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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Energetic Consequences of the DC-Electric Field Model

We analyze a solar flare observed simultaneously in soft and hard X-rays by instruments onboard Yohkoh and the Compton Gamma Ray Observatory. Assuming a simple one-dimensional coronal loop that is heated by field-aligned currents, we solve the energy balance equation to derive the DC-electric field strength necessary to explain the observed soft X-ray emission by current-dissipation. We use the derived DC-electric field to predict the number flux of electrons accelerated by thermal runaway and compare this prediction with the number flux of nonthermal thick-target electrons implied by impulsive phase hard X-ray observations. We find that runaway acceleration can account for the large flux (approx. greater than 10(exp 36 1/s) of nonthermal electrons provided the loop filling factor is approx. less than 10(exp -3) such that heating and acceleration occur in filamented structures within the loop.

Zarro, Dominic M.↗
NASA NTRS2009

Heating of the Solar Corona and its Loops

At several million degrees, the solar corona is more than two orders of magnitude hotter than the underlying solar surface. The reason for these extreme conditions has been a puzzle for decades and is considered one of the fundamental problems in astrophysics. Much of the coronal plasma is organized by the magnetic field into arch-like structures called loops. Recent observational and theoretical advances have led to great progress in understanding the nature of these loops. In particular, we now believe they are bundles of unresolved magnetic strands that are heated by storms of impulsive energy bursts called nanoflares. Turbulent convection at the solar surface shuffles the footpoints of the strands and causes them to become tangled. A nanoflare occurs when the magnetic stresses reach a critical threshold, probably by way of a mechanism called the secondary instability. I will describe our current state of knowledge concerning the corona, its loops, and how they are heated.

Klimchuk, James A.↗
NASA NTRS1993

On-board closed-loop congestion control for satellite based packet switching networks

NASA LeRC is currently investigating a satellite architecture that incorporates on-board packet switching capability. Because of the statistical nature of packet switching, arrival traffic may fluctuate and thus it is necessary to integrate congestion control mechanism as part of the on-board processing unit. This study focuses on the closed-loop reactive control. We investigate the impact of the long propagation delay on the performance and propose a scheme to overcome the problem. The scheme uses a global feedback signal to regulate the packet arrival rate of ground stations. In this scheme, the satellite continuously broadcasts the status of its output buffer and the ground stations respond by selectively discarding packets or by tagging the excessive packets as low-priority. The two schemes are evaluated by theoretical queuing analysis and simulation. The former is used to analyze the simplified model and to determine the basic trends and bounds, and the later is used to assess the performance of a more realistic system and to evaluate the effectiveness of more sophisticated control schemes. The results show that the long propagation delay makes the closed-loop congestion control less responsive. The broadcasted information can only be used to extract statistical information. The discarding scheme needs carefully-chosen status information and reduction function, and normally requires a significant amount of ground discarding to reduce the on-board packet loss probability. The tagging scheme is more effective since it tolerates more uncertainties and allows a larger margin of error in status information. It can protect the high-priority packets from excessive loss and fully utilize the downlink bandwidth at the same time.

Chu, Pong P.↗
NASA NTRS1995

Testing the DC-electric field model in a solar flare observed by Yohkoh and the Compton Gamma-Ray Observatory

We apply a DC-electric field model to the analysis of soft and hard X-ray observations of a solar flare observed by Yohkoh and the Compton Gamma Ray Observatory (CGRO) on 6 September 1992. The flare was observed simultaneously in the soft X-ray Ca XIX line by the Yohkoh Bragg Crystal Spectrometer (BCS) and in hard X-rays (greater than 50 keV) by the CGRO Burst and Transient Spectrometer Experiment (BATSE). A strong stationary component of Ca XIX emission was present at the start of impulsive hard X-ray emission indicating an extended phase of heating prior to the production of energetic nonthermal electrons. We interpret the preflare Ca XIX emission as a signature of Joule heating by field-aligned currents. We relate the temporal variation of impulsive hard X-ray emission to the rate of runaway electron acceleration by the DC-electric field associated with the current. We find that the initial rise in hard X-ray emission is consistent with electron acceleration by a DC-electric field that increased from a preflare value of less than approximately 10(exp -5) V/cm to approximately (9 +/- 1) x 10(exp -5) V/cm at the time of the first hard X-ray peak and then remained constant during the rest of the impulsive phase. We attribute the increase in electric field strength to the formation of a current sheet at the reconnection point of two loop structures. The decrease in hard X-ray emission after flare maximum is consistent with a reduction in the number of runaway electrons due to an increase in coronal density produced by chromospheric evaporation. The increased density quenches the runaway process by enhancing collisional thermalization of electrons. To avoid the generation of an unrealistically large magnetic field, the flaring region must be highly filamented into greater than approximately 10(exp 6) oppositely directed current channels of approximately 30 cm width with an initial preflare current of approximately 3 x 10(exp 10) A per channel.

Zarro, D. M.↗
NASA NTRS2011

International Space Station Active Thermal Control Sub-System On-Orbit Pump Performance and Reliability Using Liquid Ammonia as a Coolant

The International Space Station (ISS) contains two Active Thermal Control Sub-systems (ATCS) that function by using a liquid ammonia cooling system collecting waste heat and rejecting it using radiators. These subsystems consist of a number of heat exchangers, cold plates, radiators, the Pump and Flow Control Subassembly (PFCS), and the Pump Module (PM), all of which are Orbital Replaceable Units (ORU's). The PFCS provides the motive force to circulate the ammonia coolant in the Photovoltaic Thermal Control Subsystem (PVTCS) and has been in operation since December, 2000. The Pump Module (PM) circulates liquid ammonia coolant within the External Active Thermal Control Subsystem (EATCS) cooling the ISS internal coolant (water) loops collecting waste heat and rejecting it through the ISS radiators. These PM loops have been in operation since December, 2006. This paper will discuss the original reliability analysis approach of the PFCS and Pump Module, comparing them against the current operational performance data for the ISS External Thermal Control Loops.

Morton, Richard D.↗
NASA NTRS2021

The Dynamic Formation of Pseudostreamers

Streamers and pseudostreamers structure the corona at the largest scales, as seen in both eclipse and coronagraph white-light images. Their inverted-goblet appearance encloses broad coronal loops at the Sun and tapers to a narrow radial stalk away from the star. The streamer associated with the global solar dipole magnetic field is long-lived, predominantly contains a single arcade of nested loops within it, and separates opposite-polarity interplanetary magnetic fields with the heliospheric current sheet anchored at its apex. Pseudostreamers, on the other hand, are transient, enclose double arcades of nested loops, and separate like-polarity fields with a dense plasma sheet. We use numerical magnetohydrodynamic simulations to calculate, for the first time, the formation of pseudostreamers in response to photospheric magnetic-field evolution. Convective transport of a minority-polarity flux concentration, initially positioned under one side of a streamer, through the streamer boundary into the adjacent, pre-existing coronal hole forms the pseudostreamer. Interchange magnetic reconnection at the overlying coronal null point(s) governs the development of the pseudostreamer above – and of anew, satellite coronal hole behind – the moving minority polarity. The reconnection dynamics liberate coronal-loop plasma that can escape into the heliosphere along so-called separatrix-web (“S-Web”)arcs, which reach far from the heliospheric current sheet and the solar equatorial plane, and can explain the origin of high-latitude slow solar wind. We describe the implications of our results for in-situ and remote-sensing observations of the corona and heliosphere as obtained, most recently, by Parker Solar Probe and Solar OrbiteR.

Roger B. Scott↗
DOE OSTI2025

Packaging a 650V/400A GaN Half-bridge Power Module with Ultra-low Parasitics for Electric Vehicle Drive Applications

This paper proposes a compact and efficient half-bridge power module with three 650 V / 150 A GaN dies in parallel. The power module incorporates a main power printed circuit board (PCB), an interface PCB, and a flex PCB to achieve low parasitics in both power loop and gate-side connection, resolving the issue of high parasitics typically encountered with wire bonding in high-current applications. Additionally, the interface PCB decouples the design constraints between the power loop and the gate loops. The proposed design is optimized with a vertical loop configuration to reduce power loop inductance through magnetic flux cancellation. Finite element analysis indicates that the power loop inductance is 0.58 nH at 100 MHz, while the maximum die junction temperature reaches 131 °C under an ambient temperature of 65 °C and a load current of 385 A. The proposed multi-piece PCB structure reduces the inductance of the drive circuit to minimize EMI and to mitigate false triggering. At the same time, it reduces impedance mismatches across different driver circuits, thereby achieving dynamic current sharing in multi-chip parallel configurations. Under simulation conditions of 400 V / 385 A, the current imbalance among chips was limited to 5 A. A 400 V / 385 A double-pulse test was conducted to experimentally validate the performance of the proposed power module.

30 DIRECT ENERGY CONVERSION↗
NASA NTRS1977

Multiple feedback control apparatus for power conditioning equipment

An improved feedback control system to govern the cyclic operation of the power switch of a non-dissipative power conditioning equipment. The apparatus includes two or three control loops working in unison. The first causes the output DC level to be compared with a reference, and the error amplified for control purposes. The second utilizes the AC component of the voltage across the output filter inductor or the current through the output filter capacitor, and the third loop senses the output transients.

Biess, John↗
NASA NTRS1983

The stability of coronal loops - Finite-length and pressure-profile limits

Results are described from a quickly converging, necessary-and-sufficient, MHD-stability test for coronal-loop models. The primary stabilizing influence arises from magnetic line tying at the photosphere, and this end conditions requires a series expansion of possible loop excitations. The stability boundary is shown to quickly approach a limit as the number of terms increases, providing a critical length for the loop in proportion to its transverse magnetic scale. Several models of force-free-field profiles are tested and the stability behavior of a localized current channel, embedded in an external current-free region, is shown to be superior to that of other, broader, current profiles. Pressure-gradient effects, leading to increased or decreased stability, are shown to be amplified by line tying. Long loops must either conduct low net current, or exhibit an axial-field reversal coexisting with a low-pressure core. The limits on stability depend on the magnetic aspect ratio, the plasma-to-magnetic pressure ratio, and the field orientation at the loop edge. Applications of these results to the structure of coronal loops are described.

Einaudi, G.↗
NASA NTRS2022

Development of a Loop Antenna Deployment System for TEM-Based Subsurface Mars Water Detection

The subsurface of Mars has the potential to harbor existing deposits of liquid water, which are of great interest both scientifically (in the search for life) and as resources for future astronauts living on the red planet. However, the depth to a potential subsurface aquifer may be kilometers deep, which is well beyond what current surface or orbital approaches can survey while also confirming the unique signature for liquid water. Inspired by critical technology for exploring deep aquifers on Earth, we are developing the Transient H2O Reconnaissance (TH2OR) instrument at NASA’s Jet Propulsion Laboratory (JPL). TH2OR operates on the principle of transient electromagnetics (TEM), which leverages induction and electromotive force to induce a current in a subsurface water body using a loop-shaped antenna that provides both transmit and receive functions when placed on the surface. On Mars, TEM may be even more effective given the relative dryness of the subsurface compared to a more conductive, saline, liquid, water body on Earth. However, to probe deep within the subsurface (below 5 km) a large enclosed antenna is needed – specifically, a 100-m diameter effective loop or a shape with roughly equivalent area that can transmit at low frequencies (kHz-Hz). The deployment of a large-scale structure on the surface is complicated by the fact that the transmit wire must be both lightweight and robust to contact with the surface. Further, TH2OR may be delivered to the surface by a non-mobile vehicle, so it is desired that the deployment can be activated from a static location. This paper provides an overview of the deployment trade study, focusing on our current, favored approach, using a projectile wire launcher. Building on past approaches in the literature, we have developed and fielded an Earth-based, gas-projectile prototype for launching a triangle-shaped antenna onto analogue terrain. Our results compare simulated launch performance to actual field tests conducted under Earth gravity and pressure conditions. We discuss how Earth performance maps to a prospective Mars deployment under reduced gravity and pressure. We also provide lessons learned and next steps towards the development of an integrated TH2OR instrument for finding water on Mars.

Stamenkovic, Vlada↗
NASA NTRS1988

Current-driven resistive ballooning modes in axially bounded solar flare plasmas

The most unstable current-driven resistive modes of an axially bounded coronal loop are found in computer simulations to exhibit the spatial structure of ballooning modes. The observed modes are not confined to mode rational surfaces, but instead have broad radial extent. A theory assuming ballooning mode spatial structure predicts that a minimum current should be required for linear instability, and that, when the mode is unstable, the linear growth rate scales linearly with the resistivity eta below a critical resistivity, and scales as cu root of eta for larger resistivities. Both predictions are borne out by simulation results. Both theory and simulation analyses of the mode suggest that the strong radial structure of the mode near the ends of the system is the primary contributing factor to the instability of the mode. A helical current sheet is formed in the nonlinear evolution of the mode near the edge of the current channel and is accompanied by a strong radial gradient in the current and partial current reversal.

Otani, Niels F.↗
DOE OSTI2022

Flow Sensor Test Article (F-STAr) (Design and Fabrication Status Report)

The Flow Sensor Test Article (F-STAr) is a test article currently under construction for the Mechanisms Engineering Test Loop (METL). F-STAr was designed to provide high sodium flowrate capabilities for sensor calibration, component testing, and fluid studies. Figure 1 shows two solid model views of the new test article. F-STAr includes a high-capacity pump that can provide a nominal flowrate of 120 GPM; a test section support structure that can accommodate a wide array of sub-test articles and their instrumentation; and finally, a heating and cooling system to aid in controlling the testing environment. Initially, F-STAr will be configured to test liquid metal flow sensors, specifically field shift sensors like the Eddy Current Flow Sensors (ECFS) based on the RDT C4-7T standard. To test these sensors, two test sections were designed that attempt to model Sodium Fast Reactor (SFR) outlet conditions. Figure 2 shows models of the “Full-Scaled Test Section” (FSTS) that represents a generic SFR fuel handling socket and a “Pseudo-Scaled Test Section” (PSTS) that represents a generic array of scaled fuel handling sockets. While F-STAr will be configured to test ECFS’s, it can also be outfitted to meet other experimental needs. For example, F-STAr could be setup with a test section that includes a fluidic diode or a component test investigating the performance of hydrodynamic bearings. Other test sections include studies of sodium thermal hydraulics like thermal striping. Overall, F-STAr is a flexible test article designed to accommodate many needs. This report will provide a status update on the design and construction of F-STAr. Manufacturing of all components has commenced, and several components have already been completed. These components include the pump and test section assembly stand. Other components, such as the heater, have been completed but were rejected due to the vendor not meeting the requirements of the purchase order. Lastly, the submersible flowmeter and main flange components are under construction, and their status will be reviewed in this report. Overall, most of the F-STAr components and parts will be completed by the end of September 2022.

42 ENGINEERING↗
NASA NTRS1991

VERDEX: A virtual environment demonstrator for remote driving applications

One of the key areas of the National Advanced Robotics Centre's enabling technologies research program is that of the human system interface, phase 1 of which started in July 1989 and is currently addressing the potential of virtual environments to permit intuitive and natural interactions between a human operator and a remote robotic vehicle. The aim of the first 12 months of this program (to September, 1990) is to develop a virtual human-interface demonstrator for use later as a test bed for human factors experimentation. This presentation will describe the current state of development of the test bed, and will outline some human factors issues and problems for more general discussion. In brief, the virtual telepresence system for remote driving has been designed to take the following form. The human operator will be provided with a helmet-mounted stereo display assembly, facilities for speech recognition and synthesis (using the Marconi Macrospeak system), and a VPL DataGlove Model 2 unit. The vehicle to be used for the purposes of remote driving is a Cybermotion Navmaster K2A system, which will be equipped with a stereo camera and microphone pair, mounted on a motorized high-speed pan-and-tilt head incorporating a closed-loop laser ranging sensor for camera convergence control (currently under contractual development). It will be possible to relay information to and from the vehicle and sensory system via an umbilical or RF link. The aim is to develop an interactive audio-visual display system capable of presenting combined stereo TV pictures and virtual graphics windows, the latter featuring control representations appropriate for vehicle driving and interaction using a graphical 'hand,' slaved to the flex and tracking sensors of the DataGlove and an additional helmet-mounted Polhemus IsoTrack sensor. Developments planned for the virtual environment test bed include transfer of operator control between remote driving and remote manipulation, dexterous end effector integration, virtual force and tactile sensing (also the focus of a current ARRL contract, initially employing a 14-pneumatic bladder glove attachment), and sensor-driven world modeling for total virtual environment generation and operator-assistance in remote scene interrogation.

Stone, Robert J.↗
NASA NTRS1985

The structure of high-temperature solar flare plasma in non-thermal flare models

Analytic differential emission measure distributions have been derived for coronal plasma in flare loops heated both by collisions of high-energy suprathermal electrons with background plasma, and by ohmic heating by the beam-normalizing return current. For low densities, reverse current heating predominates, while for higher densities collisional heating predominates. There is thus a minimum peak temperature in an electron-heated loop. In contrast to previous approximate analyses, it is found that a stable reverse current can dominate the heating rate in a flare loop, especially in the low corona. Two 'scaling laws' are found which relate the peak temperature in the loop to the suprathermal electron flux. These laws are testable observationally and constitute a new diagnostic procedure for examining modes of energy transport in flaring loops.

Emslie, A. G.↗
DOE OSTI2024

Shallow Geothermal Resources for Cooling Applications at the University of Hawai‘i

Scientists at Berkeley Lab have teamed up with The University of Hawai‘i at Manoa (UH Manoa) through the U.S. Department of Energy’s (DOE’s) Energy Transitions Initiative Partnership Project (ETIPP) to evaluate the technological and market feasibility of shallow geothermal heat exchanger (GHE) technology for building cooling, energy efficiency, and emissions reduction applications in Hawai’i. The team is assessing the data necessary to model the feasibility of deploying this technology, the actual models that will be used, and what hurdles need to be overcome to install a demonstration case. UH has an abundance of geologic and geothermal data and is looking to the national labs’ expertise to execute this analysis. UH is also interested in investigating policy, regulatory, and business conditions advantageous for implementation of a pilot project, and more broad deployment of this technology in Hawai‘i. In many locations around the world, the demands for heating and cooling are roughly balanced over the course of the year, so GHEs do not cause significant long-term changes in subsurface temperature. This is not the case in Hawai’i, where the demand for heating is very small, meaning that over time, GHEs will add heat to the subsurface. If temperatures increase significantly, GHE systems will not work as designed. Regional groundwater flow has the potential to sweep heated water away from boreholes, thereby maintaining the functionality of the GHE system. Significant regional groundwater flow requires two things: a sufficiently large driving hydraulic head gradient (usually closely related to surface topography), and sufficient porosity and permeability to enable groundwater to flow in large enough quantities to enable near-borehole temperatures to be maintained at ambient values. Hawai‘i’s volcanic terrain offers ample surface topographic variation. The lava itself shows an extremely large range of porosity and permeability, making it crucial to select sites with large enough values of these properties. Numerical modeling of coupled groundwater and heat flow can be used to determine how large is large enough. Both closed-loop and open-loop systems are being investigated. Another option being considered is using cool seawater as the source of chill. Currently work is progressing on two fronts. A hydrogeologic model for a closed-loop system is being developed for the Stan Sheriff Center at the UH Manoa campus, where a subsurface karst system immediately downgradient of the borefield may provide efficient removal of heated groundwater. The team will also develop a technoeconomic model for this site to compare the cost of cooling using a GHE system with the costs of operating the current air conditioning system. At the state scale, geographic information system (GIS) layers of various attributes relevant for GHE are being combined to develop an overall favorability map for employing GHE in Hawai‘i.

Doughty, C↗
NASA NTRS1989

Computer simulation of a pilot in V/STOL aircraft control loops

The objective was to develop a computerized adaptive pilot model for the computer model of the research aircraft, the Harrier II AV-8B V/STOL with special emphasis on propulsion control. In fact, two versions of the adaptive pilot are given. The first, simply called the Adaptive Control Model (ACM) of a pilot includes a parameter estimation algorithm for the parameters of the aircraft and an adaption scheme based on the root locus of the poles of the pilot controlled aircraft. The second, called the Optimal Control Model of the pilot (OCM), includes an adaption algorithm and an optimal control algorithm. These computer simulations were developed as a part of the ongoing research program in pilot model simulation supported by NASA Lewis from April 1, 1985 to August 30, 1986 under NASA Grant NAG 3-606 and from September 1, 1986 through November 30, 1988 under NASA Grant NAG 3-729. Once installed, these pilot models permitted the computer simulation of the pilot model to close all of the control loops normally closed by a pilot actually manipulating the control variables. The current version of this has permitted a baseline comparison of various qualitative and quantitative performance indices for propulsion control, the control loops and the work load on the pilot. Actual data for an aircraft flown by a human pilot furnished by NASA was compared to the outputs furnished by the computerized pilot and found to be favorable.

Vogt, William G.↗
DOE OSTI2026

Supervisory Control and Data Acquisition for Electrochemical Separation Experimentation

The Python-based program is a laboratory automation tool designed to control and monitor electrochemical systems. The tool was developed for capacitive deionization (CDI) experiments, but it can be used for any system that requires controlled voltage or current segments and multi-parameter monitoring. The program integrates hardware components to run user-defined experimental parameters, providing operational control of a programmable power supply, peristaltic pump, and data acquisition devices. Currently, the program is structured with a workflow that includes an initialization (or pre-run) phase, a main loop, and a post-experiment stabilization (or post-run) phase. The initialization phase prepares and stabilizes the cell, ensuring that the electrodes and solution reach a baseline state before the experiment begins. The main loop consists of multiple voltage segments that repeat, controlling the experiment while recording key parameters such as time, voltage, current, pH, and conductivity. Finally, the post-experiment stabilization phase allows the system to stabilize after the experiment, returning the cell and solution to equilibrium conditions before ending the sequence. The program is designed with four variations, each tailored to different experimental needs. All variations include both the initialization and post-experiment stabilization stages, which run for a set amount of time, voltage, current, and flow rate before and after the main experiment block. The main loop runs for a set number of cycles, as defined by the user input, and each cycle is composed of 2 or 4 segments. The 4 program variations are described as follows: Program 1: The main program includes 2 segments. Each segment is defined to have a set duration, flow rate, voltage, and current. This program measures conductivity, flow rate, voltage, and current. Program 2: The main program expands Program 1 to include 4 segments. Each segment has a specified duration, flow rate, voltage, and current. Like Program 1, it measures conductivity, flow rate, voltage, and current. Program 3: The main program consists of 2 segments, each defined by time, flow rate, voltage, and current. In addition to conductivity, flow rate, voltage, and current, Program 3 collects pH and temperature data through a 4-channel data acquisition device. Program 4: This program independently controls two channels of a multi-channel power supply simultaneously. While conductivity can only be measured for one cell at a time, the dual-channel control makes it possible to operate two cells simultaneously under different voltage/current conditions. The main program includes 2 segments.For each program, all measurements are automatically logged and integrated into a single Excel output file. Data are displayed in numerical format and plotted, both in real time, to track system performance. A key feature of the program is its ability to synchronize all outputs so that every measurement shares a single timestamp, ensuring accurate alignment of voltage, current, pH, conductivity, and pH data.By combining hardware control, real-time monitoring, and unified data collection, this program significantly reduces manual workload and minimizes errors, making it a reliable platform for researchers, engineers, and laboratory technicians conducting CDI experiments, among other electrochemical tests.

Valentino, Lauren [Argonne National Laboratory (AN↗
NASA NTRS1997

Force Balance and Substorm Effects in the Magnetotail

A model of the quiet time middle magnetotail is developed using a consistent orbit tracing technique. The momentum equation is used to calculate geocentric solar magnetospheric components of the particle and electromagnetic forces throughout the current sheet. Ions generate the dominant x and z force components. Electron and ion forces almost cancel in the y direction because the two species drift earthward at comparable speeds. The force viewpoint is applied to a study of some substorm processes. Generation of the rapid flows seen during substorm injection and bursty bulk flow events implies substantial force imbalances. The formation of a substorm diversion loop is one cause of changes in the magnetic field and therefore in the electromagnetic force. It is found that larger forces are produced when the cross-tail current is diverted to the ionosphere than would be produced if the entire tail current system simply decreased. Plasma is accelerated while the forces are unbalanced resulting in field lines within a diversion loop becoming more dipolar. Field lines become more stretched and the plasma sheet becomes thinner outside a diversion loop. Mechanisms that require thin current sheets to produce current disruption then can create additional diversion loops in the newly thinned regions. This process may be important during multiple expansion substorms and in differentiating pseudoexpansions from full substorms. It is found that the tail field model used here can be generated by a variety of particle distribution functions. However, for a given energy distribution the mixture of particle mirror or reflection points is constrained by the consistency requirement. The study of uniqueness also leads to the development of a technique to select guiding center electrons that will produce charge neutrality all along a flux tube containing nonguiding center ions without the imposition of a parallel electric field.

Kaufmann, Richard L.↗