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DOE OSTI2026

Geometric scaling of laser-driven proton focusing from hemispherical foils

We systematically characterize the focusing behavior of laser-driven proton beams from hemispherical targets of various diameters using mesh radiography. The proton focal location is inferred to be near the geometrical center for the smallest tested hemisphere (Ψ = 𝐷 hemi /𝐷 Laser = 6.1). However, larger hemispheres (Ψ = 14.6) degrade the focusing behavior and behave more like flat foils with focal location significantly inside the hemisphere. We also infer a tight virtual focus of 9 ± 3 𝜇⁢m through a mesh transition analysis.

Griff-McMahon, J. [Princeton Univ., NJ (United Sta↗

DOE OSTI2021

High-power non-perturbative laser delivery diagnostics at the final focus of 100-TW-class laser pulses

Controlling the delivery of multi-terawatt and petawatt laser pulses to final focus, both in position and angle, is critical to many laser applications such as optical guiding, laser–plasma acceleration, and laser-produced secondary radiation. We present an online, non-destructive laser diagnostic, capable of measuring the transverse position and pointing angle at focus. The diagnostic is based on a unique double-surface-coated wedged-mirror design for the final steering optic in the laser line, producing a witness beam highly correlated with the main beam. By propagating low-power kilohertz pulses to focus, we observed spectra of focus position and pointing angle fluctuations dominated by frequencies below 70 Hz. The setup was also used to characterize the excellent position and pointing angle correlation of the 1 Hz high-power laser pulses to this low-power kilohertz pulse train, opening a promising path to fast non-perturbative feedback concepts even on few-hertz-class high-power laser systems.

47 OTHER INSTRUMENTATION↗

DOE OSTI2023

Hybrid achromatic microlenses with high numerical apertures and focusing efficiencies across the visible

Abstract Compact visible wavelength achromats are essential for miniaturized and lightweight optics. However, fabrication of such achromats has proved to be exceptionally challenging. Here, using subsurface 3D printing inside mesoporous hosts we densely integrate aligned refractive and diffractive elements, forming thin high performance hybrid achromatic imaging micro-optics. Focusing efficiencies of 51–70% are achieved for 15μm thick, 90μm diameter, 0.3 numerical aperture microlenses. Chromatic focal length errors of less than 3% allow these microlenses to form high-quality images under broadband illumination (400–700 nm). Numerical apertures upwards of 0.47 are also achieved at the cost of some focusing efficiency, demonstrating the flexibility of this approach. Furthermore, larger area images are reconstructed from an array of hybrid achromatic microlenses, laying the groundwork for achromatic light-field imagers and displays. The presented approach precisely combines optical components within 3D space to achieve thin lens systems with high focusing efficiencies, high numerical apertures, and low chromatic focusing errors, providing a pathway towards achromatic micro-optical systems.

47 OTHER INSTRUMENTATION↗

DOE OSTI2024

Ultracompact mirror device for forming 20-nm achromatic soft-X-ray focus toward multimodal and multicolor nanoanalyses

Abstract Nanoscale soft-X-ray microscopy is a powerful analysis tool in biological, chemical, and physical sciences. To enhance its probe sensitivity and leverage multimodal soft-X-ray microscopy, precise achromatic focusing devices, which are challenging to fabricate, are essential. Here, we develop an ultracompact Kirkpatrick-Baez (ucKB) mirror, which is ideal for the high-performance nanofocusing of broadband-energy X-rays. We apply our advanced fabrication techniques and short-focal-length strategy to realize diffraction-limited focusing over the entire soft-X-ray range. We achieve a focus size of 20.4 nm at 2 keV, which represents a significant improvement in achromatic soft-X-ray focusing. The ucKB mirror extends soft-X-ray fluorescence microscopy by producing a bicolor nanoprobe with a 1- or 2-keV photon energy. We propose a subcellular chemical mapping method that allows a comprehensive analysis of specimen morphology and the distribution of light elements and metal elements. ucKB mirrors will improve soft-X-ray nanoanalyses by facilitating photon-hungry, multimodal, and polychromatic methods, even with table-top X-ray sources.

Science & Technology - Other Topics↗

DOE OSTI2026

The role of focusing geometry in MeV x-ray production from petawatt laser–solid interaction

Relativistic laser–plasma interactions provide a compact and flexible route to generating bright, ultrashort pulses of MeV x rays, with applications in high-energy density science, nuclear physics, and radiography. Despite extensive study of intensity scaling in laser-driven electron acceleration, the role of focusing geometry and focal-volume effects in MeV radiation production remains insufficiently understood. Here, we present experimental and kinetic simulation results from the Texas Petawatt Laser (120 J, 140 fs) in which the focusing geometry (f/3 or f/1.5) is varied, while the laser energy and pulse duration are fixed. Experimentally, the f/3 geometry produces approximately three times more MeV radiation than the f/1.5 geometry, despite its twofold lower nominal vacuum intensity. This result is based on the time-integrated radiation per unit solid angle, as measured along the diagnostic line of sight. Three-dimensional particle-in-cell simulations reproduce this trend when a modest (10s of μm) effective focal plane shift is introduced, demonstrating that relativistic laser–plasma coupling is highly sensitive to focal geometry in the presence of a preplasma. This behavior is consistent with differences in interaction length and effective intensity at the critical surface between the two configurations. The sensitivity of the tightly focused f/1.5 configuration ($z_R ≈$⁠ 5 μ m) reflects the combined influence of thermal lensing and an extended preplasma, while the f/3 geometry (⁠$z_R ≈$ 80 μ m) remains comparatively robust. These results demonstrate a breakdown of conventional intensity scaling and identify focusing geometry as a critical control parameter for MeV electron and x-ray generation at petawatt powers. Implications for laser–plasma-based radiographic facilities are also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

The influence of laser focusing conditions on the direct laser acceleration of electrons

Direct laser acceleration of electrons during a high-energy, picosecond laser interaction with an underdense plasma has been demonstrated to be substantially enhanced by controlling the laser focusing geometry. Experiments using the OMEGA EP facility measured electrons accelerated to maximum energies exceeding 120 times the ponderomotive energy under certain laser focusing, pulse energy, and plasma density conditions. Two-dimensional particle-in-cell simulations show that the laser focusing conditions alter the laser field evolution, channel fields generation, and electron oscillation, all of which contribute to the final electron energies. The optimal laser focusing condition occurs when the transverse oscillation amplitude of the accelerated electron in the channel fields matches the laser beam width, resulting in efficient energy gain. Through this observation, a simple model was developed to calculate the optimal laser focal spot size in more general conditions and is validated by experimental data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Focusing of relativistic electron beams with permanent magnetic solenoid

Achieving strong focusing of MeV electron beams is a critical requirement for advanced beam applications such as compact laboratory x-ray sources, high gradient accelerators, and ultrafast electron scattering instrumentation. To address these needs, a compact radially magnetized permanent magnetic solenoid (PMS) has been designed, fabricated, and tested. The solenoid provides a compact and inexpensive solution for delivering high axial magnetic fields (1 T) to focus MeV electron beams. Field characterization of the solenoid demonstrates good agreement with analytical models, validating the PMS design. The electron beam test employs a high-brightness photoinjector to study the focusing properties of the PMS. The results indicate a focal length of less than 10 cm and a significant reduction in beam size with small spherical aberrations. Two application cases are evaluated: angular magnification in ultrafast electron diffraction setups and strong focusing for Compton scattering or other microfocus uses.

Electron diffraction↗

DOE OSTI2020

Photon scattering by a 4π -spherically-focused ultrastrong electromagnetic wave

The scattering of high-power probe laser pulses by tightly focused ultrastrong laser pulses has been investigated through a semiclassical approach using a perturbative method based on the Born approximation. Under a 4π-spherically-focused ultrastrong light field, the electric permittivity and magnetic permeability tensors for vacuum are calculated from the Euler-Heisenberg Lagrangian to show the nonlinear birefringent property of vacuum. And, from permittivity and permeability tensors, the scattering potential is derived for the Born approximation. The first-order solution of the Born approximation is taken as an electric field scattered from the 4π-spherically-focused laser pulse when a probe laser pulse propagates through the focused laser field. The differential cross section of the nonlinear birefringent vacuum is derived, and the number of photons scattered from the nonlinear birefringent vacuum is analyzed in the laser power range of 10-1000 PW.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

3D small-gain formula allowing strong focusing and harmonic lasing for a ring-based x-ray free electron laser oscillator

We present a detailed derivation of a formula for the small-gain calculation for an x-ray free electron laser oscillator (XFELO) based on a medium-energy (3–4 GeV) storage ring. We found harmonic lasing and strong focusing are essential for this beam energy range. Taking the small-signal low-gain formula developed by Kim and his colleagues, we modified it in such a way that the gain can be calculated without the “no focusing approximation,” and a strong focusing can be applied, as well as harmonic lasing. In this formula, the gain is represented as a product of two factors with one of them depending only on the harmonic number, undulator period, and gap. Using this factor, we show that it is favorable to use harmonic lasing to achieve hard x-ray FEL working in the small-signal low-gain regime with the medium-energy electron beam. Our formula also allows FEL optimization by varying the vertical gradient of the undulator, the vertical dispersion, and the horizontal and vertical focusing, independently. As an example, we applied this formula to study the feasibility of an XFELO option for the National Synchrotron Light Source II (NSLS-II) upgrade. Since a quite high peak current is required for the FEL, collective effects of beam dynamics in medium-energy synchrotrons significantly affect the electron beam parameters. We carried out a multiparameter optimization taking collective effects into account. Note, even though our example is for a ring-based XFELO at 3 to 4 GeV, the formula and, in particular, the approach developed here may be applied to other types of FELs. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗

DOE OSTI2024

Signatures of vacuum birefringence in low-power flying focus pulses

Vacuum birefringence produces a differential phase between orthogonally polarized components of a weak electromagnetic probe in the presence of a strong electromagnetic field. Despite representing a hallmark prediction of quantum electrodynamics, vacuum birefringence remains untested in pure light configurations due to the extremely large electromagnetic fields required for a detectable phase difference. Here, we exploit the programmable focal velocity and extended focal range of a flying focus laser pulse to substantially lower the laser power required for detection of vacuum birefringence. In the proposed scheme, a linearly polarized x-ray probe pulse counterpropagates with respect to a flying focus pulse, whose focus moves at the speed of light in the same direction as the x-ray probe. The peak intensity of the flying focus pulse overlaps the probe over millimeter-scale distances and induces a polarization ellipticity on the order of 10 − 10 , which lies within the detection sensitivity of existing x-ray polarimeters. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Ultrabright Electron Bunch Injection in a Plasma Wakefield Driven by a Superluminal Flying Focus Electron Beam

Here, we propose a new method for self-injection of high-quality electron bunches in the plasma wakefield structure in the blowout regime utilizing a “flying focus” produced by a drive beam with an energy chirp. In a flying focus the speed of the density centroid of the drive bunch can be superluminal or subluminal by utilizing the chromatic dependence of the focusing optics. We first derive the focal velocity and the characteristic length of the focal spot in terms of the focal length and an energy chirp. We then demonstrate using multidimensional particle-in-cell simulations that a wake driven by a superluminally propagating flying focus of an electron beam can generate GeV-level electron bunches with ultralow normalized slice emittance (~30 nm rad), high current (~17 kA), low slice energy spread (~0.1%), and therefore high normalized brightness (> 10 19 A/ m 2 /rad 2 ) in a plasma of density ~10 19 cm –3 . The injection process is highly controllable and tunable by changing the focal velocity and shaping the drive beam current. Nearterm experiments at FACET II where the capabilities to generate tens of kA, < 10 fs drivers are planned, could potentially produce beams with brightness near 10 20 A / m 2 / rad 2 .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Self-Focused Pulse Propagation Is Mediated by Spatiotemporal Optical Vortices

We show that the dynamics of high-intensity laser pulses undergoing self-focused propagation in a nonlinear medium can be understood in terms of the topological constraints imposed by the formation and evolution of spatiotemporal optical vortices (STOVs). STOVs are born from point phase defects on the sides of the pulse nucleated by spatiotemporal phase shear. These defects grow into closed loops of spatiotemporal vorticity that initially exclude the pulse propagation axis, but then reconnect to form a pair of toroidal vortex rings that wrap around it. STOVs constrain the intrapulse flow of electromagnetic energy, controlling the focusing-defocusing cycles and pulse splitting inherent to nonlinear pulse propagation. Here, we illustrate this in two widely studied but very different regimes, relativistic self-focusing in plasma and nonrelativistic self-focusing in gas, demonstrating that STOVs mediate nonlinear propagation irrespective of the detailed physics.

42 ENGINEERING↗

DOE OSTI2020

Focusing a round coherent beam by spatial filtering the horizontal source

This paper illustrates the use of spatial filtering with a horizontal slit near the source to enlarge the horizontal coherence in an experimental station and produce a diffraction-limited round focus at an insertion device beamline for X-ray photon correlation spectroscopy experiments. Simple expressions are provided to guide the optical layout, and wave propagation simulations confirm their applicability. The two-dimensional focusing performance of Be compound refractive lenses to produce a round diffraction-limited focus at 11 keV capable of generating a high-contrast speckle pattern of an aerogel sample is demonstrated. The coherent scattering patterns have comparable speckle sizes in both horizontal and vertical directions. The focal spot sizes are consistent with hybrid ray-tracing calculations. Producing a two-dimensional focus on the sample can be helpful to resolve speckle patterns with modern pixel array detectors with high visibility. This scheme has now been in use since 2019 for the 8-ID beamline at the Advanced Photon Source, sharing the undulator beam with two separate beamlines, 8-ID-E and 8-ID-I at 7.35 keV, with increased partially coherent flux, reduced horizontal spot sizes on samples, and good speckle contrast.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Physical Sciences Vistas: Perspectives on Excellence in Mission-Focused Science, Technology, and Engineering at Los Alamos Laboratory (Issue 1, 2020)

This is the first 2020 issue of Physical Sciences Vistas, with a focus on “excellence in mission-focused science, technology, and engineering.” Excellence in mission-focused ST&E comprises one of the four elements of the Laboratory Agenda, focusing on sustaining and enhancing LANL’s science base. This issue highlights the diverse efforts of personnel in our Physical Sciences Directorate (ALDPS) to enhance science, technology, and engineering at the Laboratory. As we reflect on work at the Laboratory, mostly from our homes due to COVID-19, it is gratifying to see the important, diverse contributions to ST&E across ALDPS.

36 MATERIALS SCIENCE↗

NASA NTRS1971

A study of transient stimulated Raman scattering and self-focusing in the picosecond time regime

Two third order processes, stimulated Raman scattering and self-focusing, with picosecond pulses are studied. In the case of transient stimulated scattering, the gain is reduced from the steady state value, and qualitatively new features, such as shortening and delay of the Stokes pulse relative to the laser pulse, appear. These predictions are extended to realistic laser pulses, and experiments confirm all of the theoretical predictions. The self-focusing and frequency broadening of picosecond pulses is studied in the absence of stimulated Raman scattering in several materials with large orientational Kerr constants. Measurements of the relaxation time indicate that the orientational Kerr effect is important in the self-focusing of picosecond pulses. Self-focused filaments are observed to propagate with constant diameters over a distance greater than 10 cm, but disappear before the end of a 20 cm cell. The filaments radiate light continuously along their path and the spectrum of the light shows that the frequency content extends symmetrically for several hundred wave numbers on either side of the laser frequency.

Reintjes, J. F.↗

NASA NTRS1976

Prediction of sonic boom at a focus

The behavior of sonic boom at a focus has been reviewed for the purpose of extending present sonic boom computational methods to include focal zones. The geometry of a focal zone - whether a smooth caustic, a cusped caustic, or a perfect focus to a point - determines the character of focused signatures. The seeming contradiction of various experimental data can be resolved by noting these differences. A ray acoustic analysis has been developed for quantitative determination of caustic geometry. The only reliable theory presently available for signatures at a focus is for a smooth caustic. There has been some controversy between theoretical and experimental values of a constant in the scaling law for this case. It has been found that this discrepancy can be resolved by accounting for the finite thickness of real sonic boom shock waves. These findings have been incorporated into an existing sonic boom computer program.

Plotkin, K. J.↗

NASA NTRS1976

The effect of adiabatic focusing upon charged-particle propagation in random magnetic fields

The charged particles considered are scattered by random fields while they propagate along the diverging lines of force of a spatially inhomogeneous guiding field. Their longitudinal transport is described in terms of the eigenfunctions of a Sturm-Liouville operator which incorporates the effect of adiabatic focusing along with that of scattering. The relaxation times and characteristic velocities which appear in this matrix formulation of the transport problem are graphed and tabulated. Explicit formulas which describe the particle-density profile that results from a localized impulsive injection are derived for two different regimes. In the first regime, where focusing is relatively weak, a diffusive mode of propagation is dominant, but coherent modes are also present, and they become prominent as the intensity of focusing increases. In the second regime, where focusing is strong and where diffusion does not occur, the propagation is purely coherent. The existence of this supercoherent mode of particle transport opens up many possibilities for the interpretation of astrophysical phenomena.

Earl, J. A.↗

NASA NTRS1977

Scanning and focusing mechanisms of METEOSAT radiometer

The scanning and focusing mechanisms settled onboard the METEOSAT Radiometer are described. A large camera which will take line by line pictures of the earth from a geostationary satellite in the same manner as a TV picture using both the spin of the spacecraft and the tilt of a telescope is included. The scanning mechanism provides the + or - 9 degrees tilt angle of the telescope through 2,500 elementary steps of 1.256 0.0001 radian. As the radiometer image quality is closely dependent on the characteristics of the scanning law, the mechanism is required to fulfill functional performances specifications particularly severe in terms of linearity of the scan curve, accuracy of each step as well as repeatability of the short-term scanning. The focusing mechanism allows + or - 12 millimeters shift of the telescope focus by step increments of 0.140 mm. The focus adjustment is achieved by moving a dihedral reflector according to a pure straight-line motion. The main requirements of each mechanism are summarized and their design and performances are described in detail.

Jouan, J.↗