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DOE OSTI2025

Beam focusing and consequences for Doppler backscattering measurements

The phenomenon of focusing of microwave beams in a plasma near a turning-point caustic is discussed by exploiting the analytical solution to the Gaussian beam-tracing equations in the two-dimensional (2-D) linear-layer problem. The location of maximum beam focusing and the beam width at that location are studied in terms of the beam initial conditions. This focusing must be taken into account to interpret Doppler backscattering (DBS) measurements. We find that the filter function that characterises the scattering intensity contribution along the beam path through the plasma is inversely proportional to the beam width, predicting enhanced scattering from the beam focusing region. We show that the DBS signal enhancement for decreasing incident angles between the beam path and the density gradient is due to beam focusing and not due to forward scattering, as was originally proposed by (Gusakov et al., (Plasma Phys. Contr. Fusion, vol. 56, 2014, p. 0250092014, 2017); Plasma Phys. Rep. vol. 43(6), 2017, pp. 605–613). The analytic beam model is used to predict the measurement of the k y density-fluctuation wavenumber power spectrum via DBS, showing that, in an NSTX-inspired example, the spectral exponent of the turbulent, intermediate-to-high k y density-fluctuation spectrum might be quantitatively measurable via DBS, but not the spectral peak corresponding to the driving scale of the turbulent cascade.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Flying focus with arbitrary directionality for spatiotemporal control of laser intensity

Flying focus techniques produce laser pulses whose focal points travel at arbitrary, controllable velocities. While this flexibility can enhance a broad range of laser-based applications, existing techniques constrain the motion of the focal point to the propagation direction of the pulse. Here, we introduce a flying focus configuration that decouples the motion of the focus from the propagation direction. Here, a chirped laser pulse focused and diffracted by a diffractive lens and grating creates a focal point that can move both along and transverse to the propagation direction. The focal length of the lens, grating period, and chirp can be tuned to control the direction and velocity of the focus. Simulations demonstrate this control for a holographic configuration suited to high-power pulses, in which two off-axis pump beams with different focal lengths encode the equivalent phase of a chromatic lens and grating in a gas or plasma. For low-power pulses, conventional solid-state or adaptive optics can be used instead. Multi-dimensional control over the focal trajectory enables new configurations for applications, including laser wakefield acceleration of ions, nonlinear Thomson scattering, and surface-plasmon emission of THz radiation.

Classical optics↗

DOE OSTI2022

In-Situ Nanoscale Focusing of Extreme Ultraviolet Solid-State High Harmonics

Extreme ultraviolet light delivering radiation with a wavelength shorter than approximately 100 nm is now available from solid-state sources. However, despite exceptional progress, efficient focusing of extreme ultraviolet photons to their ultimate diffraction limit remains a formidable challenge because of the precision of the focusing by curved, optical surfaces. Here we integrate coherent short-wavelength high-order harmonics from a MgO crystal, with a high-numerical-aperture, nanostructured, focusing element etched onto the surface of the crystal itself. We focus extreme ultraviolet light, seventh harmonic of an 800-nm laser, with a zone plate of numerical aperture 0.35, down to a waist radius of 150 nm, with 18% focusing efficiency. The estimated intensity approaches 10 7 W/cm 2 . Future developments may demonstrate nanoscale laser ablation and miniaturization of extreme ultraviolet coherent sources on a chip.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Rapidly tunable ultrabroadband flying focus using adaptive optics and an axiparabola

A programmable ultrabroadband flying focus was produced using adaptive optics and an axiparabola with a continuous wave superluminescent diode. A deformable mirror and spatial light modulator were used to add a programmable amount of radial group delay, and an axiparabola was used to create an extended focus by imparting spherical aberration. Three different flying focus trajectories were measured using spectral interferometry, two with uniform velocity and one with an accelerating velocity. Here, the temporal response function width of the flying focus optics alone was calculated to be 52 ± 6 fs, and the focal spot size was measured to be (1.2 ± 0.1) × larger than the diffraction-limited spot size through the extended focus.

Markland, H. S. [University of Rochester, NY (Unit↗

DOE OSTI2020

Final Focus Solenoid Design Considerations

Radiography utilizing intense relativistic electron beams requires a final focus magnet to produce a small beam spot on the x-ray conversion target. A solenoid magnet is generally used for the final focus magnet. This note addresses design considerations of the final focus solenoid that impact the spot size. The spot size on target is a function of the beam size entering the final focus magnet, the beam emittance and energy spread and spherical aberration inherent in a solenoid magnet. The present final focus solenoid designs for both Axis 1 and Axis 2 of the DARHT facility are evaluated. A new design is proposed for both Axis 1 and Axis 2.

43 PARTICLE ACCELERATORS↗

DOE OSTI2020

The Dark Energy Spectrographic Instrument (DESI) Guide-Focus Assembly

The specific research of the DESI project is to study in detail the expansion history of the Universe over the past 10 billion years. In order to do this, the project designed, fabricated, tested and commissioned the DESI instrument which has been deployed at the Mayall Telescope at the Kitt Peak National Observatory near Tucson, Arizona. The DESI project was conducted by approximately 30 US and foreign national laboratories. Our CRADA with the The Institut de Física d’Altes Energies (IFAE) in Barcelona (Spain) involved both research planning for eventual observing on the DESI telescope; and in providing hardware jointly designed by LBNL and IFAE; ten guide and focus sensor systems (GFAs) that either provide feedback to the Mayall telescope tracking system or provide focus position information to the DESI corrector hexapod. The key major goals of this CRADA were achieved.For survey planning, Drs. Fernandez, Fosalba, Garcia-Bellido, and Gaztañaga were all important contributors to the working groups to which they were assigned. Their application of redshift techniques, development of simulations to support target selection, exploration of the use of alternative observables to extract cosmological information like AP and void statistics, and the use of PAU data to assist in the optimization of targeting selections have been vital in the early planning for targets during commissioning. The major role in the project involved Drs. Castander, Miquel, Padilla, and Sànchez. They were all directly involved with the development of the Guide-Focus Assembly (GFA) hardware, software and filter validation. In order to accomplish the goals of the DESI Project, the Mayall telescope must track DESI targeted galaxies for up to 15 minutes and the DESI corrector must be repositioned on its hexapod system for different telescope orientations. The guide and focus assemblies (GFA) provide in this information. There are ten GFA modules on the focal plane, six providing tracking information and four providing focus information. A common GFA design supports both functions by a simple switching of its operating mode. IFAE designed, fabricated, tested and delivered twelve GFAs. Once received at LBNL, the GFAs were integrated with the focal plane. This was an iterative process as the GFA’s were delivered as they were made. Our working relationship with the IFAE scientists and engineers was remarkable given the distance and time zone issues. The GFAs have performed extremely well during the commissioning phase of the instrument.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Focusing Ions at Atmospheric Pressure using Nonlinear DC Voltage Sequences Applied to a Stacked Ring Ion Guide

Many modern ion mobility (IM) and mass spectrometers (MS) operate under low pressure (= 10 Torr) and employ high voltage radiofrequencies (RF) to provide ion confinement. Unfortunately, RF effectiveness drastically decreases as pressure increases, and few techniques for focusing ions at elevated pressures exist. Here we demonstrate a new approach for focusing ions at atmospheric pressure (AP) by applying nonlinear DC voltage sequences following quadratic and power (exponential) functions to a stacked ring ion guide. We used ion trajectory simulations to rigorously explore how ions react to nonlinear electric fields and validate the simulations with a set of ion current measurements performed at AP. Ion trajectory simulations show that ions initially defocus near the entrance of the device but then become intensely focused as they travel through the device. Contour plots for both nonlinear voltage sequences show electric field lines that increasingly curve inwards as a function of distance, resulting in spatial ion focusing. Experimental ion current and spot size measurements were performed at AP using a 10-cm stacked ring ion guide and a segmented Faraday cup detector. Quadratic sequences produced ~5% smaller spot sizes (~22.8 mm) and ~25% higher ion current compared to a linear voltage sequence (~24.0 mm). Alternatively, power sequences produced ~64% smaller spot sizes (~8.7 mm), albeit with ~10x lower ion current. However, both nonlinear voltage sequences produced similar ion currents at the center of the Faraday cup detector, indicating that higher ion densities are achieved when using nonlinear voltage gradients. These results demonstrate a new way to focus ions at AP, and the capabilities demonstrated here provide fundamental insights on how to keep ions inside analytical devices at elevated pressures without RF.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Community Planning for Solar: Conducting Focus Groups for Solar Planning

This guide is designed to assist community officials, volunteers, and regional planning agency staff in conducting preliminary community meetings to learn about attitudes towards solar energy in your community. The guide will provide the key steps, timelines, facilitators' guide, and tips for hosting successful focus groups. Focus groups are meetings with a small group that represent a diversity of perspectives in your community. These differ from an open meeting in that focus groups include very specific questions that are prepared in advance, and all participants are given time to respond and understand various perspectives about solar energy. The guide concludes with a suggested template for reporting the results of your focus group or community meeting to your community more broadly. Holding community focus groups is part of assessing community preferences, as part of the Community Planning for Solar toolkit (ag.umass.edu/solarplanning). This guide is designed to help municipalities in Massachusetts and other states proactively plan for solar development in their communities. For more information, visit the UMass Clean Energy Extension (CEE) website (ag.umass.edu/clean-energy).

14 SOLAR ENERGY↗

DOE OSTI2020

Methodology for deriving the telescope focus function and its uncertainty for a heterodyne pulsed Doppler lidar

Doppler lidars provide two measured parameters, radial velocity and signal-to-noise ratio, from which winds and turbulent properties are routinely derived. Attenuated backscatter, which gives quantitative information on aerosols, clouds, and precipitation in the atmosphere, can be used in conjunction with the winds and turbulent properties to create a sophisticated classification of the state of the atmospheric boundary layer. Calculating attenuated backscatter from the signal-to-noise ratio requires accurate knowledge of the telescope focus function, which is usually unavailable. Inaccurate assumptions of the telescope focus function can significantly deform attenuated backscatter profiles, even if the instrument is focused at infinity. Here, we present a methodology for deriving the telescope focus function using a co-located ceilometer for pulsed heterodyne Doppler lidars. The method was tested with Halo Photonics StreamLine and StreamLine XR Doppler lidars but should also be applicable to other pulsed heterodyne Doppler lidar systems. The method derives two parameters of the telescope focus function, the effective beam diameter and the effective focal length of the telescope. Additionally, the method provides uncertainty estimates for the retrieved attenuated backscatter profile arising from uncertainties in deriving the telescope function, together with standard measurement uncertainties from the signal-to-noise ratio. The method is best suited for locations where the absolute difference in aerosol extinction at the ceilometer and Doppler lidar wavelengths is small.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1973

Automatic focus control for facsimile camera

Focus control performs function of automatically focusing facsimile camera throughout object field being scanned. It does this by determining and adjusting focus of imaging sensor accordingly. Since facsimile camera images a scene by scanning discrete strips, it is possible to have entire three-dimensional scene in perfect focus at point of imaging by use of focus control.

Sinclair, A. R.↗

NASA NTRS1974

Space and velocity focusing in time-of-flight mass spectrometers

A focusing equation is developed describing the relationship between space and velocity focusing for all one-dimensional time-of-flight mass spectrometers with constant electric fields. As a result of this equation, first-order double time focusing in one dimension is impossible. The possibility of large improvements in the resolving power of the time-of-flight mass spectrometers is discussed on this basis. The focusing equation also leads to an expression for the minimum time resolution obtainable. This second equation is applied to the conventional Wiley and McLaren (1955) two-field time-of-flight mass spectrometer with and without time-lag focusing, and to the mirror instrument of Karataev et al. (1972).

Stein, R.↗

NASA NTRS1975

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

This paper describes the effects of strong adiabatic focusing in terms of eigenfunctions of an operator which incorporates both scattering by random fields and focusing by a spatially inhomogeneous guiding field. It is found that focused transport differs from rectilinear transport in the following ways: (1) the coherent velocity toward stronger fields is larger than that toward weaker fields; (2) coherent effects are more prominent relative to diffusive effects when focusing is present; and (3) initial anisotropies at injection have a minimal influence upon rectilinear transport but they have a pronounced effect on focused transport. These features explain certain well-known discrepancies between the diffusive picture and the observed profiles of solar particle events. In particular, they explain the so-called scatter-free propagation of kilovolt flare electrons.

Earl, J. A.↗

NASA NTRS1978

Criteria for the selection of focusing ultrasonic probes

The principles of operation employed in the focusing of a sound field are considered, taking into account the use of solid and liquid coupling media. The focusing limits for a given transducer are investigated. As a diffraction phenomenon, focusing is a function of the system dimensions, the frequency, and the sound velocity. The frequency and the material used for the lenses are in most cases determined in accordance with considerations regarding sound propagation. Changes in the focus are therefore effected mainly by the selection of transducer and lens dimensions. The functions of the focusing factor for a normal immersion probe and a direct contact angle probe are represented in graphs. The deviation of the appropriate parametric values for an ultrasonic probe is illustrated with the aid of examples.

Schlengermann, U.↗

NASA NTRS1993

Quantitative results from the focusing schlieren technique

An iterative theoretical approach to obtain quantitative density data from the focusing schlieren technique is proposed. The approach is based on an approximate modeling of the focusing action in a focusing schlieren system, and an estimation of an appropriate focal plane thickness. The theoretical approach is incorporated in a computer program, and results obtained from a supersonic wind tunnel experiment evaluated by comparison with CFD data. The density distributions compared favorably with CFD predictions. However, improvements to the system are required in order to reduce noise in the data, to improve specifications of a depth of focus, and to refine the modeling of the focusing action.

Cook, S. P.↗

NASA NTRS1999

Three-Dimensional Simulations of Electron Beams Focused by Periodic Permanent Magnets

A fully three-dimensional (3D) model of an electron beam focused by a periodic permanent magnet (PPM) stack has been developed. First, the simulation code MAFIA was used to model a PPM stack using the magnetostatic solver. The exact geometry of the magnetic focusing structure was modeled; thus, no approximations were made regarding the off-axis fields. The fields from the static solver were loaded into the 3D particle-in-cell (PIC) solver of MAFIA where fully 3D behavior of the beam was simulated in the magnetic focusing field. The PIC solver computes the time-integration of electromagnetic fields simultaneously with the time integration of the equations of motion of charged particles that move under the influence of those fields. Fields caused by those moving charges are also taken into account; thus, effects like space charge and magnetic forces between particles are fully simulated. The electron beam is simulated by a number of macro-particles. These macro-particles represent a given charge Q amounting to that of several million electrons in order to conserve computational time and memory. Particle motion is unrestricted, so particle trajectories can cross paths and move in three dimensions under the influence of 3D electric and magnetic fields. Correspondingly, there is no limit on the initial current density distribution of the electron beam, nor its density distribution at any time during the simulation. Simulation results including beam current density, percent ripple and percent transmission will be presented, and the effects current, magnetic focusing strength and thermal velocities have on beam behavior will be demonstrated using 3D movies showing the evolution of beam characteristics in time and space. Unlike typical beam optics models, this 3D model allows simulation of asymmetric designs such as non- circularly symmetric electrostatic or magnetic focusing as well as the inclusion of input/output couplers.

Kory, Carol L.↗

NASA NTRS2016

Modeling a Miniaturized Scanning Electron Microscope Focusing Column - Lessons Learned in Electron Optics Simulation

This presentation discusses work done to assess the design of a focusing column in a miniaturized Scanning Electron Microscope (SEM) developed at the NASA Marshall Space Flight Center (MSFC) for use in-situ on the Moon-in particular for mineralogical analysis. The MSFC beam column design uses purely electrostatic fields for focusing, because of the severe constraints on mass and electrical power consumption imposed by the goals of lunar exploration and of spaceflight in general. The resolution of an SEM ultimately depends on the size of the focused spot of the scanning beam probe, for which the stated goal here is a diameter of 10 nanometers. Optical aberrations are the main challenge to this performance goal, because they blur the ideal geometrical optical image of the electron source, effectively widening the ideal spot size of the beam probe. In the present work the optical aberrations of the mini SEM focusing column were assessed using direct tracing of non-paraxial rays, as opposed to mathematical estimates of aberrations based on paraxial ray-traces. The geometrical ray-tracing employed here is completely analogous to ray-tracing as conventionally understood in the realm of photon optics, with the major difference being that in electron optics the lens is simply a smoothly varying electric field in vacuum, formed by precisely machined electrodes. Ray-tracing in this context, therefore, relies upon a model of the electrostatic field inside the focusing column to provide the mathematical description of the "lens" being traced. This work relied fundamentally on the boundary element method (BEM) for this electric field model. In carrying out this research the authors discovered that higher accuracy in the field model was essential if aberrations were to be reliably assessed using direct ray-tracing. This led to some work in testing alternative techniques for modeling the electrostatic field. Ultimately, the necessary accuracy was attained using a BEM/Fourier series hybrid approach. The presentation will give background remarks about the MSFC mini Lunar SEM concept and electron optics modeling, followed by a description of the alternate field modeling techniques that were tried, along with their incorporation into a ray-trace simulation. Next, the validation of this simulation against commercially available software will be discussed using an example lens as a test case. Then, the efficacy of aberration assessment using direct ray-tracing will be demonstrated, using this same validation case. The discussion will include practical error checks of the field solution. Finally, the ray-trace assessment of the MSFC mini Lunar SEM concept will be shown and discussed. The authors believe this presentation will be of general interest to practitioners of modeling and simulation, as well as those with a general optics background. Because electron optics and photon optics share many basic concepts (e.g., lenses, images, aberrations, etc.), the appeal of this presentation need not be restricted to just those interested in charged particle optics.

Modeling Miniaturizing Scanning↗

NASA NTRS2017

Methods for Reducing Singly Reflected Rays on the Wolter-I Focusing Figures of the FOXSI Rocket Experiment

In high energy solar astrophysics, imaging hard X-rays by direct focusing offers higher dynamic range and greater sensitivity compared to past techniques that used indirect imaging. The Focusing Optics X-ray Solar Imager (FOXSI) is a sounding rocket payload which uses seven sets of nested Wolter-I figured mirrors that, together with seven high-sensitivity semiconductor detectors, observes the Sun in hard X-rays by direct focusing. The FOXSI rocket has successfully flown twice and is funded to fly a third time in Summer 2018. The Wolter-I geometry consists of two consecutive mirrors, one paraboloid, and one hyperboloid, that reflect photons at grazing angles. Correctly focused X-rays reflect twice, once per mirror segment. For extended sources, like the Sun, off-axis photons at certain incident angles can reflect on only one mirror and still reach the focal plane, generating a pattern of single-bounce photons that can limit the sensitivity of the observation of faint focused X-rays. Understanding and cutting down the singly reflected rays on the FOXSI optics will maximize the instrument's sensitivity of the faintest solar sources for future flights. We present an analysis of the FOXSI singly reflected rays based on ray-tracing simulations, as well as the effectiveness of different physical strategies to reduce them.

FOXSI Rocket Experiment↗

DOE OSTI2020

On the competition between mixing rate and uniformity in a coaxial hydrodynamic focusing mixer

Fast microfluidic mixers for use with line-of-sight integrating detection schemes pose unique challenges. Such detectors typically cannot discriminate signal from slow moving (e.g. near internal walls) and fast-moving portions of the fluid stream. This convolves reaction rate dynamics with fluid flow residence time dynamics. Further, the small cross sections of typical three-dimensional hydrodynamic focusing devices lead to lower detection signals. The current study focuses on achieving both small time scales of mixing and homogenous residence times. This is achieved by injecting sample through a center capillary and hydrodynamically focusing using a sheath flow within a tapered second capillary. The current design also features a third, larger coaxial capillary. The mixed stream flows into the large cross-section of this third capillary to decelerate and expand the stream by up to 14-fold to improve line-of-sight signal strength of reaction products. Hydrodynamic focusing, mixing, and expansion are studied using analytical and numerical models and also studied experimentally using a fluorescein-iodide quenching reaction. The experimentally validated models are used to explore trade-offs between mixing rate and uniformity. For the first time, this work presents detailed analysis of the Lagrangian time history of species transport during mixing inside coaxial capillaries to measure mixing nonuniformity. The mixing region enables order 100 μs mixing times and residence time widths of the same order (140 μs).

42 ENGINEERING↗