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DOE OSTI2025

The total neutron cross section of liquid and solid ammonia

Ammonia is a material of interest for future neutron moderators at high-power sources due to its high hydrogen density, low melting point, and resistance to polymerization in an intense radiation field. Its performance in such applications cannot currently be calculated due to the absence of suitable computer models for the interaction of neutrons with ammonia under relevant conditions. In an effort to develop suitable scattering kernels for computer simulations of moderator performance, we have conducted a series of Density Functional Theory and Molecular Dynamics calculations of the molecular-level thermal properties of ammonia at various temperatures within both the solid and liquid phases. In this paper, we compare computer calculations for the energy-dependent total neutron cross section of ammonia, based on these models, to experimental measurements of those cross sections at temperatures of 221 K, 180 K, and 35 K. The experimental data were collected over an energy range from 0.1 meV to 10 eV using time-of-flight techniques at the Low Energy Neutron Source (LENS) facility at Indiana University. This comparison provides a first validation in the development of thermal scattering libraries for Monte Carlo source design simulations based on liquid and solid ammonia. In conclusion, we also provide some insights into where additional development of tools for creating such models may be needed.

Ammonia↗

DOE OSTI2021

Trapped Electrons and Ions as Particle Detectors

Electrons and ions trapped with electromagnetic fields have long served as important high-precision metrological instruments, and more recently have also been proposed as a platform for quantum information processing. Here we point out that these systems can also be used as highly sensitive detectors of passing charged particles, due to the combination of their extreme charge-to-mass ratio and low-noise quantum readout and control. In particular, these systems can be used to detect energy depositions many orders of magnitude below typical ionization scales. As illustrations, we suggest some applications in particle physics. We outline a nondestructive time-of-flight measurement capable of sub-eV energy resolution for slowly moving, collimated particles. We also show that current devices can be used to provide competitive sensitivity to models where ambient dark matter particles carry small electric millicharges $\ll$e. Furthermore, our calculations may also be useful in the characterization of noise in quantum computers coming from backgrounds of charged particles.

47 OTHER INSTRUMENTATION↗

DOE OSTI2014

Generation-based memory synchronization in a multiprocessor system with weakly consistent memory accesses

In a multiprocessor system, a central memory synchronization module coordinates memory synchronization requests responsive to memory access requests in flight, a generation counter, and a reclaim pointer. The central module communicates via point-to-point communication. The module includes a global OR reduce tree for each memory access requesting device, for detecting memory access requests in flight. An interface unit is implemented associated with each processor requesting synchronization. The interface unit includes multiple generation completion detectors. The generation count and reclaim pointer do not pass one another.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Generation-based memory synchronization in a multiprocessor system with weakly consistent memory accesses

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Pilot decision space for sonic boom impact resolution

A system for predicting pressure waves in a sonic boom footprint calculates alternative footprints and pressure waves along a flight path based on speed and altitude modifiers. The available, adjustable parameters are bounded within a flight envelope and along an approved flight corridor. The system receives and incorporates data from external sources, such as weather data, that impacts sonic boom pressure wave predictions and aircraft performance characteristics.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Tomographic Reconstruction of the Neutron Time-Energy Spectrum from a Dense Plasma Focus

A dense plasma focus (DPF) nuclear fusion device is an attractive pulsed neutron source in many applications, due to its relatively large neutron yield, produced in a short time duration. In order to design a DPF that generates neutrons within a specified time profile, or generates a neutron energy spectrum with specific properties, it is necessary to be able to characterize and model the results of the fusion process releasing the neutrons. The time-energy spectrum of fusion neutrons is an ideal quantity to use to validate multiphysics codes that simulate the pinch and fusion processes, because it is a quantity that requires the physics of each of the stages leading up to and ending in the fusion reaction to be simulated correctly. In particular, since DPF fusion neutrons are not monoenergetic -- and there can often be several fusion pinches creating neutrons -- a computer simulation matching high quality neutron spectrum measurements provides great confidence in the fidelity of the simulation. In order to make such a comparison, it is first necessary to have quality measurements from which to infer the spectrum. In this work we pose neutron spectroscopy as the classical tomographic inverse problem from neutron time of flight data at multiple distances, but enhanced by using an additional measurement of the time profile of the fusion pinch near its source and by using detector pairs set up in a geometry that allows for scatter background subtraction. The detector pairs enhance the quality of the time of flight measurements, and the additional constraint posed by the measured time profile allows for reconstructions discretized as finely as the time measurements and in energy as finely as 100 keV, without the problem being underdetermined. We present results from a Deuterium-fueled DPF at the U.S. Department of Energy's Nevada National Security Site and show that we can infer the time-energy spectrum from our measurements for both single and multi-pinch fusion reactions with equal fidelity.

Catenacci, Jared↗

DOE OSTI2023

Improvements of Nuclear Data Evaluations for Lead Isotopes in Support of Next Generation Lead-Cooled Fast Systems

The neutron evaluation of the isotopes that comprise natural lead were undertaken as a part of DOE-NEUP Project #19-16739. The goal of the project was to update the neutron cross sections to account for new differential measurements and incorporate the most up-to-date physics. Shortcomings in the lead cross sections was made known by several independent reports. The work performed here repeated the simulation of all the “benchmark” validation systems and concluded that the major issue is the scattering cross sections in the major lead isotopes above 100 keV. Re-evaluation of 206,207,208 Pb included both the resolved resonance region and fast region evaluations of the cross sections. Combined these regions cover energies from thermal to 20 MeV. The most drastic improvement is the resolved resonance region evaluation of 208 Pb which is now extended from 1.0 to 1.5 MeV. Parameterization of these resonances in the R-matrix provides a superior reconstruction of not only the experimental cross section but also the scattering distributions via the Blatt-Biedenharn formalism. Fast region evaluations of the three major isotopes were done to include new inelastic experimental data from the neutron Time-of-Flight facility at CERN. The culmination of all the changes to the cross section is a drastic improvement in the scattering kernel as shown in Rensselaer Polytechnic Institute (RPI) Quasi-Differential scattering measurements and improved prediction of keff for fast integral experiments. Alongside the new cross sections, new nuclear data covariance (uncertainties) have been computed and are included in the evaluation. Little is changed in the magnitude of the uncertainties but the correlations within the covariance display non-trivial changes. The new evaluations of 206,207,208 Pb have been submitted to the National Nuclear Data Center to be included in the ENDF/B-VIII.1 library. While the cross sections have been updated extensively, knowledge and modeling of the cross sections between 1.0 and 3.0 MeV for the isotopes remain a challenge. Most notably is the double differential elastic cross section for 208 Pb and 206 Pb. New quasi-differential measurements for pure samples of these two nuclei would go a long way in reducing compensating errors in the evaluations. Qualitatively, the project has produced a prosperous collaboration between the nuclear data group at RPI with staff scientists at Brookhaven National Laboratory, Naval Nuclear Laboratory, Oak Ridge National Laboratory, Los Alamos National Laboratory, Lawrence Livermore National Laboratory, and Sandia National Laboratories. Quantitatively this is reflected in seven conference presentations, at least one journal submission, and one doctoral thesis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2019

Tomographic Reconstruction of the Neutron Time-Energy Spectrum from a Dense Plasma Focus

A dense plasma focus (DPF) nuclear fusion generator is an attractive pulsed neutron source in many applications, due to its relatively large neutron yield, produced in a short time duration. In order to design a DPF that generates neutrons within a specified time profile, or generates a neutron energy spectrum with specific properties, it is necessary to understand and be able to fully characterize the results of the fusion process releasing the neutrons. The time-energy spectrum of fusion neutrons is an ideal quantity to use to validate multiphysics codes that simulate the pinch and fusion processes, because it is a quantity that requires the physics of each of the stages leading up to and ending in the fusion reaction to be simulated correctly. In particular, since DPF fusion neutrons are not monoenergetic – and there can often be several fusion pinches creating neutrons – a computer simulation matching high quality neutron spectrum measurements provides great confidence in the fidelity of the simulation. In order to make such a comparison, it is first necessary to have quality measurements from which to infer the spectrum. In this work we pose neutron spectroscopy as the classical tomographic inverse problem from neutron time of flight data at multiple distances, but enhanced by using detector pairs designed to reduce the scatter background and with an additional measurement of the time profile of the fusion pinch near its source. The detector pairs enhance the quality of the time of flight measurements and the additional constraint posed by the measured time profile allows for temporal resolution in the spectrum reconstruction that is equal to the measurement resolution, which can be subnanosecond, and energy resolution in the 10’s of keV, without the problem being underconstrained. We present results from a Deuterium-fueled DPF at the U.S. Department of Energy’s Nevada National Security Site and show that we can infer the time-energy spectrum from our measurements for both single and multi-pinch fusion reactions with equal fidelity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Neutron Leakage Spectra Sensitivities for ICSBEP Benchmarks

Neutron leakage spectra have been measured, simulated, and investigated by many groups. These spectra have many uses, including determining shielding requirements and calculating dose for radiation protection purposes, validating nuclear data, and determining material composition. It has even been proposed to use measurements of neutron leakage spectra to determine the soil composition of Mars. As part of the Los Alamos National Laboratory (LANL) Experiments Underpinned by Computational Learning for Improvements in nuclear Data (EUCLID) Laboratory Directed Research Development (LDRD) project, the authors are working on developing methods to calculate sensitivities to neutron leakage spectra. This may allow nuclear data evaluators to better use neutron leakage spectra data to constrain or adjust nuclear data. This may also be particularly useful as many neutron leakage spectra measurements do not require fissile material and can be performed with well characterized neutron sources. Neutron leakage spectra measurements are usually performed by placing a detector at the outside of a nuclear system. This may be a reactor, a neutron generator, or a neutron source. Certain detection systems can use pulse height data to infer neutron energies, other detector systems rely on other ways of determining neutron energy (for example, a Bonner sphere with multiple moderator thicknesses can be used to measure neutron spectrum). These measurements typically rely on some unfolding of the measured results. For pulsed systems like the "Livermore Pulsed Spheres," time-of-flight information can also help to constrain the neutron energy spectra data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2014

Solving fractional Schrödinger-type spectral problems: Cauchy oscillator and Cauchy well

This paper is a direct offspring of the work of Garbaczewski and Stephanovich [“Lévy flights and nonlocal quantum dynamics,” J. Math. Phys. 54, 072103 (2013)] where basic tenets of the nonlocally induced random and quantum dynamics were analyzed. A number of mentions were made with respect to various inconsistencies and faulty statements omnipresent in the literature devoted to so-called fractional quantum mechanics spectral problems. Presently, we give a decisive computer-assisted proof, for an exemplary finite and ultimately infinite Cauchy well problem, that spectral solutions proposed so far were plainly wrong. As a constructive input, we provide an explicit spectral solution of the finite Cauchy well. The infinite well emerges as a limiting case in a sequence of deepening finite wells. The employed numerical methodology (algorithm based on the Strang splitting method) has been tested for an exemplary Cauchy oscillator problem, whose analytic solution is available. An impact of the inherent spatial nonlocality of motion generators upon computer-assisted outcomes (potentially defective, in view of various cutoffs), i.e., detailed eigenvalues and shapes of eigenfunctions, has been analyzed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Anomalous low-frequency conductivity in easy-plane XXZ spin chains

Using the framework of generalized hydrodynamics, we compute here the low-frequency spin conductivity σ ( ω ) of XXZ spin chains with easy-plane anisotropy. We find that for almost all values of the anisotropy - 1 < Δ < 1 , the low-frequency conductivity scales anomalously with frequency, as σ ( ω ) ~ 1 / ω . We interpret this anomalous response as a consequence of quasiparticles undergoing Lévy flights. For special values of the anisotropy, the divergence is cut off at low frequencies, so σ ( ω ) has a finite dc limit. These results reveal a hitherto unknown mechanism for anomalous response in integrable systems and also provide a physical explanation of the discontinuous behavior of the spin Drude weight. We use our method to recover that at the isotropic point Δ = 1 , σ ( ω ) ~ ω - 1 / 3 . We support our results with extensive numerical studies using matrix-product operator methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

Effect of high current electron beam in a 30 MeV radio frequency linac for neutron-time-of-flight applications

A high power pulsed radio frequency electron linac is designed by BARC, India to accelerate 30 MeV, 10 A, 10 ns beam for neutron-time-of-flight applications. It will be used as a neutron generator and will produce ∼10{sup 12}–10{sup 13} n/s. It is essential to reduce the beam instability caused by space charge effect and the beam cavity interaction. In this paper, the wakefield losses in the accelerating section due to bunch of RMS (Root mean square) length 2 mm (at the gun exit) is analysed. Loss and kick factors are numerically calculated using CST wakefield solver. Both the longitudinal and transverse wake potentials are incorporated in beam dynamics code ELEGANT to find the transverse emittance growth of the beam propagating through the linac. Beam loading effect is examined by means of numerical computation carried out in ASTRA code. Beam break up start current has been estimated at the end of the linac which arises due to deflecting modes excited by the high current beam. At the end, transverse beam dynamics of such high current beam has been analysed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2018

A Method For Determining The Radially-Averaged Effective Impact Area For An Aircraft Crash Into A Structure

This report presents a methodology for deriving the equations which can be used for calculating the radially-averaged effective impact area for a theoretical aircraft crash into a structure. Conventionally, a maximum effective impact area has been used in calculating the probability of an aircraft crash into a structure. Whereas the maximum effective impact area is specific to a single direction of flight, the radially-averaged effective impact area takes into consideration the real life random nature of the direction of flight with respect to a structure. Since the radially-averaged effective impact area is less than the maximum effective impact area, the resulting calculated probability of an aircraft crash into a structure is reduced.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Towards modelling AR Sco: calibration – reproducing high-energy pulsar emission and testing convergence to Aristotelian electrodynamics

In recent years, kinetic simulations have been crucial to further our understanding of pulsar electrodynamics. Yet, due to the large-scale separation between the gyro-period and the stellar rotation period, resolving the particle gyration has been computationally unfeasible for realistic pulsar parameters. The main aim of this work is comparing our gyro-phase-resolved model with a gyro-centric pulsar model, where our model solves the general equations of motion with included radiation reaction using a higher order numerical solver with adaptive time-steps. Specifically, we aim to (i) reproduce a pulsar’s high-energy emission maps, namely one with 10 per cent of the surface B-field strength of Vela, and the spectra produced by an independent gyro-centric pulsar emission model; and (ii) test convergence of these results to the radiation-reaction limit of Aristotelian electrodynamics. (iii) Additionally, we identify the effect that a large $E_{\parallel }$-field has on the trajectories and radiation calculations. We find that we can reproduce the curvature radiation emission maps and spectra well, using 10 per cent field strengths of the Vela pulsar and injecting our particles at a higher altitude in the magnetosphere. Using sufficiently large $E_{\parallel }$-fields, our numeric results converge to the analytic radiation-reaction limit trajectories. Additionally, we illustrate the importance of accounting for the $\mathbf {E}\times \mathbf {B}$-drift in the particle trajectories and radiation calculations, validating the Harding and collaborators’ model approach. Lastly, we found that our model deals very well with the high-radiation-reaction and high-field regimes present in pulsars.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

Coastal Ohio Wind Project for Reduced Barriers to Deployment of Offshore Wind Energy

The Coastal Ohio Wind Project was created to establish the viability of wind turbines on the coastal and offshore regions of Northern Ohio. The project’s main goal was to improve operational unit strategies used for environmental impact assessment of offshore turbines on lake wildlife by optimizing and fusing data from the multi-instrument surveillance system and providing an engineering analysis of potential design/operational alternatives for offshore wind turbines. The project also developed a general economic model for offshore WTG deployment to quantify potential revenue losses due to wind turbine shutdown related to ice and avian issues. In a previous phase of this project (Award Number: DE-FG36-06GO86096), we developed a surveillance system that was used to collect different parameters such as passage rates, flight paths, flight directions, and flight altitudes of nocturnal migrating species, movements of birds and bats, and bird calls for assessing patterns and peak passage rates during migration. To derive such parameters we used thermal IR imaging cameras, acoustic recorders, and marine radar Furuno (XANK250), which was coupled with a XIR3000B digitizing card from Russell Technologies and open source radR processing software. The integration yielded a development of different computational techniques and methods, which we further developed and optimized as a combined surveillance system. To accomplish this task we implemented marine radar calibration, optimization of processing parameters, and fusion of the multi-sensor data in order to make inferences about the potential avian targets. The main goal of the data fusion from the multi-sensor environment was aimed at reduction of uncertainties while providing acceptable confidence levels with detailed information about the migration patterns. Another component comprised of an assessment of wind resources in a near lake environment and an investigation of the effectiveness of ice coating materials to mitigate adverse effects of ice formation on wind turbine structures. Firstly, a Zephir LiDAR system was acquired and installed at Woodlands School in Huron, Ohio, which is located near Lake Erie. Wind resource data were obtained at ten measurement heights, 200m, 150m, 100m, 80m, 60m, 40m, 38m, 30m, 20m, and 10m. The Woodlands School’s wind turbine anemometer also measured the wind speed at the hub height. These data were collected for approximately one year. The hub anemometer data correlated well with the LiDAR wind speed measurements at the same height. The data also showed that on several days different power levels were recorded by the turbine at the same wind speed as indicated by the hub anemometer. The corresponding LiDAR data showed that this difference can be attributed to variability in the wind over the turbine rotor swept area, which the hub anemometer could not detect. The observation suggests that single point hub wind velocity measurements are inadequate to accurately estimate the power generated by a turbine at all times since the hub wind speed is not a good indicator of the wind speed over the turbine rotor swept area when winds are changing rapidly. To assess the effectiveness of ice coatings to mitigate the impact of ice on turbine structures, a closed-loop icing research tunnel (IRT) was designed and constructed. By controlling the temperature, air speed, water content and liquid droplet size, the tunnel enabled consistent and repeatable ice accretion under a variety of conditions with temperatures between approximately 0°C and -20°C and wind speeds up to 40 miles per hour in the tunnel’s test section. The tunnel’s cooling unit maintained the tunnel temperature within ±0.2°C. The coatings evaluated in the study were Boyd Coatings Research Company’s CRC6040R3, MicroPhase Coatings Inc.’s PhaseBreak TP, ESL and Flex coatings. Similar overall performance was observed in all coatings tested in that water droplets form on the test articles beginning at the stagnation region and spreading in the downstream direction in time. When comparing ice accumulation characteristics for the four coatings tested, for ice thickness during accumulation the CRC6040R3 had the least, followed by the ESL, Flex, and TP. However, when comparing the coatings’ ability to reduce ice adhesion, the Flex showed the highest adhesion reduction, followed by the ESL, TP and CRC 6040R3 coatings. The ice accumulated on the Flex coated surface shed under gravity when rotated 90 degrees following the tests while the other coatings required application of varying degrees of force to remove the ice. In conclusion, the ice coatings tested were not sufficient in preventing ice accumulation on all surfaces. However, Flex coating shows promise in mitigating ice on the rotor blades under the gravitational and centrifugal forces. Only the effect of gravity in shedding the ice was considered in this study. Further research will be needed to evaluate this coating on rotating blades in the icing tunnel to characterize its effectiveness. Lastly, the development of economic feasibility models used existing approaches adapted for offshore deployment in marine settings to one more suitable for Lake Erie deployment. Two different wind turbine models were tested and dynamic return on investment (ROI) model scenarios were generated. For the purpose of estimating power generation three bladed wind turbines of 3 MW capacity were selected including Model1- Leitwind LTW101-3.000-kW and Model2-Vostro V90-3.0 MW. The analysis were based on the revenue aspect of decision making of deploying wind turbines in the Ohio coastal region. The installation cost, maintenance and operational aspects were disregarded due to unavailability of data. The adjusted varying price (residential and industrial sector) and projected future price of electricity in different years suggested that the Leitwind model could generate $\$ $32.4 million of revenue in 25 years if the supply electricity is in the residential sector, while it would be $\$ $14.7million if the supply is in the industrial sector. For the Vostro model these figures are $\$ $28.6 million for residential sector and $\$ $12.9 million for industrial sector for 25 years.

17 WIND ENERGY↗

DOE OSTI2021

Understanding Growth Dynamics and Yield Prediction of Sorghum Using High Temporal Resolution UAV Imagery Time Series and Machine Learning

Unmanned aerial vehicles (UAV) carrying multispectral cameras are increasingly being used for high-throughput phenotyping (HTP) of above-ground traits of crops to study genetic diversity, resource use efficiency and responses to abiotic or biotic stresses. There is significant unexplored potential for repeated data collection through a field season to reveal information on the rates of growth and provide predictions of the final yield. Generating such information early in the season would create opportunities for more efficient in-depth phenotyping and germplasm selection. This study tested the use of high-resolution time-series imagery (5 or 10 sampling dates) to understand the relationships between growth dynamics, temporal resolution and end-of-season above-ground biomass (AGB) in 869 diverse accessions of highly productive (mean AGB = 23.4 Mg/Ha), photoperiod sensitive sorghum. Canopy surface height (CSM), ground cover (GC), and five common spectral indices were considered as features of the crop phenotype. Spline curve fitting was used to integrate data from single flights into continuous time courses. Random Forest was used to predict end-of-season AGB from aerial imagery, and to identify the most informative variables driving predictions. Improved prediction of end-of-season AGB (RMSE reduction of 0.24 Mg/Ha) was achieved earlier in the growing season (10 to 20 days) by leveraging early- and mid-season measurement of the rate of change of geometric and spectral features. Early in the season, dynamic traits describing the rates of change of CSM and GC predicted end-of-season AGB best. Late in the season, CSM on a given date was the most influential predictor of end-of-season AGB. The power to predict end-of-season AGB was greatest at 50 days after planting, accounting for 63% of variance across this very diverse germplasm collection with modest error (RMSE 1.8 Mg/ha). End-of-season AGB could be predicted equally well when spline fitting was performed on data collected from five flights versus 10 flights over the growing season. This demonstrates a more valuable and efficient approach to using UAVs for HTP, while also proposing strategies to add further value.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

An Open Source Perovskite Solar Cell Curve Tracer

When developing systems for perovskite solar cells (PSCs), it is important to have a testing platform that closely resembles your deployed systems. While developing a 1 U CubeSat, the Big Red Sat-1 at the University of Nebraska-Lincoln, we found a lack of passive curve tracing instrumentation, which we needed for our mission. To that end, we developed a benchtop passive curve tracer that leverages the Ossila Solar Simulator as an AM1.5 light source. This device utilizes a ladder of switched resistors and a precision voltage and current measurement to achieve the curve tracing. It also integrates a common-anode multiplexer to switch through multipixel PSCs. Finally, the solar cell holder is separate from the main measurement system, so various substrates sizes and pixel counts can be supported. This system is tested using various PSCs. It has been open sourced to enable reuse in future systems that may benefit from the lower power consumption and flight heritage.

14 SOLAR ENERGY↗

DOE OSTI2014

Sub-nanosecond time-resolved ambient-pressure X-ray photoelectron spectroscopy setup for pulsed and constant wave X-ray light sources

An apparatus for sub-nanosecond time-resolved ambient-pressure X-ray photoelectron spectroscopy studies with pulsed and constant wave X-ray light sources is presented. A differentially pumped hemispherical electron analyzer is equipped with a delay-line detector that simultaneously records the position and arrival time of every single electron at the exit aperture of the hemisphere with ∼0.1 mm spatial resolution and ∼150 ps temporal accuracy. The kinetic energies of the photoelectrons are encoded in the hit positions along the dispersive axis of the two-dimensional detector. Pump-probe time-delays are provided by the electron arrival times relative to the pump pulse timing. An average time-resolution of (780 ± 20) ps (FWHM) is demonstrated for a hemisphere pass energy E{sub p} = 150 eV and an electron kinetic energy range KE = 503–508 eV. The time-resolution of the setup is limited by the electron time-of-flight (TOF) spread related to the electron trajectory distribution within the analyzer hemisphere and within the electrostatic lens system that images the interaction volume onto the hemisphere entrance slit. The TOF spread for electrons with KE = 430 eV varies between ∼9 ns at a pass energy of 50 eV and ∼1 ns at pass energies between 200 eV and 400 eV. The correlation between the retarding ratio and the TOF spread is evaluated by means of both analytical descriptions of the electron trajectories within the analyzer hemisphere and computer simulations of the entire trajectories including the electrostatic lens system. In agreement with previous studies, we find that the by far dominant contribution to the TOF spread is acquired within the hemisphere. However, both experiment and computer simulations show that the lens system indirectly affects the time resolution of the setup to a significant extent by inducing a strong dependence of the angular spread of electron trajectories entering the hemisphere on the retarding ratio. The scaling of the angular spread with the retarding ratio can be well approximated by applying Liouville's theorem of constant emittance to the electron trajectories inside the lens system. The performance of the setup is demonstrated by characterizing the laser fluence-dependent transient surface photovoltage response of a laser-excited Si(100) sample.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗