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Approaches to Inertial Confinement Fusion

LASER INDIRECT DRIVE

The indirect-drive approach to inertial confinement fusion (ICF) uses a complex chain of energy transfers to drive a highly controlled implosion of a cryogenic, spherical capsule containing fusion fuel. At its hottest and most dense state (called stagnation), the fuel reaches pressures approaching 300 Gbar and is confined for a fraction of a nanosecond.

With laser indirect drive (LID), as seen in Figure A-1, lasers are directed onto the inner walls of a cylindrical cavity called a hohlraum, at the center of which sits the spherical, fuel-filled implosion capsule. The hohlraum is made primarily of heavy metals (Au or DU), which efficiently convert the energy of the laser light into X rays. Acting as an X-ray oven, the inner walls of the hohlraum provide a symmetric bath of X-ray radiation that reaches a blackbody temperature up to ~250 eV (for reference, the blackbody temperature at the surface of the sun is ~0.5 eV).

The spherical fusion capsule at the center of the hohlraum consists of a shell (called an ablator) that is made of plastic, beryllium, or diamond that encloses the fusion fuel, which is DT ice and gas. The capsule must be cryogenically cooled before the experiment so that a layer of DT ice forms on its inner surface (providing a fuel layer that can trap the energy from the initial fusion reactions) and to keep the initial pressure low (to make the capsule easier to implode). It must also be extremely symmetric and smooth, since defects in its initial stage will be amplified under compression.

As the X rays from the hohlraum illuminate the capsule, the material at the capsule surface is heated and expands away from the main capsule, or ablates. Since every action has an equal and opposite reaction, the remaining capsule material responds to this ablation by moving inward, imploding the capsule. The laser power is designed to launch a series of exquisitely timed shocks into the capsule, which compress and heat the fuel to fusion-relevant temperatures (>4,000 eV).

To reach these temperatures, and to amplify the ~100 million atmospheres (Mbar) of pressure generated via X-ray ablation to obtain the hundreds of billions of atmospheres (Gbar) of pressure needed for ignition, the capsule must be imploded on itself by a factor of ~30 at a very high velocity (~400 km/s). This implosion, which is like compressing a balloon to the size of a BB, must be highly symmetric and controlled to maintain a uniform compression of the increasingly hot and dense fuel.

As the drive pressure reaches its maximum, the very center of the fuel becomes hot enough to produce initial fusion reactions. If the remainder of cooler, dense fuel has enough inertia to hold itself together (confine itself) long enough to trap the energetic fusion reaction products from these initial reactions, it can return their energy to the dense fuel layer as additional heat. If the confinement time is sufficient, this self-heating can increase temperatures to 20,000 eV, exponentially increasing both the participating fuel volume and rate of fusion reactions, leading to an explosive release of energy called ignition.

LID is a complex and challenging effort. The laser energy, which is currently limited to 1.8 MJ, must be delivered with precise timing and spatial control into the cylindrical hohlraum in such a way that the hohlraum X rays produce highly uniform irradiation and well-timed ablative shocks to the spherical capsule. Small imperfections in the target and asymmetries in the X-ray drive can be amplified

greatly by the rapid, high convergence ratio implosion and, if not adequately controlled, disrupt the capsule and quench ignition. The first ignition efforts on NIF were hampered by—among others—laser-plasma interactions in the hohlraum that led to energy losses in the drive (but which were ultimately harnessed to provide symmetry control), engineering features on the capsules (such as the fill tube and thin plastic “tent” that suspended the capsule in the hohlraum), and capsule imperfections (bumps and voids). A decade of extraordinary efforts enabled the inertial fusion community to measure, understand, and mitigate many of these complexities.

Outlook

The earliest LID designs fielded on NIF were part of the National Ignition Campaign (NIC), which ended in 2012. These experiments led to the discovery that the laser plasma instability could be used to control beam energy deposition on the hohlraum, which provided a way to control the large-scale symmetry of the implosions. However, NIC implosions had time-dependent drive asymmetries and perturbations seeded by capsule features and imperfections that precluded the control needed for robust performance.

The High-Foot campaign, which followed NIC, used higher powers in the early part of the laser pulse to reduce instability growth in the ablation front. This change led to higher implosion velocities and yields (around 25 kJ of fusion energy, compared to ~5 kJ for NIC), but at the cost of reduced compression. The reduced compression helped enable high-resolution imaging of the implosions that revealed the importance of the capsule perturbations, such as tent scars.

Next, designs using high density carbon (HDC/diamond) ablators and shorter pulses were tested. The hohlraum gas fill was lower density than for NIC, which reduced Stimulated Raman Scattering (SRS) and increased the efficiency of the conversion of laser light to X rays. While this improved symmetry control, the low gas fills led to a faster filling of the hohlraum with plasma. Significant progress was made on reducing effects of engineering features; for example, the fill tube size was reduced five-fold. Fusion yields doubled, to ~55 kJ, with evidence that a significant fraction of the yields arose from self-heating.

Most recently, HYBRID campaigns increased capsule size to increase the energy delivered to the target and optimized both design parameters and capsule quality to improve the symmetry of the implosions. Yields increased again, to almost 200 kJ. On August 8, 2021, a HYBRID-E implosion produced a fusion yield of 1.3 MJ. This corresponds to a gain of 0.7 relative to the incident laser energy of 1.8 MJ and a capsule gain of about 5 (fusion yield relative to the energy absorbed by the capsule). While this achievement is short of ignition as defined in the 1997

NRC study,¹ it is well above the gain of 0.3 milestone as outlined in the report as the point where “fusion reactions occur over a sufficient region to induce propagation of the thermonuclear burn into the denser, colder, outer fuel.”

The August 8th LID shot on NIF provided a convincing demonstration of significant self-heating, reaching temperatures and yields far beyond any previous experiment and unobtainable by compression alone. It offers significant validation of the hot-spot concept for ICF, and detailed data that can be used to test and constrain the complex multi-scale codes used in ICF target design. It also highlights the difficulty of operating in a fundamentally nonlinear regime, where small changes in the initial conditions or drive can lead to large changes in outcome. Clearly, there is much fundamental science that remains to be done.

LASER DIRECT DRIVE

The laser direct-drive (LDD) approach to hot-spot ignition has many similarities to LID, but irradiates a spherical fuel capsule directly with laser photons instead of X rays from a laser-driven hohlraum. (See Figure A-2 for illustration.) This has the advantage of a significant increase of driving energy (on NIF, the laser delivers 1.8 MJ of energy while the hohlraum delivers ~0.2 MJ), which enables much larger capsules, but comes at the cost of introducing a source of direct asymmetry, since the laser beams hit the target surface directly. Furthermore, NIF is presently configured to deliver its laser beams into the poles of a cylindrical hohlraum, and not to the surface of a spherical capsule. Thus, much of present-day LDD research is focused on scaling experiments performed on the 30 kJ Omega laser. In a sense, LID is better for drive homogeneity/smoothing, while LDD is better for efficiency and coupling, potentially, although it is susceptible to different laser plasma instabilities.

The spherical concentric layers of a LDD ICF target typically consist of a central region of DT vapor surrounded by a cryogenic DT-fuel layer and a thin, nominally plastic layer, called the ablator. The incident laser drive is designed to be as spatially uniform as possible on the outer surface of the capsule, using multiple laser beams with a peak, overlapped intensity of <10¹⁵ watts/cm². The intensity of the laser pulse is varied over nanosecond time scales to produce the desired profile of ablation pressure. As with LID, the ablation process causes the target to accelerate and implode via the rocket effect, reaching a peak implosion velocity in the 300 to 500 km/s range, depending on the implosion design. As the implosion proceeds, the laser energy acts on an increasingly small surface and encounters previously ablated material, called coronal plasma, that typically absorbs 60-70 percent of the laser energy. The hydrodynamic efficiency of converting that absorbed laser energy to inward kinetic energy of the shell via the rocket effect is about 9 percent. This gives a conversion efficiency of incident laser energy to shell kinetic energy of about 6 percent for laser direct drive.

As the DT-fuel layer decelerates, the initial DT vapor and the fuel mass that was thermally ablated from the inner surface of the DT-ice layer are compressed and form a central hot-spot plasma having a pressure of ~100 Gbar, in which fusion reactions occur for a few tenths of a nanosecond around stagnation. ICF relies on the 3.5 MeV DT-fusion alpha particles depositing their energy in the hot-spot plasma, causing the hot-spot temperature to rise sharply and a thermonuclear burn wave to propagate out through the surrounding nearly-degenerate, cold dense DT fuel, producing significantly more energy than was used to heat and compress the fuel. If the inertia of the compressed DT shell confines the hot-spot plasma long enough for alpha heating to trigger the ignition instability, the LDD capsule will achieve energy gain. The onset of central-hot-spot ignition is predicted to occur when the product of the temperature and areal density of the hot-spot plasma reach a minimum of 5 keV and 0.3 g/cm².

Outlook

Laser direct-drive ICF is studied on the OMEGA laser facility, through both focused experiments to understand the fundamental physics, such as energy coupling, and integrated subscale targets that are designed for ignition on NIF but hydrodynamically scaled to the laser energy available at OMEGA. Hydrodynamic

scaling uses a smaller target but maintains critical parameters such as shell convergence, hot-spot pressure, shell adiabat, and implosion velocities, enabling studies of hot-spot formation for spherically symmetric, LDD, DT-layered implosions that scale to burning plasma and ignition designs on MJ-scale lasers in both polar and spherical illumination geometries. (See also Figure A-3.)

A fuel hot-spot pressure in excess of 50 Gbar was demonstrated for direct-drive, layered deuterium-tritium implosions on OMEGA.

The influence of laser plasma interactions on energy coupling and preheat, and the seeding of hydrodynamic instabilities by laser imprint, target imperfections, and engineering features have been investigated on OMEGA and at ignition-relevant scales on the National Ignition Facility.

Low-mode implosion asymmetry has been studied using X-ray imagers and nuclear diagnostics with multiple lines of sight, characterizing the in-flight shell asymmetry and the hot-spot flow velocity at stagnation.

Focused experiments have examined the physics of multi-shock interactions with matter to identify the sensitivity of material release to details of radiation preheat and kinetic effects.

The fusion neutron yield for OMEGA DT cryogenic implosions has been increased by more than a factor of three as guided by statistical modeling of past experiments, thereby achieving an energy-scaled generalized Lawson parameter (defined in Chapter 3) of 0.8 (assuming ~1.35 MJ absorbed energy with 2.0 MJ incident energy) and an extrapolated fusion yield of almost 1 MJ.

MAGNETIC DIRECT DRIVE AND MAGNETO-INERTIAL FUSION

Magnetic direct drive (MDD) fusion is distinct from the two laser fusion concepts in that the implosive force is provided by the interaction of direct current through a cylindrical target with its own self-generated magnetic field, rather than by photons. Just as parallel currents running along parallel wires will tend to draw two wires together, current running through a cylinder will tend to implode the cylinder, with implosion pressures that increase with the square of the current and the inverse square of the radius. For example, Sandia’s Z machine can deliver more than 20 MA of current to a fuel-filled metal cylinder, generating pressures around 1 Gbar at stagnation. Importantly, the pressure on an imploding MDD target increases as long as current flows. This is in contrast to LID and LDD, where pressure decreases along with decreasing surface area.

Two other features distinguish MDD from laser-driven ICF concepts. First, the wall-plug efficiency of MDD tends to be much higher than that of laser drivers. For example, NIF’s capacitor banks store ~400 MJ of energy and its laser delivers about 2 MJ to cm-scale LID hohlraums (0.5 percent wall-plug efficiency). The capacitor banks on Z store 20 MJ and deliver about 1 MJ to cm-scale cylindrical MDD targets (~5 percent wall-plug efficiency). Second, the time scales of MDD tend to be longer than that of lasers, with current risetimes of ~100 ns, rather than the ~2 ns of a NIF laser drive. Thus, while the energy density of MDD is comparable to that of NIF, the power density is much lower. Combined with the inherently two-dimensional (cylindrical) compression of MDD—as opposed to the three-dimensional (spherical) compression of LID and LDD, pulsed power drivers can access distinct target designs and concepts for fusion.

One way to harness the distinct power delivery of MDD is the concept of Magneto-Inertial Fusion (MIF), which operates at pressures of ~1-10 Gbar rather than the ~100-300 Gbar of traditional ICF. Here, the committee notes a target concept called Magnetized Liner Inertial fusion (MagLIF), as depicted in Figure A-4. Where laser ICF uses spherical compression, high power, and high pressure to reach the Lawson (Pt) and confinement (ρR) requirements for self-heating and gain, MIF relies on preheat, external magnetic fields, longer times, and larger volumes

to approach those requirements. In particular, MagLIF uses the following ideas for MDD fusion:

• Preheat: Where spherical implosions of a cryogenic target can create multi-keV temperatures at convergence ratios (CR) of about 30 from shock and compressional heating alone, reaching those temperatures with cylindrical compression would require much higher convergence ratios that would exacerbate instabilities. Preheating MagLIF fuel to temperatures of ~100 eV using a ~2 kJ laser pulse enables relatively slow (~100 km/s) implosions that

• can reach multi-keV temperatures at CR ~30 while preserving the inertial integrity and stability of the imploding cylindrical liner.
• Premagnetization: Where spherical implosions can achieve ρR sufficient to trap the energy from charged fusion products at CR ~30, the fuel ρR in a cylindrical MDD implosion is ~10× smaller than required for inertial confinement. Worse, large preheat temperatures and long (~20 ns) implosion times make conductive heat losses a serious concern for MIF. Introducing an external axial magnetic field before the implosion solves both of these problems: the magnetic field inhibits radial conduction losses, keeping the fuel hot during the implosion, and the initial magnetic field is flux-compressed by the implosion to such a degree that it effectively traps and confines charged fusion products that are emitted in the radial direction. In the axial direction, MDD has sufficient areal density to inertially confine charged fusion products.

Outlook

The MagLIF concept with DD fuel has demonstrated yields above 10¹³ neutrons on Sandia’s Z machine, which, due to the ~100× smaller cross section of the DD reaction compared to DT, is equivalent to ~10¹⁵ DT neutrons, or ~2 kJ of DT fusion energy. This is roughly equivalent to LID experiments at NIF without self-heating. Furthermore, analysis of primary and secondary neutron spectra indicates that ~40 percent of the charged tritons produced in one branch of the DD reaction are confined by the combination of large BR (magnetic radial confinement) and ρZ (axial inertial confinement). It is important to note that a BR sufficient to trap these 1 MeV tritons would also be sufficient to trap the 3.5 MeV alpha particles from DT reactions. However, the demonstrated efficacy of this confinement does not mean that present-day MagLIF targets would have appreciable self-heating, since the stagnation plasmas have ρTau ~20× less than is required for energy deposition that effectively feeds back into the fusing plasma.

While these experiments have demonstrated the fundamental soundness of the MIF concept, there are both practical and physics-based limitations to what can be done with present U.S. pulsed power capabilities. On the practical side, Sandia’s Z machine is not an ignition facility: many of its principal components are more than 35 years old, many are becoming less reliable with age, and none were built to handle high yields. Even if the facility could handle high yields, scaling calculations indicate that significantly higher preheat energies (~30 kJ 15X) and implosion currents (~50 MA 3X) are needed to bring the MagLIF concept into the burning plasma regime.

Extensive work has been done to understand and mitigate the risks associated with scaling MDD to larger drivers and targets. The required axial magnetic fields

for a burning MagLIF plasma are only 20T and have been demonstrated by existing technology. Experiments using one quad of NIF to preheat fuel-filled cylinders with the required ~30 kJ of laser preheat are ongoing in a cross–lab collaboration. These experiments include novel diagnostics that can detect mix from various target components (mix is a concern for MIF because, unlike conductive heat losses, radiative heat losses from high-Z impurities in the hot fuel are not inhibited by the external magnetic field). Extensive work has been done to understand the sources, evolution, scaling, and mitigation of the magneto-Raleigh-Taylor instability, which can lead to non-uniform and ill-confined stagnation plasmas. Finally, current-scaling studies are under way to anticipate and understand current-loss mechanisms on any potential future driver.

With its relatively low pressures, pulsed power fusion operates in a much less demanding physical regime than laser-driven ICF. With its relatively low power densities and high energy densities, it offers opportunities for robust target concepts that do not require the high finesse of multi-shock spherical compression. And with its high wall-plug efficiency, pulsed power fusion has clear paths to high-gain targets that may offer advantages for fusion energy. It should be noted, however, that pulsed power as a driver technology and MDD as a fusion drive are supported at a relatively modest level in the United States, with a relatively small pool of experts. For example, most U.S. hydrocodes do not include the magnetohydrodynamics packages that enable MDD target design, and there is a single NNSA Center of Excellence that is devoted to pulsed power science. These resources may be further stressed by the increasing maintenance needs of an aging Z facility (which, in addition to ICF also supports radiation effects, materials properties, and fundamental science experiments) and the absence of a mid-scale (~10 MA) pulsed power facility in the United States that could advance fundamental pulsed power science and train the next generation of scientists.