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Microgravity acceleration measurement and environment characterization science (17-IML-1)

The Space Acceleration Measurement System (SAMS) is a general purpose instrumentation system designed to measure the accelerations onboard the Shuttle Orbiter and Shuttle/Spacelab vehicles. These measurements are used to support microgravity experiments and investigation into the microgravity environment of the vehicle. Acceleration measurements can be made at locations remote from the SAMS main instrumentation unit by the use of up to three remote triaxial sensor heads. The prime objective for SAMS on the International Microgravity Lab (IML-1) mission will be to measure the accelerations experienced by the Fluid Experiment System (FES). The SAMS acceleration measurements for FES will be complemented by low level, low frequency acceleration measurements made by the Orbital Acceleration Research Experiment (OARE) installed on the shuttle. Secondary objectives for SAMS will be to measure accelerations at several specific locations to enable the acceleration transfer function of the Spacelab module to be analyzed. This analysis effort will be in conjunction with similar measurements analyses on other Spacelab missions.

Source record

Analysis of Spacelab 3 residual acceleration data

A data reduction plan is being developed to efficiently process residual acceleration data, making such data more accessible to principal investigators of low-gravity experiments. Accelerometer data collected during the Spacelab 3 mission is being processed using a prototype version of this plan. The plan addresses various aspects of acceleration data analysis: the identification of disturbances that are intolerable to experiments, the investigation of acceleration orientations, the definition and characterization of the background acceleration corresponding to a given experiment time line, the isolation and examination of particular significant disturbances, and the identification of disturbance sources. Acceleration magnitude, frequency, and orientation are discussed: transient accelerations can have magnitudes as large as 0.01 g with frequency components no greater than 0.001 g. These accelerations fluctuate rapidly in orientation. The occurrence of disturbance sources in an orbiter is tentatively identified as a random process, whereas the response of the orbiter to given accelerations is considered deterministic. The need to continue monitoring of residual accelerations in orbiting space laboratories is stressed.

Rogers, Melissa J. B.

Particle acceleration in cosmic plasmas; Proceedings of the Workshop, Bartol Research Inst., Newark, DE, Dec. 4-6, 1991

The present volume on particle acceleration in cosmic plasmas discusses transport theory, particle acceleration in the sun, heliosphere, and galaxy, particle acceleration at nonrelativistic shocks, and stochastic particle acceleration. Attention is given to particle acceleration in relativistic flows and shocks, simulations, composition and sources of high-energy cosmic rays, electron acceleration, and observation priorities and perspectives. Topics addressed include particle acceleration in the magnetosphere, particle transport from a turbulence perspective, numerical simulations of time-dependent cosmic ray mediated shocks, and solar flare plasma. Also discussed are relativistic shock waves and the excitation of plerions, ion acceleration at collisionless shock interactions, ultrahigh-energy cosmic rays from Fanaroff Riley, and constraints on electron acceleration in the Crab Nebula.

Zank, G. P.

The influence of source acceleration on acoustic signals

The effect of aircraft acceleration on acoustic signals is often ignored in both analytical studies and data reduction of flight test measurements. In this study, the influence of source acceleration on acoustic signals is analyzed using computer simulated signals for an accelerating point source. Both rotating and translating sources are considered. Using a known signal allows an assessment of the influence of source acceleration on the received signal. Aircraft acceleration must also be considered in the measurement and reduction of flyover noise. Tracking of the aircraft over an array of microphones enables ensemble averaging of the acoustic signal, thus increasing the confidence in the measured data. This is only valid when both the altitude and velocity remain constant. For an accelerating aircraft, each microphone is exposed to differing flight velocities, Doppler shifts, and smear angles. Thus, averaging across the array in the normal manner is constrained by aircraft acceleration and microphone spacing. In this study computer simulated spectra, containing acceleration, are averaged across a 12 microphone array mimicking a flight test with accelerated profile in which noise data was obtained. Overlapped processing is performed is performed in the flight test measurements in order to alleviate spectral smearing.

Kelly, Jeffrey J.

Cycle-Powered Short Radius (1.9 m) Centrifuge: Effect of Exercise Versus Passive Acceleration on Heart Rate in Humans

In addition to extensive use of lower extremity physical exercise training as a countermeasure for the work capacity component of spaceflight deconditioning, some form of additional head-to-foot (+Gz) gravitational (orthostatic) stress may be required to further attenuate or prevent the signs and symptoms (nausea, vertigo, instability, fatigue) of the general reentry syndrome (GRS) that can reduce astronaut performance during landing. Orthostatic (head-to-foot) stress can be induced by standing, by lower body negative pressure, and by +Gz acceleration. One important question is whether acceleration training alone or with concurrent leg exercise would provide sufficient additive stimulation to attenuate the GRS. Use of a new human-powered centrifuge may be the answer. Thus, the purpose for this study was to compare heart rate (HR), i.e., a stress response during human-powered acceleration, in four men (35-62 yr) and two women (30-31 yr) during exercise acceleration versus passive acceleration (by an off-board operator) at 100% (maximal acceleration = A(max)), and at 25%, 50%, and 75% of A(max). Mean (+/-SE) A(max) was 43.7 +/- 1.3 rpm (+3.9 +/- 0.2Gz). Mean HR at exercise A(max) was 189 +/- 13 b/min (50-70 sec run time), and 142 +/- 22 b/min at passive A(max) (40-70 sec run time). Regression of mean HR on the various +Gz levels indicated explained variance (correlations squared) of r(exp 2) = 0.88 (exercise) and r(exp 2) = 0.96 (passive): exercise HR of 107 +/- 4 (25%) to 189 +/- 13 (100%) b/min were 43-50 b/min higher (p less than 0.05) than comparable passive HR of 64 +/- 2 to 142 +/- 22 b/min. Thus, exercise adds significant physiological stress during +Gz acceleration. Inflight use of this combined exercise and acceleration countermeasure may maintain work capacity as well as normalize acceleration and orthostatic tolerances which could attenuate or perhaps eliminate the GRS.

Greenleaf, J. E.

Summary Report of Mission Acceleration Measurements for STS-89: Launched January 22, 1998

Support of microgravity research on the 89th flight of the Space Transportation System (STS-89) and a continued effort to characterize the acceleration environment of the Space Shuttle Orbiter and the Mir Space Station form the basis for this report. For the STS-89 mission, the Space Shuttle Endeavour was equipped with a Space Acceleration Measurement System (SAMS) unit, which collected more than a week's worth of data. During docked operations with Mir, a second SAMS unit collected approximately a day's worth of data yielding the only set of acceleration measurements recorded simultaneously on the two spacecraft. Based on the data acquired by these SAMS units, this report serves to characterize a number of acceleration events and quantify their impact on the local nature of the accelerations experienced at the Mechanics of Granular Materials (MGM) experiment location. Crew activity was shown to nearly double the median root-mean-square (RMS) acceleration level calculated below 10 Hz, while the Enhanced Orbiter Refrigerator/Freezer operating at about 22 Hz was a strong acceleration source in the vicinity of the MGM location. The MGM science requirement that the acceleration not exceed q I mg was violated numerous times during their experiment runs; however, no correlation with sample instability has been found to this point. Synchronization between the SAMS data from Endeavour and from Mir was shown to be close much of the time, but caution with respect to exact timing should be exercised when comparing these data. When orbiting as a separate vehicle prior to docking, Endeavour had prominent structural modes above 3 Hz, while Mir exhibited a cluster of modes around 1 Hz. When mated, a transition to common modes was apparent in the two SAMS data sets. This report is not a comprehensive analysis of the acceleration data, so those interested in further details should contact the Principal Investigator Microgravity Services team at the National Aeronautics and Space Administration's John H. Glenn Research Center.

Hrovat, Kenneth

Testing of a Loop Heat Pipe Subjective to Variable Accelerations: Temperature Stability - Part 2

The effect of accelerating forces on the performance of loop heat pipes (LHP) is of interest and importance to terrestrial and space applications. LHP's are being considered for cooling of military combat vehicles and for spinning spacecraft. In order to investigate the effect of an accelerating force on LHP operation, a miniature LHP was installed on a spin table. Variable accelerating forces were imposed on the LHP by spinning the table at different angular speeds. Several patterns of accelerating forces were applied, i.e. continuous spin at different speeds and periodic spin at different speeds and frequencies. The resulting accelerations ranged from 1.17 g's to 4.7 g's. This paper presents the second part of the experimental study, i.e. the effect of an accelerating force on the LHP operating temperature. It has been known that in stationary tests the LHP operating temperature is a function of the evaporator power and the condenser sink temperature when the compensation temperature is not actively controlled. Results of this test program indicate that any change in the accelerating force will result in a chance in the LHP operating temperature through its influence on the fluid distribution in the evaporator, condenser and compensation chamber. However, the effect is not universal, rather it is a function of other test conditions. A steady, constant acceleration may result in an increase or decrease of the operating temperature, while a periodic spin will lead to a quasi-steady operating temperature over a sufficient time interval. In addition, an accelerating force may lead to temperature hysteresis and changes in the temperature oscillation. In spite of all these effects, the LHP continued to operate without any problems in all tests.

Ku, Jentung

Neural Network Based Representation of UH-60A Pilot and Hub Accelerations

Neural network relationships between the full-scale, experimental hub accelerations and the corresponding pilot floor vertical vibration are studied. The present physics-based, quantitative effort represents an initial systematic study on the UH-60A Black Hawk hub accelerations. The NASA/Army UH-60A Airloads Program flight test database was used. A 'maneuver-effect-factor (MEF)', derived using the roll-angle and the pitch-rate, was used. Three neural network based representation-cases were considered. The pilot floor vertical vibration was considered in the first case and the hub accelerations were separately considered in the second case. The third case considered both the hub accelerations and the pilot floor vertical vibration. Neither the advance ratio nor the gross weight alone could be used to predict the pilot floor vertical vibration. However, the advance ratio and the gross weight together could be used to predict the pilot floor vertical vibration over the entire flight envelope. The hub accelerations data were modeled and found to be of very acceptable quality. The hub accelerations alone could not be used to predict the pilot floor vertical vibration. Thus, the hub accelerations alone do not drive the pilot floor vertical vibration. However, the hub accelerations, along with either the advance ratio or the gross weight or both, could be used to satisfactorily predict the pilot floor vertical vibration. The hub accelerations are clearly a factor in determining the pilot floor vertical vibration.

Kottapalli, Sesi

Summary Report of Mission Acceleration Measurements for STS-89

Support of microgravity research on the 89th flight of the Space Transportation System (STS-89) and a continued effort to characterize the acceleration environment of the Space Shuttle Orbiter and the Mir Space Station form the basis for this report. For the STS-89 mission, the Space Shuttle Endeavour was equipped with a Space Acceleration Measurement System (SAMS) unit, which collected more than a week's worth of data. During docked operations with Mir, a second SAMS unit collected approximately a day's worth of data yielding the only set of acceleration measurements recorded simultaneously on the two spacecraft. Based on the data acquired by these SAMS units, this report serves to characterize a number of acceleration events and quantify their impact on the local nature of the accelerations experienced at the Mechanics of Granular Materials (MGM) experiment location. Crew activity was shown to nearly double the median root-mean-square (RMS) acceleration level calculated below 10 Hz, while the Enhanced Orbiter Refrigerator/Freezer operating at about 22 Hz was a strong acceleration source in the vicinity of the MGM location. The MGM science requirement that the acceleration not exceed plus or minus 1 mg was violated numerous times during their experiment runs; however, no correlation with sample instability has been found to this point. Synchronization between the SAMS data from Endeavour and from Mir was shown to be close much of the time, but caution with respect to exact timing should be exercised when comparing these data. When orbiting as a separate vehicle prior to docking, Endeavour had prominent structural modes above 3 Hz, while Mir exhibited a cluster of modes around 1 Hz. When mated, a transition to common modes was apparent in the two SAMS data sets. This report is not a comprehensive analysis of the acceleration data, so those interested in further details should contact the Principal Investigator Microgravity Services team at the National Aeronautics and Space Administration's John H. Glenn Research Center.

Hrovat, Kenneth

Outlook towards deployable continual learning for particle accelerators

Particle accelerators are high power complex machines. To ensure uninterrupted operation of these machines, thousands of pieces of equipment need to be synchronized, which requires addressing many challenges including design, optimization and control, anomaly detection and machine protection. With recent advancements, machine learning (ML) holds promise to assist in more advance prognostics, optimization, and control. While ML based solutions have been developed for several applications in particle accelerators, only few have reached deployment and even fewer to long term usage, due to particle accelerator data distribution drifts caused by changes in both measurable and non-measurable parameters. In this paper, we identify some of the key areas within particle accelerators where continual learning can allow maintenance of ML model performance with distribution drifts. Particularly, we first discuss existing applications of ML in particle accelerators, and their limitations due to distribution drift. Next, we review existing continual learning techniques and investigate their potential applications to address data distribution drifts in accelerators. By identifying the opportunities and challenges in applying continual learning, this paper seeks to open up the new field and inspire more research efforts towards deployable continual learning for particle accelerators.

43 PARTICLE ACCELERATORS

Cluster for Research Excellence (CRE) for Accelerator Physics

The purpose of this Cooperative Research and Development Agreement (CRADA) was to establish a Cluster of Research Excellence (CRE) for Accelerator Physics and broaden the accelerator physics collaboration between Northern Illinois University (NIU) and Fermilab. The CRE was based in both Fermilab’s Accelerator Division and in NIU’s Department of Physics. A research agenda and strategy for the CRE for Accelerator Physics included specific research topics, experiments, and research facility upgrades. The scope of the research program covered two thrusts with subtopics in the Accelerator Science Research Program utilizing the infrastructure of FAST, IOTA, the Fermilab Accelerator Complex, and the Illinois Accelerator Research Center (IARC). Specific areas of proposed exploration included: 1.Tests of novel “nonlinear integrable” systems including beam self-fields; 2.Experimental tests of phase-space diffusion and chaos in intense beams; 3.Investigate technically feasible approaches towards next generation intenseneutrino facilities; 4.Understanding optical control of charged particle beams; 5.Exploitation of bright electron beams from FAST for novel applications; 6. Conduct research into accelerator-based ‘precision science’, such as Muon g-2, EDM, Mu2e, etc.

43 PARTICLE ACCELERATORS

Plasma Dynamics and Nonthermal Particle Acceleration in 3D Nonrelativistic Magnetic Reconnection

Understanding plasma dynamics and nonthermal particle acceleration in 3D magnetic reconnection has been a long-standing challenge. In this paper, we explore these problems by performing large-scale fully kinetic simulations of multi-X-line plasmoid reconnection with various parameters in both the weak- and strong-guide-field regimes. In each regime, we have identified its unique 3D dynamics that lead to field-line chaos and efficient acceleration, and we have achieved nonthermal acceleration of both electrons and protons into power-law spectra. The spectral indices agree well with a simple Fermi acceleration theory that includes guide-field dependence. In the low-guide-field regime, the flux rope kink instability governs the 3D dynamics for efficient acceleration. The weak dependence of the spectra on the ion-to-electron mass ratio and β ($\ll$1) implies that the particles are sufficiently magnetized for Fermi acceleration in our simulations. While both electrons and protons are injected at reconnection exhausts, protons are primarily injected by perpendicular electric fields through Fermi reflections and electrons are injected by a combination of perpendicular and parallel electric fields. The magnetic power spectra agree with in situ magnetotail observations, and the spectral index may reflect a reconnection-driven size distribution of plasmoids instead of the Goldreich–Sridhar vortex cascade. As the guide field becomes stronger, the oblique flux ropes of large sizes capture the main 3D dynamics for efficient acceleration. Intriguingly, the oblique flux ropes can also experience flux rope kink instability, to drive extra 3D dynamics. This work has broad implications for 3D reconnection dynamics and particle acceleration in heliophysics and astrophysics.

79 ASTRONOMY AND ASTROPHYSICS

Energy Conversion and Electron Acceleration and Transport in 3D Simulations of Solar Flares

Recent observations and simulations indicate that solar flares undergo extremely complex 3D evolution, making 3D particle transport models essential for understanding electron acceleration and interpreting flare emissions. In this study, we investigate this problem by solving Parker’s transport equation with 3D MHD simulations of solar flares. By examining energy conversion in the 3D system, we evaluate the roles of different acceleration mechanisms, including reconnection current sheet (CS), termination shock (TS), and supra-arcade downflows (SADs). We find that large-amplitude turbulent fluctuations are generated and sustained in the 3D system. The model results demonstrate that a significant number of electrons are accelerated to hundreds of keV and even a few MeV, forming power-law energy spectra. These energetic particles are widely distributed, with concentrations at the TS and in the flare looptop region, consistent with results derived from recent hard X-ray (HXR) and microwave (MW) observations. By selectively turning particle acceleration on or off in specific regions, we find that the CS and SADs effectively accelerate electrons to several hundred keV, while the TS enables further acceleration to MeV. However, no single mechanism can independently account for the significant number of energetic electrons observed. Instead, the mechanisms work synergistically to produce a large population of accelerated electrons. Our model provides spatially and temporally resolved electron distributions in the whole flare region and at the flare footpoints, enabling synthetic HXR and MW emission modeling for comparison with observations. These results offer important insights into electron acceleration and transport in 3D solar flare regions.

79 ASTRONOMY AND ASTROPHYSICS

Horizontal vestibuloocular reflex evoked by high-acceleration rotations in the squirrel monkey. IV. Responses after spectacle-induced adaptation

The horizontal angular vestibuloocular reflex (VOR) evoked by sinusoidal rotations from 0.5 to 15 Hz and acceleration steps up to 3,000 degrees /s(2) to 150 degrees /s was studied in six squirrel monkeys following adaptation with x2.2 magnifying and x0.45 minimizing spectacles. For sinusoidal rotations with peak velocities of 20 degrees /s, there were significant changes in gain at all frequencies; however, the greatest gain changes occurred at the lower frequencies. The frequency- and velocity-dependent gain enhancement seen in normal monkeys was accentuated following adaptation to magnifying spectacles and diminished with adaptation to minimizing spectacles. A differential increase in gain for the steps of acceleration was noted after adaptation to the magnifying spectacles. The gain during the acceleration portion, G(A), of a step of acceleration (3,000 degrees /s(2) to 150 degrees /s) increased from preadaptation values of 1.05 +/- 0.08 to 1.96 +/- 0.16, while the gain during the velocity plateau, G(V), only increased from 0.93 +/- 0.04 to 1.36 +/- 0.08. Polynomial fits to the trajectory of the response during the acceleration step revealed a greater increase in the cubic than the linear term following adaptation with the magnifying lenses. Following adaptation to the minimizing lenses, the value of G(A) decreased to 0.61 +/- 0.08, and the value of G(V) decreased to 0.59 +/- 0.09 for the 3,000 degrees /s(2) steps of acceleration. Polynomial fits to the trajectory of the response during the acceleration step revealed that there was a significantly greater reduction in the cubic term than in the linear term following adaptation with the minimizing lenses. These findings indicate that there is greater modification of the nonlinear as compared with the linear component of the VOR with spectacle-induced adaptation. In addition, the latency to the onset of the adapted response varied with the dynamics of the stimulus. The findings were modeled with a bilateral model of the VOR containing linear and nonlinear pathways that describe the normal behavior and adaptive processes. Adaptation for the linear pathway is described by a transfer function that shows the dependence of adaptation on the frequency of the head movement. The adaptive process for the nonlinear pathway is a gain enhancement element that provides for the accentuated gain with rising head velocity and the increased cubic component of the responses to steps of acceleration. While this model is substantially different from earlier models of VOR adaptation, it accounts for the data in the present experiments and also predicts the findings observed in the earlier studies.

NASA Discipline Neuroscience

Spectral Power-law Formation by Sequential Particle Acceleration in Multiple Flare Magnetic Islands

We present a first-principles model of pitch-angle and energy distribution function evolution as particles are sequentially accelerated by multiple flare magnetic islands. Data from magnetohydrodynamic (MHD) simulations of an eruptive flare/coronal mass ejection provide ambient conditions for the evolving particle distributions. Magnetic islands, which are created by sporadic reconnection at the self-consistently formed flare current sheet, contract and accelerate the particles. The particle distributions are evolved using rules derived in our previous work. In this investigation, we assume that a prescribed fraction of particles sequentially "hops" to another accelerator and receives an additional boost in energy and anisotropy. This sequential process generates particle number spectra that obey an approximate power law at mid-range energies and presents low- and high-energy breaks. We analyze these spectral regions as functions of the model parameters. We also present a fully analytic method for forming and interpreting such spectra, independent of the sequential acceleration model. The method requires only a few constrained physical parameters, such as the percentage of particles transferred between accelerators, the energy gain in each accelerator, and the number of accelerators visited. Our investigation seeks to bridge the gap between MHD and kinetic regimes by combining global simulations and analytic kinetic theory. The model reproduces and explains key characteristics of observed flare hard X-ray spectra as well as the underlying properties of the accelerated particles. Our analytic model provides tools to interpret high-energy observations for missions and telescopes, such as RHESSI, FOXSI, NuSTAR, Solar Orbiter, EOVSA, and future high-energy missions.

magnetic reconnection

Early-time γ -ray constraints on cosmic-ray acceleration in the core-collapse SN 2023ixf with the Fermi Large Area Telescope

Context. While supernova remnants (SNRs) have been considered the most relevant Galactic cosmic ray (CR) accelerators for decades, core-collapse supernovae (CCSNe) could accelerate particles during the earliest stages of their evolution and hence contribute to the CR energy budget in the Galaxy. Some SNRs have indeed been associated with TeV γ -rays, yet proton acceleration efficiency during the early stages of an SN expansion remains mostly unconstrained. Aims. The multi-wavelength observation of SN 2023ixf, a Type II supernova (SN) in the nearby galaxy M 101 (at a distance of 6.85 Mpc), opens the possibility to constrain CR acceleration within a few days after the collapse of the red super-giant stellar progenitor. With this work, we intend to provide a phenomenological, quasi-model-independent constraint on the CR acceleration efficiency during this event at photon energies above 100 MeV. Methods. We performed a maximum-likelihood analysis of γ -ray data from the Fermi Large Area Telescope up to one month after the SN explosion. We searched for high-energy, non-thermal emission from its expanding shock, and estimated the underlying hadronic CR energy reservoir assuming a power-law proton distribution consistent with standard diffusive shock acceleration. Results. We do not find significant γ -ray emission from SN 2023ixf. Nonetheless, our non-detection provides the first limit on the energy transferred to the population of hadronic CRs during the very early expansion of a CCSN. Conclusions. Under reasonable assumptions, our limits would imply a maximum efficiency on the CR acceleration of as low as 1%, which is inconsistent with the common estimate of 10% in generic SNe. However, this result is highly dependent on the assumed geometry of the circumstellar medium, and could be relaxed back to 10% by challenging spherical symmetry. Consequently, a more sophisticated, inhomogeneous characterisation of the shock and the progenitor’s environment is required before establishing whether or not Type II SNe are indeed efficient CR accelerators at early times.

79 ASTRONOMY AND ASTROPHYSICS

Numerical simulations of laser-driven experiments of ion acceleration in stochastic magnetic fields

We present numerical simulations used to interpret laser-driven plasma experiments at the GSI Helmholtz Centre for Heavy Ion Research. The mechanisms by which non-thermal particles are accelerated in astrophysical environments, e.g., the solar wind, supernova remnants, and gamma ray bursts, is a topic of intense study. When shocks are present, the primary acceleration mechanism is believed to be first-order Fermi, which accelerates particles as they cross a shock. Second-order Fermi acceleration can also contribute, utilizing magnetic mirrors for particle energization. Despite this mechanism being less efficient, the ubiquity of magnetized turbulence in the universe necessitates its consideration. Another acceleration mechanism is the lower-hybrid drift instability, arising from gradients of both density and magnetic field, which produce lower-hybrid waves with an electric field that energizes particles as they cross these waves. With the combination of high-powered laser systems and particle accelerators, it is possible to study the mechanisms behind cosmic-ray acceleration in the laboratory. In this work, we combine experimental results and high-fidelity three-dimensional simulations to estimate the efficiency of ion acceleration in a weakly magnetized interaction region. We validate the FLASH magneto-hydrodynamic code with experimental results and use OSIRIS particle-in-cell code to verify the initial formation of the interaction region, showing good agreement between codes and experimental results. We find that the plasma conditions in the experiment are conducive to the lower-hybrid drift instability, yielding an increase in energy ΔE of ~ 264 keV for 242 MeV calcium ions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Ion beam divergence characteristics of three-grid accelerator systems

A comprehensive experimental investigation of the geometrical and operating conditions which affect most strongly the ion beam divergence of three-grid accelerator systems is presented. Three-grid accelerator systems are shown to offer significant improvements in ion beam focusing over two-grid accelerator systems. These improvements are greatest for low, but limited, net-to-total accelerating voltage ratio ranges and small screen-to-accelerator grid separation ratios (i.e., high perveance grid sets). Ion beam focusing gains are negligible at a net-to-total accelerating voltage ratio near unity. Low decelerator grid impingement currents and low ion beam divergence angles require that the decelerator hole diameter be about twenty five percent larger than the accelerator hole diameter, also that the decelerator grid be spaced as close as is practically possible to the accelerator grid.

Aston, G.