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At least 1,117 records · Page 62

ERS-1 scatterometer calibration and validation activities at ECMWF. B: From radar backscatter characteristics to wind vector solutions

Calibration and validation activities for the ERS-1 scatterometer were carried out at ECMWF (European Center for Medium range Weather Forecast) complementary to the 'Haltenbanken' field campaign off the coast of Norway. At a Numerical Weather Prediction (NWP) center a wealth of verifying data is available both in time and space. This data is used to redefine the wind retrieval procedure given the instrumental characteristics. It was found that a maximum likelihood estimation procedure to obtain the coefficients of a reformulated sigma deg to wind relationship should use radar measurements in logarithmic rather than physical space, and use winds as the wind components rather than wind speed and direction. Doing this, a much more accurate transfer function than the one currently operated by ESA was derived. Sigma deg measurement space shows no signature of a separation in an upwind solution cone and a downwind solution cone. As such signature was anticipated in ESA's wind direction ambiguity removal algorithm, reconsideration of the procedure is necessary. Despite the fact that revisions have to be made in the process of wind retrieval; a grid potential is shown for scatterometry in meteorology and climatology.

Stoffelen, AD↗

Operator-assisted planning and execution of proximity operations subject to operational constraints

Future multi-vehicle operations will involve multiple scenarios that will require a planning tool for the rapid, interactive creation of fuel-efficient trajectories. The planning process must deal with higher-order, non-linear processes involving dynamics that are often counter-intuitive. The optimization of resulting trajectories can be difficult to envision. An interaction proximity operations planning system is being developed to provide the operator with easily interpreted visual feedback of trajectories and constraints. This system is hosted on an IRIS 4D graphics platform and utilizes the Clohessy-Wiltshire equations. An inverse dynamics algorithm is used to remove non-linearities while the trajectory maneuvers are decoupled and separated in a geometric spreadsheet. The operator has direct control of the position and time of trajectory waypoints to achieve the desired end conditions. Graphics provide the operator with visualization of satisfying operational constraints such as structural clearance, plume impingement, approach velocity limits, and arrival or departure corridors. Primer vector theory is combined with graphical presentation to improve operator understanding of suggested automated system solutions and to allow the operator to review, edit, or provide corrective action to the trajectory plan.

Grunwald, Arthur J.↗

Interactive computer modeling of combustion chemistry and coalescence-dispersion modeling of turbulent combustion

An interactive computer code for simulation of a high-intensity turbulent combustor as a single point inhomogeneous stirred reactor was developed from an existing batch processing computer code CDPSR. The interactive CDPSR code was used as a guide for interpretation and direction of DOE-sponsored companion experiments utilizing Xenon tracer with optical laser diagnostic techniques to experimentally determine the appropriate mixing frequency, and for validation of CDPSR as a mixing-chemistry model for a laboratory jet-stirred reactor. The coalescence-dispersion model for finite rate mixing was incorporated into an existing interactive code AVCO-MARK I, to enable simulation of a combustor as a modular array of stirred flow and plug flow elements, each having a prescribed finite mixing frequency, or axial distribution of mixing frequency, as appropriate. Further increase the speed and reliability of the batch kinetics integrator code CREKID was increased by rewriting in vectorized form for execution on a vector or parallel processor, and by incorporating numerical techniques which enhance execution speed by permitting specification of a very low accuracy tolerance.

Pratt, D. T.↗

Postprocessing for the UCLA climate model

Postprocessing programs written to analyze the results of a general circulation model are described. The model history data is interpolated to pressure surfaces, converted from 64-bit Cyber words to 32 bit IBM words, and transferred to tape for further analysis. The time average program reads the interpolation output tape and produces 15-day time averages. The model outputs a very detailed record for selected grid points. This data is sent to a tape in Cyber full words. The conversion program changes the format of the tape from 64 bit Cyber words to 32 bit IBM words, processing a month of data at a time. The grid-point history sorting program inputs the converted grid point history tape and sorts it by time. The end product is a tape with a time history of each field for every point. After the PBP data has been stored, it can be plotted. The plotting package is flexible, and allows the choice of fields and grid points. The one-dimensional fields are plotted as functions of time, and a daily summary is also produced. For the two-dimensional fields, time-height cross sections and daily summaries are produced. The model plotting package produces plots for all fields on the time average and pressure tapes. These plots include world maps, polar projections, zonal means, vectors, streamlines, and latitude-height plots.

Abeles, J.↗

Lunar Navigation Determination System - LaNDS

A portable comprehensive navigational system has been developed that both robotic and human explorers can use to determine their location, attitude, and heading anywhere on the lunar surface independent of external infrastructure (needs no Lunar satellite network, line of sight to the Sun or Earth, etc.). The system combines robust processing power with an extensive topographical database to create a real-time atlas (GIS Geospatial Information System) that is able to autonomously control and monitor both single unmanned rovers and fleets of rovers, as well as science payload stations. The system includes provisions for teleoperation and tele-presence. The system accepts (but does not require) inputs from a wide range of sensors. A means was needed to establish a location when the search is taken deep in a crater (looking for water ice) and out of view of Earth or any other references. A star camera can be employed to determine the user's attitude in menial space and stellar map in body space. A local nadir reference (e.g., an accelerometer that orients the nadir vector in body space) can be used in conjunction with a digital ephemeris and gravity model of the Moon to isolate the latitude, longitude, and azimuth of the user on the surface. That information can be used in conjunction with a Lunar GIS and advanced navigation planning algorithms to aid astronauts (or other assets) to navigate on the Lunar surface.

Quinn, David↗

Structural Dynamics Observations in Space Launch System Green Run Hot Fire Testing

The Space Launch System (SLS) Core Stage (CS) Thrust Vector Control (TVC) system is comprised of eight mechanical feedback Shuttle heritage Type III TVC actuators and four RS-25 engines, each attached to a Shuttle heritage gimbal block/bearing. Two actuators are used to move each engine in two planes perpendicular to one another (i.e., pitch and yaw). The TVC system design leverages hardware from the Space Shuttle program as well as new hardware designed specifically for the Core Stage. The Green Run Hot Fire (GRHF) of the SLS Core Stage provided a flight-like ground test environment for verification of integrated vehicle TVC performance. A TVC model coupled to a vehicle structural dynamic model has been developed previously and incrementally validated in subsystem tests and simulations. Still, some aspects of TVC performance in GRHF were not anticipated. The ensuing investigation demonstrated the need for well-instrumented test environments, various levels of modeling fidelity, test-representative structural models, and caution in reuse of legacy components. This paper is the sixth installment in a seven-paper series surveying the design, engineering, test validation, and flight performance of the Core Stage Thrust Vector Control system. It introduces the salient structural dynamic phenomena uncovered in ambient and hot fire testing. During the Green Run test campaign, a comparison of ambient and hot fire step responses showed a significant change in apparent damping due to the presence of friction, challenging long standing assumptions that friction could be neglected. Additionally, the characteristic response of the engine and thrust structure during GRHF proved to be more complex than anticipated, as evidenced by the available actuator, thrust structure, and engine measurements. While the string-potentiometer based test instrumentation was intended to allow for reconstruction of the engine angles along the two control axes, the geometric placement, location uncertainty, and responses in overlapping frequency spectra revealed additional phenomena requiring further analysis and post-processing. The observations from both modal and frequency response testing during the Green Run ambient and hot fire configurations led to Engine and Core Stage FEM (finite element model) updates. When evidence of unexpected engine motion was found in engine section accelerometer data, the authors pursued additional structural analysis leading to FEM updates associated with the TVC gimbal and thrust structure. Through collaboration between structures, TVC, and flight control disciplines, the test-informed models and root-cause analysis led to confident flight rationale for the first flight of the SLS launch vehicle.

Richard K. Moore↗

Structural Dynamics Observations in Space Launch System Green Run Hot Fire Testing

The Space Launch System (SLS) Core Stage (CS) Thrust Vector Control (TVC) system is comprised of eight mechanical feedback Shuttle heritage Type III TVC actuators and four RS-25 engines, each attached to a Shuttle heritage gimbal block/bearing. Two actuators are used to move each engine in two planes perpendicular to one another (i.e., pitch and yaw). The TVC system design leverages hardware from the Space Shuttle program as well as new hardware designed specifically for the Core Stage. The Green Run Hot Fire (GRHF) of the SLS Core Stage provided a flight-like ground test environment for verification of integrated vehicle TVC performance. A TVC model coupled to a vehicle structural dynamic model has been developed previously and incrementally validated in subsystem tests and simulations. Still, some aspects of TVC performance in GRHF were not anticipated. The ensuing investigation demonstrated the need for well-instrumented test environments, various levels of modeling fidelity, test-representative structural models, and caution in reuse of legacy components. This paper is the sixth installment in a seven-paper series surveying the design, engineering, test validation, and flight performance of the Core Stage Thrust Vector Control system. It introduces the salient structural dynamic phenomena uncovered in ambient and hot fire testing. During the Green Run test campaign, a comparison of ambient and hot fire step responses showed a significant change in apparent damping due to the presence of friction, challenging long standing assumptions that friction could be neglected. Additionally, the characteristic response of the engine and thrust structure during GRHF proved to be more complex than anticipated, as evidenced by the available actuator, thrust structure, and engine measurements. While the string-potentiometer based test instrumentation was intended to allow for reconstruction of the engine angles along the two control axes, the geometric placement, location uncertainty, and responses in overlapping frequency spectra revealed additional phenomena requiring further analysis and post-processing. The observations from both modal and frequency response testing during the Green Run ambient and hot fire configurations led to Engine and Core Stage FEM (finite element model) updates. When evidence of unexpected engine motion was found in engine section accelerometer data, the authors pursued additional structural analysis leading to FEM updates associated with the TVC gimbal and thrust structure. Through collaboration between structures, TVC, and flight control disciplines, the test-informed models and root-cause analysis led to confident flight rationale for the first flight of the SLS launch vehicle.

Richard Moore↗

The Dipper Satellite: A Medium-Class Explorer Mission to the Threshold of Space

The Dipper satellite will carry out an unprecedented, systematic, and focused in-situ exploration of the Earth's lower ionosphere and thermosphere below 200 km that will produce a pivotal base of knowledge that will significantly advance our understanding of knowledge that will significantly advance our understanding of how our near-space environment works. The satellite will carry comprehensive in-situ probes to measure vector electric and magnetic fields, plasma density and temperature, ion velocities, ion and neutral composition and winds, energetic particles including suprathermal electrons, gravity waves, and lightning bursts. The satellite will include a propulsion system and tapered body that will provide over 10,000 excursions to altitudes below 200 km with over 3000 dips to altitudes below 150 km. With this instrument complement, spacecraft, and orbit, the Dipper mission will gather the necessary combined electrodynamics and neutral dynamics measurements to provide an understanding of the Earth's critical boundary region where the ionized gases of space and the neutral gases of the atmosphere are coupled, and where impinging forces and momentum are deposited from the magnetosphere above and from the troposphere, stratosphere, and mesosphere below. In exploring those physical processes in the lower ionosphere which can only be measured in-situ, the Dipper mission addresses four main science objectives. The Dipper will: 1) reveal how ion-neutral coupling creates a global system of dynamo electric fields and currents; 2) provide first-hand understanding of how magnetospheric currents close in the ionosphere and reveal the effects on the upper atmosphere of magnetospheric energy and momentum deposition; 3) discover the degree of upwards coupling and energy deposition due to thunderstorm electric fields and determine their significance; 4) determine the dynamics and composition of the Earth's lower thermosphere, including its response to gravity, tidal, and planetary waves on a range of spatial scales. A proposal to design, build, operate, and analyze data from instruments on the Dipper spacecraft within the schedule and budget constraints of NASA's MIDEX program was submitted to NASA in 1998. This presentation summarizes the main features of the mission.

Pfaff, R. F., Jr.↗

Comparison Tools for Assessing the Microgravity Environment of Space Missions, Carriers and Conditions

The microgravity environment of the NASA Shuttles and Russia's Mir space station have been measured by specially designed accelerometer systems. The need for comparisons between different missions, vehicles, conditions, etc. has been addressed by the two new processes described in this paper. The Principal Component Spectral Analysis (PCSA) and Quasi-steady Three-dimensional Histogram QTH techniques provide the means to describe the microgravity acceleration environment of a long time span of data on a single plot. As described in this paper, the PCSA and QTH techniques allow both the range and the median of the microgravity environment to be represented graphically on a single page. A variety of operating conditions may be made evident by using PCSA or QTH plots. The PCSA plot can help to distinguish between equipment operating full time or part time, as well as show the variability of the magnitude and/or frequency of an acceleration source. A QTH plot summarizes the magnitude and orientation of the low-frequency acceleration vector. This type of plot can show the microgravity effects of attitude, altitude, venting, etc.

DeLombard, Richard↗

MISTiC Winds, a Micro-Satellite Constellation Approach to High Resolution Observations of the Atmosphere Using Infrared Sounding and 3D Winds Measurements

MISTiC(TM) Winds is an approach to improve short-term weather forecasting based on a miniature high resolution, wide field, thermal emission spectrometry instrument that will provide global tropospheric vertical profiles of atmospheric temperature and humidity at high (3-4 km) horizontal and vertical ( 1 km) spatial resolution. MISTiCs extraordinarily small size, payload mass of less than 15 kg, and minimal cooling requirements can be accommodated aboard a 27U-class CubeSat or an ESPA-Class micro-satellite. Low fabrication and launch costs enable a LEO sunsynchronous sounding constellation that would collectively provide frequent IR vertical profiles and vertically resolved atmospheric motion vector wind observations in the troposphere. These observations are highly complementary to present and emerging environmental observing systems, and would provide a combination of high vertical and horizontal resolution not provided by any other environmental observing system currently in operation. The spectral measurements that would be provided by MISTiC Winds are similar to those of NASA's AIRS that was built by BAE Systems and operates aboard the AQUA satellite. These new observations, when assimilated into high resolution numerical weather models, would revolutionize short-term and severe weather forecasting, save lives, and support key economic decisions in the energy, air transport, and agriculture arenasat much lower cost than providing these observations from geostationary orbit. In addition, this observation capability would be a critical tool for the study of transport processes for water vapor, clouds, pollution, and aerosols. Key remaining technical risks are being reduced through laboratory and airborne testing under NASA's Instrument Incubator Program.

Maschhoff, K. R.↗

A Parallel Processing Algorithm for Remote Sensing Classification

A current thread in parallel computation is the use of cluster computers created by networking a few to thousands of commodity general-purpose workstation-level commuters using the Linux operating system. For example on the Medusa cluster at NASA/GSFC, this provides for super computing performance, 130 G(sub flops) (Linpack Benchmark) at moderate cost, $370K. However, to be useful for scientific computing in the area of Earth science, issues of ease of programming, access to existing scientific libraries, and portability of existing code need to be considered. In this paper, I address these issues in the context of tools for rendering earth science remote sensing data into useful products. In particular, I focus on a problem that can be decomposed into a set of independent tasks, which on a serial computer would be performed sequentially, but with a cluster computer can be performed in parallel, giving an obvious speedup. To make the ideas concrete, I consider the problem of classifying hyperspectral imagery where some ground truth is available to train the classifier. In particular I will use the Support Vector Machine (SVM) approach as applied to hyperspectral imagery. The approach will be to introduce notions about parallel computation and then to restrict the development to the SVM problem. Pseudocode (an outline of the computation) will be described and then details specific to the implementation will be given. Then timing results will be reported to show what speedups are possible using parallel computation. The paper will close with a discussion of the results.

Gualtieri, J. Anthony↗

Numerical modeling of Bridgman growth of PbSnTe in a magnetic field

In this work we study heat and mass transport, fluid motion, and solid/liquid phase change in the process of steady Bridgman growth of Pb(.8)Sn(.2)Te (LTT) in an axially-imposed uniform magnetic field under terrestrial and microgravity conditions. In particular, this research is concerned with the interrelationships among segregation, buoyancy-driven convection, and magnetic damping in the LTT melt. The main objectives are to provide a quantitative understanding of the complex transport phenomena during solidification of the nondilute binary of LTT, to provide estimates of the strength of magnetic field required to achieve the desired diffusion-dominated growth, and to assess the role of magnetic damping for space and earth based control of the buoyancy-induced convection. The problem was solved by using FIDAP and numerical results for both vertical and horizontal growth configurations with respect to the acceleration of gravity vector are presented.

Yao, Minwu↗

Venus and Beyond Using the Ariane ASAP Launch Capability

The cost of executing planetary missions in the next ten years is expected to decrease significantly. The principle reason is that new technology is reducing spacecraft mass while increasing capability. Another reason is that launch costs are expected to decrease. A move in this direction is to permit important planetary missions to fly as secondary payloads, and this opportunity is now provided by the French on the Ariane 5 using the Ariane Structure for Auxiliary Payloads (ASAP). The ASAP will fly on GEO missions, and can boost up to eight 100 kg (or 200 kg, if paired) payloads into the elliptical geosynchronous transfer orbit (GTO), which delivers large communication satellites to GEO. An efficient multi-burn method has been developed by this author to deliver these small spacecraft from GTO to Mars and other destinations. This method, referred to here as Moon-Earth Gravity Assist (MEGA), requires 3 or more major maneuvers together with close flybys of the earth and moon. An example for a Mars 2003 mission (not to scale) is shown in Figure 1, where, once in GTO, the first burn sends the spacecraft beyond the Moon to a distance of 1.2 million kilometers. At apogee, the second burn targets to an encounter with the Moon such that a swingby returns the spacecraft to the Earth with a 300 km perigee, and with an inclination such that a perigee burn will send the spacecraft off to Mars with the required escape velocity vector. Details of this method, specifically for Mars missions, can be found in Reference 3. A similar strategy works for Venus, with some caveats. This method is required to work for any Ariane 5 launch date over a three month period, to ensure a high probability of getting off the ground. The launch period is provided by fixing the Earth escape date (3rd burn), but allowing the high ellipse (beyond the Moon) period to vary by one or two months, and also allowing a one to two month wait time in GTO (or other orbit) before the first burn is performed. Figure 2 shows the trajectory profiles for the early and late GTO launch dates for a Mars 2003 mission. Venus. which is an inner planet, poses special problems for the MEGA process. The escape direction is reverse that of Earth's motion, and the GTO apogee arrival

Penzo, Paul A.↗

Fiber Optic Sensing Monitors Strain and Reduces Costs

In applications where stress on a structure may vary widely and have an unknown impact on integrity, a common engineering strategy has been overbuilding to ensure a sufficiently robust design. While this may be appropriate in applications where weight concerns are not paramount, space applications demand a bare minimum of mass, given astronomical per-pound launch costs. For decades, the preferred solution was the tactic of disassembly and investigation between flights. Knowing there must be a better way, Dr. Mark Froggatt, of Langley Research Center, explored alternate means of monitoring stresses and damage to the space shuttle. While a tear-it-apart-and-have-a-look strategy was effective, it was also a costly and time consuming process that risked further stresses through the very act of disassembly and reassembly. An alternate way of monitoring the condition of parts under the enormous stresses of space flight was needed. Froggatt and his colleagues at Langley built an early-warning device to provide detailed information about even minuscule cracks and deformations by etching a group of tiny lines, or grating, on a fiber optic cable five-thousandths of an inch thick with ultraviolet light. By then gluing the fiber to the side of a part, such as a fuel tank, and shining a laser beam down its length, reflected light indicated which gratings were under stress. Inferring this data from measurements in light rather than in bonded gauges saved additional weight. Various shuttle components now employ the ultrasonic dynamic vector stress sensor (UDVSS), allowing stress detection by measuring light beamed from a built-in mini-laser. By measuring changes in dynamic directional stress occurring in a material or structure, and including phase-locked loop, synchronous amplifier, and contact probe, the UDVSS proved especially useful among manufacturers of aerospace and automotive structures for stress testing and design evaluation. Engineers could ensure safety in airplanes and spaceships with a narrower, not overbuilt, margin of safety. For this development, in 1997, Discover Magazine named Froggatt a winner in the "Eighth Annual Awards for Technological Innovation" from more than 4,000 entries.

Source record↗

Influence of Vibrotactile Feedback on Controlling Tilt Motion After Spaceflight

We hypothesize that adaptive changes in how inertial cues from the vestibular system are integrated with other sensory information leads to perceptual disturbances and impaired manual control following transitions between gravity environments. The primary goals of this ongoing post-flight investigation are to quantify decrements in manual control of tilt motion following short-duration spaceflight and to evaluate vibrotactile feedback of tilt as a sensorimotor countermeasure. METHODS. Data is currently being collected on 9 astronaut subjects during 3 preflight sessions and during the first 8 days after Shuttle landings. Variable radius centrifugation (216 deg/s, <20 cm radius) in a darkened room is utilized to elicit otolith reflexes in the lateral plane without concordant canal or visual cues. A Tilt-Translation Sled (TTS) is capable of synchronizing pitch tilt with fore-aft translation to align the resultant gravitoinertial vector with the longitudinal body axis, thereby eliciting canal reflexes without concordant otolith or visual cues. A simple 4 tactor system was implemented to provide feedback when tilt position exceeded predetermined levels in either device. Closed-loop nulling tasks are performed during random tilt steps or sum-of-sines (TTS only) with and without vibrotactile feedback of chair position. RESULTS. On landing day the manual control performance without vibrotactile feedback was reduced by >30% based on the gain or the amount of tilt disturbance successfully nulled. Manual control performance tended to return to baseline levels within 1-2 days following landing. Root-mean-square position error and tilt velocity were significantly reduced with vibrotactile feedback. CONCLUSIONS. These preliminary results are consistent with our hypothesis that adaptive changes in vestibular processing corresponds to reduced manual control performance following G-transitions. A simple vibrotactile prosthesis improves the ability to null out tilt motion within a limited range of motion disturbances.

Wood, S. J.↗

A finite element conjugate gradient FFT method for scattering

An extension of a two dimensional formulation is presented for a three dimensional body of revolution. With the introduction of a Fourier expansion of the vector electric and magnetic fields, a coupled two dimensional system is generated and solved via the finite element method. An exact boundary condition is employed to terminate the mesh and the fast fourier transformation (FFT) is used to evaluate the boundary integrals for low O(n) memory demand when an iterative solution algorithm is used. By virtue of the finite element method, the algorithm is applicable to structures of arbitrary material composition. Several improvements to the two dimensional algorithm are also described. These include: (1) modifications for terminating the mesh at circular boundaries without distorting the convolutionality of the boundary integrals; (2) the development of nonproprietary mesh generation routines for two dimensional applications; (3) the development of preprocessors for interfacing SDRC IDEAS with the main algorithm; and (4) the development of post-processing algorithms based on the public domain package GRAFIC to generate two and three dimensional gray level and color field maps.

Collins, Jeffery D.↗

Improvements to the Unstructured Mesh Generator MESH3D

The AIRPLANE process starts with an aircraft geometry stored in a CAD system. The surface is modeled with a mesh of triangles and then the flow solver produces pressures at surface points which may be integrated to find forces and moments. The biggest advantage is that the grid generation bottleneck of the CFD process is eliminated when an unstructured tetrahedral mesh is used. MESH3D is the key to turning around the first analysis of a CAD geometry in days instead of weeks. The flow solver part of AIRPLANE has proven to be robust and accurate over a decade of use at NASA. It has been extensively validated with experimental data and compares well with other Euler flow solvers. AIRPLANE has been applied to all the HSR geometries treated at Ames over the course of the HSR program in order to verify the accuracy of other flow solvers. The unstructured approach makes handling complete and complex geometries very simple because only the surface of the aircraft needs to be discretized, i.e. covered with triangles. The volume mesh is created automatically by MESH3D. AIRPLANE runs well on multiple platforms. Vectorization on the Cray Y-MP is reasonable for a code that uses indirect addressing. Massively parallel computers such as the IBM SP2, SGI Origin 2000, and the Cray T3E have been used with an MPI version of the flow solver and the code scales very well on these systems. AIRPLANE can run on a desktop computer as well. AIRPLANE has a future. The unstructured technologies developed as part of the HSR program are now targeting high Reynolds number viscous flow simulation. The pacing item in this effort is Navier-Stokes mesh generation.

Thomas, Scott D.↗

Simulation of auroral double layers

Some basic properties of plasma double layers are deduced from a particle-in-cell computer simulation and related to parallel electric-field structures above the auroral regions. The simulation results on the processes leading to double-layer formation are examined, particularly in relation to the transient stage and double-layer structure and stability. It is concluded that: (1) a large potential difference applied to a finite-length plasma will be concentrated in a shocklike localized region instead of occurring over the entire length of the system; (2) the initial stage in double-layer formation is dominated by a large-potential pulse propagating in the direction of the induced electrostatic drift; (3) the entire potential is dropped over a specific scale length once the double layer has formed; and (4) this scale length is expected to be of the order of 1 km for a double layer above a discrete auroral arc with a potential of 10 kV and the electric-field vector parallel to the magnetic-field vector.

Hubbard, R. F.↗