should decrease E_aL; however, this is under the assumption that all laser beams can be fully injected into the hohlraum. If an LEH is small enough that some of the laser energy is blocked outside the hohlraum, greater laser energy will be needed to generate the required radiation temperature inside the hohlraum. Thus, the optimum LEH size should be a trade-off between clearance for the laser beams and available laser energy.

Φ_LEH (mm)	1.6	2	2.4	2.8	3.2	3.6
C₄₀	1.7 × 10⁻³	2.5 × 10⁻³	3.4 × 10⁻³	5.1 × 10⁻³	7.1 × 10⁻³	9.2 × 10⁻³
C₄₄	1.0 × 10⁻³	1.5 × 10⁻³	2.1 × 10⁻³	3.0 × 10⁻³	4.2 × 10⁻³	5.5 × 10⁻³
C₆₀	1.6 × 10⁻⁶	1.2 × 10⁻⁵	2.8 × 10⁻⁵	4.8 × 10⁻⁵	6.7 × 10⁻⁵	8.4 × 10⁻⁵
C₆₄	1.7 × 10⁻⁶	2.4 × 10⁻⁵	5.3 × 10⁻⁵	9.0 × 10⁻⁵	1.2 × 10⁻⁴	1.6 × 10⁻⁴
C₈₀	8.6 × 10⁻⁴	9.6 × 10⁻⁴	1.0 × 10⁻³	1.0 × 10⁻³	8.1 × 10⁻⁴	4.2 × 10⁻⁴
C₈₄	3.2 × 10⁻⁴	3.6 × 10⁻⁴	3.9 × 10⁻⁴	3.8 × 10⁻⁴	3.1 × 10⁻⁴	1.6 × 10⁻⁴
C₈₈	4.9 × 10⁻⁴	5.5 × 10⁻⁴	5.9 × 10⁻⁴	5.8 × 10⁻⁴	4.6 × 10⁻⁴	2.4 × 10⁻⁴
ϵ_rms	2.6 × 10⁻³	3.5 × 10⁻³	4.7 × 10⁻³	6.8 × 10⁻³	9.3 × 10⁻³	1.2 × 10⁻²
E_aL (MJ)	1.19	1.38	1.61	1.88	2.19	2.54
E_L (MJ)	1.32	1.53	1.79	2.08	2.43	2.82
LEH loss (MJ)	0.40	0.63	0.91	1.24	1.62	2.05

Table 1. C_lm, ϵ_rms, E_aL, E_L, and LEH loss of an octahedral hohlraum with R_H = 4R_C for the CH Rev5 capsule, with Φ_LEH varying from 1.6 to 3.6 mm. Here, the LEH loss is the amount of input laser energy lost via the LEHs and is given by E_loss/η_aLη_LX. In each case, the input laser energy E_L is chosen to give a radiation temperature of 300 eV.

View all Tables

Φ_LEH (mm)	1.6	2	2.4	2.8	3.2	3.6
C₄₀	3.9 × 10⁻⁵	5.6 × 10⁻⁵	7.7 × 10⁻⁵	1.0 × 10⁻⁴	1.3 × 10⁻⁴	1.8 × 10⁻⁴
C₄₄	2.4 × 10⁻⁵	3.4 × 10⁻⁵	4.7 × 10⁻⁵	6.1 × 10⁻⁵	8.0 × 10⁻⁵	1.1 × 10⁻⁴
C₆₀	1.1 × 10⁻⁶	1.5 × 10⁻⁵	3.3 × 10⁻⁵	5.1 × 10⁻⁵	7.1 × 10⁻⁵	9.7 × 10⁻⁵
C₆₄	1.1 × 10⁻⁶	2.9 × 10⁻⁵	6.3 × 10⁻⁵	9.7 × 10⁻⁵	1.4 × 10⁻⁴	1.8 × 10⁻⁴
C₈₀	2.3 × 10⁻⁴	2.7 × 10⁻⁴	3.1 × 10⁻⁴	3.3 × 10⁻⁴	3.4 × 10⁻⁴	3.2 × 10⁻⁴
C₈₄	8.8 × 10⁻⁵	1.0 × 10⁻⁴	1.2 × 10⁻⁴	1.2 × 10⁻⁴	1.3 × 10⁻⁴	1.2 × 10⁻⁴
C₈₈	1.3 × 10⁻⁴	1.6 × 10⁻⁴	1.8 × 10⁻⁴	1.9 × 10⁻⁴	1.9 × 10⁻⁴	1.8 × 10⁻⁴
ϵ_rms	3.4 × 10⁻⁴	3.9 × 10⁻⁴	4.5 × 10⁻⁴	5.3 × 10⁻⁴	7.2 × 10⁻⁴	6.0 × 10⁻⁴
E_aL (MJ)	1.57	1.76	1.98	2.25	2.56	2.92
E_L (MJ)	1.74	1.95	2.21	2.50	2.85	3.24
LEH loss (MJ)	0.40	0.63	0.91	1.24	1.62	2.05

Table 2. C_lm, ϵ_rms, E_aL, E_L, and LEH loss of an octahedral hohlraum with R_H = 5R_C for the CH Rev5 capsule, with Φ_LEH varying from 1.6 to 3.6 mm. The LEH loss is the same as in Table I, and is given here for comparison with E_L.

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To have sufficient LEH clearance for the laser beams, the lower limit of LEH size is determined by three factors: (1) the focal spot size of the laser beam at the LEH, (2) the LEH closure caused by radiation, and (3) laser pointing error. Again considering the CH Rev5 capsule, the LEH closure under a 300 eV ignition pulse is about 0.29 mm according to our 1D multigroup radiation transfer hydrodynamic code RDMG.49–51 Taking the pointing error as 0.08 mm for a laser beam of round shape with 1.2 mm diameter at the LEH, we estimate a LEH diameter Φ_LEH ∼ 2 mm.21 Detail 2D simulations using LARED-Integration have shown that a value of Φ_LEH = 2.4 mm can leave enough room52 for this ignition target design. However, owing to the uncertainties in the simulation,53 the LEH size should be determined with convincing experimental evidence before pursuing an ignition-scale laser system based on the octahedral hohlraum. Nevertheless, it remains a challenging task to determine the LEH size of an ignition target at a small-scale laser facility, because it is impossible to create ignition radiation inside an ignition-scale hohlraum with a small laser energy.

In this paper, we propose to use the prepulse of an ignition pulse to determine the LEH size of ignition-scale hohlraums via LEH closure behavior, and we present experimental evidence based on multiple diagnostics at the SGIII laser facility with the hohlraum, laser pre-pulse, and laser beam size at an ignition scale. As shown in Fig. 5 of Ref. 52, the LEH radius from simulations is a function of time under an ignition pulse, and it closes during the prepulse at low laser power but opens up again during the main pulse at high laser power. It is worth mentioning that this phenomenon has been clearly observed in NIF experiments.54 Qualitatively, during the low-power part of the laser pulse, radiation-ablated plasma accumulates at the LEH and leads to a decrease in the open area of the LEH. On arrival of the main pulse, the ablated plasma is heated by the high-intensity laser, and the thermal pressure of the hot plasma pushes away the plasma entering the LEH, resulting in opening-up of the LEH.52 This indicates that a given LEH size will be acceptable for the main pulse as long as it provides clearance for the laser beam during the prepulse. Thus, it should be possible to determine the appropriate LEH size for an ignition hohlraum by examining the LEH behavior during a prepulse generated at a small laser facility with an energy output lower than an ignition laser facility.

II. EXPERIMENTAL DESIGN

In the experiment, we consider an Au octahedral hohlraum of ignition-scale Φ_H = 8.8 mm for a high-foot ignition scheme.55 Note that LEH closure is caused mainly by radiation ablation if there is sufficient LEH clearance for the laser beams. In this case, a 2-LEH hohlraum has similar LEH closure behavior to a 6-LEH hohlraum under the same radiation drive. Hence, it is reasonable to use an ignition-scale hohlraum with two LEHs for this experiment. The hohlraum is initially filled with 1.3 mg/cm³ C₅H₁₂ gas at 0.4 atm pressure and room temperature. The required radiation temperature T_r and drive laser from LARED-Integration are presented in Fig. 1(a) for Φ_LEH = 2.2 mm. As can be seen, the prepulse is composed of a picket, a first step, and a second step, with a laser power lower than 50 TW. The first and second steps start at 1.49 and 6 ns, respectively. The main pulse starts at 8.2 ns, rising rapidly to 500 TW within 0.8 ns. From postprocessing of 2D simulations, we can define various plasma interface positions for the LEH. As can be seen in Fig. 1(b), for all values of the electron density except for the very low N_e = 0.1N_c, the LEH radius keeps closing during the whole prepulse and then opens up after the main pulse starts, similar to what is shown in Fig. 5 of Ref. 52. Here, N_c is the laser critical density, ∼1.1 × 10²¹/λ² cm⁻³, where the laser wavelength λ is in micrometers. From 2D simulations, the beams have LEH clearance at Φ_LEH ≥ 2.2 mm, but they are severely blocked by LEH closure at Φ_LEH = 1.4 mm.

Figure 1.(a) Required T_r (red curve) on the capsule of a high-foot scheme and the derived laser pulse (black curve) from 2D simulations for a 2-LEH spherical hohlraum with Φ_H = 8.8 mm and Φ_LEH = 2.2 mm. Only the prepulse (black solid curve) is considered in this experiment. (b) Post-processed time-dependent positions of plasma interface with electron density N_e = 0.1N_c, 0.2N_c, 0.6N_c, and N_c and positions of 50% peak x-ray emissions with energies between 0.8 and 1 keV or above 1.8 keV. The pink region is the laser channel. (c) Schematic of laser beam configuration and ignition-scale 2-LEH spherical hohlraum. The laser beams at 55° (orange) have a 1 mm diameter round shape at the LEH, and those at other angles have a 0.5 mm diameter. (d) Initial fields of view of the six flat-response x-ray detectors (FXRDs) and filtered M-band x-ray detectors (MXRDs), with the spots on the wall representing the laser depositions.

The SGIII laser facility has an output of 180 kJ, an order of magnitude lower than the NIF, and is sufficiently flexible to create a ∼10 ns laser pulse with power up to 50 TW. Hence, we can determine the LEH size by creating the prepulse inside an ignition-scale hohlraum with an ignition-scale laser beam size at SGIII. SGIII has 48 laser beams with injection angles of 28.5°, 35°, 49.5°, and 55°. Here, 55° happens to be the design angle of the octahedral hohlraum.19–22 The laser pointing error is 0.07 mm. Figure 1(c) shows a schematic of the 2-LEH spherical hohlraum injected by the 48 laser beams for this experiment. Every beam has a round shape at its LEH, with a super-Gaussian spatial profile $\propto \exp [- {(2 r / Φ_{Q})}^{m}]$ produced using continuous phase plates (CPPs), with m ∼ 5. Here, r is the spatial position along the radial direction of the LEH, and it includes 96% of the laser energy in the range r ≤ Φ_Q/2. We use custom CPPs to have Φ_Q = 1 mm for the 16 beams at 55°, and the SGIII standard CPPs to have Φ_Q = 0.5 mm for the beams at other angles. We take Φ_Q as the beam size at the LEHs. According to our design, the 48 laser beams deliver about 110 kJ and 50 TW to create the prepulse in Fig. 1(a). In the experiment, to examine the LEH closure behavior at different LEH sizes, we take the LEH diameter as 1.4, 1.6, 1.8, 2, and 2.4 mm, respectively.

III. DIAGNOSTICS AND DISCUSSION

Various diagnostics56 are used to provide experimental evidence to determine the LEH size. LEH closure is observed by an x-ray framing camera (XFC) through the upper LEH at 0° in two ranges of 0.8–1 keV (N-band emission of Au, mainly from the equilibrium region ablated by radiation) and 2–3 keV (M-band emission of Au, mainly from the nonequilibrium corona where most of the laser energy is absorbed). Time-integrated images of x-rays in 2–3 keV are also observed by a pinhole camera through the upper LEH at 16°. The x-ray emissions observed outside the LEH can provide important information on LEH closure. The x-ray fluxes of 0.1–5 keV are measured by an array of flat-response x-ray detectors (FXRDs) through the upper LEHs at 16°, 42°, and 64° and from the lower LEHs at 0°, 20°, and 42° with respect to the hohlraum axis. The M-band flux of x-rays $>$ 1.8 keV, largely emitted from the M-band of Au, is measured by an array of filtered M-band x-ray detectors (MXRDs) placed at the same places as the FXRDs. The measured fluxes vary with the viewing angles of the FXRDs and MXRDs, depending on the proportions of laser spot, re-emission wall, and LEH in their fields of view. The initial fields of view of all FXRDs and MXRDs are shown in Fig. 1(d) for Φ_LEH = 2.2 mm. The FXRDs and MXRDs at the upper 16° and 64° and the lower 64° positions can only see re-emissions from the wall. Laser spots can be viewed only by the FXRDs and MXRDs at the upper and lower 42° positions, with a proportion less than 10%. The on-axis FXRD and MXRD at 0° measure emissions from the plasmas accumulated around the hohlraum axis. Stimulated Brillouin and Raman backscattered lights are measured by a full-aperture backscatter station (FABS) and a near backscatter station (NBS) installed for beams at 55°. The total laser backscatter fraction is less than 4% for all shots, which is reasonable for such a prepulse with intensity less than 2.3 × 10¹⁴ W/cm².

On the left of Fig. 2, we present the time-resolved raw XFC images for shot SGIII20170323148 with Φ_LEH = 1.4 mm and shot SGIII20170324150 with Φ_LEH = 2 mm. The bright ring-shaped regions in these images are contributed by x-ray emissions from the ablated plasmas of the LEH edge. As can be seen, the LEH closure behaves similarly in the two x-ray bands for the same shot, but very differently between the two shots. The LEH with Φ_LEH = 1.4 mm closes before 6 ns and then opens up, while for Φ_LEH = 2 mm it continues to close at all times. This difference can be seen more clearly in the middle panels of Fig. 2, in which we present images along the temporal profiles of the drive laser together with the nominal radiation temperature T_r. Here, T_r is derived from the fluxes measured by the FXRDs,31 varying with their fields of view. As can be seen, the LEH with Φ_LEH = 1.4 mm opens up after 6 ns when the second step pulse arrives with a rapid rise in power to about 50 TW. By contrast, the LEH with Φ_LEH = 2 mm continues to close throughout the pulse. From the XFC images, we can define the LEH radius as the central location of the sharp slope of the ring region,54 and we show the time variation of this radius on the right of Fig. 2 for shots with Φ_LEH = 1.4 and 2 mm. It is obviously the high laser power of the second step that causes the transition from closure to opening up for Φ_LEH = 1.4 mm and slows down the closure for Φ_LEH = 2 mm. For comparison, we adopt this definition of the LEH radius in post-shot 2D simulations with LARED-Integration. The simulation results are also presented on the right of Fig. 2, from which it can be seen that they agree qualitatively with the observations.

Figure 2.(Left) Time-resolved raw images from an x-ray framing camera (XFC) at four different times and for two x-ray energy ranges of 0.8–1 and 2–3 keV for shot SGIII20170323148 with 1.4 mm diameter LEHs (upper) and shot SGIII20170324150 with 2 mm diameter LEHs (lower). (Middle) Drive laser power (light cyan dashed curve) and T_r (solid curves) with an error bar of 3% for shots SGIII20170323148 (upper) and SGIII20170324150 (lower). The small images match those on the left, except that the upper ones at 2.5 and 5.5 ns are for shot SGIII20170323149. (Right) Time-dependent LEH radius, defined as the half peak width of x-ray emissions of 0.8–1 keV, from XFC images (symbols with error bars of ±75 µm) and from post-shot 2D simulation (orange solid line) for shots with 1.4 mm diameter LEHs (upper) and 2 mm diameter LEHs (lower), with the red dashed line indicating the laser beam size. The mode 1 azimuthal asymmetry of the XFC images is due to the axis deviation between each pinhole and the XFC and to the axis deviation between the XFC and the target, which are considered in the error bars.

Severe LEH closure for the case with Φ_LEH = 1.4 mm is confirmed by the interesting x-ray images from the pinhole camera for time-integrated M-band emissions of 2–3 keV. As can be seen in Fig. 3(a), the pinhole image of shot SGIII20170323149 has a strong emission ring (orange) from the inner edge of the LEH to the outer part of the laser channel, indicating strong M-band emission from the dense and hot plasmas that are ablated from the LEH edge and heated either directly by the lasers or by the hotter plasmas in the laser channel via electron heat conduction. Between the orange region and the LEH center, especially around the central part of the laser channel, M-band emissions become weak (light blue and blue) because of the relatively low density of the very hot laser plasmas in this region. The image in Fig. 3(a) clearly reveals that the radiation-ablated plasmas from the LEH edge strongly influence the clearance of the laser channel for Φ_LEH = 1.4 mm. The time-integrated M-band emission images for Φ_LEH = 2 mm are quite different. As can be seen in Fig. 3(c), the time-integrated M-band emission is strong in a ring (light blue) between the LEH edge and the laser channel. The outer edge of this ring corresponds to the expanded LEH, which is too cold to emit many M-band x-rays, while the inner edge is at a low density and therefore is also unable to emit many M-band x-rays. The image in Fig. 3(c) clearly indicates that Φ_LEH = 2 mm provides sufficient clearance for the laser beams. Compared with the XFC image at 2–3 keV for shot SGIII20170324150 in Fig. 2, the time-integrated emission of this light blue ring is contributed mainly by the LEH closure plasmas at around 6.5 ns and later times. It is worth mentioning that the clear physical characteristics revealed by the images in Figs. 3(a) and 3(c) can be used to distinguish whether an LEH is open or not.

Figure 3.(a) Time-integrated x-ray image at 2–3 keV observed by the pinhole camera at 16° from the upper side and (b) its field of view for shot SGIII20170323149 with 1.4 mm diameter LEHs. (c) and (d) Corresponding image and field of view for shot SGIII20170324150 with 2 mm diameter LEHs. The red dashed circle is the LEH edge and the yellow dashed circle is the outer boundary of the 1 mm diameter laser beam. Note that the size scales of the two images are different.

The severe LEH closure in the case of Φ_LEH = 1.4 mm is also confirmed by the temporal behavior of the M-band fluxes measured by the MXRDs. As can be seen in Fig. 4, the severe LEH closure for Φ_LEH = 1.4 mm leads to a strong M-band flux with very different temporal behavior from that for Φ_LEH ≥ 1.8 mm. The M-band flux for Φ_LEH = 1.4 mm rises rapidly at 6 ns when the second step laser arrives, but rises much more slowly for Φ_LEH ≥ 1.8 mm. In addition, the maximum M-band flux for Φ_LEH = 1.4 mm is about 18 times stronger than that for Φ_LEH ≥ 1.8 mm. In particular, from the on-axis MXRD, it is found that the M-band flux is quite strong for Φ_LEH = 1.4 mm, while it is at a low noise level for Φ_LEH ≥ 1.8 mm, except in the case Φ_LEH = 2.4 mm, which is somewhat abnormal. We have two shots for Φ_LEH = 1.6 mm. For shot SGIII20201009152, similar to Φ_LEH = 1.4 mm, the M-band flux from all MXRDs rises rapidly at 6 ns to a remarkably high maximum value. However, for shot SGIII20201010155, the M-band fluxes from all MXRDs behave similarly to those for Φ_LEH ≥ 1.8 mm. This indicates that 1.6 mm may be a critical size for this model and that an LEH size Φ_LEH ≥ 1.8 mm provides sufficient clearance for the laser beams. Thus, the measured M-band fluxes from MXRDs again provide strong evidence to determine the LEH size.

Figure 4.Temporal behaviors of the M-band fluxes measured by the six MXRDs for shots with Φ_LEH = 1.4, 1.6, 1.8, 2, and 2.4 mm, with an error bar of 10%. The burrs on the curves are due to diagnostic noise at low fluxes. Note that the flux scale for Φ_LEH = 1.4 mm is different from the others.

In Fig. 5, we compare the behavior of T_r for different values of Φ_LEH. As can be seen, for a given FXRD, T_r exhibits similar behavior for all shots with Φ_LEH ≥ 1.8 mm, but there are remarkable differences in the case of Φ_LEH = 1.4 mm. First, for all FXRDs, for Φ_LEH = 1.4 mm, T_r rises more rapidly before the second step laser reaches its flat top and is much higher than that for Φ_LEH ≥ 1.8 mm. Second, the T_r difference between on-axis and off-axis FXRDs for Φ_LEH = 1.4 mm is significantly smaller than for Φ_LEH ≥ 1.8 mm. This indicates that the accumulated plasmas at the LEH lead to strong x-ray emission and severe LEH closure for Φ_LEH = 1.4 mm. Third, T_r for Φ_LEH ≥ 1.8 mm continues to rise during the flat top of the second laser step and reaches a maximum when the laser ends, while T_r for Φ_LEH = 1.4 mm begins to decrease soon after the second step laser starts. This is a strong indication of severe LEH closure for Φ_LEH = 1.4 mm.

Figure 5.Temporal behavior of T_r (solid curves) derived using the measured fluxes from six FXRDs for shots with Φ_LEH = 1.4, 1.6, 1.8, 2, and 2.4 mm. The laser power (light gray dashed lines) is shown for reference.

It should be noted here that T_r for Φ_LEH = 1.4 mm is much higher than for all other cases with larger Φ_LEH. Normally, a smaller Φ_LEH leads to a higher T_r inside the hohlraum because of lower radiation loss via the smaller LEH area. However, this is not the case for Φ_LEH = 1.4 mm, where the small size of the LEHs causes parts of the laser beams with Φ_Q = 1 mm to hit the LEH edge and the outer wall of the hohlraum, leading to strong x-ray emission outside the hohlraum. As a result, only part of the laser energy can be injected into the hohlraum, and a much lower T_r is generated inside the hohlraum than that measured by FXRDs outside the hohlraum. Thus, the much higher T_r for Φ_LEH = 1.4 mm from the FXRDs indicates a much lower T_r inside the hohlraum than in the cases with LEH clearance. It is interesting to note that the highest T_r of this “LEH closure” shot comes from the Up64 FXRD, which, although it sees a low flux (as shown in Fig. 4) because it views at a large angle to the hohlraum axis, also sees the hot LEH plasmas.

For an “LEH clearance” shot, the T_r values from all off-axis FXRDs are very close. This can be easily understood from their fields of view in Fig. 1(d), which are largely or even fully occupied by re-emissions from the wall. Note that from Fig. 5, the maximum T_r of the “LEH clearance” shots does not seem to be so sensitive to Φ_LEH once the differences of input laser energy are taken into account. In fact, from the energy balance, T_r increases about 3% from Φ_LEH = 1.4 to 2.4 mm inside such a 2-LEH spherical hohlraum with Φ_H = 8.8 mm, which is within the error bar of the FXRDs. We have two shots for Φ_LEH = 1.6 mm, whose T_r from off-axis FXRDs behave similarly to that for Φ_LEH ≥ 1.8 mm, although the T_r from the on-axis FXRD rises rapidly at around 6 ns. Again, this indicates that Φ_LEH = 1.6 mm is a critical size for the model in this experiment. Considering the laser beam diameter of 1 mm at the LEHs and the laser pointing error of 0.07 mm, the LEH closure is less than 0.6 mm in diameter under the ignition prepulse used in this experiment, which is in agreement with NIF data. From the NIF, the measured LEH closure is about 0.515 mm in diameter according to Ref. 57 and 0.526 and 0.406 mm for the low-foot and high-foot schemes, respectively, according to Ref. 54. To leave enough room for the laser pointing accuracy, we determine that the LEH diameter should be 0.8 mm larger than the laser focal spot at the LEH.

IV. SUMMARY

We have proposed to use the prepulse of the ignition pulse to determine the LEH size for the ignition target via the LEH closure behavior at a small laser facility, and we have adopted this approach to determine the LEH size at the SGIII facility with convincing evidence from multiple diagnostics. As a result, we have found that it is safe to take an LEH 0.8 mm larger in diameter than the laser size at the LEH for the model in this experiment. Considering a laser with 1.2 mm diameter at the LEH, we can take Φ_LEH = 2 mm for an ignition octahedral hohlraum. This means that the octahedral hohlraum has the same total LEH area as that of an NIF cylindrical hohlraum.13,58,59 The latter needs a larger LEH size for its inner beams, which are much larger than the outer beams44,54 to suppress the serious LPIs arising from their long propagation distances inside the hohlraum. Taking Φ_LEH = 2 mm and assuming a laser backscatter of 10%, according to Tables I and II, 1.53 and 1.95 MJ are required to drive the 8.864 mm diameter and 11.08 mm diameter octahedral hohlraums, respectively,

Our work reported here has successfully demonstrated the feasibility of octahedral hohlraums for inertial confinement fusion and is crucially important for determining the appropriate dimensions for an octahedrally configured laser system to give a predictable and reproducible fusion gain.23 It has also provided a novel way to determine the LEH size for an ignition-scale target at a small-scale laser facility. Note that the LEH closure is related to the prepulse. Hence, if a prepulse can ablate more plasmas and lead to more severe LEH closure, then a larger LEH will be required. Point designs with octahedral hohlraums for NIF capsules CH Rev5 and Be Rev6 are presented in Refs. 52 and 60 respectively, and a paper on point design for the recently proposed novel ignition capsule61 is under preparation, which can mitigate the hydrodynamic instabilities by using CH as the outermost ablator layer, while keeps high-density carbon as the main ablator for maintaining the advantage of short laser pulses.

ACKNOWLEDGMENTS

Acknowledgment. The authors thank the entire SGIII operations, diagnostics, and target teams at the Research Center of Laser Fusion, China Academy of Engineering Physics for their outstanding support during the experiment. All simulations were performed on a supercomputer in China. We especially acknowledge all the referees of this paper for providing very beneficial and important suggestions and questions to improve the quality of the paper. This work is supported by the National Natural Science Foundation of China (Grant No. 12035002).

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