Visualizing Fast Electron Energy Transport Into Laser-Compressed High-Density Fast-Ignition Targets

ARTICLES PUBLISHED ONLINE: 11 JANUARY 2016 | DOI: 10.1038/NPHYS3614

Visualizing fast electron energy transport into laser-compressed high-density fast-ignition targets

L. C. Jarrott1†, M. S. Wei2*, C. McGuey1, A. A. Solodov3,4, W. Theobald3, B. Qiao1, C. Stoeckl3, R. Betti3,4, H. Chen5, J. Delettrez3, T. Döppner5, E. M. Giraldez2, V. Y. Glebov3, H. Habara6, T. Iwawaki6, M. H. Key5, R. W. Luo2, F. J. Marshall3, H. S. McLean5, C. Mileham3, P. K. Patel5, J. J. Santos7, H. Sawada8, R. B. Stephens2, T. Yabuuchi6 and F. N. Beg1*

Recent progress in kilojoule-scale high-intensity lasers has opened up new areas of research in radiography, laboratory astrophysics, high-energy-density physics, and fast-ignition (FI) laser fusion. FI requires ecient heating of pre-compressed high-density fuel by an intense relativistic electron beam produced from laser–matter interaction. Understanding the details of electron beam generation and transport is crucial for FI. Here we report on the first visualization of fast electron spatial energy deposition in a laser-compressed cone-in-shell FI target, facilitated by doping the shell with copper and imaging the K-shell radiation. Multi-scale simulations accompanying the experiments clearly show the location of fast electrons and reveal key parameters aecting energy coupling. The approach provides a more direct way to infer energy coupling and guide experimental designs that significantly improve the laser-to-core coupling to 7%. Our findings lay the groundwork for further improving eciency, with 15% energy coupling predicted in FI experiments using an existing megajoule-scale laser driver.

usion ignition and burn may be achieved through inertial its energy into the compressed core. In two-dimensional (2D) confinement fusion (ICF) by compressing tritium (T) and/or computer simulations of an idealized electron FI scenario, a core Fdeuterium (D) fuel to high enough temperatures (∼10 keV) of radius ∼40 µm and peak density of ∼500 g cm−3 can be heated to initiate fusion reactions, producing high-energy neutrons to ignition with as little as 25 kJ of electron beam energy (∼2 MeV and α-particles. If assembled properly, with excellent spherical Maxwellian-distributed electrons in a parallel beam)5. compression symmetry, fuel areal density exceeding ∼1 g cm−2, The first experiment to undertake both the compression of a and very little mixing of cold material into the hotspot, a shell and heating by fast electrons used nine driver beams (2.5 kJ, thermonuclear burn wave sustained by α-particle heating could unshaped, laser wavelength λ = 532 nm) and a 0.1 PW short- propagate throughout the bulk of the fuel. Conventional ICF pulse laser directed into a cone-in-shell target at Japan’s Institute seeks to achieve ignition by symmetrically imploding a hollow of Laser Engineering (ILE). That team reported a significant spherical ‘capsule’ consisting of an ablator and inner lining of neutron yield enhancement and an inferred coupling efficiency of cryogenically frozen DT fuel. The fuel is forced inwards, forming 15–30% of the short-pulse laser energy into the fuel6,7. More recent a high-temperature ‘hotspot’ in the centre. Experiments conducted understanding indicates that this was an optimistic result. Follow-up at the National Ignition Facility1 have produced fuel areal densities experiments with the same driver found insufficient compression, exceeding 1 g cm−2, significant α-particle heating, and fuel energy being approximately ten times lower than was previously estimated, gain exceeding unity2. But, ignition has not yet been achieved. and a much lower (∼1.6%) coupling efficiency8. Alternative approaches for high-energy-gain ICF include fast Subsequent work on the Omega Laser Facility at the Labo- ignition (FI; ref. 3) and shock ignition4. These schemes separate ratory for Laser Energetics (LLE) using much more substantial the compression and heating phases of the implosion, using a compression-laser drive energy (18 kJ, 54 beams, λ = 351 nm), a more stable compression followed by a short burst of localized pulse shape designed to compress the fuel on a lower adiabat, and a heating. By separating these two aspects, the fuel can be compressed higher energy heating pulse (1 kJ, 0.1 PW), showed an unambiguous isochorically (without a central hotspot), thereby reducing the fuel neutron yield enhancement of two to three times through optimiza- density requirements or increasing the mass of fuel that can be tion of the timing between the driver beams and the heating pulse. compressed, potentially leading to higher gain. The heating pulse With this enhancement, a coupling efficiency of 3.5 ± 1.0% of the in electron FI is generated by a separate short-pulse petawatt (PW) short-pulse energy into heating of the entire core was inferred9. laser that creates an intense, MeV electron beam which deposits More recent experiments, using novel 8 keV X-ray backlighting

1Center for Energy Research, Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, California 92093, USA. 2General Atomics, San Diego, California 92186-5608, USA. 3Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA. 4Fusion Science Center, University of Rochester, Rochester, New York 14623, USA. 5Lawrence Livermore National Laboratory, Livermore, California 94550, USA. 6Graduate School of Engineering, Osaka University, Suita, 565-0871 Osaka, Japan. 7University of Bordeaux, CELIA (Centre Lasers Intenses et Applications), UMR 5107, F-33405 Talence, France. 8Department of Physics, University of Nevada, Reno, Nevada 89557, USA. †Present address: Lawrence Livermore National Laboratory, Livermore, California 94550, USA. *e-mail: [email protected]; [email protected]

ARTICLES NATURE PHYSICS DOI: 10.1038/NPHYS3614

a Cu-doped CD (23 µm) b 0.25 µ CH (15 m) Initial pulse Optimized pulse OMEGA driver beams 0.20

µm) R (435 0.15 10 ps OMEGA EP

0.10 Hollow Au cone Driver beam power (TW)

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X-ray Spherical spectrometer crystal 0.00 imager 0.0 0.5 1.0 1.5 2.0 2.5 Time (ns)

Figure 1 | Configuration of the target, experimental layout, and laser parameters. a, Schematics of the cone-in-shell target, laser beams and main diagnostics. b, OMEGA ultraviolet driver beam pulse shape. radiography, provided the first time-resolved characterization of A baseline Cu Kα emission was observed in the imploding the fuel assembly, validating simulations and demonstrating that shell on all shots; they were generated by suprathermal electrons substantial areal density (∼0.3 g cm−2) hydrocarbon plasmas can be (∼20 keV) from the OMEGA beams interacting with the ablating assembled at the cone tip10. The series of experiments and mod- shell surface. An additional signal due to fast electrons produced elling so far have provided a more complete evaluation of the FI by the OMEGA-EP laser was measured in integrated shots. The concept, but the primary figure of merit has remained neutron yield, recorded 2D Cu Kα images (see Supplementary Fig. 1) showed that which gives only global information of energy deposition and no emission due to suprathermal electrons originated from the in-flight detailed information about the fast electron characteristic or spa- shell, whereas the additional emission due to fast electrons was tial energy deposition, thus limiting guidance for further improve- emitted from a tight region within 150 µm surrounding the cone tip. ment. These limitations motivated the development of the methods The two emission regions had distinctly different geometries. and results reported in this article, where we directly visualized Several interesting features in the Cu Kα images were observed fast electron transport and spatial energy deposition, providing a when using the targets with the small (10 µm) tip cone. Figure 2a–c more direct way to calculate energy coupling into compressed FI shows the data from integrated shots at three different delays targets. Through optimization of the target design and implosion with the OMEGA-EP beam energy of 500 J (after subtraction of a process, we have demonstrated an improved energy coupling (up typical OMEGA-only shot datum and flat-field background). Fast- to 7%) from the short-pulse laser to the entire compressed plasma electron-induced Cu Kα emission was found to be peaked off the on OMEGA. outside of the cone wall and extended as far as ∼100 µm up from the The experiments described in this work used a cone-in-shell tip, indicating fast electrons were created, not at the cone tip, but in target (see Methods for target details) that consisted of a re-entrant an extended pre-formed plasma that filled the cone to a large offset hollow gold cone in a two-layer plastic shell composed of an outer distance. This is consistent with the pre-formed plasma density CH ablator layer and an inner CD ‘fuel’ layer doped with Cu at profile (see Supplementary Fig. 2) predicted by the 2D HYDRA ∼1 atomic percent. Figure 1 shows the experimental layout with (ref. 12) radiation-hydrodynamic simulation of the measured laser a sketch of the target. The Cu-dopant enables the characterization pre-pulse interacting with the inner Au cone wall. The critical of fast electron spatial energy deposition via 2D imaging of Cu Kα density surface of the simulated pre-plasma was found to move back radiation by a spherically bent, quartz crystal11, whereas the total ∼100 µm from the cone tip along the axis. photon number is measured by a calibrated X-ray spectrometer. Most importantly, the Cu Kα images provide unprecedented In our early set of experiments, modelled after the previous spatial information about where the fast electrons deposit their work by Theobald et al.9, cone-in-shell targets used a small tip energy in the compressed plasma. As shown in Fig. 2a–c, fast- (10 µm diameter) Au cone with ∼0.8 atmosphere air trapped inside electron-induced Cu Kα emission is from a large, diffused spot. The the shell. In the latest, optimized experiment, the target design brightness, characteristic shape and size change as a function of was modified: the targets were pre-evacuated to increase core the time delay between the OMEGA-EP and OMEGA beams. The density, and the gold cone tip diameter was increased to 40 µm size of the emission region and its decreasing radius with time are to reduce side-wall-generated pre-plasma, thereby enabling fast consistent with the simulated size and location of the imploding electron generation closer to the compressed core. The power of shell approaching stagnation from the 2D radiation-hydrodynamics the driver laser pulse picket (Fig. 1b) was also reduced to lower the code, DRACO (ref. 13). Figure 2d–f shows the fuel assembly profiles adiabat of the inner portion of the shell. In all cases, the cone-in- for the mass density and plasma temperature at the corresponding shell target was first imploded using 54 beams from the OMEGA-60 delay times from the DRACO simulation using the experimental ultraviolet laser with a total energy of 18 kJ (330 J/beam). The 10 ps driver and target parameters. At an early time, 3.65 ns, 100 ps OMEGA-EP infrared short-pulse beam (with energy varied from before the cone tip has been destroyed, the compressed shell is still 250 to 1,500 J and a peak intensity up to 4 × 1019 W cm−2) was imploding inwards with an areal density of 0.1 g cm−2 along the cone focused onto the inner cone tip at various time delays relative to the axis (angularly averaged mean areal density of ∼0.04 g cm−2) and OMEGA driver (see Methods). remains cold. The hot and relatively low-density plasma just outside

NATURE PHYSICS DOI: 10.1038/NPHYS3614 ARTICLES

3.65 ns 3.75 ns 3.85 ns a bc 1.0 m) m) m) 100 100 100 μ μ μ Cu K α

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−100 −100 −100 Transverse position ( Transverse position ( Transverse position ( 0.0 −100 0 100 −100 0 100 −100 0 100 Axial position (μm) Axial position (μm) Axial position (μm)

Figure 2 | Experimentally measured and simulated Cu Kα images. a–c, Measured Cu Kα emission attributable to fast electrons produced by the OMEGA-EP beam at three corresponding delays (3.65 ns, 3.75 ns and 3.85 ns, relative to the OMEGA driver beam) from the imploded cone-in-shell target with the small tip (10 µm) cone. Black lines indicate the approximate position of the cone. d–f, Contour plots of fuel mass density and electron temperature produced by the OMEGA ultraviolet driver beam from 2D radiation-hydrodynamic simulations at the same delay times. The density node immediately in front of the cone tip is composed of the hot compressed residual air, while the horseshoe shape in d–f is the shell before stagnation. g–i, Simulated Cu Kα images from the hybrid particle-in-cell transport simulations. The details of the simulations are described in the text as well as in Methods. the cone tip is composed of compressed air that was initially trapped Supplementary Information). Compared to the OMEGA-only shots, inside the shell. At the later time, 3.85 ns, 100 ps after the implosion- integrated shots showed increasing Cu Kα yield (energy deposited) driven shocks have broken through the cone tip, the imploded shell as a function of the OMEGA-EP laser energy, with an enhancement material is further compressed towards the cone tip and also heated of up to ∼70% at high (kJ) OMEGA-EP laser energies in our early to a temperature of several hundred eV, which could contribute set of experiments using the 10 µm tip cone targets. It is noted that to the reduced signals in the forward direction in Fig. 2c, as the with the small tip cones, OMEGA-EP contrast improvement did Cu Kα line emission shifts outside the imaging crystal bandwidth not lead to a noticeable increase in the fast-electron-induced Cu Kα with increased plasma temperature14,15. Once the cone tip is broken, yield measured by both the X-ray spectrometer and the 2D Cu Kα implosion-produced plasma fills the cone, resulting in an overall image data. This strongly suggests that the fast electron source reduction in the Cu Kα signal, as seen both in the observed image position in the small tip cone target remained far from the tip even (Fig. 2c) and the total yield measured by the calibrated X-ray with high-contrast laser pulses. This could be due to piling up of spectrometer (not shown here). This limiting factor makes the joint the pre-plasma as a result of the interaction of the OMEGA-EP shots at later delay futile even though the core density continues to laser (either by the pre-pulse and/or the rising edge of the main increase with peak areal density, reaching 0.3 g cm−2 at maximum pulse) with the cone wall tens of micrometres back from the compression at 4.05 ns (ref. 10). cone tip. A scan of Cu Kα yield versus OMEGA-EP laser energy (Fig. 3) The increasing trend of energy coupling with OMEGA-EP beam was also performed in integrated experiments with the short- energy was also found in the measured fusion neutron yield, where 6 6 pulse beam at a fixed delay (3.65 ± 0.1 ns), for example, before a factor of 2.4 ± 0.6 (from 2.4 × 10 to 5.8 × 10 Ny ) enhancement the cone-tip-breakout time. The yield was measured using a was observed when increasing the heating beam energy from 0 J calibrated X-ray spectrometer whose collection eﬃciency is not (OMEGA-only implosion) to full energy (1.2 kJ) (not shown here). dependent on the plasma temperature, which was then used The Cu Kα enhancement from the core region along with the to infer the total energy deposited by the fast electrons into neutron yield enhancement give two independent figures of merit the assembled fuel (discussed below with details described in for energy coupling to the high-density core.

ARTICLES NATURE PHYSICS DOI: 10.1038/NPHYS3614

the core being incapable of stopping fast electrons with a hard 1.5 energy spectrum. ) −1 2.0 Cu K The developed experimental platform and the benchmarked simulation tools led to a clear understanding of the underlying Fast electron induced 1.0 α yield (10 physics and limiting factors on energy coupling, which facilitated 1.5 photons sr a new target design to compare the eﬃcacy of diﬀerent schemes 11 and geometries with an aim to achieve higher energy coupling to 0.5 11 photons sr the core. This study shows that it is crucial to minimize pre-plasma 1.0 yield (10 within the cone (to shorten the source-to-core distance) and to α 0.0 delay the cone-tip-breakout time to assemble a denser core which

−1 will more eﬃciently stop energetic electrons owing to the linearly 0.5 LC, 10 μm, 0.8 atm ) μ increasing stopping power with core areal density16. Elimination of

Total Cu K HC, 10 m, 0.8 atm HC, 40 μm, vacuum the pre-plasma inside the cone, which can be accomplished using a Driver contribution 0.0 wider cone tip together with improved laser contrast, would spawn 0 500 1,000 1,500 fast electrons closer to the core and result in greater overlap with Heating beam energy (J) the core region, considering the electron beam’sinherent divergence. DRACO simulations of cone-in-shell target implosion using an opti- Figure 3 | Spectrally measured Cu Kα yield as a function of OMEGA-EP mized driver pulse (with a reduced picket power to lower the adiabat short-pulse energy. Data taken with fixed OMEGA-EP delay from the and improve shock timing) together with a vacuum shell attached temperature-insensitive X-ray spectrometer diagnostic. Total Kα yield to a large (40 µm) tip cone have predicted an improved fuel assem- shown on the left y-axis includes the ultraviolet driver beam contribution bly10,17. The cone-tip-breakout time was predicted to be delayed by (marked by the grey horizontal bar) and the fast electron contribution ∼140 ps and the areal density (along the cone axis, not angularly (shown on the right y-axis), all of which has been corrected for dopant averaged) at the time of cone-tip breakout was predicted to increase variation. Data shown in blue and green were obtained from the early set of to 0.36 g cm−2, as compared to 0.1 g cm−2 before the optimization. experiments with the 10 µm tip cone and 0.8 atm air trapped inside the Fast electrons with energy up to 1 MeV completely range out within shell for the LC (low contrast) and the HC (high contrast) OMEGA-EP laser such a high-density CD core16. The peak areal density at maximum pulse cases, respectively. Data shown in red were from the latest, optimized compression was predicted to increase to 0.6 g cm−2, twice that of experiment with the improved target design utilizing a 40 µm tip cone and the recently measured highest value before the optimization10. pre-evacuated shell. Error bars are 24%, which corresponds to the The latest integrated experiments have tested this improved tar- uncertainty in the absolute calibration of the spectrometer by comparison get and implosion design, and indeed have obtained a significant to a single-photon counting camera (dominant), the image-plate detector increase in the observed Cu Kα yield. As shown in Fig. 3 (red dots), uncertainty and the error in a weighted least squares regression analysis of the measured Cu Kα yield due to fast electrons produced by the the data, all added in quadrature. OMEGA-EP beam with an energy of 500 J in the optimized experiment is ∼6.7 × 1010 photons sr−1, a factor of four increase compared To assess how much OMEGA-EP heating beam energy was with the earlier set of experiments (1.5 × 1010 photons sr−1). With coupled to the imploded cone-in-shell FI targets from the measured the OMEGA-EP beam energy >1 kJ, the observed yield is tripled Cu Kα data, and to gain further insight into the causes of the (from 4 × 1010 to 12 × 1010 photons sr−1). Furthermore, a stop- observed emission profiles and yield values, an integrated multi- ping power analysis of the gold cone thickness showed that fast code modelling approach was undertaken to simulate each step electrons with kinetic energy near the peak Cu Kα cross-section of the process from implosion to energy deposition, as described would be completely stopped within the 10-µm-thick cone, resulting in Methods. As shown in Fig. 2g–i, the simulated Cu Kα image in a fast electron distribution entering the assembled fuel, with and the yield confirmed the experimental results, reproducing the a strong correlation between the energy deposited and the num- measured yield and the main observed features, such as the peaked ber of Cu Kα photons produced, with an energy deposition factor emission outside the cone wall at a large distance from the tip of 1.5×10−10 J/(photons sr−1) (see Supplementary Information for and the diminishing signal in the forward direction in the core details). Energy coupling from the OMEGA-EP laser to the core due to reduced collection efficiency of the imager and the large in the optimized experiment has been inferred to be ∼5–7%. This opacity as a result of the hot and dense fuel, particularly at later is the highest coupling efficiency ever reported in integrated FI time delay (3.85 ns). The temporal behaviour of the simulated experiments with an 18 kJ ultraviolet driver and 1 kJ short-pulse Cu Kα yield for each delay is consistent with the experimentally heating laser. observed yield trend, where the yield increases from 1.5 to Further improvements to the core energy coupling could be 1.7 × 1010 photons sr−1 for delays of 3.65 ns and 3.75 ns, then reduces achieved by increasing the core density, together with guiding fast to 1.2 × 1010 photons sr−1 at 3.85 ns, after cone-tip breakout. electron transport to create a parallel beam using either externally Matching simulations with experiments provided the essential applied axial magnetic fields18 or self-generated resistive magnetic information on the total energy of fast electrons (with a two- fields in an engineered target19,20, which would result in changes temperature distribution for the energy spectrum, with T1 and in the absolute Cu Kα emission and the emission profile, which T2 being 0.3 and 4.0 MeV, respectively, and an isotropic angular would be measurable with this platform. A detailed analysis using distribution) as well as the fraction of energy deposited into the the ZUMA transport code21,22 taking into account collisions and core. It was estimated that 25% of the laser energy was transferred scattering was performed in a 2D cylindrical geometry to evalu- to fast electrons, and only ∼4.8% of fast electron energy (that is, ate the dependence of fast electron energy coupling on the beam 1.2% of laser energy) was deposited into the imploded plasma, energy spectrum and the core areal density. It was then validated predominantly in regions above 1 g cm−3. This low-energy coupling by comparing the inferred energy deposition on OMEGA using was found to be limited by three combined factors: the large the measured Cu Kα yield with the simulated energy deposition distance from the fast electron source to the core due to pre- using similar areal density and laser conditions to the experiments. plasma filling the cone (see a simulated pre-plasma density profile These simulations, with details described in Methods, suggest that shown in Supplementary Fig. 2); the large angular divergence of the spectrum (hence, stopping range) of the fast electrons must the fast electron source; and the relatively low areal density of be compatible with the core areal density to maximize coupling,

NATURE PHYSICS DOI: 10.1038/NPHYS3614 ARTICLES

100 Received 24 March 2015; accepted 20 November 2015; published online 11 January 2016 40%

) References −2 30% 1. Moses, E. Ignition on the National Ignition Facility: a path towards inertial 20% fusion energy. Nucl. Fusion 49, 104022 (2009). 1% 10% 2. Hurricane, O. et al. Fuel gain exceeding unity in an inertially confined fusion implosion. Nature 506, 343–348 (2014). 10−1 3. Tabak, M. et al. Ignition and high gain with ultrapowerful lasers. Phys. Plasmas 1, 1626–1634 (1994). 5% 4. Betti, R. et al. Shock ignition of thermonuclear fuel with high areal density.

Core areal density (g cm density areal Core Phys. Rev. Lett. 98, 155001 (2007). 5. Atzeni, S. et al. Fast ignitor target studies for the HiPER project. Phys. Plasmas 15, 056311 (2008). OMEGA/EP OMEGA/EP optimized 1% 6. Kodama, R. et al. Fast heating of ultrahigh-density plasma as a step towards NIF/ARC predicted laser fusion ignition. Nature 412, 798–802 (2001). 10−2 10−1 100 101 7. Kodama, R. et al. Nuclear fusion: fast heating scalable to laser fusion ignition. Nature 418, 933–934 (2002). Fast electron temperature (MeV) 8. Arikawa, Y. et al. A experimental study on the energy coupling efficiency from the heating laser to core plasma in the fast ignition experiment. Bull. Am. Phys. Figure 4 | Dependence of fast electron energy-coupling eciency on core Soc. 58, BAPS.2013.DPP.YO5.1 (2013). areal density and electron beam temperature. Simulations used a parallel 9. Theobald, W. et al. Initial cone-in-shell fast-ignition experiments on OMEGA. beam with an exponential energy distribution. Inferred fast electron Phys. Plasmas 18, 056305 (2011). energy-coupling eciency to the imploded core for three cases: early 10. Theobald, W. et al. Time-resolved compression of a capsule with a cone to high experiments (red dotted) without optimization and the latest, optimized density for fast-ignition laser fusion. Nature Commun. 5, 5785 (2014). experiment (solid red) with the improved target and implosion design on 11. Stoeckl, C. et al. A spherical crystal imager for OMEGA EP. Rev. Sci. Instrum. OMEGA, and the predicted high coupling on NIF (dashed blue). The 83, 033107 (2012). 12. Marinak, M., Haan, S., Dittrich, T., Tipton, R. & Zimmerman, G. A comparison horizontal bars mark the corresponding range of the core areal density of three-dimensional multimode hydrodynamic instability growth on various (angularly averaged) in each case. National Ignition Facility capsule designs with HYDRA simulations. Phys. Plasmas 5, 1125–1132 (1998). as shown in Fig. 4. It shows that a source with slope temperature 13. Radha, P. et al. Multidimensional analysis of direct-drive, plastic-shell T ≤ 400 keV deposits almost no energy past the cone. Further, the implosions on OMEGA. Phys. Plasmas 12, 056307 (2005). very low angularly averaged areal density (∼0.04 g cm−2) in the 14. Akli, K. et al. Temperature sensitivity of Cu Kα imaging efficiency using a assembled core in our early experiments was incapable of stop- spherical Bragg reflecting crystal. Phys. Plasmas 14, 023102 (2007). ping MeV electrons, and the 10–15-µm-thick Au cone tip and 15. Pérez, F., Kemp, A., Divol, L., Chen, C. & Patel, P. Deflection of MeV electrons walls had similar areal density (0.02–0.03 g cm−2), resulting in <5% by self-generated magnetic fields in intense laser-solid interactions. Phys. Rev. Lett. 111, 245001 (2013). overall fast electron energy coupling to the core, ηfe-c. This core 16. Solodov, A. & Betti, R. 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With experimentally inferred laser-to-electron conversion efficien- 55, BAPS.2010.DPP.JP9.119 (2010). cies exceeding 30%, the total laser energy coupled to the core would 22. Jarrott, L. C. et al. Fast electron transport and spatial energy deposition be >15%, which is very encouraging for FI ICF. in Cu-doped fast ignition plasmas. Bull. Am. Phys. Soc. 59, Furthermore, it is worth noting that this platform and the BAPS.2014.DPP.CI1.4 (2014). technique have already been applied to further study FI energy 23. Park, H.-S. et al. High-adiabat high-foot inertial confinement fusion implosion coupling, exploring various methods to achieve high coupling, such experiments on the National Ignition Facility. Phys. Rev. Lett. 112, as magnetic guiding of fast electrons with engineered FI targets17 055001 (2014). 24. Crane, J. et al. Journal of Physics: Conference Series Vol. 244, 032003 (IOP and the use of laser-driven proton beams for FI (ref. 25), as well as Publishing, 2010). future experiments incorporating laser channelling for FI (ref. 26). 25. McGuffey, C. et al. 9th Int. Conf. Inertial Fusion Sci. Appl. Vol. 9, 181 (2015). This platform can also be extended to larger, NIF-scale facilities, 26. Ivancic, S. et al. Channeling of multikilojoule high-intensity laser beams in an where fast electron coupling can be diagnosed at ignition-scale areal inhomogeneous plasma. Phys. Rev. E 91, 051101 (2015). densities. Such a study can be explored using the multi-kJ high- intensity NIF-ARC laser at present being commissioned. This would Acknowledgements be a significant step forward for FI ICF. This material is based on work supported by the US Department of Energy National Nuclear Security Administration under the National Laser User Facility programme with Methods Award Number DE-NA0000854, DE-NA0002033, the OFES Fusion Science Center (FSC) grant No DE-FC02-04ER54789, the OFES ACE Fast Ignition grant No. Methods and any associated references are available in the online DE-FG02-95ER54839, and NNSA cooperative agreement DE-NA0001944. The support version of the paper. of the DOE does not constitute an endorsement by the DOE of the views expressed in

ARTICLES NATURE PHYSICS DOI: 10.1038/NPHYS3614 this article. J.J.S. participated in this work thanks to funding from the French National LSP PIC modelling, L.C.J. for the ZUMA modelling; targets were manufactured by Agency for Research (ANR) and the competitiveness cluster Alpha—Route des Lasers E.M.G., R.W.L. and R.B.S.; M.S.W., C.McGuffey and F.N.B. led the writing of the through project TERRE ANR-2011-BS04-014. The authors would like to acknowledge manuscript with significant contributions from A.A.S., L.C.J., W.T., H.S.M. and R.B.S.; excellent support provided by the Omega Laser Facility staff and the GA target figures were prepared by L.C.J., A.A.S. and M.S.W. fabrication group. The authors are thankful to S. Chawla for HYDRA simulations and C. Dorrer for the measured OMEGA-EP pre-pulse information. Additional information Supplementary information is available in the online version of the paper. Reprints and Author contributions permissions information is available online at www.nature.com/reprints. F.N.B. and M.S.W. designed and executed the experiment as principal investigators with Correspondence and requests for materials should be addressed to M.S.W. or F.N.B. help from L.C.J., C.McGuffey, W.T., A.A.S., R.B., J.D., M.H.K., F.J.M., H.S.M., P.K.P., J.J.S., H.S., T.Y. and R.B.S.; C.S., H.C., T.D., V.Y.G., H.H., T.I. and C.Mileham developed and operated diagnostics; data analysis was performed by L.C.J., C.McGuffey and W.T.; Competing financial interests simulations were performed by A.A.S. for the DRACO/LSP modelling, B.Q. for the The authors declare no competing financial interests.

NATURE PHYSICS DOI: 10.1038/NPHYS3614 ARTICLES

Methods Simulations. DRACO (ref. 13) is a radiation-hydrodynamic code used to simulate Target. The cone-in-shell targets were fabricated by General Atomics and were the cone-in-shell target implosion and fuel assembly. Here, a 2D cylindrical closely related to those used in ref. 9, for which the implosion has been geometry was used. The simulation capability was significantly enhanced, well-characterized and benchmarked10. They included a hollow gold cone including an improved radiation transport, an Eulerian scheme, nonlocal thermal with an inner full opening angle of 34◦ ± 1◦, a sidewall thickness of 10 or 15 µm, electron transport and cross-beam energy transfer. and a flat tip with 10 or 40 µm inner diameter and 15 µm thickness. The hollow The implicit particle-in-cell (PIC) code, LSP (ref. 27), was used with its laser gold cone was inserted into a laser-drilled hole in a 38-µm-thick plastic shell injection package to simulate the laser pre-plasma interaction inside the cone to with a 15 µm outer CH ablator layer and a 23 µm inner strong deuterated plastic provide the fast electron energy and angular distribution for the LSP transport (SCD) layer uniformly doped with Cu at ∼1 at.%. The shell outer diameter was modelling. The laser spatial profile was set to a double Gaussian fit as calculated 870 µm. The thickness of the CH ablator was chosen to prevent direct heating of from the measured wavefront on shot. The temporal profile was set to a sin2 shape the inner, doped CD layer by the OMEGA ultraviolet driver, as well as to avoid with full period 11.92 ps, which was equal to the FWHM of a Gaussian fit to the neutron generation from the hot coronal plasma, therefore assuring the measured estimated experimental pulse shape. The simulation was run for 15 ps with 60 time neutrons originated only from the compressed CD core. In earlier experiments steps per laser cycle and 16 cells per laser wavelength. LSP PIC simulations with the cone-in-shell targets using the small tip (10 µm diameter) Au cone, the included the pre-plasma profiles (density, temperature and ionization) due to the shell was not evacuated pre-shot. The trapped air inside the shell had 0.8 atm OMEGA-EP pre-pulse interacting with the Au cone from the 2D pressure. The improved targets used in the latest experiment had the Au cone with radiation-hydrodynamic code HYDRA (ref. 12) modelling, which was performed a large inner diameter (40 µm) with the same tip thickness, and the shells were in 2D cylindrical geometry using the experimentally measured pre-pulse. The pre-evacuated. The Cu-dopant level in the inner SCD shells ranged from 0.7 to HYDRA-simulated pre-plasma density profile showed that the critical density 1.3 at.% over the course of the three experimental campaigns owing to variation in surface (along the cone axis) before the arrival of the main short pulse was at target fabrication, although a precision of ±0.05 at.% was maintained within each ∼100 µm from the solid density cone tip (see Supplementary Information). The campaign. Differences in dopant level have been taken into account in the LSP PIC-simulated fast electron source showed a characteristic two-temperature yield calculations. distribution for the energy spectrum, with T1 and T2 being 0.3 and 4.0 MeV respectively, with an isotropic angular distribution. Detailed results of the LSP PIC Laser. The cone-in-shell target was imploded using 54 beams of the OMEGA-60 simulations were described in ref. 28 and will be the subject of a future publication. ultraviolet laser (with SG4 phase plates, without smoothing by spectral dispersion Hybrid PIC simulations using the LSP code were then performed to model fast (SSD)) with a total energy of 18 kJ (330 J/beam) using a shaped pulse designed to electron transport and energy deposition, with the PIC-simulated fast electron drive a low-adiabat implosion for the fuel assembly in the earlier experiments. In source being injected from the inside of the cone at a location of 100 µm before the the latest, optimized experiment with the improved target and implosion design, cone tip and using the DRACO-simulated fuel density and temperature profiles at the power in the shaped driver pulse picket was reduced by half, but the energy per the experimental time delays during the implosion as input. The inside of the Au beam was kept the same (330 J) as before and SSD was applied. In integrated cone was uniformly filled with Au pre-plasma at an electron density of experiments, the 10 ps OMEGA-EP short-pulse beam (with energy varied from 250 5 × 1022 cm−3. The simulated fast-electron-induced Cu Kα emission from the to 1,500 J) was timed and focused to the smallest spot achievable, which was imploded core was reconstructed taking into account the plasma r80 =15–20 µm (radius containing 80% of beam energy), with a pointing accuracy temperature-dependent Cu Kα emissivity and core plasma opacity calculated using of 15 µm relative to the cone axis by conducting a dedicated alignment shot then the PrismSpect code29, the crystal imager collection efficiency, and 3D projection monitoring on subsequent shots using a high-frame-rate alignment camera. along the imager diagnostic line of sight. With this, the reconstructed 2D Cu Kα Between shot days, the laser energy contrast on the OMEGA-EP laser was emission profile and the total Kα yield in the simulation could then be directly improved by two orders of magnitude (from ∼100 to ∼1 mJ in the 3 ns pedestal compared with experiment. The effect of electric and magnetic fields on fast pre-pulse). This improvement allowed for measurements of the dependence of the electron transport in our experiments and the resultant Cu Kα emission was found fast electron coupling efficiency and spatial distribution on laser contrast. The to be insignificant (see Supplementary Information). chosen time delays between the OMEGA-EP and the OMEGA driver was Hybrid transport modelling using the ZUMA code21 without fields, but determined by 2D DRACO radiation-hydrodynamic simulations of the implosion including collisions and scattering, were performed to examine the dependence of and the cone-tip breakout; the latter was verified to be accurate to within 50 ps in electron energy coupling on the electron spectrum and core areal density. ZUMA previous experiments10. modelling used a parallel fast electron beam with a Boltzmann energy distribution, with its slope temperature varied from 0.1 to 10 MeV. A 10-µm-thick carbon disk Diagnostics. A high-magnification (14.7) high-resolution (20 µm), narrow-band (20 µm radius) was used to represent the plasma core with a 10-µm-thick solid (6 eV) spherical Bragg crystal imager11 using a quartz crystal mirror was density Au disk (20 µm radius) at the front to mimic the cone tip. The density of the fielded to image Kα1 radiation (8.048 keV) from the Cu-dopant atoms. A carbon disk was varied to provide a core areal density from 0.01 to 6.4 g cm−2. Fuji image-plate dosimeter (super-resolution, SR type) was used as the detector to record the image. References A calibrated X-ray spectrometer using a cylindrically bent HOPG crystal in the 27. Welch, D., Rose, D., Cuneo, M., Campbell, R. & Mehlhorn, T. Integrated von Hamos geometry recorded the Cu K-shell and ionic line emission in the range simulation of the generation and transport of proton beams from laser-target 7.5–9.5 keV. The spectrometer was calibrated for Cu Kα line emission by interaction. Phys. Plasmas 13, 063105 (2006). comparing in situ measurements of the total signal seen on the spectrometer’s 28. Qiao, B. et al. Fast electron generation and transport from ten-picosecond image-plate film in units of photostimulated luminescence (PSL) with the total laser-plasma interactions in the cone-guided fast ignition. Bull. Am. Phys. Soc. number of photons detected by an absolutely calibrated single-photon counting 58, BAPS.2013.DPP.YO5.5 (2013). camera in separate laser experiments. 29. MacFarlane, J., Golovkin, I., Wang, P., Woodruff, P. & Pereyra, N. Spect3d—a The relative timing between OMEGA and OMEGA-EP in joint shots was multi-dimensional collisional-radiative code for generating diagnostic monitored in the laser chain and measured in situ via characteristic X-ray signatures based on hydrodynamics and pic simulation output. High Energy signatures on the neutron timing diagnostic. Density Phys. 3, 181–190 (2007).