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DOE OSTI2026

XFEL imaging techniques for high energy density and inertial fusion energy research at HED-HiBEF

The imaging platform developed at the High Energy Density-Helmholtz International Beamline for Extreme Fields (HED-HiBEF) instrument at the European X-ray Free Electron Laser (XFEL) and its applications to HED and fusion related research are presented. The platform combines the XFEL beam with the high-intensity short-pulse laser ReLaX and the high-energy nanosecond-pulse laser DiPOLE-100X. The spatial resolution is better than 500 nm and the temporal resolution of the order of 50 fs. The influence of the XFEL source in the x-ray imaging method is discussed. Free-propagation x-ray phase contrast imaging and Talbot-Lau imaging setups are shown. We show examples of blast waves and converging cylindrical shocks in aluminum, resonant absorption measurements of specific charged states in copper with ReLaX and planar shocks in polystyrene material generated by DiPOLE-100X. For the first time, we show the application of Talbot-Lau interferometry to convergent cylindrical shocks as well as resonant absorption processes. We also discuss the possibilities introduced by combining this imaging platform with a kJ-class laser.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Staged Z-pinch experiment at the double-EAGLE pulsed power facility

The staged Z-pinch is a potential high-energy gain fusion concept where a high atomic number liner implodes on a deuterium target using a pulsed multi-MA current source. Over the past several years this concept has been studied on 0.5–1.0 MA facilities using Ar and Kr gas puffs injected at R = 1.2 cm. Neutron yield up to (2.5 ± 0.34) x 10 10 was measured, Ruskov et al (2023 IEEE Trans. Plasma Sci. 51 3310–6). Here, in this study, we present experimental results from the 4 MA, 110 ns current rise time Double-EAGLE facility at L3Harris (currently, Fisica Inc.) where a larger radius nozzle created gas density profiles peaked at R = 2.5 cm. Modeling with the MACH2 and FLASH codes indicates that the larger radius allows stronger acceleration of the liner plasma and generation of shock waves that preheat a target plasma layer next to the liner to temperatures $T_i >$1 keV. The resulting counter thermal pressure on the liner plasma limits the growth of the Magneto-Rayleigh–Taylor (MRT) instability at the liner-vacuum boundary and the implosion proceeds in a relatively stable manner. Near bang time the enormous target plasma thermal pressure smoothens the MRT perturbations developed during the earlier implosion stages. Time integrated x-ray pinhole images with cutoff energy of 100 eV confirm that a long (∼3 cm), stable and uniform high energy density plasma column is formed in the final implosion stage. Consistent neutron yield in the 10 10 –10 11 range was measured for both Ar and Kr liners imploding on a deuterium target.

Physics - Plasma physics↗

DOE OSTI2026

Recent advances in plasma control and physics research in the Large Helical Device

The Large Helical Device (LHD), the largest superconducting helical system in the world, is equipped with advanced heating and diagnostic tools, facilitating plasma control and physics research. Data assimilation was employed for electron temperature control using a real-time Thomson scattering system and real time prediction code. A virtual LHD environment enabled visualization of escaping high-energy tritium ions and demonstrated that these ions impact the rear side of the divertor plate. Pioneering results crucial to plasma control have also been achieved. Real-time wall conditioning using Lithium granule dropping improved bulk ion energy and particle transport while simultaneously enhancing the heavy impurity transport. Progress has also been made in the investigation of turbulence-driven transport. At the confinement bifurcation, ion-scale turbulence decreased, while electron-scale turbulence increased. A change in the anisotropy of turbulent eddies was also observed at the confinement bifurcation. Coexistence of local and non-local turbulence was identified in electron-scale turbulence. Non-local turbulence exhibited the rapid spatial propagation of perturbations throughout the plasma, while local turbulence followed the temperature gradient. A transition between drift-wave turbulence and magnetohydrodynamics (MHD) turbulence was observed with the turbulence minimized at the transition condition. Machine learning analysis was employed to evaluate the temperate and density conditions of this turbulence transition. Then, real-time control of fueling and heating was applied to maintain the turbulence transition condition, improving the energy confinement enhancement factor by 20%. In addition, evidence was obtained for collisionless ion heating by energetic-ion-driven geodesic acoustic modes and MHD bursts. These achievements represent unique contributions to the development of fusion reactors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Particle-in-cell simulations of burning inertial confinement fusion capsule implosions

Anomalies observed in the neutron spectral shift of high-yield shots at the National Ignition Facility (NIF) suggest the presence of suprathermal ions [E. P. Hartouni et al., Nat. Phys. 19, 72 (2023)], implying that kinetic effects play a significant role in burning inertial confinement fusion (ICF) plasmas. Furthermore, recent measurements of reaction-in-flight (RIF) neutrons offer a direct probe of the stopping power in the burning fuel region of high-energy alpha particles and up-scattered fuel ions. We have developed the particle-in-cell code PICNIC, an exactly energy-conserving particle-in-cell Monte-Carlo collision (PIC-MCC) code to simulate the burn stage in ICF. We present results from 1D spherical simulations of NIF shot N210808, which was the first to exceed the Lawson criterion for laser fusion. We find that the suprathermal ions generated by large-angle Rutherford and nuclear elastic scattering (NES) with fusion alphas produce an alpha knock-on neutron (AKN) signal consistent with the extent and relative yield of the AKN spectrum identified in ignition experiments at the NIF. Furthermore, we also find that the inclusion of large-angle scattering physics does not explain the anomalously large spectral shift observed in the experiment.

High-energy-density plasmas↗

DOE OSTI2025

Synthesis and characterization of electron beam irradiation-induced damage in polycrystalline metal thin films

High-energy physics research, industrial sterilizing, and material processing depend extensively on electron beam accelerators. Exit windows are crucial components of such electron accelerator systems, maintaining vacuum integrity inside the machine while providing mechanical strength, thermal stability, and radiation resistance at the beam-target interface. In this study, thin metallic films of Ni, Ti, Cr, and V were explored for use in electron beam exit windows, and their properties were compared with the properties of their bulk counterparts. Simulation results of metal foils predicted Ti to exhibit less beam power dissipation compared to Ni. However, Ni possesses superior mechanical and structural properties compared to Ti. The performance of these films under electron beam irradiation was examined by depositing thin layers of these films on silicon and metallic substrates using magnetron sputtering and exposing them to e-beam irradiation in a controlled setup. The deposited films were subjected to a dose of approximately 66 kGy at a beam energy of 10 MeV and characterized prior to and postexposure to the beam using field emission scanning electron microscopy, atomic force microscopy, x-ray diffraction (XRD), and nanoindentation. Particular emphasis was given to characteristics like the grain structure, surface morphology, dislocation density, and hardness. XRD patterns revealed irradiation-induced changes in peak intensities, while the crystallinity remained largely unchanged. Nanoindentation results showed that the pristine and irradiated Ti and Ni films were twice as hard when compared to bulk Ti and Ni samples, regardless of the substrate type used (Si or bulk Ti, or Ni). These results emphasize the superior mechanical properties of thin metal films compared to their bulk counterparts. In conclusion, this study advances the optimization of thin film materials for robust and efficient e-beam applications, ensuring improved durability and operational reliability.

AFM↗

DOE OSTI2026

Beyond $\rho ^{2/3}$ scaling: microscopic origins and multimessengers of high-density nuclear symmetry energy

The nature and Equation of State (EOS) of dense neutron-rich matter are still very poorly known, while they have broad impacts on many interesting issues in both astrophysics and nuclear physics. In particular, the nuclear symmetry energy $E_{\textrm{sym}}(\rho )$ encoding the cost to make nuclear matter more neutron-rich has been the most uncertain component of the EOS of dense neutron-rich nucleonic matter. It significantly affects the radii, tidal deformations, cooling rates, and frequencies of various oscillation modes of isolated neutron stars as well as the strain amplitude and frequencies of gravitational waves from their mergers, besides its many effects on the structures of nuclei as well as the dynamics and observables of their collisions. Siemens (1970s) observed that $E_{\textrm{sym}}(\rho )$ scales as $(\rho /\rho _0)^{2/3}$ near the saturation density $\rho _0$ of nuclear matter, since both the kinetic part and the potential contribution (quadratic in momentum) exhibit this dependence. The scaling holds if: (1) the nucleon isoscalar potential is quadratic in momentum, and (2) the isovector interaction is weakly density-dependent. After examining many empirical evidences and understanding theoretical findings in the literature, we conclude that: (1) Siemens’ $\rho ^{2/3}$ scaling is robust and serves as a valuable benchmark for both nuclear theories and experiments up to $2\rho _0$ but breaks down at higher densities, (2) Experimental and theoretical findings about $E_{\textrm{sym}}(\rho )$ up to $2\rho _0$ are broadly consistent, but uncertainties remain large for its curvature $K_{\textrm{sym}}(\rho )$ and higher-order parameters, (3) Above $2\rho _0$ , uncertainties grow due to poorly constrained spin-isospin-dependent tensor and three-body forces as well as the resulting nucleon short-range correlations. Looking forward, combining signals from both observations of neutron stars and terrestrial heavy-ion reaction experiments is the most promising path to finally constraining the high-density $E_{\textrm{sym}}(\rho )$ and the EOS of supradense neutron-rich matter. Multiple examples of community efforts to further constrain the high-density $E_{\textrm{sym}}(\rho )$ using both real and mocked data of present and future high-precision observations of neutron stars, as well as heavy-ion collisions involving high-energy rare isotopes, are briefly reviewed.

Li, Bao-An [East Texas A & M Univ., Commerce, TX (↗

DOE OSTI2025

High-energy X-ray radiography with apodized petawatt laser beams

We have produced laser wakefield-accelerated electron beams with energies of 2 GeV in Target Area 1 of the ZEUS facility. These electron beams oscillate in the accelerating structure that is produced in the wake of an ultrashort laser pulse (25 fs). These ’betatron’ oscillations result in the emission of a collimated (4 mrad divergence) beam of high-energy X-ray/gamma photons (on the order of several hundred keV). In this work, we demonstrate the capabilities of the ZEUS laser system by showing that apodizing the laser beam in the near field allows for the production of high-quality betatron X-rays for radiography purposes. This demonstrates that a high-power, large-aperture laser beam could be split into multiple parts to drive betatron X-ray sources from multiple angles or temporal delays into a High Energy Density (HED) target to be probed, enabling pump-probe measurements at multiple temporal delays or tomography on a single shot.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Microstructure-Based Understanding of High-Temperature Deformation Behaviors in Laser Powder Bed Fusion (LPBF) 316H Stainless Steel

This report presents the results of high-temperature mechanical property testing and microstructural analysis of laser powder bed fusion (LPBF) 316H stainless steel (SS) conducted during Fiscal Year 2025 (FY25) under the U.S. Department of Energy, Office of Nuclear Energy’s Advanced Materials and Manufacturing Technologies (AMMT) program. The study builds upon prior work by expanding the mechanical property test matrix and advancing a microstructure-based mechanistic understanding of LPBF 316H SS performance, with a focus on the solution annealed (SA, 1100°C for 1 hour) materials. High-temperature tension, creep, fatigue, and creep-fatigue tests were performed. Thermal aging studies were conducted. Advanced characterization techniques, including scanning electron microscopy (SEM), scanning transmission electron microscopy (STEM), and high-energy synchrotron X-ray diffraction, were employed to investigate the microstructural evolution during thermal aging and mechanical testing. It was discovered that the as-built (AB) LPBF 316H SS exhibited precipitation kinetics during thermal aging that are 10–100 times faster than its wrought counterpart due to the presence of high densities of preferred nucleation sites, while the precipitation kinetics in SA LPBF 316H was under investigation. The accelerated precipitation of embrittling phases such as sigma phase in LPBF 316H SS compared to its wrought counterpart led to significant impacts on creep ductility. The influence of laser printing parameters and build orientations on fatigue and creep-fatigue performance was observed. In assessing the creep-fatigue performance, it was discovered that the SA LPBF 316H samples failed in less than 200 cycles under 595°C, 0.5% (strain amplitude) with a 60-minute hold time. This work establishes a mechanistic framework for predicting the long-term behavior of LPBF 316H SS, supporting its rapid qualification under the ASME BPVC. The findings contribute to the broader goal of enabling the deployment of advanced materials in next-generation nuclear energy systems. An outlook for FY26 work, including continued aging studies, mechanical testing, and microstructural characterization, is provided.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Closure models for the feedback of energetic particles on plasma turbulence

Energetic particles interact with the plasma surrounding them, resonating with certain types of plasma waves to stabilize them while destabilizing others, and changing the character of the background turbulence in ways that have not been fully quantified or understood. Interaction with the turbulent background plasma is key to the acceleration of many types of energetic particles including high-energy cosmic rays, solar energetic particles, and pick-up ions. The acceleration of particles is a process that would ideally be described by a kinetic model, a type of model that follows a probability distribution function (PDF) for all particles in 7-dimensional (x, y, z, v x , v y , v z , t) space. Because of the high dimensionality of a kinetic model, simulations that solve kinetic equations use the largest computational resources currently available, and are yet unable to simulate a realistic number of particles, reach the large scales necessary for astrophysical problems, and use high-precision numerical methods. Two available alternatives to kinetic plasma models have been explored for this problem, with limited success. One is a multi-fluid model produced by a cumulant discarding closure, which evolves coupled equations for the velocity, magnetic field, and internal energy for both the background plasma and the fluid of energetic particles. However, simulations that solve multi-fluid magnetohydrodynamic (MHD) equations are able to include the interaction with energetic particles only in crude ways, typically as an add-on pressure term. The second alternative is to use a hybrid method to couple a fluid description of the background plasma to a kinetic model or a Fokker–Planck model for the energetic particles. These methods are hampered by the physical modeling of the coupling. In this work, we develop a new model, which follows the PDF for all particles; this can be viewed as a step toward physical realism above a multi-fluid MHD model, while also being more computationally efficient than a kinetic model. The equations we develop model both the background plasma and the energetic particles self-consistently. Over the last decade, similar PDF methods have been developed to a high level of sophistication to model reactive flows and turbulent combustion for engineering applications. For treatment of the feedback of the energetic particles on a background plasma, a PDF closure approach should evaluate the mean characteristics, including the density, with better statistical quality than will particle-sampling procedures.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Combustion synthesis of nanoscale magnesium borides with improved hydrogen uptake and release

The overarching goal of the reported project was to develop reversible metal hydrides that can be dehydrogenated and recharged at relatively low temperatures and pressures. The project complemented the research on reversible metal hydrides for hydrogen storage conducted by the Hydrogen Materials – Advanced Research Consortium (HyMARC). The students involved were trained at both the University of Texas at El Paso (UTEP) and Sandia National Laboratories (SNL). The research objectives were to fabricate nanoscale magnesium boride powders with different B/Mg atomic ratios and to investigate the effects of B/Mg ratio and particle size on the hydrogenation properties of the obtained materials. Magnesium diboride (MgB 2 ) and tetraboride (MgB 4 ) were synthesized by using combustion synthesis and by heating in a tube furnace. The latter method resulted in materials with significantly reduced impurity levels. An effective method for the removal of magnesium oxide impurities was identified. High-energy ball milling produced submicron MgB 2 and MgB 4 powders. However, hydrogenation experiments at pressures up to 700 bar have not shown any uptake of hydrogen. Thermogravimetric analysis of the decomposition of the obtained MgB 2 and MgB 4 demonstrated higher thermodynamic stability of the latter. Thus, the boron-rich nature and phase stability of magnesium borides with high B/Mg ratios make them poor candidates for direct hydrogenation. However, the synthesized MgB 4 is a promising energetic additive to solid fuels for high-speed air-breathing propulsion as it offers a lower oxidation onset temperature and greater energy density than MgB 2 .

08 HYDROGEN↗

DOE OSTI2026

Characterizing the γ-Ray Emission from Low-luminosity AGN

A majority of the active galactic nuclei (AGN) in the local Universe are classified as low-luminosity AGN (LLAGN), having bolometric luminosities ≲10 42 erg s −1 . Although high-energy γ-ray emission is predicted from both the jets and disks of LLAGN, to date only four have been detected by the Fermi Large Area Telescope (Fermi-LAT). In this work, we therefore conduct a comprehensive study of all the LLAGN from the Palomar spectroscopic survey of bright, northern galaxies, including both subthreshold and detected γ-ray sources, using 14.4 yr of LAT data. Our analysis results in a new detection of one LLAGN, as well as a detection of the subthreshold population using a stacking technique. We find that the signal from the subthreshold sample is consistent with being dominated by star formation activity, although a contribution from compact jets or a mixed contribution from jetted and nonjetted systems is also feasible. On the other hand, the individually detected LLAGN are likely dominated by jet emission. We perform detailed spectral modeling for a subset of these sources and find that the γ-ray signal can be explained by synchrotron self-Compton radiation if the inner jet emission region is weakly magnetized, with its total energy density being strongly particle dominated and only slowly moving. With this work we also publicly release our Python-based stacking library for analyzing subthreshold source populations with the LAT based on a proven technique used in numerous studies.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Maximum Energy of Particles Accelerated in Gamma-Ray Burst Afterglow Shocks

Particle acceleration in relativistic collisionless shocks remains an open problem in high-energy astrophysics. Particle-in-cell (PIC) simulations predict that electron acceleration in weakly magnetized shocks proceeds via small-angle scattering, leading to a maximum electron energy significantly below the Bohm limit. This upper bound on electron energy manifests observationally as a characteristic synchrotron cutoff, providing a direct probe of the underlying acceleration physics. Gamma-ray burst (GRB) afterglows offer an exceptional laboratory for testing these predictions. Here, we model the spectral evolution of GRB afterglows during the relativistic deceleration phase, incorporating PIC-motivated acceleration prescriptions and self-consistently computing synchrotron and synchrotron self-Compton emission. We find that low-energy bursts in low-density environments, typical of short GRBs, exhibit a pronounced synchrotron cutoff in the GeV band within minutes to hours after the trigger. Applying our framework to GRB 190114C and GRB 130427A, we find that current observations are insufficient to discriminate between PIC-motivated acceleration and the Bohm limit, primarily due to poor photon statistics in the Fermi-Large Area Telescope band. Nevertheless, future MeV–TeV afterglow observations can break model degeneracies and place substantially tighter constraints on the mechanisms responsible for particle acceleration in relativistic shocks. To this end, we simulate a fiducial nearby short GRB as a promising probe of the cutoff location, for which the two acceleration scenarios are cleanly distinguishable and the detection of such an event in the near future remains feasible.

Wu, Zhao-Feng [Purdue University, West Lafayette, ↗

DOE OSTI2026

Evidence for Neutrino Emission from X-Ray Bright Seyfert Galaxies in the Southern Hemisphere Using Enhanced Starting Track Events with IceCube

IceCube recently reported the observation of TeV neutrinos from the nearby Seyfert galaxy NGC 1068, and the corresponding neutrino flux is significantly higher than the upper limit implied by observations of GeV–TeV gamma rays. This suggests that neutrinos are produced near the supermassive black hole, where the radiation density is high enough to obscure gamma rays. We use a set of muon neutrinos with interaction vertices inside the detector, which have good sensitivity to sources in the southern sky, from IceCube data recorded between 2011 and 2021. We then search for individual and collective neutrino signals from 14 Seyfert galaxies in the southern sky selected from the Swift Burst Alert Telescope AGN Spectroscopic Survey. Using the correlations between keV X-rays and TeV neutrinos predicted by disk–corona models, and assuming production characteristics similar to NGC 1068, a collective neutrino signal search reveals an excess of $6.{7}_{-3.2}^{+4.0}$ events, which is inconsistent with background expectations at the 3σ level of significance. In this Letter, we present new independent evidence that Seyfert galaxies contribute to the extragalactic flux of high-energy neutrinos.

Seyfert galaxies↗

NASA NTRS1969

High-energy, high-power, long-life battery

High-energy-density primary battery achieves energy densities of up to 130 watt hrs./lb. The electrochemical couple consists of a lithium anode, a copper-fluoride cathode, and uses methyl formate/lithium hexafluoroarsenate for the electrolyte. Once achieved, battery life is approximately 30 hours.

Abens, S. G.↗

NASA NTRSDate not supplied

Solvent-Free Preparation of High Energy, Binder-Free Electrodes Enabled by Dry Compressible Holey Graphene

Graphene is an atomically thick sheet consisting of a graphitic carbon network with excellent mechanical strength, electrical and thermal conductivity, and chemical stability. Holey graphene, a structural derivative of graphene, has an array of through-the-thickness holes across the lateral surface of the nanosheet. The presence of these holes has minimal detrimental effect on the graphene properties and leads to enhanced performance in applications such as electronics, sensors, and energy storage. For example, these holes allow more facile cross-plane ion and gas transport than intact graphene, making holey graphene an ideal electrode material for electrochemical energy storage. This presentation will focus on the ability of holey graphene to be compression molded into robust articles or architectures under solvent-free conditions without the need for potentially parasitic binders. The unique dry compressibility of holey graphene has enabled facile fabrication of high mass loading electrodes with both high density and high porosity, which have found use in supercapacitors and various high-energy battery systems such as lithium-oxygen, lithium-sulfur, and lithium-selenium batteries.

Yi Lin↗

DOE OSTI2025

Vortex-Controlled Quasiparticle Multiplication and Self-Growth Dynamics in Superconducting Resonators

Even in the quantum limit, non-equilibrium quasiparticle (QP) populations induce QP poisoning that irreversibly relaxes the quantum state and significantly degrades the coherence of transmon qubits. A particularly detrimental yet previously unexplored mechanism arises from QP multiplication facilitated by vortex trapping in superconducting quantum circuits, where a high-energy QP relaxes by breaking additional Cooper pairs and amplifying the QP population due to the locally reduced excitation gap and enhanced quantum confinement within the vortex core. Here we directly resolve this elusive QP multiplication process by revealing vortex-controlled QP self-generation in a highly nonequilibrium regime preceding the phonon bottleneck of QP relaxation. At sufficiently low fluence, femtosecond-resolved magneto-reflection spectroscopy directly reveals a continuously increasing QP population that is strongly dependent on magnetic-field-tuned vortex density and absent at higher excitation fluences. Quantitative analysis of the emergent QP pre-bottleneck dynamics further reveals that, although the phonon population saturates within $\simeq$10~ps, both free and trapped QPs continue to grow in a self-sustained manner--hallmarks of the long-anticipated QP-vortex interactions in nonequilibrium superconductivity. We estimate a substantial increase of $\sim$34% in QP density at vortex densities of $\sim$ 100 magnetic flux quanta per $\mathrm{Î¼m^{2}}$. Our findings establish a powerful spectroscopic tool for uncovering QP multiplication and reveal vortex-assisted QP relaxation as a critical materials bottleneck whose mitigation will be essential for resolving QP poisoning and enhancing coherence in superconducting qubits.

Park, Joong M. [Ames Lab]↗

DOE OSTI2025

Likelihood-Based Particle Identification in the Short-Baseline Near Detector

Accurate particle identification is crucial in any high-energy physics experiment, allowing scientists to understand the unique interactions and mechanisms at play in a detector. In this project, I develop and study a new particle identification (PID) algorithm for the Short-Baseline Near Detector, a likelihood-based approach, different from out current $\chi^2$ method. A likelihood estimation offers a more physically motivated strategy for PID. The distribution random energy losses of charged particles traveling through a medium are described by the Vavilov probability density function. By using this model, we can account for random energy losses and construct likelihood functions specific to each particle type, potentially enabling a more accurate method for PID.

Vanderwaal, Sophia [U. Alabama, Huntsville] (ORCID↗

DOE OSTI2026

Ultra high-energy cosmic rays from relativistic outflows in accretion induced collapse of white dwarfs

When a rapidly-rotating, highly magnetized white dwarf (WD) approaches the Chandrashekhar limit through mass accretion, it can undergo an accretion-induced collapse (AIC) to form a proto-neutron star or protomagnetar. The protomagnetar can drive a magnetically-dominated relativistic outflow, whose low entropy can lead to efficient formation of heavy nuclei. In this work, we propose that such relativistic outflows from AIC of WDs can contribute as sources of ultra high-energy cosmic rays (UHECRs). We model the acceleration of heavy nuclei in these relativistic outflows, and show that AICs can dominantly power the observed UHECRs, if a majority of them host relativistic outflows. Accounting for uncertainties in the acceleration mechanisms and AIC rates, AICs can contribute $\sim$ a few $10^{43} - 10^{45}\ {\rm erg \ Mpc}^{-3} {\rm yr}^{-1}$ in UHECR energy generation rate density, assuming iron-like nuclei.