Fusion Target Design Research Articles

Quantum computation of stopping power for inertial fusion target design

Stopping power is the rate at which a material absorbs the kinetic energy of a charged particle passing through it-one of many properties needed over a wide range of thermodynamic conditions in modeling inertial fusion implosions. First-principles stopping calculations are classically challenging because they involve the dynamics of large electronic systems far from equilibrium, with accuracies that are particularly difficult to constrain and assess in the warm-dense conditions preceding ignition. Here, we describe a protocol for using a fault-tolerant quantum computer to calculate stopping power from a first-quantized representation of the electrons and projectile. Our approach builds upon the electronic structure block encodings of Su et al. [PRX Quant. 2, 040332 (2021)], adapting and optimizing those algorithms to estimate observables of interest from the non-Born-Oppenheimer dynamics of multiple particle species at finite temperature. We also work out the constant factors associated with an implementation of a high-order Trotter approach to simulating a grid representation of these systems. Ultimately, we report logical qubit requirements and leading-order Toffoli costs for computing the stopping power of various projectile/target combinations relevant to interpreting and designing inertial fusion experiments. We estimate that scientifically interesting and classically intractable stopping power calculations can be quantum simulated with roughly the same number of logical qubits and about one hundred times more Toffoli gates than is required for state-of-the-art quantum simulations of industrially relevant molecules such as FeMoco or P450.

Laser-direct-drive fusion target design with a high-Z gradient-density pusher shell.

Laser-direct-drive fusion target designs with solid deuterium-tritium (DT) fuel, a high-Z gradient-density pusher shell (GDPS), and a Au-coated foam layer have been investigated through both 1D and 2D radiation-hydrodynamic simulations. Compared with conventional low-Z ablators and DT-push-on-DT targets, these GDPS targets possess certain advantages of being instability-resistant implosions that can be high adiabat (α≥8) and low hot-spot and pusher-shell convergence (CR_{hs}≈22 and CR_{PS}≈17), and have a low implosion velocity (v_{imp}<3×10^{7}cm/s). Using symmetric drive with laser energies of 1.9 to 2.5MJ, 1D lilac simulations of these GDPS implosions can result in neutron yields corresponding to ≳50-MJ energy, even with reduced laser absorption due to the cross-beam energy transfer (CBET) effect. Two-dimensional draco simulations show that these GDPS targets can still ignite and deliver neutron yields from 4 to ∼10MJ even if CBET is present, while traditional DT-push-on-DT targets normally fail due to the CBET-induced reduction of ablation pressure. If CBET is mitigated, these GDPS targets are expected to produce neutron yields of >20MJ at a driven laser energy of ∼2MJ. The key factors behind the robust ignition and moderate energy gain of such GDPS implosions are as follows: (1) The high initial density of the high-Z pusher shell can be placed at a very high adiabat while the DT fuel is maintained at a relatively low-entropy state; therefore, such implosions can still provide enough compression ρR>1g/cm^{2} for sufficient confinement; (2) the high-Z layer significantly reduces heat-conduction loss from the hot spot since thermal conductivity scales as ∼1/Z; and (3) possible radiation trapping may offer an additional advantage for reducing energy loss from such high-Z targets.

Correcting Hohlraum Drive Asymmetry with Glow Discharge Polymerization Coated Capsule Shims

In inertial confinement fusion target design, the shape discrepancy between the cylindrical hohlraum and the spherical capsule creates a low mode asymmetry in the implosion. One way to correct such asymmetry is to shim the target capsule surface with extra mass in specific locations following a three-dimensional P4 Legendre mode. Previously, the desired surface pattern was precision machined out of the capsule. The resulting 2DConA experiments that investigated the implosion’s shape demonstrated the shimming method’s success. However, machining leaves large defects on the capsule surface that will degrade neutron yield in a DT implosion. An alternative shimming approach is to grow the pattern on the capsule surface using a glow discharge polymerization coating process in a stencil lithography application. In this paper, we discuss the fabrication, characterization, and challenges of making shimmed target capsules with this new method.

Equation of state of tungsten-doped carbon based on QEOS model for laser fusion

Tungsten-doped diamond is employed as a promising ablator material in high-gain laser fusion target design. Unlike for pure carbon, reports on the equation of state (EOS) of tungsten-doped carbon are limited, particularly in the high-pressure range over Mbar, which is relevant to laser fusion. To complement the radiation-hydrodynamic simulations of laser fusion, we developed the EOS of tungsten-doped carbon by combining the quotidian EOS model and large-scale atomistic simulations, which provide fundamental material parameters. In this manner, the EOS of doped carbon can be efficiently constructed. The influence of tungsten doping on the diamond material parameters and EOS was observed. The application of the developed EOS was shown via typical radiation-hydrodynamic simulations of laser fusion.

Surface structure on diamond foils generated by spatially nonuniform laser irradiation

Here we report on the effects of material strength factors on the generation of surface structure due to nonuniform laser irradiation. The influence of material strength on the generation of perturbation on a diamond surface subjected to nonuniform laser irradiation was experimentally investigated. Our previous investigations suggested that stiffer and denser materials reduce surface perturbation due to spatially nonuniform laser irradiation, which was reproduced well by calculations with multi-dimensional hydrodynamic simulation code. In this work, we found that local fractures due to yield strength failure are generated by high degrees of irradiation non-uniformity. A characteristic crack-like surface structure was observed, which was not reproduced by the 2D simulation code calculations at all. The 2D simulations showed that the pressure at the diamond surface locally exceeds the Hugoniot elastic limit due to nonuniform irradiation, implying the potential for development of surface perturbations. We also measured the areal-density distribution of perturbations for single-crystal diamond and diamond with a thin high atomic number (high-Z) coating on its surface. The experimental results imply that the combination of a stiff material and thin high-Z coating can suppress the solid-strength effects caused by large irradiation non-uniformity. The knowledge given here is applicable to inertial confinement fusion target design, laser material processing, and universal problems involving solids and high-energy-density plasmas.

First-principles equation-of-state table of beryllium based on density-functional theory calculations.

Beryllium has been considered a superior ablator material for inertial confinement fusion (ICF) target designs. An accurate equation-of-state (EOS) of beryllium under extreme conditions is essential for reliable ICF designs. Based on density-functional theory (DFT) calculations, we have established a wide-range beryllium EOS table of density ρ = 0.001 to 500 g/cm3 and temperature T = 2000 to 108 K. Our first-principle equation-of-state (FPEOS) table is in better agreement with the widely used SESAME EOS table (SESAME 2023) than the average-atom INFERNO and Purgatorio models. For the principal Hugoniot, our FPEOS prediction shows ∼10% stiffer than the last two models in the maximum compression. Although the existing experimental data (only up to 17 Mbar) cannot distinguish these EOS models, we anticipate that high-pressure experiments at the maximum compression region should differentiate our FPEOS from INFERNO and Purgatorio models. Comparisons between FPEOS and SESAME EOS for off-Hugoniot conditions show that the differences in the pressure and internal energy are within ∼20%. By implementing the FPEOS table into the 1-D radiation-hydrodynamic code LILAC, we studied the EOS effects on beryllium-shell-target implosions. The FPEOS simulation predicts higher neutron yield (∼15%) compared to the simulation using the SESAME 2023 EOS table.

Conceptual research on Z-pinch driven fusion-fission hybrid reactor

The Z-pinch driven fusion-fission hybrid reactor (Z-FFR) concept, proposed by CAEP, utilizes high-energy neutrons produced by Z-pinch driven inertial confinement fusion (ICF) to drive the sub-critical fission reactor for energy release. The Z-FFR innovative concepts such as local-holistic-ignition fusion target and advanced sub-critical power reactor, and it has advantages in security, economy and environment, and might promisingly be a millennial energy source which could effectively solve the climate problem and deal with the energy crisis. This paper introduces the current status of the conceptual research on Z-FFR in CAEP. The principle, structure and operation characteristics of the energy system are expounded in three aspects, the fusion-target design, the low-repetitive Z-pinch driver and the sub-critical fission reactor. The costs of the system are estimated, and the future developmental roadmap is put forward.

Mitigation of two-plasmon decay in direct-drive inertial confinement fusion through the manipulation of ion-acoustic and Langmuir wave damping

The extended Zakharov model of the two-plasmon decay instability in an inhomogeneous plasma [D. F. DuBois et al., Phys. Rev. Lett. 74, 3983 (1995); D. A. Russell and D. F. DuBois, Phys. Rev. Lett. 86, 428 (2001)] is further generalized to include the evolution of the electron distribution function in the quasi-linear approximation [cf., e.g., K. Y. Sanbonmatsu et al. Phys. Plasmas 7, 2824 (2000); D. A. Russell et al., paper presented at the Workshop on SRS/SBS Saturation, Wente Vineyards, Livermore, CA, 2–5 April 2002]. This makes it possible to investigate anomalous absorption of laser light and hot electron production due to the two-plasmon decay instability of multiple overlapping electromagnetic waves. Scalings of hot-electron production in the (stationary) nonlinearly saturated regime relevant to recent experiments [B. Yaakobi et al., Phys. Plasmas 19, 012704 (2012); D. H. Froula et al., Phys. Rev. Lett. 108, 165003 (2012)] have been obtained. They indicate a sensitivity to ion-acoustic wave (IAW) damping and to the collisional absorption of Langmuir waves. Such a sensitivity might be exploited in inertial confinement fusion target design by the use of mid-Z ablators.

Multiple spherically converging shock waves in liquid deuterium

To achieve ignition, inertial confinement fusion target designs use a sequence of shocks to compress the target before it implodes. To minimize the entropy acquired by the fuel, the strength and timing of these shocks will be precisely set during a series of tuning experiments that adjust the laser pulse to achieve optimal conditions. We report measurements of the velocity and timing of multiple, converging shock waves inside spherical targets filled with liquid (cryogenic) deuterium. These experiments produced the highest reported shock velocity observed in liquid deuterium (Us = 135 km/s at ∼25 Mb) and observed an increase in shock velocity due to spherical convergence. These direct-drive experiments are best simulated when hydrodynamic codes use a nonlocal model for the transport of absorbed laser energy from the coronal plasma to the ablation surface.

LIFE Pure Fusion Target Designs: Status and Prospects

Analysis and radiation-hydrodynamics simulations for expected high-gain fusion target performance on a demonstration 1-GWe Laser Inertial Fusion Energy (LIFE) power plant are presented. The required laser energy driver is 2.2 MJ at a 0.351-μm wavelength, and a fusion target gain greater than 60 at a repetition rate of 16 Hz is the design goal for economic and commercial attractiveness. A scaling-law analysis is developed to benchmark the design parameter space for hohlraum-driven central hot-spot ignition. A suite of integrated hohlraum simulations is presented to test the modeling assumptions and provide a basis for near-term experimental resolution of the key physics uncertainties on the National Ignition Facility.

Single crystal growth and formation of defects in deuterium-tritium layers for inertial confinement nuclear fusion

We identify vapor-etched grain boundary grooves on the solid-vapor interface as the main source of surface roughness in the deuterium-tritium (D–T) fuel layers, which are solidified and then cooled. Current inertial confinement fusion target designs impose stringent limits to the cross-sectional area and total volume of these grooves. Formation of these grain boundaries occurs over time scales of hours as the dislocation network anneals and is inevitable in a plastically deformed material. Therefore, either cooling on a much shorter time scale or a technique that requires no cooling after solidification should be used to minimize the roughness.

Increased efficiency of short-pulse laser-generated proton beams from novel flat-top cone targets

Ion-driven fast ignition (IFI) may have significant advantages over electron-driven FI due to the potentially large reduction in the amount of energy required for the ignition beam and the laser driver. Recent experiments at the Los Alamos National Laboratory’s Trident facility employing novel Au flat-top cone targets have produced a fourfold increase in laser-energy to ion-energy efficiency, a 13-fold increase in the number of ions above 10MeV, and a few times increase in the maximum ion energy compared to Au flat-foil targets. Compared to recently published scaling laws, these gains are even greater. If the efficiency scales with intensity in accordance to flat-foil scaling, then, with little modification, these targets can be used to generate the pulse of ions needed to ignite thermonuclear fusion in the fast ignitor scheme. A proton energy of at least 30MeV was measured from the flat-top cone targets, and particle-in-cell (PIC) simulations show that the maximum cutoff energy may be as high as 40–45MeV at modest intensity of 1×1019W∕cm2 with 20J in 600fs. Simulations indicate that the observed energy and efficiency increase can be attributed to the cone target’s ability to guide laser light into the neck to produce hot electrons and transport these electrons to the flat-top of the cone where they can be heated to much higher temperatures, creating a hotter, denser sheath. The PIC simulations also elucidate the critical parameters for obtaining superior proton acceleration such as the dependence on laser contrast/plasma prefill, as well as longitudinal and transverse laser pointing, and cone geometry. These novel cones have the potential to revolutionize inertial confinement fusion target design and fabrication via their ability to be mass produced. In addition, they could have an impact on the general physics community studying basic electron and radiation transport phenomena or as better sources of particle beams to study equations of state and warm dense matter, or for hadron therapy, as new radioisotope generators, or for compact proton radiography sources.

Revisiting Nonlocal Electron-Energy Transport in Inertial-Fusion Conditions

Correct modeling of the electron-energy transport is essential for inertial confinement fusion target design. Various transport models have been proposed in order to extend the validity of a hydrodynamical description into weakly collisional regimes, taking into account the nonlocality of the electron transport combined with the effects of self-generated magnetic fields. We have carried out new experiments designed to be highly sensitive to the modeling of the heat flow on the Ligne d'Intégration Laser facility, the prototype of the Laser Megajoule. We show that two-dimensional hydrodynamic simulations correctly reproduce the experimental results only if they include both the nonlocal transport and magnetic fields.

Measurements of low-level prepulse on Nike KrF laser

The krypton fluoride (KrF) laser is a leading candidate driver for inertial fusion energy. Some of the current fusion target designs call for targets with thin metallic coatings. These targets could be particularly susceptible to preheat by a low-level laser prepulse. Knowledge of the prepulse can be important in understanding and modeling the behavior of such targets. This paper presents measurements of low-level prepulse on target with the Nike KrF laser. Sources of prepulse are discussed and measurements are performed under several specific laser conditions in order to evaluate the relative contribution of these sources to the overall prepulse. Prepulse is found to be ∼2×10−7 from peak intensity for approximately 120ns prior to the main laser pulse. Prepulse energy density on target is ∼2J∕cm2. The first laser amplifier in the time- and angle-multiplexed section of the laser is found to be the dominant source of prepulse.

Thick-Liquid Blanket Configuration and Response for the HIF Point Design

This paper describes the thick-liquid blanket system of the Robust Point Design (RPD-2002). RPD-2002 is the first self-consistent description of a heavy-ion fusion accelerator, final focus, target, magnet shielding, and thick-liquid blanket design. The 120 beams are delivered to the target from two sides, in 9x9 arrays, with 5.4° between rows giving a maximum beam angle from the target axis of 24°. The chamber employs thick-liquid protection, using liquid jets that have been demonstrated to have the required geometric precision in scaled water experiments. Other aspects of the chamber design, not directly related to the beam-line shielding, have been kept the same as the HYLIFE-II design.

Improved performance of direct-drive inertial confinement fusion target designs with adiabat shaping using an intensity picket

Hydrodynamic instabilities seeded by laser imprint and surface roughness limit the compression ratio and neutron yield in the direct-drive inertial confinement fusion target designs. New improved-performance designs use adiabat shaping to increase the entropy of only the outer portion of the shell, reducing the instability growth. The inner portion of the shell is kept on a lower entropy to maximize shell compressibility. The adiabat shaping is implemented using a high-intensity picket in front of the main-drive pulse. The picket launches a strong shock that decays as it propagates through the shell. This increases the ablation velocity and reduces the Rayleigh–Taylor growth rates. In addition, as shown earlier [T.J.B. Collins and S. Skupsky, Phys. Plasmas 9, 275 (2002)], the picket reduces the instability seed due to the laser imprint. To test the results of calculations, a series of the picket pulse implosions of CH capsules were performed on the OMEGA laser system [T.R. Boehly, D.L. Brown, R.S. Craxton et al., Opt. Commun. 133, 495 (1997)]. The experiments demonstrated a significant improvement in target yields for the pulses with the picket compared to the pulses without the picket. Results of the theory and experiments with adiabat shaping are being extended to future OMEGA and the National Ignition Facility’s [J.A. Paisner, J.D. Boyes, S.A. Kumpan, W.H. Lowdermilk, and M.S. Sorem, Laser Focus World 30, 75 (1994)] cryogenic target designs.

The control of laser-plasma parametric instabilities and thetemperature of suprathermal electrons with ultrabroad bandwidth frequencymodulated laser pulse

The development of the capability of selectively exciting or suppressing aspecific laser-plasma parametric instability will result in a betterunderstanding on the rich interplay between laser-plasma instabilities,nonlinear wave collapse and strong turbulence; it is also very important toinertial confinement fusion target designs and other advanced applications.The progress in the development of ultraintense, ultrashort pulse lasers hasallowed for the exploration of many new regimes in the field of laser-plasmainteraction. In this paper, one of the possible applications of the ultrabroadbandwidth associated with these ultrashort laser pulses were explored. Thebehaviour of ultrabroad bandwidth frequency modulated (UBFM) laser excitedsimulated Raman scattering (SRS)was studied using a 1½D electromagnetic particle-in-cell code. Theresults show that, according to the properties of parametric instability, onecan already either enhance or reduce the intensity of selected instability forvarious applications by a readily available UBFM laser pulse.

Effects of radiation on direct-drive laser fusion targets

The role played by radiation in the radiation-preheated direct-drive laser fusion target design is discussed. The soft x-rays emitted during the foot of the laser pulse—at a few 1012 W/cm2—preheat the low-opacity foam ablator which helps to control the Rayleigh–Taylor instability. The foam opacity is, however, thick enough to stop that radiation, keeping the fuel on a low adiabat. Radiation effects are also important in the blow-off corona of the target because they establish a long scale-length plasma. This may help to shield the ablation region from the nonuniformities in the laser absorption.

A unified self-consistent model for calculating ion stopping power in ICF plasma

A new unified self-consistent ion stopping power model for use in ion-driven inertial confinement fusion (ICF) target design has been developed. This model includes sophisticated treatments for electron density distribution of an atom in plasmas and a full random phase approximation stopping function that extrapolates the zero temperature Lindhard stopping function to arbitrary temperatures. It is shown that this model provides accurate ion stopping power for cold materials, including both low-Z and high-Z elements. For finite temperature plasmas, the model accounts for the stopping effects due to electrons in ground states, excited states, resonance states, and continuum states in a self-consistent manner. There is no separation treatment for “bound” and “free” electrons. Hence, the model enables the calculations of ion stopping power to be made within a single model for a wide range of beam and target conditions relevant to ICF studies.

Computational modeling of direct-drive fusion pellets and KrF-driven foil experiments

FAST is a radiation transport hydrodynamics code that simulates laser matter interactions of relevance to direct-drive laser fusion target design. FAST solves the Euler equations of compressible flow using the Flux-Corrected Transport finite volume method. The advection algorithm provides accurate computation of flows from nearly incompressible vortical flows to those that are highly compressible and dominated by strong pressure and density gradients. In this paper we describe the numerical techniques and physics packages. FAST has also been benchmarked with Nike laser facility experiments in which linearly perturbed, low adiabat planar plastic targets are ablatively accelerated to velocities approaching 107 cm/s. Over a range of perturbation wavelengths, the code results agree with the measured Rayleigh–Taylor growth from the linear through the deeply nonlinear regimes. FAST has been applied to the two-dimensional spherical simulation design to provide surface finish and laser bandwidth tolerances for a promising new direct-drive pellet that uses a foam ablator.