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DOE OSTI2021

Surrogate approximation of the Grad–Shafranov free boundary problem via stochastic collocation on sparse grids

In magnetic confinement fusion devices, the equilibrium configuration of a plasma is determined by the balance between the hydrostatic pressure in the fluid and the magnetic forces generated by an array of external coils and the plasma itself. The location of the plasma is not known a priori and must be obtained as the solution to a free boundary problem. The partial differential equation that determines the behavior of the combined magnetic field depends on a set of physical parameters (location of the coils, intensity of the electric currents going through them, magnetic permeability, etc.) that are subject to uncertainty and variability. The confinement region is in turn a function of these stochastic parameters as well. In this work, we consider variations on the current intensities running through the external coils as the dominant source of uncertainty. This leads to a parameter space of dimension equal to the number of coils in the reactor. With the aid of a surrogate function built on a sparse grid in parameter space, a Monte Carlo strategy is used to explore the effect that stochasticity in the parameters has on important features of the plasma boundary such as the location of the x-point, the strike points, and shaping attributes such as triangularity and elongation. Furthermore, the use of the surrogate function reduces the time required for the Monte Carlo simulations by factors that range between 7 and over 30.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2014

Bulk ion acceleration and particle heating during magnetic reconnection in a laboratory plasma

Bulk ion acceleration and particle heating during magnetic reconnection are studied in the collisionless plasma of the Magnetic Reconnection Experiment (MRX). The plasma is in the two-fluid regime, where the motion of the ions is decoupled from that of the electrons within the ion diffusion region. The reconnection process studied here is quasi-symmetric since plasma parameters such as the magnitude of the reconnecting magnetic field, the plasma density, and temperature are compatible on each side of the current sheet. Our experimental data show that the in-plane (Hall) electric field plays a key role in ion heating and acceleration. The electrostatic potential that produces the in-plane electric field is established by electrons that are accelerated near the electron diffusion region. The in-plane profile of this electrostatic potential shows a “well” structure along the direction normal to the reconnection current sheet. This well becomes deeper and wider downstream as its boundary expands along the separatrices where the in-plane electric field is strongest. Since the in-plane electric field is 3–4 times larger than the out-of-plane reconnection electric field, it is the primary source of energy for the unmagnetized ions. With regard to ion acceleration, the Hall electric field causes ions near separatrices to be ballistically accelerated toward the outflow direction. Ion heating occurs as the accelerated ions travel into the high pressure downstream region. This downstream ion heating cannot be explained by classical, unmagnetized transport theory; instead, we conclude that ions are heated by re-magnetization of ions in the reconnection exhaust and collisions. Two-dimensional (2-D) simulations with the global geometry similar to MRX demonstrate downstream ion thermalization by the above mechanisms. Electrons are also significantly heated during reconnection. The electron temperature sharply increases across the separatrices and peaks just outside of the electron diffusion region. Unlike ions, electrons acquire energy mostly from the reconnection electric field, and the energy gain is localized near the X-point. However, the increase in the electron bulk flow energy remains negligible. These observations support the assertion that efficient electron heating mechanisms exist around the electron diffusion region and that the heat generated there is quickly transported along the magnetic field due to the high parallel thermal conductivity of electrons. Classical Ohmic dissipation based on the perpendicular Spitzer resistivity is too small to balance the measured heat flux, indicating the presence of anomalous electron heating.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Modeling of Supercritical CO2 Shell-and-Tube Heat Exchangers Under Extreme Conditions. Part I: Correlation Development

Abstract High-temperature supercritical CO2 Brayton cycles are promising possibilities for future stationary power generation and hybrid electric propulsion applications. Heat exchangers are critical components in supercritical CO2 thermal cycles and require accurate correlations and comprehensive performance modeling under extreme temperatures and pressures. In this paper (Part I), new Colburn and friction factor correlations are developed to quantify shell-side heat transfer and friction characteristics of flow within heat exchangers in the shell-and-tube configuration. Using experimental and computational fluid dynamics (CFD) data sets from existing literature, multivariate regression analysis is conducted to achieve correlations that capture the effect of multiple critical geometric parameters. These correlations offer superior accuracy and versatility as compared to previous studies and predict the thermohydraulic performance of about 90% of the existing experimental and CFD data within ±15%. Supplementary thermohydraulic performance data are acquired from CFD simulations with supercritical CO2 as working fluid to validate the developed correlations and demonstrate its capability to be applied to supercrtical CO2 heat exchangers.

Engineering↗

DOE OSTI2022

Coupling Subsurface and Above-Surface Models for Optimizing the Design of Borefields and District Heating and Cooling Systems

Accurate dynamic energy simulation is important for the design and sizing of district heating and cooling systems with geothermal heat exchange for seasonal energy storage. Current modeling approaches in building and district energy simulation tools typically consider heat conduction through the ground between boreholes without flowing groundwater. While detailed simulation tools for subsurface heat and mass transfer exist, these fall short in simulating above-surface energy systems. To support the design and operation of such systems, the study developed a coupled model including a software package for building and district energy simulation, and software for detailed heat and mass transfer in the subsurface. For the first, it uses the open-source Modelica Buildings Library, which includes dynamic simulation models for building and district energy and control systems. For the heat and mass transfer in the soil, it uses the TOUGH simulator. The TOUGH family of codes can model heat and multi-phase, multi-component mass transport for a variety of fluid systems, as well as chemical reactions, in fractured porous media. The study validated the coupled modeling approach by comparing the simulation results with one from the g-function based ground response model. It then looked into effects when the water table and the regional groundwater flow are considered in the ground, from the perspective of heat exchange between borehole and ground, and the electrical consumption of the district heating and cooling systems. To access the simulation models, please find the links in the submission: -- For coupled approach validation: see model Buildings.Fluid.Geothermal.Borefields.Examples.BorefieldsWithTough and Buildings.Examples.DistrictReservoirNetworks.Examples.Reservoir3Variable_TOUGH from the "Modelica Building Library" resource, branch issue1495_tough_interface, commit a2667c0. -- For the study of the effect of water table: see model Buildings.Examples.DistrictReservoirNetworks.Examples.Reservoir3Variable_TOUGH from he "Modelica Building Library" resource, branch issue1495_tough_interface_moreIO, commit 760de49. -- For the study of the effect of regional groundwater flow: see Buildings.Examples.DistrictReservoirNetworks.Examples.Reservoir3Variable_TOUGH from he "Modelica Building Library" resource, branch issue1495_tough_interface_moreIO_3D, commit c2a2d2a. The coupling interface script "GrounResponse.py" can be found from the above links in the folder Buildings/Resources/Python-Sources. Also, the needed files for TOUGH simulation are in the folder Buildings/Resources/Python-Sources/ToughFiles that can be accessed through the above links. A brief description of these files is given below; detailed specifications for the first three files may be found in the TOUGH3 Users Guide (Jung et al., 2018) https://tough.lbl.gov/documentation/tough-manuals/. (1) INCON - initial conditions for each grid block (2) INFILE - main input file with material properties and control parameters (3) MESH - description of the computational grid (4) readsave - Modelica/TOUGH interface program: read the final output of TOUGH simulation after TOUGH time step and prepare for transfer to Modelica for next Modelica time step (5) readsave.inp - input parameters for program readsave (6) writeincon - Modelica/TOUGH interface program: write the output of Modelica after Modelica time step and prepare for transfer to TOUGH as initial conditions for the next TOUGH step (7) writeincon.inp - input parameters for program writeincon

15 GEOTHERMAL ENERGY↗

DOE OSTI2023

Efficient Thermal Energy Storage with Radial Flow in Packed Beds

Thermal energy storage (TES) is a way to store excess heat in order to generate power later. These types of systems are valuable in the solar industry, where power production can still occur when sunlight is not available. This not only increases system flexibility, it drives down the cost of electricity. One option to store thermal energy is with a packed bed where the storage media resides in a cylindrical container. Flow from one end of the cylinder to the other deposits or recovers heat (axial flow). While a promising technology in terms of energy storage, it exhibits a high pressure drop that lowers overall system efficiency. This project seeks to flow the heat transfer fluid through the storage media in the radial direction. This system offers the potential to retain reasonable thermal performance while substantially lowering the pressure drop. The overall goal was to assess the performance of radial flow experimentally and numerically. Three main designs were considered in this work. The first system utilized a central pipe and four receiving pipes near the wall. The second system utilized a central pipe and an annulus with holes near the wall. The last approach considered segmenting the bed so only select zones would receive flow in the radial direction. In a high-aspect ratio system, the hole patterns in the piping are important for ensuring even flow into the bed, and a major design effort was testing holes patterns to promote even flow. The four pipe system was shown to be not feasible, as preferential flow paths occur that do not allow even and full heating of the packed bed. The annular system can lead to even flow, but the results show this is better accomplished through larger piping instead of considering variations in the hole pattern along the axial length of the pipe. Segmenting the bed can lead to similar exergetic performance when compared to axial or radial flow. However, the pressure drop in the segmented design is likely too high for practical implementation. A baseline commercial design showed exergetic efficiencies for axial, radial, and radial segments of 81.6%, 82.8%, and 80.2%, respectively. Pressure drop for the axial and radial results were 2.36 psi and 2.45 psi, respectively, with segments being nearly an order of magnitude higher. At these large scales, the aspect ratio of the system is important. From a baseline of 0.64, an aspect ratio of 0.32 for radial flow showed an exergetic efficiency of 86% but a pressure drop of 5.39 psi. All of these results provide new insights into packed bed thermal energy storage with radial flow. Competing effects must be considered when designing a radial system, and results show a radial design can show strong thermal results at the expense of system efficiencies from pressure drop. The COMSOL models used in this analysis are available to the public and other researchers. Public benefits include a potential increase in the efficiency of packed bed thermal energy storage. Higher efficiency in storage promotes green energy technologies while reducing costs.

14 SOLAR ENERGY↗

NASA NTRS1982

Performance of PTFE-lined composite journal bearings

Plain cylindrical journal bearings consisting of aramid fiber reinforced epoxy outer shells and glass fiber reinforced PTFE lubricating liners were evaluated. All materials in these bearings are electrically nonconductive; thus eliminating the problem of galvanic corrosion sometimes encountered with metal bearings installed in dissimilar metal mountings. Friction and wear characteristics were determined for loads, temperatures, and oscillating conditions that are typical of current airframe bearing applications. Friction and wear characteristics were found to be compatible with most airframe bearing requirements from -23 C to 121 C. Contamination with MIL H-5606 hydraulic fluid increased wear of the PTFE liners at 121 C, but did not affect the structural integrity of the aramid/epoxy composite.

Sliney, H. E.↗

NASA NTRS1988

Control of the interface between (He-3)-rich and (He-4)-rich phases using electric fields

A microgravity dilution refrigerator is considered, and it is shown that electric-field generated forces can be used to control the interface line between (He-3)-rich and (He-3)-poor phases. Fields as high as 13 MV/m are obtained in the present v-shaped geometry which correspond to positioning forces comparable to gravity. Good agreement is found between experimental results on the movements of the interface line and calculations obtained with a two-fluid model.

Israelsson, Ulf E.↗

NASA NTRS1987

Robotic mobile servicing platform for space station

The semi-autonomous inspection and servicing of the Space Station's major thermal, electrical, mechanical subsystems are critical needs for the safe and reliable operation of the station. A conceptual design is presented of a self-intelligent, small and highly mobile robotic platform. Equipped with suitable inspection sensors (cameras, ammonia detectors, etc.), this system's primary mission is to perform routine, autonomous inspection of the Station's primary subsystems. Typical tasks include detection of leaks from thermal fluid or refueling lines, as well as detection of micro-meteroid damage to the primary structure. Equipped with stereo cameras and a dexterous manipulator, simple teleoperator repairs and small On-orbit Replacement Unit (ORU) changeout can also be accomplished. More difficult robotic repairs would be left to the larger, more sophisticated Mobile Remote Manipulator System (MRMS). An ancillary function is to ferry crew members and equipment around the station. The primary design objectives were to provide a flexible, but uncomplicated robotic platform, one which caused minimal impact to the design of the Station's primary structure but could accept more advanced telerobotic technology as it evolves.

Lowenthal, S. H.↗

NASA NTRS1998

The Role of Marangoni Convection for the FZ-Growth of Silicon

Fluctuations of the electrical resistivity due to inhomogeneous dopant distribution are still a serious problem for the industrial processing yield of doped silicon crystals. In the case of silicon floating-zone growth, the main sources of these inhomogeneities are time- dependent flows in the liquid phase during the growth process. Excluding radio frequency (RF) induced convection, buoyancy and thermocapillary (Marangoni) convection are the two natural reasons for fluid flow. Both originate from temperature/concentration gradients in the melt, buoyancy convection through thermal/concentrational volume expansion, and thermocapillary convection through the temperature/concentration dependence of the surface tension. To improve the properties of grown crystals, knowledge of the strength, the characteristic, and the relation of these two flow mechanisms is essential. By the use of microgravity, the effect and the strength of buoyancy (gravity dependent) and thermocapillary (gravity independent) convection can be separated and clarified. Applying magnetic fields, both convective modes can be influenced: fluid flow can either be damped (static magnetic fields) or overlaid by a regular flow regime (rotating magnetic fields). Two complementary approaches have been pursued: Silicon full zones (experiments on the German sounding rockets TEXUS 7, 12, 22, 29, and 36) with the maximum temperature at half of the zone height and silicon half zones (experiments on the Japanese sounding rockets TR-IA4 and 6) with the maximum temperature at the top of the melt. With the full zone arrangement, the intensity and the frequency of the dopant striations could be determined and the critical Marangoni number could be identified. The half zone configuration is suited to classify the flow pattern and to measure the amplitude and the frequency of temperature fluctuations in the melt by inserting thermocouples or temperature sensors into the melt. All experiments have been carried out in monoellipsoid mirror furnaces. Typical zone geometries are approx. 8 to 14 mm in diameter and height. The crystals grown under microgravity are compared to crystals grown in static axial magnetic fields (B<5 tesla) and in transversal rotating magnetic fields (B<7.5 mT / f=50 Hz). Experimental results are completed by 3D numerical simulations: the obtained temperature and concentration distribution in the melt confirm the damping effect of rotating magnetic fields and explain the change in the radial segregation under static magnetic fields.

Dold, P.↗

NASA NTRS2009

Windage Power Loss in Gas Foil Bearings and the Rotor-Stator Clearance of High Speed Generators Operating in High Pressure Environments

Closed Brayton Cycle (CBC) and Closed Supercritical Cycle (CSC) engines are prime candidates to convert heat from a reactor into electric power for robotic space exploration and habitation. These engine concepts incorporate a permanent magnet starter/generator mounted on the engine shaft along with the requisite turbomachinery. Successful completion of the long-duration missions currently anticipated for these engines will require designs that adequately address all losses within the machine. The preliminary thermal management concept for these engine types is to use the cycle working fluid to provide the required cooling. In addition to providing cooling, the working fluid will also serve as the bearing lubricant. Additional requirements, due to the unique application of these microturbines, are zero contamination of the working fluid and entirely maintenance-free operation for many years. Losses in the gas foil bearings and within the rotor-stator gap of the generator become increasingly important as both rotational speed and mean operating pressure are increased. This paper presents the results of an experimental study, which obtained direct torque measurements on gas foil bearings and generator rotor-stator gaps. Test conditions for these measurements included rotational speeds up to 42,000 revolutions per minute, pressures up to 45 atmospheres, and test gases of nitrogen, helium, and carbon dioxide. These conditions provided a maximum test Taylor number of nearly one million. The results show an exponential rise in power loss as mean operating density is increased for both the gas foil bearing and generator windage. These typical "secondary" losses can become larger than the total system output power if conventional design paradigms are followed. A nondimensional analysis is presented to extend the experimental results into the CSC range for the generator windage.

Bruckner, Robert J.↗

NASA NTRS2019

Full Facility Shock Frame Simulations of the Electric Arc Shock Tube

Radiative heating computations are performed for high speed lunar return experiments conducted in the Electric Arc Shock Tube (EAST) facility at NASA Ames Research Center. The nonequilibrium radiative transport equations are solved via NASA's in-house radiation code NEQAIR using flow field input from US3D flow solver. The post-shock flow properties for the 10 km/s Earth entry conditions are computed using the stagnation line of a blunt-body and a full facility CFD (Computational Fluid Dynamics) simulation of the EAST shock tube. The shocked gas in the blunt-body flow achieves a thermochemical equilibrium away from the shock front whereas EAST flow exhibits a nonequilibrium behavior due to strong viscous dissipation of the shock by boundary layer. The full-tube flow calculations capture the influence of the boundary layer on the shocked gas state and provide a realistic fluid dynamic input for the radiative predictions. The integrated radiance behind the shock is calculated in NEQAIR for wavelength regimes from Vacuum-UltraViolet (VUV) to InfraRed (IR), which are pertinent to the emission characteristics of high enthalpy shock waves in air. These radiance profiles are validated against corresponding EAST shots. The full-tube simulations successfully predict a sharp radiance peak at the shock front which gets smeared in the test data due to the spatial resolution in the measurements. The full facility based radiance behind the shock shows a slightly better match with the test data in the VUV and Red spectral regions, as compared to that from a blunt-body based predictions. The UV radiance is very similar for both geometries and under-predicts the test behavior. The IR test data matches better with the blunt-body based predictions where the full-tube simulations show a significant over-prediction.

Radiation↗

DOE OSTI2013

Methods of forming semiconductor devices and devices formed using such methods

Single source precursors are subjected to carbon dioxide to form particles of material. The carbon dioxide may be in a supercritical state. Single source precursors also may be subjected to supercritical fluids other than supercritical carbon dioxide to form particles of material. The methods may be used to form nanoparticles. In some embodiments, the methods are used to form chalcopyrite materials. Devices such as, for example, semiconductor devices may be fabricated that include such particles. Methods of forming semiconductor devices include subjecting single source precursors to carbon dioxide to form particles of semiconductor material, and establishing electrical contact between the particles and an electrode.

36 MATERIALS SCIENCE↗

DOE OSTI2014

Modular cathode assemblies and methods of using the same for electrochemical reduction

Modular cathode assemblies are useable in electrolytic reduction systems and include a basket through which fluid electrolyte may pass and exchange charge with a material to be reduced in the basket. The basket can be divided into upper and lower sections to provide entry for the material. Example embodiment cathode assemblies may have any shape to permit modular placement at any position in reduction systems. Modular cathode assemblies include a cathode plate in the basket, to which unique and opposite electrical power may be supplied. Example embodiment modular cathode assemblies may have standardized electrical connectors. Modular cathode assemblies may be supported by a top plate of an electrolytic reduction system. Electrolytic oxide reduction systems are operated by positioning modular cathode and anode assemblies at desired positions, placing a material in the basket, and charging the modular assemblies to reduce the metal oxide.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Modular cathode assemblies and methods of using the same for electrochemical reduction

25 ENERGY STORAGE↗

DOE OSTI2024

Design and Performance Evaluation of a Resistive Control Using a Hydraulic PTO System for the TALOS Wave Energy Converter

This study is focused on developing a numerical model to evaluate the performance of a hydraulic PTO system for the TALOS Wave Energy Converter. The WEC device is described and the architecture of the hydraulic PTO system is presented with detail. The WEC is modeled using WEC-Sim, and the PTO is modeled using the Simscape Fluids library from Simulink. The hydraulic PTO is based on a constant pressure configuration that is suitable for WEC passive control. The hydraulic system is composed by a set of rectifying valves and two hydraulic accumulators that reduce the stiffness of the system and also serve as energy storage devices. One of the advantages of this hydraulic PTO architecture is the possibility of controlling the electric generator to operate around the optimal efficiency operating point. The main components of the hydraulic PTO are off-the-shelf devices that are commercially available, which will facility a future deployment of the designed system. The design variables used for this study are the accumulator size, the maximum pressure in the accumulators, the hydraulic motor maximum displacement, and the shaft speed in the electric generator. The performance of the system is evaluated individually, using sinusoidal inputs that replicates regular wave conditions. In addition to this, the numerical model of the PTO is coupled to a WEC-Sim simulation of the TALOS Wave Energy Converter with six PTOs to generate a wave-to-wire model. The main objective of this work is to present a comprehensive design methodology that could serve as a guideline for future research efforts focused on implementing control algorithms on multi degree of freedom WECs.

hydraulic systems↗

NASA NTRS1994

Inertial currents in isotropic plasma

The magnetospheric convection electric field contributes to Birkeland currents. The effects of the field are to polarize the plasma by displacing the bounce paths of the ions from those of electrons, to redistribute the pressure so that it is not constant along magnetic field lines, and to enhance the pressure gradient by the gradient of the bulk speed. Changes in the polarization charge during the convection of the plasma are neutralized by electrons in the form of field-aligned currents that close through the ionosphere. The pressure drives field-aligned currents through its gradient in the same manner as in quasi-static plasmas, but with modifications that are important if the bulk speed is of the order of the ion thermal speed; the variations in the pressure along field lines are maintained by a weak parallel potential drop. These effects are described in terms of the field-aligned currents in steady state, isotropic, MHD plasma. Solutions are developed by taking the MHD limit ot two-fluid solutions and illustrated in the special case of Maxwellian plasma for which the temperature is constant along magnetic field lines. The expression for the Birkeland current density is a generalization of Vasyliunas' expression for the field-aligned current density in quasi-static plasma and provides a unifying expression when both pressure gradients and ion inertia operate simultaneously as sources of field-aligned currents. It contains a full account of different aspects of the ion flow (parallel and perpendicular velocity and vorticity) that contribute to the currents. Contributions of ion inertia to field-aligned currents will occur in regions of strong velocity shear, electric field reversal, or large gradients in the parallel velocity or number density, and may be important in the low-latitude boundary layer, plasma sheet boundary layer, and the inner edge region of the plasma sheet.

Heinemann, M.↗

NASA NTRS1993

Inertial Currents in Isotropic Plasma

The magnetospheric convection electric field contributes to Birkeland currents. The effects of the field are to polarize the plasma by displacing the bounce paths of the ions from those of electrons, to redistribute the pressure so that it is not constant along magnetic field lines, and to enhance the pressure gradient by the gradient of the bulk speed. Changes in the polarization charge during the convection of the plasma are neutralized by electrons in the form of field-aligned currents that close through the ionosphere. The pressure drives field-aligned currents through its gradient in the same manner as in quasi-static plasma, but with modifications that are important if the bulk speed is of the order of the ion thermal speed; the variations in the pressure along field lines are maintained by a weak parallel potential drop. These effects are described in terms of the field-aligned currents in steady state, isotropic, MED plasma. Solutions are developed by taking the MHD limit of two-fluid solutions and illustrated in the special case of Maxwellian plasma for which the temperature is constant along magnetic field lines. The expression for the Birkeland current density is a generalization of Vasyliunas' expression for the field-aligned current density in quasi-static plasma and provides a unifying expression when both pressure gradients and ion inertia operate simultaneously as sources of field-aligned currents. It contains a full account of different aspects of the ion flow (parallel and perpendicular velocity and vorticity) that contribute to the currents. Contributions of ion inertia to field-aligned currents will occur in regions of strong velocity shear, electric field reversal, or large gradients in the parallel velocity or number density, and may be important in the low-latitude boundary layer, plasma sheet boundary layer, and the inner edge region of the plasma sheet.

Heinemann, M.↗

NASA NTRS1994

Inertial currents in isotropic plasma

The magnetospheric convection electric field contributes to Birkeland currents. The effects of the field are to polarize the plasma by displacing the bounce paths of the ions from those of electrons, to redistribute the pressure so that it is not constant along magnetic field lines, and to enhance the pressure gradient by the gradient of the bulk speed. Changes in the polarization charge during the convection of the plasma are neutralized by electrons in the form of field-aligned currents that close through the ionosphere. The pressure drives field-aligned currents through its gradient in the same manner as in quasi-static plasma, but with modifications that are important if the bulk speed is of the order of the ion thermal speed; the variations in the pressure along field lines are maintained by a weak parallel potential drop. These effects are described in terms of the field-aligned currents in steady state, isotropic, magnetohyrodynamic (MHD) plasma. Solutions are developed by taking the MHD limit of two-fluid solutions and illustrated in the special case of Maxwellian plasma for which the temperature is constant along magnetic field lines. The expression for the Birkeland current density is a generalization of Vasyliunas' expression for the field-aligned current density in quasi-static plasma and provides a unifying expression when both pressure gradients and ion inertia operate simultaneously as sources of field-aligned currents. It contains a full account of different aspects of the ion flow (parallel and perpendicular velocity and vorticity) that contribute to the currents. Contributions of ion inertia to field-aligned currents will occur in regions of strong velocity shear, electric field reversal, or large gradients in the parallel velocity or number density, and may be important in the low-latitude boundary layer, plasma sheet boundary layer, and the inner edge region of the plasma sheet.

Heinemann, M.↗