Physics principles of inertial confinement fusion and U.S. program overview

Inertial confinement fusion (ICF) has existed as a field of study since the 1970s, but the field was born out of the Cold War. In the decades since the 1960s, pioneering research developing the principles and technologies of ICF has culminated in the creation of three major Department of Energy facilities that still exist today: the National Ignition Facility (NIF) at Lawrence Livermore National Laboratory, the OMEGA laser at the Laboratory for Laser Energetics, and the $Z$ pulsed power facility at Sandia National Laboratories. While the technology of ICF facilities themselves is interesting, this review concentrates upon the physics principles of the targets fielded on U.S. ICF facilities and upon results from the last decade of research. While there have been periods of frustration on the road to ICF ignition, recent research has demonstrated great leaps in understanding what aspects of the implosions need more control. Tangible progress in ICF is evident as burning plasmas and ignited plasmas have recently been generated, repeatedly, on the NIF stemming from decades of science and engineering understanding generated from work at the three previously mentioned facilities and in the international community.

Figure 1

The reaction rates of select reactions are plotted based upon formulas given by [50] and [345] in the case of $p$-boron. The temperature region $2<T<20\mathrm{keV}$ of practical interest to ICF is highlighted. The top curve is the DT reaction rate, while the tangent line is the power-law approximation [Eq. (1)] to the DT reaction rate.

Figure 2

(a) NIF DT implosion data (as of September 2021) plotted against Eq. (11) (dashed curve). Here $G_{\text{fuel}}$ is calculated from the ratio of the fusion yield over the peak fuel kinetic energy (an approximation that neglects energy loss in the conversion of kinetic energy into internal energy at stagnation due to x rays or asymmetry). The low performing experiments that deviate from the theory expression are largely those from the National Ignition Campaign (see Sec. 3), which experienced significant hydrodynamic instability and mixing: the enhanced bremsstrahlung emission that breaks the assumptions of Eq. (11). (b) $G_{\text{fuel}}$ is plotted vs the measured burn-averaged DT fuel areal density (inferred via the neutron down-scatter ratio of 10–12 MeV neutrons over 13–15 MeV neutrons). As seen here, fusion performance rapidly falls off at low areal density (as expected since 1D inertial confinement is reduced), but surprisingly also at higher areal density (contrary to conventional wisdom; see Sec. 3e1, 3e2, 3e3), and an apparent optimum exists for fuel $\rho R\sim 0.6–0.7\mathrm{g}/{\mathrm{cm}}^2$.

Figure 3

Simulated image of a characteristic hot-spot ignition design implosion at peak compression illustrating what a configuration may look like. Black outlines illustrate material boundaries, and the breaking of perfect symmetry results from the input of realistic surface finishes and asymmetry breaking engineering features into the simulation; while initially small, these perturbations inevitably grow, as the tendency of an implosion is to act as an amplifier. Left half: density ($\mathrm{g}/{\mathrm{cm}}^3$). Right half: electron temperature (keV). A few key processes are illustrated.

Figure 4

Contour plot of $H$ showing the dependence upon $f_B$ and $T$. At fixed $T$, higher $f_B$ lowers $H$, essentially reflecting the fact that enhanced bremsstrahlung cooling makes the ignition temperature higher than it would be for pure DT and this makes ignition more difficult to achieve. If the implosion can be engineered to have a high enough optical depth to reabsorb bremsstrahlung x rays ($f_B<1$), the ignition temperature is reduced.

Figure 5

Plot of $F(T)$ for four different values of $f_B$ (solid line, 0.5; dashed line, 0.75; dotted line, 1.0; long-dashed line, 1.25). A maximum in $F(T)$ exists nearly independent of $f_B\sim 14\mathrm{keV}$, and above 14 keV the temperature $F(T)$ slowly declines due to the reaction-rate dependence. $F(T)$ is positive only when alpha heating exceeds radiative loss, and for $T\gg T_{\text{ign}}$ the sensitivity of $F$ to radiative loss is of diminishing significance.

Figure 6

An implosion with asymmetry at peak velocity is abstracted into an implosion of two asymmetric pistons. An analytic model constructed around this simple physical picture captures the principal impact of asymmetry on an implosion. Along the direction defined by the extremes of shell thickness variation (upper left image), the implosion is abstracted into an “apple core” of thin and thick pistons at opposing ends of the hot spot (upper right image). A symmetric configuration results in no center of mass motion (lower left image), while an asymmetric configuration has a net center of mass motion that carries kinetic energy. Adapted from [209].

Figure 7

Upper left panel: stagnation pressures from a suite of ensemble model simulations are plotted against the piston pressure formula $P_{\text{stag}}(\mathrm{Gbar})=0.0097\mathrm{DSR}(\%)v_{\text{imp}}^2(\mathrm{km}/\mathrm{s})/R_{\mathrm{hs}}(\mathrm{\mu }\mathrm{m})$, which is a rewriting of Eq. (26) in terms of more directly measured variables. The ratio of 10–12 MeV fusion neutrons to 13–15 MeV fusion neutrons defines DSR, which is directly related to shell $\rho R$. Lower left panel: stagnation pressures from indirect-drive DT experiments at the NIF are plotted against the piston pressure formula. Right panel: hot-spot energy inferred from indirect-drive DT experiments at the NIF are plotted against the piston formula for hot-spot energy. Key implosion campaigns are in color, where LF refers to low foot, HF indicates high foot, and HDC refers to high-density carbon experiments on NIF. The data inference of stagnation pressure and hot-spot energy follows from a procedure first described by [74] and [458]. From [209].

Figure 8

Typical targets used in laser-driven ICF are (upper left image) indirectly driven (where the laser energy is incident on a hohlraum generating a bath of x rays) or (upper right image) directly driven (where the laser beams are directly incident on the capsule). In either case, a spherical capsule is prepared at $t=0$ with a layer of DT fuel on its inside surface. As the capsule surface absorbs energy and ablates, pressure accelerates the shell of the remaining ablator and DT fuel inward, thereby producing an implosion. By the time the shell is at approximately one-fifth of its initial radius, it is imploding at a speed of many hundreds of kilometers per second, as dictated by Eq. (17). By the time the implosion reaches minimum radius, a hot spot of DT has formed, surrounded by colder and denser DT fuel. The timescales shown in the row of frames at the bottom are characteristic of plastic ablators. The timescales for higher-density ablators like high-density carbon (HDC) are generally shorter owing to their reduced thickness. From [40].

Figure 9

A simulation of instability growth on an indirect-drive ICF gas capsule implosion is shown in a variable logarithmic density color scale that ranges from low (blue) to high (red). The particular implosion design is that of the “low foot”; see Sec. 3. (a) A small amplitude mode-60 perturbation is imposed on the outside of the capsule at $t=0$. (b) By $t=10\mathrm{ns}$ the outer layer of the capsule has ablated away and the shell has been compressed. (c) By $t=15\mathrm{ns}$ the shell begins to rapidly accelerate inward. (d) By $t=16\mathrm{ns}$ perturbation growth on the outside of the capsule becomes visible. (e) By $t=18\mathrm{ns}$ the shock wave that transited the ablator and entered the gas races inward ahead of the shell. (f) By $t=19\mathrm{ns}$ instability growth on the inside of the shell develops. (g) By $t=20\mathrm{ns}$ the amplitude of instability growth exceeds the thickness of the shell. (h) By $t=21\mathrm{ns}$ the shell of the implosion has been shredded by instability.

Figure 10

Coupled hohlraum-capsule simulation images are inset on top of a typical indirect-drive target geometry. (a) At a time early in peak laser power, the shallow polar angle “inner” beams propagate to their intended location on the inner hohlraum wall unimpeded. (b) At a later time, a plasma bubble generated by the incidence of the large polar angle “outer” beams (not shown) interferes with the propagation of the inner beam, upsetting the intended x-ray symmetry inside the hohlraum. Insets: From [62].

Figure 11

Examples of laser pulse shapes, hohlraum radiation temperatures, and ablation pressures for two indirect-drive experiments at the NIF. (a) Laser power vs time for the “coasting” 1.3 MJ pulse N130501 and the “no-coasting” 1.7 MJ pulse N130812. The colloquial terms coast and no coast are misnomers since both of the pulse shapes shown result in implosions that coast. It is just that the longer duration pulse results in less coasting. (b) The resulting simulated hohlraum radiation temperatures for shot N130501 and shot N130812, with the ratio of the two shown in the inset. (c) The ablation pressure (arbitrary units) that results from $T_{\mathrm{rad}}^{7/2}$, with the ratio of the two shown in the inset. The shape of the ablation pressure in time is nearly triangular with a near-linear rise and fall. Time duration between the bang time and the peak in ablation pressure is the coast time. Insets: From [206].

Figure 12

Data from the high-foot series of experiments (2013–2014) show a clear correlation between burn-average hot-spot ion temperature as measured by neutron time-of-flight detectors (left frame), the neutron down-scatter ratio (DSR), which is the ratio of 10–12 MeV fusion neutrons to 13–15 MeV fusion neutrons and is therefore a measure of compression (middle frame), and the total fusion neutron yield (right frame).

Figure 13

The first high-foot DT implosion experiment N130501 formed a baseline to study the impact of increasing implosion velocity with different choices of coast time. Left frame: experiment N130710 increased implosion velocity by increasing laser power relative to N130501, while experiment N130812 maintained the same laser power as N130501 but extended the duration of peak laser power, therefore significantly reducing the coast time. Middle frame: experiments N130710 and N130812 were designed to have identical peak hohlraum radiation temperature and implosion velocity, but the N130812 experiment has a higher late-time hohlraum radiation temperature. Right frame: the three experiments N130501, N130710, and N130812 gave the first indications that hot-spot pressure would increase with reduced coast time, as was later proven through a series of high-foot experiments where the coast time was systematically decreased in steps. At short coast time, the hot-spot pressure was observed to drop from its maximum value: a failure mode speculated to be due to a rupture in shell caused by an asymmetry-induced perforation at low remaining mass ([204]).

Figure 14

NIF DT shot data (dots) are plotted in the space of the inferred Lawson parameter and hot-spot (thermal) temperature. The curves denote the ignition boundary estimated from $p\tau H(T)\ge 1$ and Eq. (21). The dotted and dashed curves show how the ignition boundary moves to higher temperature under different assumptions of mixing of high-$Z$ material into the DT, resulting in enhancement of bremsstrahlung x-ray losses. Solid curves,$f_B=1$; dotted curves, a 50% increase in bremsstrahlung: $f_B=1.5$; dashed curves, a 100% increase: $f_B=2.0$. (a) Data from the low-foot series (circles). (b) Data from the high-foot series (squares). In this analysis, the neutron time of flight (NTOF) inferred DD ion temperature $T_i(\mathrm{DD})$ is used as an estimate of thermal temperature since it is less sensitive to Doppler broadening effects, as previous work ([221]) measuring electron temperature ($T_{\mathrm{e}}$) has shown that $T_{\mathrm{e}}\approx T_{\mathrm{i}}(\mathrm{DD})\le T_{\mathrm{i}}(\mathrm{DT})$ for these types of implosions.

Figure 15

(a) Schematic indirect-drive target showing basic engineering elements. The tent membrane, which holds the capsule in the center of the hohlraum, is a Formvar material of thickness 15–100 nm. The most typically used tent thickness is 45 nm, which balances fragility with desire to minimize any potential hydrodynamic perturbation. (b) A fill tube through which the capsule is fueled extends out of a hole drilled through the ablator. Fill tubes range in diameter from 2 to $30\mathrm{\mu }\mathrm{m}$, depending upon the capsule material and target type. For plastic and beryllium capsules $10\mathrm{\mu }\mathrm{m}$ diameter fill tubes have been standard, while for HDC capsules $5\mathrm{\mu }\mathrm{m}$ diameters are standard. (c) The fill tube is epoxied to the capsule, where the two components contact each other and the drill hole around the tube is also grouted with epoxy. (d) Defects typically for HDC capsules are, from left to right, particles (or pits) on the outer surface of the ablator, voids in the through thickness of the ablator, and residue on the inner surface of the capsule. These defects are all potential seeds for inwardly directed hydrodynamic jets of ablator material.

Figure 16

Observed and simulated growth of an imposed perturbation on the outside surface of the capsule is plotted against the mode number of the perturbation. In this case the capsule has converged from its initial outer radius of 1137 to $650\mathrm{\mu }\mathrm{m}$. The perturbation amplitude growth is measured in terms of an increased optical depth variation using a face-on radiography technique. As shown, the predicted instability growth is largely in agreement with the data, except for the highest modes, and the high-foot implosion indeed has much less ART growth than the low-foot implosion across all modes, proving the key assertion about the high-foot tactic. From [362].

Figure 17

High resolution 3D simulations of (a) the LF implosion N120405 and (b) the HF implosion N130927 showing the impact of instability, asymmetry, and the tent perturbation. The reduced sensitivity of the HF to ART instability and tent perturbation growth is clear. Both implosions exhibit a mode-2 asymmetry, which manifest itself as a toroidal hot spot in the HF implosion, albeit the degree of hot-spot asymmetry seen in the 3D simulation is exaggerated compared to the data. Adapted from [89].

Figure 18

Two sets of repeat shots were performed using the $175\mathrm{\mu }\mathrm{m}$ ablator thickness capsule variant of the high-foot design in high-gas-fill DU hohlraums ([289]; [200]). Top row: equatorial (i.e., side) view time-integrated x-ray emission at $>6\mathrm{keV}$ photon energy ([287]). Second row: equatorial view neutron imaging system data ([481]). Except for one experiment (N141016, where the NIF laser misfired), the experiments exhibit oblate hot-spot symmetry with indications of DT fuel mass accumulation, inferred from the down-scatter neutrons, at the poles of the implosion. Scalar performance metrics are as labeled in the other rows. Fusion yield repeats to within 25%, while most other metrics repeat to better than 10%.

Figure 19

NIF DT shot data (dots) in the space of the inferred Lawson parameter and the hot-spot thermal temperature. (a) Data from the HDC (diamonds) and BigFoot (dark circles) series of experiments. (b) Data from the Hybrid-E 1100 μm radius capsule series (dark triangles).

Figure 20

(a) NIF DT shot data (dots) plotted in the space of an inferred Lawson parameter and hot-spot thermal temperature including the I-raum series (dark diamonds) and Hybrid-E 1050 μm capsule (dark squares) series. (b) Total fusion yield vs temperature across several experimental series with a legend. The significant jump in temperature and yield, setting aside the point associated with experiment N210808 (the rightmost point), is a qualitative indication of ignition reflecting that thermal instability indeed occurred.

Figure 21

(a) As-shot laser power vs time for a burning-plasma Hybrid-E experiment (N210307) and the first ignited one (N210808). The peak laser power was reduced and extended in time (conserving total laser energy) for N210808. (b) The model ([63]) inferred hohlraum radiation temperature vs time for the same two experiments. The $T_r$ for N210808 was higher than for N210307 due to the reduction in laser entrance hole size and the extension of the late-time laser pulse, despite the reduction in peak power. (c) As seen in previous series of experiments (Fig. 13), the reduction in coast time results in an increase in stagnation pressure. The black points are from other Hybrid-E experiments in the series from late 2020 to mid 2021 and use the same $1050\mathrm{\mu }\mathrm{m}$ inner radius capsule scale as N210307 and N210808.

Figure 22

NIF DT shot data of total measured fusion yield is plotted against data-inferred peak hot-spot pressure with a legend. The pressure at the center of the Sun is estimated to be between 200 and 250 Gbar.

Figure 23

Schematic of laser-direct-drive ICF. Multiple laser beams symmetrically illuminate a spherical shell containing DT fuel.

Figure 24

Typical electron density profile (blue line for DT and gray line for CD) for a direct-drive target. The conduction zone separates the ablation front from the critical surface. The region beyond the critical surface is the coronal plasma. Laser energy deposition (red line) occurs in the CD plasma.

Figure 25

Typical (a) OMEGA DT-layered target and (b) laser pulse shape. The laser pulse shape is divided into four parts: the picket, the foot, the ramp, and the main drive.

Figure 26

Normalized linear growth rates of the ablative RTI vs the normalized wave number for different Froude numbers. From [152].

Figure 27

Contour plots of ablation-induced vorticity inside the bubble of single-mode simulations of the ablative RTI. Left panels: snapshots at 1 and 2.25 ns from 2D simulations of a velocity perturbation with $\lambda =10\mathrm{\mu m}$ wavelength and $\tilde{v}=1\mathrm{\mu m}/\mathrm{ns}$ in an accelerated planar target with $g\simeq 110\mathrm{\mu m}/{\mathrm{ns}}^2$ and $v_a\simeq 3.5\mathrm{\mu m}/\mathrm{ns}$ from 2D simulations. From [42]. Right panels: similar snapshots from 3D simulations ([494]). There is no color scale, but the outer (inner) surface of the top color plot corresponds to vorticity values 12.5/ns (19/ns), and the outer (inner) surface of the bottom color plot corresponds to vorticity values 25/ns (40/ns).

Figure 28

X-ray radiographs of the 3D broadband modulations, initially produced by imprinting of the laser beam and measured at (a) 4, (b) 6, and (c) 10 ns ([445]). Bottom left panel: mode spectrum from the x-ray radiographs at 3 times ([445]). Bottom right panel: simulated distributions of the bubble sizes (number of bubbles $N$ vs bubble size $\lambda$) at three different distances traveled: $1\mathrm{\mu m}$ (red curve), $18\mathrm{\mu m}$ (black curve), and $67\mathrm{\mu m}$ (blue curve). From [406].

Figure 29

Results from 2D simulations showing the dependence of ${\alpha }_b$ on the initial rms multimode perturbation amplitude $h_0$ for different ablation velocities. From [502].

Figure 30

Simulated evolution of the IFAR vs the convergence ratio ($C_R$) for a typical OMEGA DT-layered target. The solid line is the simulated IFAR, while the dashed line is the $C_R^{-2}$ approximation.

Figure 31

RM instability at the ablation front. Perturbation evolution is shown for different wavelengths $\lambda =10,20,40,80\mathrm{\mu m}$. Simulations refer to a thick $D2$ target irradiated by $I=4\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, ${\lambda }_{\text{laser}}=0.35\mathrm{\mu m}$. The target is initialized with a surface amplitude roughness $A_0=0.1\mathrm{\mu m}$. From [302].

Figure 32

Richtmyer-Meshkov instability experiments on the Nike laser. Left panel: original streak record along with the amplitude lineouts taken across the ripples at four benchmarking times in the inserts. Right: the time-dependent Fourier amplitude of the dominant mode vs time for a $65\mathrm{\mu }\mathrm{m}$ thick target with $\lambda =45\mathrm{\mu }\mathrm{m}$ and initial peak-to-valley amplitude $2a_0\sim 3\mathrm{\mu }\mathrm{m}$, also marked at four important times: beginning of the pulse, first peak, etc. The origin of time $t\sim 0$ here and elsewhere corresponds to the instant when the laser-beam intensity reaches half maximum. The thickness of the shaded area approximately corresponds to the experimental uncertainty. From [5].

Figure 33

(a) Laser pulse shapes for a decaying-shock-wave picket and a relaxation picket. The decaying shock wave is created by the short picket at the beginning of the pulse shape. The adiabat is shaped as the shock wave decays. (b) Pulse shape for a relaxation-picket drive. The low-intensity, narrow picket in front creates a spatial density profile that is low at the ablation region and high inside the shell. The strong shock wave resulting from the high-foot intensity then propagates through this density profile, shaping the shell adiabat. From [241].

Figure 34

(a) Schematic of a shell showing a shaped adiabat between the ablation surface and the inner surface. The shaded region is the portion of the shell that is not ablated. The adiabat is higher in the ablated material and therefore reduces the RT growth of ablation-interface perturbations. From [241]. (b) Simulated in-flight adiabat shapes vs mass coordinates for the three pulses (the dashed curve is flat, the dotted curve is the decaying shock, and the solid curve is the relaxation technique). The dash-dotted curve is an analytic result for adiabat shaping from relaxation. From [10].

Figure 35

Left panel: comparison of simulated RT growth rates from flat adiabat (circles) and adiabat-shaped targets (squares) using the relaxation technique. From [10]. Right panels: measurements of the temporal evolution of the optical depth (OD) from laser imprinting perturbations driven by a flat adiabat (diamonds) and adiabat-shaped pulse (triangles) using the decaying shock technique. The different plots are for wavelengths 30, 60, and $120\mathrm{\mu m}$. From [444].

Figure 36

Hard sphere projection of the laser illumination pattern on a typical target for 60-beam OMEGA. Courtesy of A. Shvydky [Laboratory for Laser Energetics (LLE)].

Figure 37

The rms variation of the on-target illumination vs the ratio $R_{\mathrm{beam}}/R_{\text{target}}$ for OMEGA phase plates with super-Gaussian profile exponent 5. Courtesy of V. Gopalaswamy (LLE).

Figure 38

Simulated ablation-front mode spectrum from laser imprinting at the start of the main drive for OMEGA targets with 1 THz SSD and without SSD. From [155].

Figure 39

Cross sections of the density (in $\mathrm{g}/{\mathrm{cm}}^3$) from 3D simulations of (left image) a nonpicket and (right image) a single-picket pulse. Images are shown at $t=2.45$ and 2.55 ns, respectively, in the moment prior to deceleration of the implosion. From [213].

Figure 40

(a) Laser pulses and (b) simulated spectra of surface modulations. The strong picket pulse is displayed in blue and the reduced picket pulse in shown in red. Spectra are taken at the time corresponding the shells’ initial acceleration. From [213].

Figure 41

Imprinting mitigation using a preexpanded Au overcoat. Framing camera images from three shots are shown (left to right): uncoated with a prepulse, 40 nm Au without a prepulse, and 40 nm Au with a prepulse. Frame times are at 4.4 ns. The top row shows the linearized film images in gray scale. The bottom row shows the images processed using Wiener filtering with modulation transfer function correction and converted to areal mass fluctuation, displayed using the color map shown. All three shots had a preimposed $30\mathrm{\mu }\mathrm{m}$ wavelength and a $0.5\mathrm{\mu }\mathrm{m}$ amplitude ripple (grooves are oriented vertically). The uncoated shot is dominated by RT-amplified imprint from the laser speckle, while the Au-coated shots with a prepulse show much lower imprint, with the preimposed ripple amplified by RT instability as the prominent feature. The shot with 40 nm Au without a prepulse shows some imprint reduction but is still broken up by the imprint. From [226].

Figure 42

Left image: schematic of the hybrid direct-drive target design in planar geometry. Optical depth images of (a) a bare target and (b) a hybrid target after 4.2 ns. The hybrid target exhibits greatly reduced mass modulation. From [75].

Figure 43

Left images: schematic diagrams for CH targets displaying both standard bare CH shells and CH shells with a layer of foam added. Right panels: two-dimensional simulations including laser imprinting, performed with the code draco, showing significantly improved uniformity in foam targets with respect to standard targets. From [196].

Figure 44

Left panel: hot-electron fraction ($f_{\text{hot}}$) as a function of vacuum overlapped laser intensity. Single, two, and four correspond to OMEGA EP planar experiments where the beams are linearly polarized; eighteen (sixty) corresponds to OMEGA planar (spherical) experiments where the beams have polarization smoothing. For each configuration, the overlapping intensity is given by the vacuum intensity of the laser beams on the target surface. Right panel: hot-electron fraction vs the common wave gain for each experimental configuration tested. From [325].

Figure 45

Planar hot-electron measurements at the NIF. Fraction of laser energy converted to hot electrons as a function of simulated quarter critical laser intensity, for laser drive using outer beams (diamonds) and inner beams (triangles), for CH ablators (blue, green) and Si ablators (orange). Uncertainty in $f_{\text{hot}}$ is based on statistical uncertainty in the hard-x-ray data propagated through EGSnrc modeling. From [396].

Figure 46

Left image: target used in divergence experiments on OMEGA. Molybdenum spheres of different sizes are enclosed within a laser-driven plastic shell. Right panel: measured intensity of the $\mathrm{Mo}\text{−}K\alpha$ line and hard-x-ray radiation. The Monte Carlo (MC) simulation results for a divergent fast-electron beam are also shown. The curve is the best fit to the hard-x-ray data. The increase of the signals with the Mo-shell diameter indicates a wide-angle divergence of fast electrons. From [492].

Figure 47

The laser pulse (black line) and the hard-x-ray signals for DT-layered shot 77064 (red line) and all-CH shot 77062 (blue line) are plotted as a function of time. The difference in hard-x-ray signals is proportional to the hot-electron energy deposited in the DT layer. From [86].

Figure 48

(a) Light rays propagating past the target (blue curve) interact with light rays in the central region of another beam (red curve). (b) The interacting light rays seed an ion-acoustic wave near the Mach-1 surface (dashed curve). The ion-acoustic wave scatters light before it can penetrate deep into the target (dashed curves).

Figure 49

(a) CBET data (points) measured when energy transfer was relatively low due to the low seed intensities ($0.4\times {10}^{15}{\mathrm{W}/\mathrm{cm}}^2$) are shown for conditions where the many overlapping laser beams used to heat the plasma drove non-Maxwellian electron distribution functions. Calculations that assume a Maxwellian electron distribution function (dashed curve) and used the measured non-Maxwellian electron distribution function (solid curve) determined from Thomson scattering ([474]). (b) For CBET experiments at higher TOP9 (probe) beam intensities ($4\times {10}^{15}{\mathrm{W}/\mathrm{cm}}^2$) where significantly more energy was transferred, the CBET gain was measured (solid curve) to decrease as a function of time. Over this same time period where CBET was active, Thomson-scattering measurements showed a rapid increase in the ion temperature (circles); the final ion temperature was nearly a factor of 2 larger than the electron temperature. When accounting for this increased ion temperature, the linear CBET calculations (diamonds) were in excellent agreement with the measurements ([173]).

Figure 50

Equatorial shell trajectories from postprocessed simulated (solid lines) and experimental (symbols) backlit radiographs show improved coupling when the relative frequency between crossing beams is changed. The lower lines and symbols represent the baseline zero frequency detuning experiments. The upper lines and symbols represent the average of the two detuning experiments. From [306].

Figure 51

Results from three sequential implosion campaigns at OMEGA extrapolated to 1.9 MJ of symmetric illumination using the hydrodynamic scaling relations. The contours represent curves of constant extrapolated fusion yield (in kJ) (squares, circles, and diamonds are in a temporal sequence starting in 2015). The arrow points in the direction of future experiments. The increase in yield since 2015 resulted in implosions that would produce about 500–600 kJ of fusion energy at NIF laser energies of 1.9 MJ, with about a third of the yield from hydrodynamic compression and two-thirds from alpha-particle self-heating. From [159].

Figure 52

Fusion yield of OMEGA DT-layered implosions hydrodynamically scaled to 1.9 MJ of symmetric illumintation vs the no-alpha-particle Lawson parameter scaled to 1.9 MJ. Courtesy of V. Gopalaswamy (LLE).

Figure 53

(a) Mechanical drawing of the target chamber for the National Ignition Facility, with the blue cylinders indicating the beam port positions used for laser indirect drive (i.e., x-ray drive). Polar direct drive uses this beam geometry. (b) Same as (a) except for spherical direct drive, where the beams are spread uniformly around the target chamber. This is the ideal beam arrangement for laser direct drive. From [191].

Figure 54

Beam repointing schemes for polar direct drive of (a) the National Ignition Facility and (b) the OMEGA laser. The cylinders to the upper right of each image indicate the beam port locations and ring identifications, and the blue arrows indicate the beam repointing to the polar angles shown on target to achieve optimized laser-driven symmetry in the polar-direct-drive geometry. From [309].

Figure 55

Target solutions investigated to improve the implosion symmetry of polar-direct-drive implosions. (a) The measured contoured-shell thickness (diamonds) as a function of polar angle is compared to the ideal contoured profile. Reducing the mass around the equator of the target compensates for the reduced energy coupling of polar direct drive in this region. From [309]. (b) Depicted addition of a low-$Z$ ring around the capsule equator, where refraction in the plasma formed around this ring permits time-dependent tuning of the capsule drive uniformity. From [99].

Figure 56

$Z$ at Sandia National Laboratories.

Figure 57

Double-ended $Z$-pinch hohlraum concept, with (a) top and (b) bottom primary hohlraums, with each containing a notional wire-array $Z$ pinch with an internal pulse-shaping target, (c) a high-yield fusion capsule, (d) a secondary hohlraum containing the capsule, (e) an on-axis permanent shine shield and radial spoke electrode structures, (f) upper and lower electrical power feeds, (g) secondary entrance tamping foam, and (h) a $P_4$ symmetry shield.

Figure 58

Schematic of the dynamic hohlraum.

Figure 59

Schematic of the magnetic implosion of a liner.

Figure 60

Schematic of the MagLIF configuration within $Z$.

Figure 61

Schematic of MagLIF. The laser beam is green, the heated fuel is red, and the liner is black.

Figure 62

The three steps of MagLIF.

Figure 63

Schematic of the $Z$ convolute. The convolute adds the four inflow currents into one feed current.

Figure 64

Schematic of MagLIF with the new lower inductance feed and new magnetic-field coils. This feed geometry approaches the minimal inductance configuration obtained from a variational calculus method ([197], [482]).

Figure 65

Measured currents plotted as a function of time for the old (low inductance) and new (i.e., high inductance) MagLIF feeds.

Figure 66

Schematic of the AutoMag concept. The gaps in the metal would be filled with an insulator such as epoxy.

Figure 67

Radiograph of a beryllium liner implosion at different times without an axial magnetic field.

Figure 68

Radiograph of a beryllium liner implosion at a convergence of 2.7 with an applied 7 T axial magnetic field.

Figure 69

A 3D gorgon simulation compared to a self-emission x-ray image of the stagnated fuel in a MagLIF experiment at $Z$.

Figure 70

X-ray images of stagnated fuel for MagLIF experiments with and without a dielectric coating on the liner.

Figure 71

Interface positions as a function of time from lasnex simulations with and without a layer of cryogenic fuel on the inside of the liner.

Figure 72

lasnex simulated yields of optimized MagLIF with a cryogenic wetted foam layer on the inside of the liner.