Applying an external magnetic field to laser-driven inertial confinement fusion implosions is a promising approach for enhancing fusion yield. The field is compressed with the plasma, producing a magnetized hotspot that anisotropically suppresses thermal losses and traps alpha particles, making performance sensitive to the compressed field orientation. We derive a simple, readily applicable analytic model that enables rapid evaluation of the compressed field topology and show that ablation into the hotspot amplifies the central field, while the ablated ice near the hotspot edge develops a decaying, radially bent field, with a discontinuity in the field direction. The radially bent field renders thermal insulation at the hotspot edge negligible and largely independent of the applied field strength, whereas insulation in the hotspot core still depends strongly on the applied field. Applying the model to non-axial initial field configurations, we find that an initially applied mirror field provides the greatest suppression, followed by the standard axial field.

Imposing a magnetic field on inertial confinement fusion implosions magnetizes the electrons in the compressed fuel; this suppresses thermal losses, which increases temperature and fusion yield. Indirect-drive experiments at the National Ignition Facility with 12 and 26 T applied magnetic fields demonstrate up to 40% increase in temperature, 3× increase in fusion yield, and indicate that magnetization alters the radial temperature profile [Moody et al., Phys. Rev. Lett. 129, 195002 (2022); Lahmann et al., APS DPP (2022)]. In this work, we develop a semi-analytic hot-spot model, which accounts for the two-dimensional (2D) Braginskii anisotropic heat flow due to an applied axial magnetic field. First, we show that hot-spot magnetization alters the radial temperature profile, increasing the central peakedness, which is most pronounced for moderately magnetized implosions (with 8–14 T applied field), compared to both unmagnetized (with no applied field) and highly magnetized (with 26 T or higher applied field) implosions. This model explains the trend in the experimental data, which finds a similarly altered temperature profile in the 12 T experiment. Next, we derive the hot-spot model for gas-filled (Symcap) implosions, accounting for the effects of magnetization on the thermal conduction and in changing the radial temperature (and density) profiles. Using this model, we compute predicted central temperature amplification and yield enhancement scaling with the applied magnetic field. The central temperature fits the experimental data accurately, and the discrepancy in the yield suggests a systematic (independent of applied field) degradation, such as mix, and additional degradation in the reference unmagnetized shot, such as reduced laser drive, increased implosion asymmetry, or the magnetic field suppressing ablator mixing into the hot-spot.

This work supports the findings in the companion paper [Frank and Bose, "Self-generated magnetic fields in the hot spot of direct-drive cryogenic implosions at Omega," Phys. Plasmas 31(8), 082709 (2024)] by describing the incorporation of magnetohydrodynamic (MHD) solvers into the inertial confinement fusion (ICF) deceleration code DEC2D and the validation of these solvers. The Rayleigh-Taylor instability causes the self-generation of magnetic fields due to the Biermann battery effect, and the incorporation of MHD solvers into DEC2D enables modeling of these self-generated fields for direct-drive targets, as demonstrated in Frank and Bose (2024). DEC2D is a cylindrical Eulerian code with toroidal magnetic fields, in which azimuthal symmetry is assumed. DEC2D solves the non-ideal induction equation, including the fluid and Nernst advection, resistive diffusion, and the Biermann source term, incorporates the effects of magnetized heat flow and magnetic pressure in the energy equation, and includes the J(->)xB(->) term in the momentum equation. The magnetized heat flow includes both the perpendicular transport suppression and the Righi-Leduc heat flow. Alternative magnetized transport coefficients have been incorporated into DEC2D simulations, and it is found that small but non-negligible differences in yield and ion temperature are demonstrated for the different formulations. (c) 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) license (https://creativecommons.org/licenses/by-nc-nd/4.0/). https://doi.org/10.1063/5.0278219

This work reports that Biermann self-generated magnetic fields of ≈200 MG and Hall parameters of ≈1.5 are produced in the stagnation phase of direct-drive cryogenic implosions at Omega. The magnetic fields produce a drop of 2.4% in fusion yield and 1% in ion temperature. A quantitative estimate of the effect of self-generated magnetic fields on yield and ion temperature is essential, since direct measurements of these fields are not available. Reconstructed simulations of the 50 Gbar implosions, with all the stagnation measurements reproduced simultaneously by a combination of mid- and low-mode asymmetries as degradation mechanisms [Bose et al., Phys. Plasmas 25, 062701 (2018)], are used to obtain the estimates. The magnetic fields cause a decrease in yield due to the Righi–Leduc heat flow, which exceeds any benefits from heat flow suppression due to magnetization. It is important to note that both direct-drive Omega-scale implosions and indirect-drive National Ignition Facility (NIF)-scale implosions [Walsh et al., Phys. Rev. Lett. 118, 155001 (2017)] produce similar estimates for the magnetic field strength, and both show a decrease in fusion yield, with the Righi–Leduc transport as the loss mechanism. However, the yield degradation at Omega is small and lower by ≈5× compared to the indirect-drive ignition-scale NIF estimate.

Fuel–shell mix in kinetic plasma conditions is probed using nuclear and x-ray self-emission in shock-driven, D3He-gas-filled inertial confinement fusion implosions. As initial gas fill density decreases, measured nuclear yields and ion temperatures are lower than expected as compared to radiation-hydrodynamic simulations. Spatially and temporally resolved x-ray emissions indicate significant mixing at the fuel–shell interface in implosions with low initial gas fill density. This observed fuel–shell mix introduces a substantial amount of shell ions into the center of the implosion prior to and during shock flash and is the key mechanism needed in the kinetic-ion simulations to match experimental nuclear yields.

This Letter presents the first observation on how a strong, 500 kG, externally applied B field increases the mode-two asymmetry in shock-heated inertial fusion implosions. Using a direct-drive implosion with polar illumination and imposed field, we observed that magnetization produces a significant increase in the implosion oblateness (a 2.5× larger P2 amplitude in x-ray self-emission images) compared with reference experiments with identical drive but with no field applied. The implosions produce strongly magnetized electrons (ω_{e}τ_{e}≫1) and ions (ω_{i}τ_{i}>1) that, as shown using simulations, restrict the cross field heat flow necessary for lateral distribution of the laser and shock heating from the implosion pole to the waist, causing the enhanced mode-two shape.

Measured yields and ion temperatures inferred from the fusion product energy spectra can be used as metrics for the performance of an ICF implosion. This can be used to infer species separation, thermal decoupling, flows, or other effects that can cause the inferred ion temperatures to deviate from the true underlying thermal temperature and the yield ratio to deviate from the expected value. Direct inference of the impact of these effects on observed temperatures and yields can be difficult to uncover due to the underlying dependence on the shape and time evolution of the temperature and density profiles of the fusing plasma. Due to differences in the temperature dependence of the reactivities, different fusion products are emitted from different regions and times within the implosion. In order to properly account for this, a second-order analytical expression relating the apparent temperatures and yield ratios is developed. This expression can be coupled to models of yield and/or temperature altering effects to infer their burn-averaged impact on an implosion. The second-order expression shows significant improvement over lower-order expressions in synthetic data studies. Demonstrations of its applications to synthetic data coupled with models of ion thermal decoupling and radial flows are presented. In the case of thermal decoupling, both first and second-order expressions show reasonable levels of accuracy. To consistently infer the amplitude of radial flow with a <10% error, the second-order equation is required.

We report on the design and implementation of a new system used to characterize the energy-dependent x-ray transmission curve, Θ(E), through filters used in high-energy density physics diagnostics. Using an Amptek X-123-CdTe x-ray spectrometer together with a partially depleted silicon surface barrier detector, both the energy spectrum and total emission of an x-ray source have been accurately measured. By coupling these detectors with a custom PROTO-XRD x-ray source with interchangeable cathodes, accurate characterizations of Θ(E) for filters of varying materials and thicknesses have been obtained. The validity of the technique has been confirmed by accurately reproducing areal densities for high-purity filters with known x-ray transmission properties. In this paper, the experimental setup is described and the results of absorption calibrations performed on a variety of different filters are presented.

A series of thin glass-shell shock-driven DT gas-filled capsule implosions was conducted at the OMEGA laser facility. These experiments generate conditions relevant to the central plasma during the shock-convergence phase of ablatively driven inertial confinement fusion (ICF) implosions. The spectral temperatures inferred from the DTn and DDn spectra are most consistent with a two-ion-temperature plasma, where the initial apparent temperature ratio, T_{T}/T_{D}, is 1.5. This is an experimental confirmation of the long-standing conjecture that plasma shocks couple energy directly proportional to the species mass in multi-ion plasmas. The apparent temperature ratio trend with equilibration time matches expected thermal equilibration described by hydrodynamic theory. This indicates that deuterium and tritium ions have different energy distributions for the time period surrounding shock convergence in ignition-relevant ICF implosions.

A target design for mitigating the Rayleigh-Taylor instability is proposed for use in high energy density and direct-drive inertial confinement fusion experiments. In this scheme, a thin gold membrane is offset from the main target by several-hundred microns. A strong picket on the drive beams is incident upon this membrane to produce x rays which generate the initial shock through the target. The main drive follows shortly thereafter, passing through the ablated shell and directly driving the main target. The efficacy of this scheme is demonstrated through experiments performed at the OMEGA EP facility, showing a reduction of the Rayleigh-Taylor instability growth which scales exponentially with frequency, suppressing development by at least a factor of 5 for all wavelengths below 100 μm. This results in a delay in the time of target perforation by ∼40%.

Fuel-ion species dynamics in hydrodynamiclike shock-driven DT^{3}He-filled inertial confinement fusion implosion is quantitatively assessed for the first time using simultaneously measured D^{3}He and DT reaction histories. These reaction histories are measured with the particle x-ray temporal diagnostic, which captures the relative timing between different nuclear burns with unprecedented precision (∼10  ps). The observed 50±10  ps earlier D^{3}He reaction history timing (relative to DT) cannot be explained by average-ion hydrodynamic simulations and is attributed to fuel-ion species separation between the D, T, and ^{3}He ions during shock convergence and rebound. At the onset of the shock burn, inferred ^{3}He/T fuel ratio in the burn region using the measured reaction histories is much higher as compared to the initial gas-filled ratio. As T and ^{3}He have the same mass but different charge, these results indicate that the charge-to-mass ratio plays an important role in driving fuel-ion species separation during strong shock propagation even for these hydrodynamiclike plasmas.

Focusing laser light onto a very small target can produce the conditions for laboratory-scale nuclear fusion of hydrogen isotopes. The lack of accurate predictive models, which are essential for the design of high-performance laser-fusion experiments, is a major obstacle to achieving thermonuclear ignition. Here we report a statistical approach that was used to design and quantitatively predict the results of implosions of solid deuterium-tritium targets carried out with the 30-kilojoule OMEGA laser system, leading to tripling of the fusion yield to its highest value so far for direct-drive laser fusion. When scaled to the laser energies of the National Ignition Facility (1.9 megajoules), these targets are predicted to produce a fusion energy output of about 500 kilojoules-several times larger than the fusion yields currently achieved at that facility. This approach could guide the exploration of the vast parameter space of thermonuclear ignition conditions and enhance our understanding of laser-fusion physics.

Exploding pusher targets, i.e. gas-filled, large aspect-ratio shells, driven by a strong lasergenerated shock, are widely used as pulsed sources of neutrons and fast charged particles. Due to small convergence ratio, exploding pushers are little affected by fluid instabilities and are weakly sensitive to irradiation nonuniformities. Development of high spaceand time-resolution neutron and X-ray diagnostics allows for detailed comparison of experimental data with simulations, and for validation of simulation models. In particular, we refer to simulations with the DUED code of a series of direct-drive experiments performed at the OMEGA laser (reported in Refs [1, 2], and others currently being analyzed) and two indirect-drive NIF shots [3]. Comparisons provided evidence for the transition from a nearly fluid behaviour to a kinetic one, as the implosion Knudsen number Kn (ratio of ion mean-free path to compressed gas radius) becomes comparable or larger than one [1]. Agreement between predicted and measured observables worsens as Kn grows. Ion separation effects occur also for Kn < 1, i.e. in a quasi-hydrodynamic regime [2]. Here we show that in the quasi-hydrodynamic limit simulations reproduce DD and DT reaction yields, bang times, burn-widths, burn radii, compressed fuel radius, reaction-averaged ion temperatures. (For gas fills also containing 3He, the delay between D-3He bang time, instead, is not predicted.) Instrumental to the achievement of such an agreement was the introduction of ion viscosity, of a smooth transition between ion viscosity and artificial viscosity, of an appropriate limiter for momentum flux, of bulk fluid motion in the Monte Carlo neutron synthetic diagnostics. The sensitivity of the results to the shell opacity model has also been tested.

Simultaneously measured DD, DT, and D3He reaction histories are used to probe the impacts of multi-ion physics during the shock phase of inertial confinement fusion implosions. In these relatively hydrodynamiclike (burn-averaged Knudsen number ⟨NK⟩ ∼0.3) shock-driven implosions, average-ion hydrodynamic DUED simulations are able to reasonably match burnwidths, nuclear yields, and ion temperatures. However, kinetic-ion FPION simulations are able to better simulate the timing differences and time-resolved reaction rate ratios between DD, DT, and D3He reactions. FPION simulations suggest that the D3He/DT reaction rate ratio is most directly impacted by ion species separation between the 3He and T ions, whereas the D3He/DD reaction rate ratio is affected by both ion species separation and ion temperature decoupling effects.

The study of Rayleigh–Taylor instability in the deceleration phase of inertial confinement fusion implosions is carried out using the three-dimensional (3-D) radiation-hydrodynamic Eulerian parallel code DEC3D. We show that the yield-over-clean is a strong function of the residual kinetic energy (RKE) for low modes. Our analytical models indicate that the behavior of larger hot-spot volumes observed in low modes and the consequential pressure degradation can be explained in terms of increasing the RKE. These results are derived using a simple adiabatic implosion model of the deceleration phase as well as through an extensive set of 3-D single-mode simulations using the code DEC3D. The effect of the bulk velocity broadening on ion temperature asymmetries is analyzed for different mode numbers ℓ=1–12. The jet observed in low mode ℓ=1 is shown to cause the largest ion temperature variation in the mode spectrum. The vortices of high modes within the cold bubbles are shown to cause lower ion temperature variations than low modes.