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Statistical modeling of experimental and simulation databases has enabled the development of an accurate predictive capability for deuterium-tritium layered cryogenic implosions at the OMEGA laser [V. Gopalaswamy et al.,Nature 565, 581 (2019)10.1038/s41586-019-0877-0]. In this letter, a physics-based statistical mapping framework is described and used to uncover the dependencies of the fusion yield. This model is used to identify and quantify the degradation mechanisms of the fusion yield in direct-drive implosions on OMEGA. The yield is found to be reduced by the ratio of laser beam to target radius, the asymmetry in inferred ion temperatures from the ℓ=1 mode, the time span over which tritium fuel has decayed, and parameters related to the implosion hydrodynamic stability. When adjusted for tritium decay and ℓ=1 mode, the highest yield in OMEGA cryogenic implosions is predicted to exceed 2×10^{14} fusion reactions.

Hot electrons generated by laser-plasma instabilities degrade the performance of laser-fusion implosions by preheating the DT fuel and reducing core compression. The hot-electron energy deposition in the DT fuel has been directly measured for the first time by comparing the hard x-ray signals between DT-layered and mass-equivalent ablator-only implosions. The electron energy deposition profile in the fuel is inferred through dedicated experiments using Cu-doped payloads of varying thickness. The measured preheat energy accurately explains the areal-density degradation observed in many OMEGA implosions. This technique can be used to assess the viability of the direct-drive approach to laser fusion with respect to the scaling of hot-electron preheat with laser energy.

Collisionless shocks are ubiquitous in the Universe as a consequence of supersonic plasma flows sweeping through interstellar and intergalactic media. These shocks are the cause of many observed astrophysical phenomena, but details of shock structure and behavior remain controversial because of the lack of ways to study them experimentally. Laboratory experiments reported here, with astrophysically relevant plasma parameters, demonstrate for the first time the formation of a quasiperpendicular magnetized collisionless shock. In the upstream it is fringed by a filamented turbulent region, a rudiment for a secondary Weibel-driven shock. This turbulent structure is found responsible for electron acceleration to energies exceeding the average energy by two orders of magnitude.

Using highly resolved 3D radiation-hydrodynamic simulations, we identify a novel mechanism by which the deleterious impact of laser imprinting is mitigated in direct-drive inertial confinement fusion. Unsupported shocks and associated rarefaction flows, commonly produced with short laser bursts, are found to reduce imprint modulations prior to target acceleration. Optimization through the choice of laser pulse with picket(s) and target dimensions may improve the stability of lower-adiabat designs, thus providing the necessary margin for ignition-relevant implosions.

The self-similar nonlinear evolution of the multimode ablative Rayleigh-Taylor instability (ARTI) is studied numerically in both two and three dimensions. It is shown that the nonlinear multimode bubble-front penetration follows the ${\ensuremath{\alpha}}_{b}{A}_{T}({\ensuremath{\int}\sqrt{g}dt)}^{2}$ scaling law with ${\ensuremath{\alpha}}_{b}$ dependent on the initial conditions and ablation velocity. The value of ${\ensuremath{\alpha}}_{b}$ is determined by the bubble competition theory, indicating that mass ablation reduces ${\ensuremath{\alpha}}_{b}$ with respect to the classical value for the same initial perturbation amplitude. It is also shown that ablation-driven vorticity accelerates the bubble velocity and prevents the transition from the bubble competition to the bubble merger regime at large initial amplitudes leading to higher ${\ensuremath{\alpha}}_{b}$ than in the classical case. Because of the dependence of ${\ensuremath{\alpha}}_{b}$ on initial perturbation and vorticity generation, ablative stabilization of the nonlinear ARTI is not as effective as previously anticipated for large initial perturbations.

It is shown that inertial confinement fusion targets designed with low implosion velocities can be shock-ignited using laser-plasma interaction generated hot electrons (hot-$e$'s) to obtain high energy gains. These designs are robust to multimode asymmetries and are predicted to ignite even for significantly distorted implosions. Electron shock ignition requires tens of kilojoules of hot-$e$'s which can be produced only at a large laser facility like the National Ignition Facility, with the laser-to-hot-$e$ conversion efficiency greater than 10% at laser intensities $\ensuremath{\sim}{10}^{16}\text{ }\text{ }\mathrm{W}/{\mathrm{cm}}^{2}$.

Estimating the level of alpha heating and determining the onset of the burning plasma regime is essential to finding the path towards thermonuclear ignition. In a burning plasma, the alpha heating exceeds the external input energy to the plasma. Using a simple model of the implosion, it is shown that a general relation can be derived, connecting the burning plasma regime to the yield enhancement due to alpha heating and to experimentally measurable parameters such as the Lawson ignition parameter. A general alpha-heating curve is found, independent of the target and suitable to assess the performance of all laser fusion experiments whether direct or indirect drive. The onset of the burning plasma regime inside the hot spot of current implosions on the National Ignition Facility requires a fusion yield of about 50 kJ.

This Letter presents the first experimental demonstration of the capability to launch shocks of several-hundred Mbar in spherical targets--a milestone for shock ignition [R. Betti et al., Phys. Rev. Lett. 98, 155001 (2007)]. Using the temporal delay between the launching of the strong shock at the outer surface of the spherical target and the time when the shock converges at the center, the shock-launching pressure can be inferred using radiation-hydrodynamic simulations. Peak ablation pressures exceeding 300 Mbar are inferred at absorbed laser intensities of ∼3×10(15) W/cm2. The shock strength is shown to be significantly enhanced by the coupling of suprathermal electrons with a total converted energy of up to 8% of the incident laser energy. At the end of the laser pulse, the shock pressure is estimated to exceed ∼1 Gbar because of convergence effects.

A strong nonhydrodynamic mechanism generating atomic fuel-shell mix has been observed in strongly shocked inertial confinement fusion implosions of thin deuterated-plastic shells filled with 3He gas. These implosions were found to produce D3He-proton shock yields comparable to implosions of identical shells filled with a hydroequivalent 50∶50 D3He gas mixture. Standard hydrodynamic mixing cannot explain this observation, as hydrodynamic modeling including mix predicts a yield an order of magnitude lower than was observed. Instead, these results can be attributed to ion diffusive mix at the fuel-shell interface.

Monoenergetic-proton radiographs of laser-generated, high-Mach-number plasma jets colliding at various angles shed light on the structures and dynamics of these collisions. The observations compare favorably with results from 2D hydrodynamic simulations of multistream plasma jets, and also with results from an analytic treatment of electron flow and magnetic field advection. In collisions of two noncollinear jets, the observed flow structure is similar to the analytic model's prediction of a characteristic feature with a narrow structure pointing in one direction and a much thicker one pointing in the opposite direction. Spontaneous magnetic fields, largely azimuthal around the colliding jets and generated by the well-known ∇T(e)×∇n(e) Biermann battery effect near the periphery of the laser spots, are demonstrated to be "frozen in" the plasma (due to high magnetic Reynolds number Re(M)∼5×10(4)) and advected along the jet streamlines of the electron flow. These studies provide novel insight into the interactions and dynamics of colliding plasma jets.

The growth rates of the deceleration-phase Rayleigh-Taylor instability for imploding inertial confinement fusion capsules are calculated and compared with the results of numerical simulations. It is found that the unstable spectrum and the growth rates are significantly reduced by the finite ablation flow at the shell's inner surface. For typical direct-drive capsules designed for the National Ignition Facility, the unstable spectrum exhibits a cutoff for l approximately 90.

The perturbation transfer between the rear and front surface (feedout), secular distortion, and Rayleigh-Taylor (R-T) instability growth is studied for long wavelength modes in accelerated flat foils. A simple formula is derived, relating the R-T growth factor to the amplitude of the rear surface perturbation. Comparisons with two-dimensional simulations confirm the validity of the theory. {copyright} {ital 1998} {ital The American Physical Society }

The magnetic fields generated at the surface of a laser-irradiated planar solid target are mapped using ultrafast proton radiography. Thick ($50\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$) plastic foils are irradiated with 4-kJ, 2.5-ns laser pulses focused to an intensity of $4\ifmmode\times\else\texttimes\fi{}{10}^{14}\text{ }\text{ }\mathrm{W}/{\mathrm{cm}}^{2}$. The data show magnetic fields concentrated at the edge of the laser-focal region, well within the expanding coronal plasma. The magnetic-field spatial distribution is tracked and shows good agreement with 2D resistive magnetohydrodynamic simulations using the code draco when the Biermann battery source, fluid and Nernst advection, resistive magnetic diffusion, and Righi-Leduc heat flow are included.

The first experimental demonstration of Rayleigh-Taylor-induced magnetic fields due to the Biermann battery effect has been made. Experiments with laser-irradiated plastic foils were performed to investigate these illusive fields using a monoenergetic proton radiography system. Path-integrated $B$ field strength measurements were inferred from radiographs and found to increase from 10 to $100\text{ }\text{ }\mathrm{T}\text{ }\ensuremath{\mu}\mathrm{m}$ during the linear growth phase for $120\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ perturbations. Proton fluence modulations were corrected for Coulomb scattering using measured areal density profiles from x-ray radiographs.

This Letter reports the first time-gated proton radiography of the spatial structure and temporal evolution of how the fill gas compresses the wall blowoff, inhibits plasma jet formation, and impedes plasma stagnation in the hohlraum interior. The potential roles of spontaneously generated electric and magnetic fields in the hohlraum dynamics and capsule implosion are discussed. It is shown that interpenetration of the two materials could result from the classical Rayleigh-Taylor instability occurring as the lighter, decelerating ionized fill gas pushes against the heavier, expanding gold wall blowoff. This experiment showed new observations of the effects of the fill gas on x-ray driven implosions, and an improved understanding of these results could impact the ongoing ignition experiments at the National Ignition Facility.

Enhancement of the ion temperature and fusion yield has been observed in magnetized laser-driven inertial confinement fusion implosions on the OMEGA Laser Facility. A spherical CH target with a 10 atm ${\mathrm{D}}_{2}$ gas fill was imploded in a polar-drive configuration. A magnetic field of 80 kG was embedded in the target and was subsequently trapped and compressed by the imploding conductive plasma. As a result of the hot-spot magnetization, the electron radial heat losses were suppressed and the observed ion temperature and neutron yield were enhanced by 15% and 30%, respectively.

The linear stability analysis of unsteady ablation fronts, is carried out for a semi-infinite uniform medium. For a laser accelerated target, it is shown that a properly selected modulation of the laser intensity can lead to the dynamic stabilization or growth-rate reduction of a large portion of the unstable spectrum. The theory is in qualitative agreement with the numerical results obtained by using the two-dimensional hydrodynamic code ORCHID.

A multidimensional measurable criterion for central ignition of inertial-confinement-fusion capsules is derived. The criterion accounts for the effects of implosion nonuniformities and depends on three measurable parameters: the neutron-averaged total areal density ($\ensuremath{\rho}{R}_{n}^{\mathrm{tot}}$), the ion temperature (${T}_{n}$), and the yield over clean ($\mathrm{YOC}=\mathrm{\text{ratio}}$ of the measured neutron yield to the predicted one-dimensional yield). The YOC measures the implosion uniformity. The criterion can be approximated by $\ensuremath{\chi}=(\ensuremath{\rho}{R}_{n}^{\mathrm{tot}}{)}^{0.8}({T}_{n}/4.7{)}^{1.7}{\mathrm{YOC}}^{\ensuremath{\mu}}g1$ (where $\ensuremath{\rho}R$ is in $\mathrm{g}\text{ }{\mathrm{cm}}^{\ensuremath{-}2}$, $T$ in keV, and $\ensuremath{\mu}\ensuremath{\approx}0.4--0.5$) and can be used to assess the performance of cryogenic implosions on the NIF and OMEGA. Cryogenic implosions on OMEGA have achieved $\ensuremath{\chi}\ensuremath{\sim}0.02--0.03$.

Experimental observation of resistive wall mode (RWM) instability in the National Spherical Torus Experiment (NSTX) at plasma rotation levels intermediate to the ion precession drift and ion bounce frequencies suggests that low critical rotation threshold models are insufficient. Kinetic modifications to the ideal stability criterion yield a more complex relationship between plasma rotation and RWM stability. Good agreement is found between an experimental RWM instability at intermediate plasma rotation and the RWM marginal point calculated with kinetic effects included, by the MISK code. By self-similarly scaling the experimental plasma rotation profile and the collisionality in the calculation, resonances of the mode with the precession drift and bounce frequencies are explored. Experimentally, RWMs go unstable when the plasma rotation is between the stabilizing precession drift and bounce resonances.

Unique detection of electromagnetic fields and identification of field type and strength as a function of position were used to determine the nature of self-generated fields in a novel experiment with laser-generated plasma bubbles on two sides of a plastic foil. Field-induced deflections of monoenergetic 15-MeV probe protons passing through the two bubbles, measured quantitatively with proton radiography, were combined with Lorentz mapping to provide separate measurements of magnetic and electric fields. The result was absolute identification and measurement of a toroidal magnetic field around each bubble and determination that any electric field component parallel to the foil was below measurement uncertainties.

Thin-foil targets were irradiated with high-power ($1\ensuremath{\le}{P}_{L}\ensuremath{\le}210\text{ }\text{ }\mathrm{TW}$), 10-ps pulses focused to intensities of $Ig{10}^{18}\text{ }\text{ }\mathrm{W}/{\mathrm{cm}}^{2}$ and studied with $K$-photon spectroscopy. Comparing the energy emitted in $K$ photons to target-heating calculations shows a laser-energy-coupling efficiency to hot electrons of ${\ensuremath{\eta}}_{L\mathrm{\text{\ensuremath{-}}}e}=20\ifmmode\pm\else\textpm\fi{}10%$. Time-resolved x-ray emission measurements suggest that laser energy is coupled to hot electrons over the entire duration of the incident laser drive. Comparison of the $K$-photon emission data to previous data at similar laser intensities shows that ${\ensuremath{\eta}}_{L\mathrm{\text{\ensuremath{-}}}e}$ is independent of laser-pulse duration from $1\ensuremath{\le}{\ensuremath{\tau}}_{p}\ensuremath{\le}10\text{ }\text{ }\mathrm{ps}$.

High-resolution coherent transition radiation (CTR) imaging diagnoses electrons accelerated in laser---solid interactions with intensities of $\ensuremath{\sim}{10}^{19}\text{ }\text{ }\mathrm{W}/{\mathrm{cm}}^{2}$. The CTR images indicate electron-beam filamentation and annular propagation. The beam temperature and half-angle divergence are inferred to be $\ensuremath{\sim}1.4\text{ }\text{ }\mathrm{MeV}$ and $\ensuremath{\sim}16\ifmmode^\circ\else\textdegree\fi{}$, respectively. Three-dimensional hybrid-particle-in-cell code simulations reproduce the details of the CTR images assuming an initial half-angle divergence of $\ensuremath{\sim}56\ifmmode^\circ\else\textdegree\fi{}$. Self-generated resistive magnetic fields are responsible for the difference between the initial and measured divergence.

The demonstration of magnetic field compression to many tens of megagauss in cylindrical implosions of inertial confinement fusion targets is reported for the first time. The OMEGA laser [T. R. Boehly, Opt. Commun. 133, 495 (1997)10.1016/S0030-4018(96)00325-2] was used to implode cylindrical CH targets filled with deuterium gas and seeded with a strong external field (50 kG) from a specially developed magnetic pulse generator. This seed field was trapped (frozen) in the shock-heated gas fill and compressed by the imploding shell at a high implosion velocity, minimizing the effect of resistive flux diffusion. The magnetic fields in the compressed core were probed via proton deflectrometry using the fusion products from an imploding D3He target. Line-averaged magnetic fields between 30 and 40 MG were observed.

We report on the first proton radiography of laser-irradiated hohlraums. This experiment, with vacuum gold (Au) hohlraums, resulted in observations of self-generated magnetic fields with peak values approximately 10;{6} G. Time-gated radiographs of monoenergetic protons with discrete energies (15.0 and 3.3 MeV) reveal dynamic pictures of field structures and plasma flow. Near the end of the 1-ns laser drive, a stagnating Au plasma (approximately 10 mg cm;{-3}) forms at the center of the hohlraum. This is a consequence of supersonic, radially directed Au jets (approximately 1000 microm ns;{-1}, approximately Mach 4) that arise from the interaction of laser-driven plasma bubbles expanding into one another.

Time-gated, monoenergetic radiography with 15-MeV protons provides unique measurements of implosion dynamics in direct-drive inertial-confinement fusion. Images obtained during acceleration, coasting, deceleration, and stagnation display a comprehensive picture of spherical implosions. Critical information inferred from such images, hitherto unavailable, characterizes the spatial structure and temporal evolution of self-generated fields and plasma areal density. Results include the first observation of a radial electric field inside the imploding capsule. It is initially directed inward (at $\ensuremath{\sim}{10}^{9}\text{ }\text{ }\mathrm{V}/\mathrm{m}$), eventually reverses direction ($\ensuremath{\sim}{10}^{8}\text{ }\text{ }\mathrm{V}/\mathrm{m}$), and is the probable consequence of the evolution of the electron pressure gradient.

The compression of direct-drive, spherical implosions is studied using cryogenic ${\mathrm{D}}_{2}$ targets on the 60-beam, 351-nm OMEGA laser with intensities ranging from $\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{14}$ to $\ensuremath{\sim}1\ifmmode\times\else\texttimes\fi{}{10}^{15}\text{ }\text{ }\mathrm{W}/{\mathrm{cm}}^{2}$. The hard-x-ray signal from hot electrons generated by laser-plasma instabilities increases with laser intensity, while the areal density decreases. Mitigating hot-electron production, by reducing the laser intensity to $\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{14}\text{ }\text{ }\mathrm{W}/{\mathrm{cm}}^{2}$, results in areal density of the order of $\ensuremath{\sim}140\text{ }\text{ }\mathrm{mg}/{\mathrm{cm}}^{2}$, in good agreement with 1D simulations. These results will be considered in future direct-drive-ignition designs.

The first observation of ignition-relevant areal-density deuterium from implosions of capsules with cryogenic fuel layers at ignition-relevant adiabats is reported. The experiments were performed on the 60-beam, $30\mathrm{\text{\ensuremath{-}}}{\mathrm{kJ}}_{\mathrm{UV}}$ OMEGA Laser System [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)]. Neutron-averaged areal densities of $202\ifmmode\pm\else\textpm\fi{}7\text{ }\text{ }\mathrm{mg}/{\mathrm{cm}}^{2}$ and $182\ifmmode\pm\else\textpm\fi{}7\text{ }\text{ }\mathrm{mg}/{\mathrm{cm}}^{2}$ (corresponding to estimated peak fuel densities in excess of $100\text{ }\text{ }\mathrm{g}/{\mathrm{cm}}^{3}$) were inferred using an 18-kJ direct-drive pulse designed to put the converging fuel on an adiabat of 2.5. These areal densities are in good agreement with the predictions of hydrodynamic simulations indicating that the fuel adiabat can be accurately controlled under ignition-relevant conditions.

A novel method by C. Zhou and R. Betti [Bull. Am. Phys. Soc. 50, 140 (2005)] to assemble and ignite thermonuclear fuel is presented. Massive cryogenic shells are first imploded by direct laser light with a low implosion velocity and on a low adiabat leading to fuel assemblies with large areal densities. The assembled fuel is ignited from a central hot spot heated by the collision of a spherically convergent ignitor shock and the return shock. The resulting fuel assembly features a hot-spot pressure greater than the surrounding dense fuel pressure. Such a nonisobaric assembly requires a lower energy threshold for ignition than the conventional isobaric one. The ignitor shock can be launched by a spike in the laser power or by particle beams. The thermonuclear gain can be significantly larger than in conventional isobaric ignition for equal driver energy.

The highly nonlinear evolution of the single-mode Rayleigh-Taylor instability (RTI) at the ablation front of an accelerated target is investigated in the parameter range typical of inertial confinement fusion implosions. A new phase of the nonlinear bubble evolution is discovered. After the linear growth phase and a short constant-velocity phase, it is found that the bubble is accelerated to velocities well above the classical value. This acceleration is driven by the vorticity accumulation inside the bubble resulting from the mass ablation and vorticity convection off the ablation front. While the ablative growth rates are slower than their classical values in the linear regime, the ablative RTI grows faster than the classical RTI in the nonlinear regime for deuterium and tritium ablators.

Thick, 40 {mu}m plastic shells filled with 25-35 atm of D{sub 2} or D{sup 3}He were imploded on a low-adiabat ({alpha}{approx_equal}1.3) and with a low-implosion velocity ({approx}2x10{sup 7} cm/s) on the OMEGA laser to generate massive cores of compressed plasma with high areal densities optimal for fast ignition. The targets are driven by 20-kJ relaxation adiabat-shaping laser pulses to keep the inner portion of the shell nearly Fermi degenerate. The measured kinetic energy downshift of proton spectra is in good agreement with the theoretical predictions yielding burn-averaged areal densities of 0.130{+-}0.017 g/cm{sup 2} and peak {rho}R during the burn of about 0.24{+-}0.018 g/cm{sup 2}, the largest {rho}R measured on OMEGA to date. The same implosions with empty plastic shells are expected to reach 1.3 g/cm{sup 2} across the core (i.e., 2{rho}R) enough to stop fast electrons with energies up to 4.5 MeV typical of fast ignition scenarios.

The Rayleigh-Taylor unstable growth of laser-seeded, 3D broadband perturbations was experimentally measured in the laser-accelerated, planar plastic foils. The first experimental observation showing the self-similar behavior of the bubble size and amplitude distributions under ablative conditions is presented. In the nonlinear regime, the modulation sigma(rms) grows as alpha(sigma)gt(2), where g is the foil acceleration, t is the time, and alpha(sigma) is constant. The number of bubbles evolves as N(t) alpha(omegat sq.rt(9) + C)(-4) and the average size evolves aslambda(t) alpha omega(2)gt(2), where C is a constant and omega = 0.83 +/- 0.1 is the measured scaled bubble-merging rate.

The stability analysis of the n = 1 resistive wall mode is carried out for a simplified model of collisionless tokamak plasma. It is found that the trapped particle compressibility and the resonance between the mode and the precession drift frequency lead to a significant improvement of the beta stability limits. It is shown that, within the frame of the simplified model, the resistive wall mode can be fully suppressed and the plasma can be stable up to the wall beta limits for a slow plasma rotation.

The stability analysis of external magnetohydrodynamic modes is carried out for a cylindrical plasma in the presence of a resistive wall, plasma flow, and coupling to the sound wave continuous spectrum. It is confirmed that the resonance of the mode with the sound continuum produces an effective dissipation. The combined effects of dissipation and plasma flow open up a window of stability to the external kinks. This theory can explain the numerical results of A. Bondeson and D. J. Ward [Phys. Rev. Lett. {bold 72}, 2709 (1994)].

A stability analysis is carried out for the m=1 internal kink mode, in the presence of energetic circulating particles. It is found that, including the effect of finite radial particle-orbit excursion, the m=1 internal kink mode is strongly destabilized by the resonance interaction with the energetic passing particles. Such an instability could explain the experimental observations of the ``fishbone'' oscillations during tangential neutral beam injection [W. W. Heidbrink et al., Phys. Rev. Lett. 57, 835 (1986)].