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Analysis of hohlraum energetics of the SG series and the NIF experiments with energy balance model
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MATTER AND RADIATION AT EXTREMES
Matter and Radiation at Extremes xx (2016) 1e6 www.journals.elsevier.com/matter-and-radiation-at-extremes
Research Article
Analysis of hohlraum energetics of the SG series and the NIF experiments with energy balance model G.L. Ren*, Jie Liu, Wenyi Huo, Ke Lan Institute of Applied Physics and Computational Mathematics, Beijing 100094, China Received 8 September 2016; revised 24 October 2016; accepted 3 November 2016 Available online ▪ ▪ ▪
Abstract The basic energy balance model is applied to analyze the hohlraum energetics data from the Shenguang (SG) series laser facilities and the National Ignition Facility (NIF) experiments published in the past few years. The analysis shows that the overall hohlraum energetics data are in agreement with the energy balance model within 20% deviation. The 20% deviation might be caused by the diversity in hohlraum parameters, such as material, laser pulse, gas filling density, etc. In addition, the NIF's ignition target designs and our ignition target designs given by simulations are also in accordance with the energy balance model. This work confirms the value of the energy balance model for ignition target design and experimental data assessment, and demonstrates that the NIF energy is enough to achieve ignition if a 1D spherical radiation drive could be created, meanwhile both the laser plasma instabilities and hydrodynamic instabilities could be suppressed. Copyright © 2016 Science and Technology Information Center, China Academy of Engineering Physics. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
PACS codes: 52.57.-z; 52.50.Jm; 52.38.Mf Keywords: Energy balance model; Hohlraum energetics; National Ignition Facility (NIF); Shenguang (SG) series
1. Introduction Indirect drive inertial confinement fusion (ICF) uses a highZ hohlraum (cylindrical [1,2], rugby or elliptical [3,4] or spherical [5,6] hohlraum) to convert the incident laser energy into thermal X-rays, which ablate a capsule located at the hohlraum center to achieve thermonuclear ignition. A successful indirect drive ignition requires driving the implosion capsule to high velocity (~370 km/s) while keeping the cryogenic deuteriumetritium (DT) fuel layer at low entropy [2], meanwhile the imploded core must remain nearly spherical to avoid quenching the ignition of the central hotspot via minimizing the cooling mechanisms, as well as to avoid decreasing the conversion efficiency of the implosion kinetic energy into hotspot internal energy [7]. The implosion of * Corresponding author. E-mail address: [email protected] (G.L. Ren). Peer review under responsibility of Science and Technology Information Center, China Academy of Engineering Physics.
ignition gives stringent requirements of high velocity, low entropy and very high symmetry, which must be met by delicately adjusting the radiation environment inside the hohlraum. Therefore in ICF study, the hohlraum plays a crucial role in delivering the stringently-required radiation drive and symmetry within the limitation of the energy and power of the laser facility. The National Ignition Facility (NIF) in the US is configured to achieve laser driven ICF via indirect drive (ID) approach [1] by using cylindrical hohlraum. Since its completion in 2009, various ignition relevant experiments using different targets and laser pulses have been carried out on the NIF. The highest neutron yield achieved so far is ~1016 and obvious alpha particle heating of the hotspot has been observed [8,9]. In the observation, the hotspot pressure has reached 200 Gbar compared to the ignition threshold of 350 Gbar (1 Gbar ¼ 108 MPa). Nevertheless, the primary goal of achieving ignition on the NIF has not been reached yet. According to further studies on NIF experiments, many problems
http://dx.doi.org/10.1016/j.mre.2016.11.002 2468-080X/Copyright © 2016 Science and Technology Information Center, China Academy of Engineering Physics. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: G.L. Ren, et al., Analysis of hohlraum energetics of the SG series and the NIF experiments with energy balance model, Matter and Radiation at Extremes (2016), http://dx.doi.org/10.1016/j.mre.2016.11.002
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might be responsible for the failure of ignition, such as the hohlraum energetics, the low mode drive asymmetry and the hydrodynamic instability growth during the implosion, etc. Among these possible problems, the hohlraum energetics is primary because it determines the radiation drive onto the capsule. Usually, the radiation drive incident on the capsule cannot be measured directly, thus it is often inferred from the directly observed experimental data combined with numerical modeling. Such measurements include the observation of the Xray flux flowing out of the laser entrance holes (LEHs) at certain angles, and the measurement of the implosion trajectories of the capsule with backlit radiography. However, these measurements involve some complicated details not yet clarified [10]. For example, when measuring the X-ray flux from the LEH with the multiple-channeled X-ray diode detector (XRDs or DANTE), the interpretation of the measuring results is directly influenced by the dynamic LEH closure [11], which is hard to be precisely depicted. In addition, the radiation drive (or radiation temperature) inferred from different methods are not always in agreement with each other, and in many cases especially in the gasfilled hohlraum (GFH), the measured drive onto the capsule are well below the numerical prediction, which is called the ‘energy deficit’ [10,12] problem. All these complications indicate that an overall picture of the radiation drive in the NIF experiments is needed to better understand the general hohlraum energetics. The apparent ‘energy deficit’ problem found using gas-filled hohlraums on the NIF raises one fundamental question: Is the energy of NIF sufficient to achieve ignition? To be more specific, if we were able to overcome the troubling lasereplasma interaction (LPI) issues encountered in the gas-filled hohlraum and thus able to provide quasi spherical X-ray drive, will the energy of the current NIF facility be sufficient for ignition? In this work, we applied the fundamental energy balance model to analyze the overall NIF data and see how much the overall NIF data would deviate from the energy balance model. Stepping forward from that, we will try to answer the fundamental question whether NIF's energy is sufficient for ignition or not. Due to its conciseness in physical picture and easiness for utilization, the energy balance model is widely used in ignition target design and experimental data evaluation [1,13]. It builds up a physical bridge between the laser energy (or laser power) and the radiation drive inside the hohlraum. We used the energy balance model to analyze the hohlraum energetics in Shenguang (SG) series experiments as well as all kinds of ignition relevant NIF experiments. This article is organized as below. In Section 2, we briefly introduce the energy balance model. In Section 3, we assess the experimental drive data with the energy balance model, which were observed on the SG series laser facilities adopting both cylindrical and spherical hohlraums. In Section 4, we analyze the NIF data with the energy balance model. Finally, we give a summary.
hohlraum, some fraction of the lasers is backscattered out of the hohlraum, whereas the majority of the laser energy is absorbed by the wall plasmas via collisional absorption as well as non-linear absorption schemes, and then converted into Xrays, which are either absorbed by the wall or the capsule, or escape through the LEH. From the energy balance model [1], we have hEL ¼ EWall þ ELEH þ Ecap þ Er ¼ sTr4 $½ð1 aw ÞAw þ Ah þ ð1 ac ÞAc $t þ Er :
ð1Þ
here, we denote EL as the incident laser energy, h the total laser to X-ray conversion efficiency including both the laser absorption efficiency and the laser to X-ray conversion efficiency, EWall ; ELEH ; Ecap the X-ray energies absorbed by the wall, escaping from the LEHs, and absorbed by the capsule, respectively, Er the radiation energy stored inside the hohlraum, aw the hohlraum wall albedo (reflectivity), ac the capsule albedo, Aw , Ah and Ac the areas of the hohlraum wall, the LEHs and the capsule respectively, t the equivalent duration of the laser pulse, Tr the radiation temperature inside the hohlraum, s the Stefan parameter. As we know, Er is proportional to Tr4 $Vhohl , where Vhohl is the volume of the hohlraum. However, for the ICF hohlraum environment, even under the NIF ignition relevant radiation temperature range ~300 eV, Er is less than a few percent of the total laser energy and can be neglected. Thus the energy balance equation becomes hEL ¼ sTr4 $½ð1 aw ÞAw þ Ah þ ð1 ac ÞAc $t:
ð2Þ
The time derivative expression of the energy balance equation is also used in the hohlraum energetics study, which is called as the power balance equation hPL ¼ sTr4 $½ð1 aw ÞAw þ Ah þ ð1 ac ÞAc :
ð3Þ
The conversion efficiency h and wall albedo aw can be calculated self-consistently in radiation hydrodynamic simulations. In addition, aw can also be obtained analytically by assuming the Marshak wave approximation under certain incoming radiation temperature curve. As for the NIF ignition relevant targets, our calculation shows that h ~90% and aw ~90% during the main pulse with the peak Tr ~300 eV. However, it should be noted that the energy balance model is not exactly accurate because the radiation temperature is not strictly homogenous, and also the area of the hohlraum, the LEHs together with the capsule vary during the laser drive and the X-ray ablation. Therefore, it is worth to examine the adaptability of the energy balance model with various experimental data of the hohlraum energetics.
2. The energy balance model
3. Assessment of the drive data in SG series experiment with energy balance model
The energy balance model depicts the energy flow inside the indirect drive hohlraum. When lasers enter the high-Z
The energy balance model agrees well with the Nova 1-ns hohlraum experimental data [1]. Here, we applied the energy
Please cite this article in press as: G.L. Ren, et al., Analysis of hohlraum energetics of the SG series and the NIF experiments with energy balance model, Matter and Radiation at Extremes (2016), http://dx.doi.org/10.1016/j.mre.2016.11.002
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balance model to the hohlraum experiments conducted on the SGIII-prototype and SGIII laser facilities. In the SGIII-prototype experiment series, we firstly adopted the gas-filled cylindrical hohlraum of 1 mm diameter and 2.1 mm length. In this experiment, we used a flat-top laser pulse with 1 ns duration, and energy ranging from 2 kJ to 8 kJ. The experimental data and corresponding energy balance curve are plotted in Fig. 1. The horizontal axis in Fig. 1 is the absorbed laser energy with the measured backscatter laser energy being detracted. The vertical axis is the radiation temperature in the hohlraum. The red crosses are the radiation temperatures measured from the LEH with an angle of 55 to the hohlraum axis. The green stars are the equivalent radiation temperatures incident on the capsule positioned at the hohlraum center, hereafter called the “capsule radiation temperature” for convenience no matter whether there is a true capsule inside the hohlraum or not, which were calculated by our 2D radiation hydrodynamic code LARED-Integration [14]. The blue curve is plotted according to the energy balance model assuming the conversion efficiency h ¼ 0.7 for 1 ns laser pulse. Here aw was calculated by using our 1D multi-group radiation hydrodynamic code RDMG [14]. The simulation shows that the wall albedo aw is ~0.8 for the gold hohlraum experiments on SGIII-prototype. From Fig. 1, it can be seen that the energy balance model agrees with the calculated capsule radiation temperature, and meanwhile the energy balance curve is slightly lower than the measured cylindrical hohlraum radiation drive data with the deviation <20%. Besides the cylindrical hohlraum, we have also conducted hohlraum energetics experiments using spherical hohlraums on the SGIII-prototype and SGIII laser facilities. The spherical hohlraum with 6 LEHs [5,6] was recently advanced by our hohlraum physics team, which has superiority compared to the traditional cylindrical hohlraum in many key ignition target parameters, such as the drive symmetry, symmetry robustness, efficiency and even LPI. To validate the superiority of the
spherical hohlraum, we started the experiment from the spherical hohlraum with 2 LEHs on the SGIII-prototype and SGIII laser facilities. The spherical hohlraum diameter was 1.7 mm with 2 LEHs of 0.8 mm diameter at each end. In this experiment, we used a flat-top laser pulse with 1 ns duration, with energy ranging from 4.8 kJ to 6.3 kJ. The corresponding experimental data from the SGIII-prototype and energy balance curve are plotted in Fig. 2. The horizontal axis in Fig. 2 is the incident laser energy. The backscattered laser energy was measured, which is <3% of the total incident laser energy for the vacuum spherical hohlraum. The vertical axis is the radiation temperature in the hohlraum. The red squares in Fig. 2 are the radiation temperatures measured from the LEH with an angle of 55 to the hohlraum axis. The green star is the simulated equivalent radiation temperature incident on the capsule positioned at the hohlraum center. The blue curve is plotted according to the energy balance model assuming the conversion efficiency h ¼ 0.7 and the wall albedo aw ¼ 0.8. In Fig. 2, we can see that the hohlraum experimental data and the simulated capsule drive data agree well with the energy balance model for the SGIII-prototype spherical hohlraum experiment [15]. Moreover, in Fig. 3, we present the spherical hohlraum experimental data from the SGIII laser facilities and corresponding energy balance curve. In this experiment, the spherical hohlraum diameter was 3.6 mm and the LEH diameter was 1.2 mm. We used a flat-top laser pulse of 3 ns duration with the laser energy ranging from 75 kJ to 96 kJ. The horizontal axis in Fig. 3 is the incident laser energy. The backscatter laser energy fraction is measured to be <5% for the spherical hohlraum on SGIII laser. The vertical axis is the radiation temperature in the hohlraum. The red squares with error bars in Fig. 3 are the radiation temperatures measured from the LEH with an angle of 42 to the hohlraum axis. The green star is the simulated radiation temperature incident on the capsule positioned at the hohlraum center. The blue curve
SGIII-prototype, spherical hohlraum (Ф=1.7 mm, 2LEHs Ф=0.8 mm)
SGIII-prototype, cylindrical hohlraum (Ф=1 mm×2.1 mm, LEH Ф=0.8 mm)
Exp., LEH at 55° Sim. Tr on capsule Model
Exp., LEH at 55° Sim. Tr on capsule Model
Tr (eV)
Tr (eV)
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EL (kJ) Fig. 1. Absorbed laser energy v.s. the radiation temperature in the gas-filled cylindrical hohlraum for the SGIII-prototype. Experiment data (red crosses), simulation data (green stars) and energy balance model (blue line) are plotted for comparison.
EL (kJ) Fig. 2. Incident laser energy v.s. the radiation temperature in the vacuum spherical hohlraum for the SGIII-prototype. Experiment data (red crosses), simulation data (green star) and energy balance model (blue line) are plotted for comparison.
Please cite this article in press as: G.L. Ren, et al., Analysis of hohlraum energetics of the SG series and the NIF experiments with energy balance model, Matter and Radiation at Extremes (2016), http://dx.doi.org/10.1016/j.mre.2016.11.002
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SGIII laser, spherical hohlraum (Ф=3.6 mm, LEH Ф=1.2 mm)
Tr (eV)
Exp., LEH at 42° Sim. Tr on capsule Model
EL (kJ) Fig. 3. Incident laser energy v.s. the radiation temperature in the vacuum spherical hohlraum for the SGIII laser. Experiment data (red crosses), simulation data (green star) and energy balance model (blue line) are plotted for comparison.
is plotted according to the energy balance model. When using the energy balance model here, we adopted the conversion efficiency h ¼ 0.8 for the 3 ns laser pulse used in this experiment. The wall albedo aw was calculated by using our 1D multi-group radiation hydrodynamic code RDMG, and the simulation showed that the wall albedo aw was ~0.85 for the gold spherical hohlraum experiments on SGIII. Notice that we took h ¼ 0.7 and aw ¼ 0.8 for the 1 ns pulse laser at SGIIIprototype while h ¼ 0.8 and aw ¼ 0.85 for the 3 ns pulse at SGIII, because the laser to X-ray conversion efficiency usually increases with the pulse duration and the wall albedo increases with the radiation temperature. We can see from Fig. 3 that the energy balance model agrees with the experimental data and the simulated capsule drive data for the spherical hohlraum on the SGIII laser. In sum, the energy balance model agrees well with experiments of both cylindrical and spherical hohlraums fielded on relatively smaller scale (1 kJe100 kJ) laser facilities such as the Nova [1] and the SG series [14,15]. When the laser energy scales up to million joules (MJ) of the ignition relevant experiment, it is quite necessary to investigate the applicability of the energy balance model. 4. Analysis of the NIF data with the energy balance model Ever since the completion of NIF in 2009, hundreds of laser shots have been done with various kinds of target designs and laser pulses. The targets used on the NIF were diversified in many design parameters, some of which are listed in the following. Different cylindrical hohlraum sizes have been used, with the hohlraum diameter ranging from 5.4 mm to 6.7 mm, the LEH diameter from 3.1 mm to 3.7 mm, and the hohlraum length from 9.4 mm to 11 mm. For the laser pulses, the power ranges from ~300 TW up to the upper limit of 520 TW [16] while the laser energy ramps up from about 1 MJe1.9 MJ with durations ranging from 5 ns to 22 ns under different implosion schemes named with the high-foot
implosion (HF, shorter duration) [8,9] and the low-foot implosion (LF, longer duration) [2,13]. The hohlraum gas filling densities also vary from 0.03 mg/cm3 in the nearvacuum hohlraum (NVH) [17e20] to 1.6 mg/cm3 in the gasfilled hohlraum. Recently, two kinds of wall materials are used most often, one is gold, and the other is uranium. Usually, the hohlraums are made by gold, whereas some hohlraums are made according to the ‘sandwich’ design [2,16,21] with uranium as the radiation ablation layer. With all these variations in the material, size, gas fill and laser pulse of the hohlraums naturally, people tend to ask whether the hohlraum energetics performance of the ignition relevant targets meets the energy balance model or not. As described in Section 2, the physical equation of the energy balance model can be presented in two forms-the time integral form of the energy balance equation and the time differential form of the power balance equation. For convenience, we compared the NIF data with the power balance equation in the following paragraphs. The hohlraums are different in size, and the laser power required to achieve the same radiation temperature depends directly on the target geometrical configuration, including areas of the hohlraum wall, LEHs and capsule. Therefore from Eq. (3), we can define an effective hohlraum area as Aeff ¼ ð1 aw ÞAw þ Ah þ ð1 ac ÞAc :
ð4Þ
We use the ‘575’ hohlraum (diameter 5.75 mm, length 9.4 mm, LEH diameter 3.1 mm, capsule diameter 2.2 mm) as the standard hohlraum and denote the effective area of the ‘575’ hohlraum as A575 eff . Thus, we can normalize the laser power of different hohlraums to the standard according to the following scale: . Pnormalized ¼ PL $A575 ð5Þ Aeff : L eff is the normalized laser power, PL is In Eq. (5), Pnormalized L the original laser power, and Aeff refers to the original effective hohlraum area. In the normalization, we assume that the hohlraums with different sizes have the same conversion efficiency and wall albedo. We collected the experimental data [9,16e20,22e24] on the NIF and displayed them on the laser power v.s. the radiation temperature plane, as shown in Fig. 4. Here the laser power of the horizontal axis shown is normalized according to the ratio of the effective hohlraum area to that of a standard ‘575’ hohlraum instead of the original laser power in the references. For the power balance model curve shown in Fig. 4, we adopted a total laser to X-ray conversion efficiency of 0.9 and a wall albedo of 0.92, which are in consistent with our simulation for NIF ignition scale targets and the NIF data for vacuum hohlraums. As shown in Fig. 4, for all the experimental hohlraum radiation data on the NIF, they are in alignment with the energy balance model within a shifting range of ±20%. This is a direct proof that for all the diversifications of the NIF targets, the radiation drive inside the hohlraum is generally in agreement with the energy balance
Please cite this article in press as: G.L. Ren, et al., Analysis of hohlraum energetics of the SG series and the NIF experiments with energy balance model, Matter and Radiation at Extremes (2016), http://dx.doi.org/10.1016/j.mre.2016.11.002
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Tr (eV)
η=0.9, a=0.92
PL (TW) Fig. 4. Incident laser power v.s. the radiation temperature in the hohlraum for the NIF experiments. The pink line is the energy balance curve, and the two dashed pink lines present ±20% power shift for the energy balance curve. The blue squares are adapted from Kline's reference for the 430 TW gas-filled hohlraum. The dark yellow circles are data from the near vacuum hohlraum (NVH) with the high-density carbon (HDC) capsule. The dark yellow spheres are the data from the gas-filled hohlraum (GFH) with the HDC capsule. The pink dots are for the gold hohlraum from the D€oppner's reference [9], and the gray diamonds are data of the uranium hohlraum. The centered green star is the Rev. 5 Haan design point [2], and the solid square are the HF and LF design values cited from Edwards' report on the FPA2014 meeting [23]. In addition, there are some abbreviated notes for the data in the graph, the ‘PRL’ and ‘POP’ mean the citation from Physical Review Letters and the Physics of Plasmas, ‘FPA’ means the Fusion Power Association, ‘LEH’ indicates that the temperature is measured from the laser entrance holes by using Dante, and ‘intnl’ means the temperature is the internal radiation temperature inferred from the implosion data.
model. We can also see that in Fig. 4, the uranium hohlraum's drive temperatures are higher than the gold hohlraum's and they are located near the upper 20% power balance limit. As compared to gold, the higher opacity and lower heat capacity of uranium lead to a higher albedo, which means that the uranium hohlraum wall absorbs less X-ray energy and reemits more X-ray energy into the hohlraum and onto the capsule. Thus a higher capsule coupling efficiency is obtained for the uranium hohlraum in comparison to the gold hohlraum. Something interesting is that the blue squares data in Fig. 4 have nearly the same laser power of ~430 TW, with the laser energy ranging from 1.3 MJ to 1.9 MJ [16] and the laser duration rising from 3.1 ns to 4.5 ns, and at the same time the hohlraum temperature rises up from ~290 eV to as high as 320 eV. Therefore for the same laser power, the longer laser duration brings higher peak drive. This is reasonable because a longer laser will produce longer radiation drive that would result in higher albedo, and lower absorption of X-ray power in the hohlraum wall. It is worth mentioning that the NIF's 2011 Rev.5 ignition target design [2] by Haan et al. is located near the center of Fig. 4 and is reasonably close to the energy balance model. Furthermore, we made some progresses on the 6 LEHs spherical hohlraum recently. We have finished the spherical ignition target designs by using our 3D view factor code VF3D and 2D radiation hydrodynamic code LARED-Integration, and also evaluated the design value of the laser power and
radiation drive of the spherical hohlraum ignition target. The evaluation shows that our spherical ignition target also performs in accordance with the energy balance model. 5. Discussion and summary We have evaluated the hohlraum energetics of experiments fielded on relatively smaller scale (1 kJe100 kJ) laser facilities such as the SG series and found that they agreed well with the energy balance model within 20% deviation. Especially, we have also used the energy balance model to assess all kinds of NIF experimental radiation drive data at MJ scale. Given the diversifications of the NIF targets, the overall NIF radiation drive data generally agree with the energy balance model within ±20% deviation. The 20% deviation might be explained as follows. Firstly, the performance of the uranium hohlraums is around the upper 20% limit of the energy balance curve because the energy balance curve is plotted according to the gold hohlraums' performance. Meanwhile, a higher opacity and lower heat capacity of uranium compared to gold lead to a higher albedo and efficiency for the uranium hohlraums. Secondly, the radiation drive of same-sized hohlraums with the same peak laser power can be quite different if the laser energy is different. This is because different laser energy gives different radiation temperature and pulse duration at the same laser power, and the wall albedo is strongly connected to the radiation temperature and pulse duration. Thirdly, the drive data are
Please cite this article in press as: G.L. Ren, et al., Analysis of hohlraum energetics of the SG series and the NIF experiments with energy balance model, Matter and Radiation at Extremes (2016), http://dx.doi.org/10.1016/j.mre.2016.11.002
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from both NVH and gas-filled hohlraums, while the laser backscatter or the laser absorption behaves distinctively in these two kinds of hohlraums. It is worth mentioning that, the NIF point-target design [2] value is very close to the energy balance model curve within 20% deviation. In addition, the spherical target design values are also in agreement with the energy balance model. In general, all the experimental data from both small scale lasers, such as the SG series, and the large scale laser, NIF, are in accordance with the basic energy balance model for both spherical and cylindrical hohlraums. The analysis shows that the radiation drive can meet the requirements of the 1D ignition point design, which means that the NIF laser is adequate in energy to achieve ignition if a 1D spherical radiation drive could be created inside the cylindrical hohlraums in the case that LPI and hydrodynamic instabilities can be suppressed. The analysis in this paper has also shown that the energy balance model is a useful tool for indirect-drive ignition target design as well as for experimental data evaluation. Acknowledgement We thank the SGIII-prototype operations/laser team and the target fabrication team for their efforts during the experiments. This work is supported by the National Natural Science Foundation of China (Grant Nos. 11405011 and 11475033). References [1] J.D. Lindl, P. Amendt, R.L. Berger, S.G. Glendinning, S.H. Glenzer, et al., The physics basis for ignition using indirect-drive targets on the National Ignition Facility, Phys. Plasmas 11 (2004), 339. [2] S.W. Haan, J.D. Lindl, D.A. Callahan, D.S. Clark, J.D. Salmonson, et al., Point design targets, specifications, and requirements for the 2010 ignition campaign on the National Ignition Facility, Phys. Plasmas 18 (2011), 051001. [3] M. Vandenboomgaerde, J. Bastian, A. Casner, D. Galmiche, J.-P. Jadaud, et al., Prolate-spheroid (“Rugby-Shaped”) hohlraum for inertial confinement fusion, Phys. Rev. Lett. 99 (2007), 065004. [4] P. Amendt, C. Cerjan, D.E. Hinkel, J.L. Milovich, H.-S. Park, et al., Rugby-like hohlraum experimental design for demonstrating X-ray drive enhancement, Phys. Plasmas 15 (2008), 012702. [5] K. Lan, J. Liu, X.T. He, W.D. Zheng, D.X. Lai, High flux symmetry of the spherical hohlraum with octahedral 6 LEHs at the hohlraum-tocapsule radius ratio of 5.14, Phys. Plasmas 21 (2014), 010704. [6] K. Lan, J. Liu, Z.C. Li, X.F. Xie, W.Y. Huo, et al., Progress in octahedral spherical hohlraum study, Matter Radiat. Extrem. 1 (2016) 8e27. [7] R.H.H. Scott, D.S. Clark, D.K. Bradley, D.A. Callahan, M.J. Edwards, et al., Numerical modeling of the sensitivity of X-ray driven implosion to low-mode flux asymmetries, Phys. Rev. Lett. 110 (2013), 075001.
[8] O.A. Hurricane, D.A. Callahan, D.T. Casey, P.M. Celliers, C. Cerjan, et al., Fuel gain exceeding unity in an inertially confined fusion implosion, Nature 506 (2014) 343e348. [9] T. D€oppner, D.A. Callahan, O.A. Hurricane, D.E. Hinke, T. Ma, et al., Demonstration of high performance in layered deuterium-tritium capsule implosions in uranium hohlraums at the National Ignition Facility, Phys. Rev. Lett. 115 (2015), 055001. [10] S.A. MacLaren, M.B. Schneider, K. Widmann, J.H. Hammer, B.E. Yoxall, et al., Novel characterization of capsule X-ray drive at the National Ignition Facility, Phys. Rev. Lett. 112 (2014), 105003. [11] M.B. Schneider, S.A. MacLaren, K. Widmann, N.B. Meezan, J.H. Hammer, et al., The size and structure of the laser entrance hole in gas-filled hohlraum at the National Ignition Facility, Phys. Plasmas 22 (2015), 122705. [12] O.S. Jones, C.J. Cerjan, M.M. Marinak, J.L. Milovich, H.F. Robey, et al., A high-resolution integrated model of the National Ignition Campaign cryogenic layered experiments, Phys. Plasmas 19 (2012), 056315. [13] S.H. Glenzer, D.A. Callahan, A.J. MacKinnon, J.L. Kline, G. Grim, et al., Cryogenic thermonuclear fuel implosions on the National Ignition Facility, Phys. Plasmas 19 (2012), 056318. [14] W.Y. Huo, G.L. Ren, K. Lan, X. Li, C.S. Wu, et al., Simulation study of hohlraum experiments on SGIII-prototype laser facility, Phys. Plasmas 17 (2010), 123114. [15] W.Y. Huo, Z.C. Li, Y.H. Chen, X.F. Xie, J. Liu, et al., First investigation on the radiation field of the spherical hohlraum, Phys. Rev. Lett. 117 (2016), 025002. [16] J.L. Kline, D.A. Callahan, S.H. Glenzer, N.B. Meezan, J.D. Moody, et al., Hohlraum energetics scaling to 520 TW on the National Ignition Facility, Phys. Plasmas 20 (2013), 056314. [17] S. Le Pape, L. Divol, L. Berzak Hopkins, A. MacKinnon, N.B. Meezan, et al., Observation of a reflected shock in indirectly driven spherical implosion at the National Ignition Facility, Phys. Rev. Lett. 112 (2014), 225002. [18] A.J. MacKinnon, N.B. Meezan, J.S. Ross, T. D€oppner, A. Pak, et al., High density carbon ablator experiments on the National Ignition Facility, Phys. Plasmas 21 (2014), 056318. [19] L.F. Berzak Hopkins, S. Le Pape, L. Divol, N.B. Meezan, A.J. Mackinnon, et al., Near-vacuum hohlraums for driving fusion implosions with high density carbon ablators, Phys. Plasmas 22 (2015), 056318. [20] L.F. Berzak Hopkins, N.B. Meezan, S. Le Pape, L. Divol, A.J. MacKinnon, et al., First high-convergence cryogenic implosion in a near-vacuum hohlraum, Phys. Rev. Lett. 114 (2015), 175001. [21] X. Li, K. Lan, X. Meng, X.T. He, D.X. Lai, et al., Study on AuþUþAu sandwich hohlraum wall for ignition targets, Laser Part. Beams 28 (2010), 10.1017. [22] J.S. Ross, D. Ho, J. Milovich, T. D€oppner, J. McNaey, et al., High-density carbon capsule experiments on the National Ignition Facility, Phys. Rev. E 91 (2015), 021101. [23] J. Edwards, Progress and Challenges in X-ray Drive ICF on the NIF, Report on the Fusion Power Associates, 2014. [24] J.D. Moody, D.A. Callahan, D.E. Hinkel, P.A. Amendt, K.L. Baker, et al., Progress in hohlraum physics for the National Ignition Facility, Phys. Plasmas 21 (2014), 056317.
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Research Article
Analysis of hohlraum energetics of the SG series and the NIF experiments with energy balance model G.L. Ren*, Jie Liu, Wenyi Huo, Ke Lan Institute of Applied Physics and Computational Mathematics, Beijing 100094, China Received 8 September 2016; revised 24 October 2016; accepted 3 November 2016 Available online ▪ ▪ ▪
Abstract The basic energy balance model is applied to analyze the hohlraum energetics data from the Shenguang (SG) series laser facilities and the National Ignition Facility (NIF) experiments published in the past few years. The analysis shows that the overall hohlraum energetics data are in agreement with the energy balance model within 20% deviation. The 20% deviation might be caused by the diversity in hohlraum parameters, such as material, laser pulse, gas filling density, etc. In addition, the NIF's ignition target designs and our ignition target designs given by simulations are also in accordance with the energy balance model. This work confirms the value of the energy balance model for ignition target design and experimental data assessment, and demonstrates that the NIF energy is enough to achieve ignition if a 1D spherical radiation drive could be created, meanwhile both the laser plasma instabilities and hydrodynamic instabilities could be suppressed. Copyright © 2016 Science and Technology Information Center, China Academy of Engineering Physics. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
PACS codes: 52.57.-z; 52.50.Jm; 52.38.Mf Keywords: Energy balance model; Hohlraum energetics; National Ignition Facility (NIF); Shenguang (SG) series
1. Introduction Indirect drive inertial confinement fusion (ICF) uses a highZ hohlraum (cylindrical [1,2], rugby or elliptical [3,4] or spherical [5,6] hohlraum) to convert the incident laser energy into thermal X-rays, which ablate a capsule located at the hohlraum center to achieve thermonuclear ignition. A successful indirect drive ignition requires driving the implosion capsule to high velocity (~370 km/s) while keeping the cryogenic deuteriumetritium (DT) fuel layer at low entropy [2], meanwhile the imploded core must remain nearly spherical to avoid quenching the ignition of the central hotspot via minimizing the cooling mechanisms, as well as to avoid decreasing the conversion efficiency of the implosion kinetic energy into hotspot internal energy [7]. The implosion of * Corresponding author. E-mail address: [email protected] (G.L. Ren). Peer review under responsibility of Science and Technology Information Center, China Academy of Engineering Physics.
ignition gives stringent requirements of high velocity, low entropy and very high symmetry, which must be met by delicately adjusting the radiation environment inside the hohlraum. Therefore in ICF study, the hohlraum plays a crucial role in delivering the stringently-required radiation drive and symmetry within the limitation of the energy and power of the laser facility. The National Ignition Facility (NIF) in the US is configured to achieve laser driven ICF via indirect drive (ID) approach [1] by using cylindrical hohlraum. Since its completion in 2009, various ignition relevant experiments using different targets and laser pulses have been carried out on the NIF. The highest neutron yield achieved so far is ~1016 and obvious alpha particle heating of the hotspot has been observed [8,9]. In the observation, the hotspot pressure has reached 200 Gbar compared to the ignition threshold of 350 Gbar (1 Gbar ¼ 108 MPa). Nevertheless, the primary goal of achieving ignition on the NIF has not been reached yet. According to further studies on NIF experiments, many problems
http://dx.doi.org/10.1016/j.mre.2016.11.002 2468-080X/Copyright © 2016 Science and Technology Information Center, China Academy of Engineering Physics. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: G.L. Ren, et al., Analysis of hohlraum energetics of the SG series and the NIF experiments with energy balance model, Matter and Radiation at Extremes (2016), http://dx.doi.org/10.1016/j.mre.2016.11.002
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might be responsible for the failure of ignition, such as the hohlraum energetics, the low mode drive asymmetry and the hydrodynamic instability growth during the implosion, etc. Among these possible problems, the hohlraum energetics is primary because it determines the radiation drive onto the capsule. Usually, the radiation drive incident on the capsule cannot be measured directly, thus it is often inferred from the directly observed experimental data combined with numerical modeling. Such measurements include the observation of the Xray flux flowing out of the laser entrance holes (LEHs) at certain angles, and the measurement of the implosion trajectories of the capsule with backlit radiography. However, these measurements involve some complicated details not yet clarified [10]. For example, when measuring the X-ray flux from the LEH with the multiple-channeled X-ray diode detector (XRDs or DANTE), the interpretation of the measuring results is directly influenced by the dynamic LEH closure [11], which is hard to be precisely depicted. In addition, the radiation drive (or radiation temperature) inferred from different methods are not always in agreement with each other, and in many cases especially in the gasfilled hohlraum (GFH), the measured drive onto the capsule are well below the numerical prediction, which is called the ‘energy deficit’ [10,12] problem. All these complications indicate that an overall picture of the radiation drive in the NIF experiments is needed to better understand the general hohlraum energetics. The apparent ‘energy deficit’ problem found using gas-filled hohlraums on the NIF raises one fundamental question: Is the energy of NIF sufficient to achieve ignition? To be more specific, if we were able to overcome the troubling lasereplasma interaction (LPI) issues encountered in the gas-filled hohlraum and thus able to provide quasi spherical X-ray drive, will the energy of the current NIF facility be sufficient for ignition? In this work, we applied the fundamental energy balance model to analyze the overall NIF data and see how much the overall NIF data would deviate from the energy balance model. Stepping forward from that, we will try to answer the fundamental question whether NIF's energy is sufficient for ignition or not. Due to its conciseness in physical picture and easiness for utilization, the energy balance model is widely used in ignition target design and experimental data evaluation [1,13]. It builds up a physical bridge between the laser energy (or laser power) and the radiation drive inside the hohlraum. We used the energy balance model to analyze the hohlraum energetics in Shenguang (SG) series experiments as well as all kinds of ignition relevant NIF experiments. This article is organized as below. In Section 2, we briefly introduce the energy balance model. In Section 3, we assess the experimental drive data with the energy balance model, which were observed on the SG series laser facilities adopting both cylindrical and spherical hohlraums. In Section 4, we analyze the NIF data with the energy balance model. Finally, we give a summary.
hohlraum, some fraction of the lasers is backscattered out of the hohlraum, whereas the majority of the laser energy is absorbed by the wall plasmas via collisional absorption as well as non-linear absorption schemes, and then converted into Xrays, which are either absorbed by the wall or the capsule, or escape through the LEH. From the energy balance model [1], we have hEL ¼ EWall þ ELEH þ Ecap þ Er ¼ sTr4 $½ð1 aw ÞAw þ Ah þ ð1 ac ÞAc $t þ Er :
ð1Þ
here, we denote EL as the incident laser energy, h the total laser to X-ray conversion efficiency including both the laser absorption efficiency and the laser to X-ray conversion efficiency, EWall ; ELEH ; Ecap the X-ray energies absorbed by the wall, escaping from the LEHs, and absorbed by the capsule, respectively, Er the radiation energy stored inside the hohlraum, aw the hohlraum wall albedo (reflectivity), ac the capsule albedo, Aw , Ah and Ac the areas of the hohlraum wall, the LEHs and the capsule respectively, t the equivalent duration of the laser pulse, Tr the radiation temperature inside the hohlraum, s the Stefan parameter. As we know, Er is proportional to Tr4 $Vhohl , where Vhohl is the volume of the hohlraum. However, for the ICF hohlraum environment, even under the NIF ignition relevant radiation temperature range ~300 eV, Er is less than a few percent of the total laser energy and can be neglected. Thus the energy balance equation becomes hEL ¼ sTr4 $½ð1 aw ÞAw þ Ah þ ð1 ac ÞAc $t:
ð2Þ
The time derivative expression of the energy balance equation is also used in the hohlraum energetics study, which is called as the power balance equation hPL ¼ sTr4 $½ð1 aw ÞAw þ Ah þ ð1 ac ÞAc :
ð3Þ
The conversion efficiency h and wall albedo aw can be calculated self-consistently in radiation hydrodynamic simulations. In addition, aw can also be obtained analytically by assuming the Marshak wave approximation under certain incoming radiation temperature curve. As for the NIF ignition relevant targets, our calculation shows that h ~90% and aw ~90% during the main pulse with the peak Tr ~300 eV. However, it should be noted that the energy balance model is not exactly accurate because the radiation temperature is not strictly homogenous, and also the area of the hohlraum, the LEHs together with the capsule vary during the laser drive and the X-ray ablation. Therefore, it is worth to examine the adaptability of the energy balance model with various experimental data of the hohlraum energetics.
2. The energy balance model
3. Assessment of the drive data in SG series experiment with energy balance model
The energy balance model depicts the energy flow inside the indirect drive hohlraum. When lasers enter the high-Z
The energy balance model agrees well with the Nova 1-ns hohlraum experimental data [1]. Here, we applied the energy
Please cite this article in press as: G.L. Ren, et al., Analysis of hohlraum energetics of the SG series and the NIF experiments with energy balance model, Matter and Radiation at Extremes (2016), http://dx.doi.org/10.1016/j.mre.2016.11.002
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balance model to the hohlraum experiments conducted on the SGIII-prototype and SGIII laser facilities. In the SGIII-prototype experiment series, we firstly adopted the gas-filled cylindrical hohlraum of 1 mm diameter and 2.1 mm length. In this experiment, we used a flat-top laser pulse with 1 ns duration, and energy ranging from 2 kJ to 8 kJ. The experimental data and corresponding energy balance curve are plotted in Fig. 1. The horizontal axis in Fig. 1 is the absorbed laser energy with the measured backscatter laser energy being detracted. The vertical axis is the radiation temperature in the hohlraum. The red crosses are the radiation temperatures measured from the LEH with an angle of 55 to the hohlraum axis. The green stars are the equivalent radiation temperatures incident on the capsule positioned at the hohlraum center, hereafter called the “capsule radiation temperature” for convenience no matter whether there is a true capsule inside the hohlraum or not, which were calculated by our 2D radiation hydrodynamic code LARED-Integration [14]. The blue curve is plotted according to the energy balance model assuming the conversion efficiency h ¼ 0.7 for 1 ns laser pulse. Here aw was calculated by using our 1D multi-group radiation hydrodynamic code RDMG [14]. The simulation shows that the wall albedo aw is ~0.8 for the gold hohlraum experiments on SGIII-prototype. From Fig. 1, it can be seen that the energy balance model agrees with the calculated capsule radiation temperature, and meanwhile the energy balance curve is slightly lower than the measured cylindrical hohlraum radiation drive data with the deviation <20%. Besides the cylindrical hohlraum, we have also conducted hohlraum energetics experiments using spherical hohlraums on the SGIII-prototype and SGIII laser facilities. The spherical hohlraum with 6 LEHs [5,6] was recently advanced by our hohlraum physics team, which has superiority compared to the traditional cylindrical hohlraum in many key ignition target parameters, such as the drive symmetry, symmetry robustness, efficiency and even LPI. To validate the superiority of the
spherical hohlraum, we started the experiment from the spherical hohlraum with 2 LEHs on the SGIII-prototype and SGIII laser facilities. The spherical hohlraum diameter was 1.7 mm with 2 LEHs of 0.8 mm diameter at each end. In this experiment, we used a flat-top laser pulse with 1 ns duration, with energy ranging from 4.8 kJ to 6.3 kJ. The corresponding experimental data from the SGIII-prototype and energy balance curve are plotted in Fig. 2. The horizontal axis in Fig. 2 is the incident laser energy. The backscattered laser energy was measured, which is <3% of the total incident laser energy for the vacuum spherical hohlraum. The vertical axis is the radiation temperature in the hohlraum. The red squares in Fig. 2 are the radiation temperatures measured from the LEH with an angle of 55 to the hohlraum axis. The green star is the simulated equivalent radiation temperature incident on the capsule positioned at the hohlraum center. The blue curve is plotted according to the energy balance model assuming the conversion efficiency h ¼ 0.7 and the wall albedo aw ¼ 0.8. In Fig. 2, we can see that the hohlraum experimental data and the simulated capsule drive data agree well with the energy balance model for the SGIII-prototype spherical hohlraum experiment [15]. Moreover, in Fig. 3, we present the spherical hohlraum experimental data from the SGIII laser facilities and corresponding energy balance curve. In this experiment, the spherical hohlraum diameter was 3.6 mm and the LEH diameter was 1.2 mm. We used a flat-top laser pulse of 3 ns duration with the laser energy ranging from 75 kJ to 96 kJ. The horizontal axis in Fig. 3 is the incident laser energy. The backscatter laser energy fraction is measured to be <5% for the spherical hohlraum on SGIII laser. The vertical axis is the radiation temperature in the hohlraum. The red squares with error bars in Fig. 3 are the radiation temperatures measured from the LEH with an angle of 42 to the hohlraum axis. The green star is the simulated radiation temperature incident on the capsule positioned at the hohlraum center. The blue curve
SGIII-prototype, spherical hohlraum (Ф=1.7 mm, 2LEHs Ф=0.8 mm)
SGIII-prototype, cylindrical hohlraum (Ф=1 mm×2.1 mm, LEH Ф=0.8 mm)
Exp., LEH at 55° Sim. Tr on capsule Model
Exp., LEH at 55° Sim. Tr on capsule Model
Tr (eV)
Tr (eV)
3
EL (kJ) Fig. 1. Absorbed laser energy v.s. the radiation temperature in the gas-filled cylindrical hohlraum for the SGIII-prototype. Experiment data (red crosses), simulation data (green stars) and energy balance model (blue line) are plotted for comparison.
EL (kJ) Fig. 2. Incident laser energy v.s. the radiation temperature in the vacuum spherical hohlraum for the SGIII-prototype. Experiment data (red crosses), simulation data (green star) and energy balance model (blue line) are plotted for comparison.
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SGIII laser, spherical hohlraum (Ф=3.6 mm, LEH Ф=1.2 mm)
Tr (eV)
Exp., LEH at 42° Sim. Tr on capsule Model
EL (kJ) Fig. 3. Incident laser energy v.s. the radiation temperature in the vacuum spherical hohlraum for the SGIII laser. Experiment data (red crosses), simulation data (green star) and energy balance model (blue line) are plotted for comparison.
is plotted according to the energy balance model. When using the energy balance model here, we adopted the conversion efficiency h ¼ 0.8 for the 3 ns laser pulse used in this experiment. The wall albedo aw was calculated by using our 1D multi-group radiation hydrodynamic code RDMG, and the simulation showed that the wall albedo aw was ~0.85 for the gold spherical hohlraum experiments on SGIII. Notice that we took h ¼ 0.7 and aw ¼ 0.8 for the 1 ns pulse laser at SGIIIprototype while h ¼ 0.8 and aw ¼ 0.85 for the 3 ns pulse at SGIII, because the laser to X-ray conversion efficiency usually increases with the pulse duration and the wall albedo increases with the radiation temperature. We can see from Fig. 3 that the energy balance model agrees with the experimental data and the simulated capsule drive data for the spherical hohlraum on the SGIII laser. In sum, the energy balance model agrees well with experiments of both cylindrical and spherical hohlraums fielded on relatively smaller scale (1 kJe100 kJ) laser facilities such as the Nova [1] and the SG series [14,15]. When the laser energy scales up to million joules (MJ) of the ignition relevant experiment, it is quite necessary to investigate the applicability of the energy balance model. 4. Analysis of the NIF data with the energy balance model Ever since the completion of NIF in 2009, hundreds of laser shots have been done with various kinds of target designs and laser pulses. The targets used on the NIF were diversified in many design parameters, some of which are listed in the following. Different cylindrical hohlraum sizes have been used, with the hohlraum diameter ranging from 5.4 mm to 6.7 mm, the LEH diameter from 3.1 mm to 3.7 mm, and the hohlraum length from 9.4 mm to 11 mm. For the laser pulses, the power ranges from ~300 TW up to the upper limit of 520 TW [16] while the laser energy ramps up from about 1 MJe1.9 MJ with durations ranging from 5 ns to 22 ns under different implosion schemes named with the high-foot
implosion (HF, shorter duration) [8,9] and the low-foot implosion (LF, longer duration) [2,13]. The hohlraum gas filling densities also vary from 0.03 mg/cm3 in the nearvacuum hohlraum (NVH) [17e20] to 1.6 mg/cm3 in the gasfilled hohlraum. Recently, two kinds of wall materials are used most often, one is gold, and the other is uranium. Usually, the hohlraums are made by gold, whereas some hohlraums are made according to the ‘sandwich’ design [2,16,21] with uranium as the radiation ablation layer. With all these variations in the material, size, gas fill and laser pulse of the hohlraums naturally, people tend to ask whether the hohlraum energetics performance of the ignition relevant targets meets the energy balance model or not. As described in Section 2, the physical equation of the energy balance model can be presented in two forms-the time integral form of the energy balance equation and the time differential form of the power balance equation. For convenience, we compared the NIF data with the power balance equation in the following paragraphs. The hohlraums are different in size, and the laser power required to achieve the same radiation temperature depends directly on the target geometrical configuration, including areas of the hohlraum wall, LEHs and capsule. Therefore from Eq. (3), we can define an effective hohlraum area as Aeff ¼ ð1 aw ÞAw þ Ah þ ð1 ac ÞAc :
ð4Þ
We use the ‘575’ hohlraum (diameter 5.75 mm, length 9.4 mm, LEH diameter 3.1 mm, capsule diameter 2.2 mm) as the standard hohlraum and denote the effective area of the ‘575’ hohlraum as A575 eff . Thus, we can normalize the laser power of different hohlraums to the standard according to the following scale: . Pnormalized ¼ PL $A575 ð5Þ Aeff : L eff is the normalized laser power, PL is In Eq. (5), Pnormalized L the original laser power, and Aeff refers to the original effective hohlraum area. In the normalization, we assume that the hohlraums with different sizes have the same conversion efficiency and wall albedo. We collected the experimental data [9,16e20,22e24] on the NIF and displayed them on the laser power v.s. the radiation temperature plane, as shown in Fig. 4. Here the laser power of the horizontal axis shown is normalized according to the ratio of the effective hohlraum area to that of a standard ‘575’ hohlraum instead of the original laser power in the references. For the power balance model curve shown in Fig. 4, we adopted a total laser to X-ray conversion efficiency of 0.9 and a wall albedo of 0.92, which are in consistent with our simulation for NIF ignition scale targets and the NIF data for vacuum hohlraums. As shown in Fig. 4, for all the experimental hohlraum radiation data on the NIF, they are in alignment with the energy balance model within a shifting range of ±20%. This is a direct proof that for all the diversifications of the NIF targets, the radiation drive inside the hohlraum is generally in agreement with the energy balance
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Tr (eV)
η=0.9, a=0.92
PL (TW) Fig. 4. Incident laser power v.s. the radiation temperature in the hohlraum for the NIF experiments. The pink line is the energy balance curve, and the two dashed pink lines present ±20% power shift for the energy balance curve. The blue squares are adapted from Kline's reference for the 430 TW gas-filled hohlraum. The dark yellow circles are data from the near vacuum hohlraum (NVH) with the high-density carbon (HDC) capsule. The dark yellow spheres are the data from the gas-filled hohlraum (GFH) with the HDC capsule. The pink dots are for the gold hohlraum from the D€oppner's reference [9], and the gray diamonds are data of the uranium hohlraum. The centered green star is the Rev. 5 Haan design point [2], and the solid square are the HF and LF design values cited from Edwards' report on the FPA2014 meeting [23]. In addition, there are some abbreviated notes for the data in the graph, the ‘PRL’ and ‘POP’ mean the citation from Physical Review Letters and the Physics of Plasmas, ‘FPA’ means the Fusion Power Association, ‘LEH’ indicates that the temperature is measured from the laser entrance holes by using Dante, and ‘intnl’ means the temperature is the internal radiation temperature inferred from the implosion data.
model. We can also see that in Fig. 4, the uranium hohlraum's drive temperatures are higher than the gold hohlraum's and they are located near the upper 20% power balance limit. As compared to gold, the higher opacity and lower heat capacity of uranium lead to a higher albedo, which means that the uranium hohlraum wall absorbs less X-ray energy and reemits more X-ray energy into the hohlraum and onto the capsule. Thus a higher capsule coupling efficiency is obtained for the uranium hohlraum in comparison to the gold hohlraum. Something interesting is that the blue squares data in Fig. 4 have nearly the same laser power of ~430 TW, with the laser energy ranging from 1.3 MJ to 1.9 MJ [16] and the laser duration rising from 3.1 ns to 4.5 ns, and at the same time the hohlraum temperature rises up from ~290 eV to as high as 320 eV. Therefore for the same laser power, the longer laser duration brings higher peak drive. This is reasonable because a longer laser will produce longer radiation drive that would result in higher albedo, and lower absorption of X-ray power in the hohlraum wall. It is worth mentioning that the NIF's 2011 Rev.5 ignition target design [2] by Haan et al. is located near the center of Fig. 4 and is reasonably close to the energy balance model. Furthermore, we made some progresses on the 6 LEHs spherical hohlraum recently. We have finished the spherical ignition target designs by using our 3D view factor code VF3D and 2D radiation hydrodynamic code LARED-Integration, and also evaluated the design value of the laser power and
radiation drive of the spherical hohlraum ignition target. The evaluation shows that our spherical ignition target also performs in accordance with the energy balance model. 5. Discussion and summary We have evaluated the hohlraum energetics of experiments fielded on relatively smaller scale (1 kJe100 kJ) laser facilities such as the SG series and found that they agreed well with the energy balance model within 20% deviation. Especially, we have also used the energy balance model to assess all kinds of NIF experimental radiation drive data at MJ scale. Given the diversifications of the NIF targets, the overall NIF radiation drive data generally agree with the energy balance model within ±20% deviation. The 20% deviation might be explained as follows. Firstly, the performance of the uranium hohlraums is around the upper 20% limit of the energy balance curve because the energy balance curve is plotted according to the gold hohlraums' performance. Meanwhile, a higher opacity and lower heat capacity of uranium compared to gold lead to a higher albedo and efficiency for the uranium hohlraums. Secondly, the radiation drive of same-sized hohlraums with the same peak laser power can be quite different if the laser energy is different. This is because different laser energy gives different radiation temperature and pulse duration at the same laser power, and the wall albedo is strongly connected to the radiation temperature and pulse duration. Thirdly, the drive data are
Please cite this article in press as: G.L. Ren, et al., Analysis of hohlraum energetics of the SG series and the NIF experiments with energy balance model, Matter and Radiation at Extremes (2016), http://dx.doi.org/10.1016/j.mre.2016.11.002
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from both NVH and gas-filled hohlraums, while the laser backscatter or the laser absorption behaves distinctively in these two kinds of hohlraums. It is worth mentioning that, the NIF point-target design [2] value is very close to the energy balance model curve within 20% deviation. In addition, the spherical target design values are also in agreement with the energy balance model. In general, all the experimental data from both small scale lasers, such as the SG series, and the large scale laser, NIF, are in accordance with the basic energy balance model for both spherical and cylindrical hohlraums. The analysis shows that the radiation drive can meet the requirements of the 1D ignition point design, which means that the NIF laser is adequate in energy to achieve ignition if a 1D spherical radiation drive could be created inside the cylindrical hohlraums in the case that LPI and hydrodynamic instabilities can be suppressed. The analysis in this paper has also shown that the energy balance model is a useful tool for indirect-drive ignition target design as well as for experimental data evaluation. Acknowledgement We thank the SGIII-prototype operations/laser team and the target fabrication team for their efforts during the experiments. This work is supported by the National Natural Science Foundation of China (Grant Nos. 11405011 and 11475033). References [1] J.D. Lindl, P. Amendt, R.L. Berger, S.G. Glendinning, S.H. Glenzer, et al., The physics basis for ignition using indirect-drive targets on the National Ignition Facility, Phys. Plasmas 11 (2004), 339. [2] S.W. Haan, J.D. Lindl, D.A. Callahan, D.S. Clark, J.D. Salmonson, et al., Point design targets, specifications, and requirements for the 2010 ignition campaign on the National Ignition Facility, Phys. Plasmas 18 (2011), 051001. [3] M. Vandenboomgaerde, J. Bastian, A. Casner, D. Galmiche, J.-P. Jadaud, et al., Prolate-spheroid (“Rugby-Shaped”) hohlraum for inertial confinement fusion, Phys. Rev. Lett. 99 (2007), 065004. [4] P. Amendt, C. Cerjan, D.E. Hinkel, J.L. Milovich, H.-S. Park, et al., Rugby-like hohlraum experimental design for demonstrating X-ray drive enhancement, Phys. Plasmas 15 (2008), 012702. [5] K. Lan, J. Liu, X.T. He, W.D. Zheng, D.X. Lai, High flux symmetry of the spherical hohlraum with octahedral 6 LEHs at the hohlraum-tocapsule radius ratio of 5.14, Phys. Plasmas 21 (2014), 010704. [6] K. Lan, J. Liu, Z.C. Li, X.F. Xie, W.Y. Huo, et al., Progress in octahedral spherical hohlraum study, Matter Radiat. Extrem. 1 (2016) 8e27. [7] R.H.H. Scott, D.S. Clark, D.K. Bradley, D.A. Callahan, M.J. Edwards, et al., Numerical modeling of the sensitivity of X-ray driven implosion to low-mode flux asymmetries, Phys. Rev. Lett. 110 (2013), 075001.
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Please cite this article in press as: G.L. Ren, et al., Analysis of hohlraum energetics of the SG series and the NIF experiments with energy balance model, Matter and Radiation at Extremes (2016), http://dx.doi.org/10.1016/j.mre.2016.11.002