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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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At least 1,171 records · Page 65

Static Electric Fields and Lightning Over Land and Ocean in Florida Thunderstorms

Natural cloud-to-ground (CG) lightning and the charge structure of the associated clouds behave differently over land and ocean. Existing literature has raised questions over the years on the behavior of thunderstorms and lightning over oceans, and there are still open scientific questions. We expand on the observational datasets by obtaining identical electric field observations over coastal land, near-shore, and deep ocean regions during both clear air and thunderstorm periods. Oceanic observations were obtained using two 3-meter NOAA buoys that were instrumented with Campbell Scientific electric field mills to measure the static electric fields. These data were compared to selected electric field records from the existing on-shore electric field mill suite of 31 sensors at Kennedy Space Center (KSC). CG lightning occurrence times, locations and peak current values for both on-shore and ocean were provided by the U.S. National Lightning Detection Network. The buoy instruments were first evaluated on-shore at the Florida coast, to calibrate field enhancements and to confirm proper behavior of the system in elevated-field environments. The buoys were then moored 20NM and 120NM off the coast of KSC in February (20NM) and August (120NM) 2014. Statistically larger CG peak currents were reported over the deep ocean for first strokes and for subsequent strokes with new contacts points. Storm-related static fields were significantly larger at both oceanic sites, likely due to decreased screening by nearby space charge. Time-evolution of the static field during storm development and propagation indicated weak or missing lower positive charge regions in most storms that initiated over the deep ocean, supporting one mechanism for the observed high peak currents in negative first strokes over the deep ocean. This project also demonstrated the practicality of off-shore electric field measurements for safety-related decision making at KSC.

Lightning↗

Static Electric Fields and Lightning Over Land and Ocean in Florida Thunderstorms

Natural cloud-to-ground (CG) lightning and the charge structure of the associated clouds behave differently over land and ocean. Existing literature has raised questions over the years on the behavior of thunderstorms and lightning over oceans, and there are still open scientific questions. We expand on the observational datasets by obtaining identical electric field observations over coastal land, near-shore, and deep ocean regions during both clear air and thunderstorm periods. Oceanic observations were obtained using two 3-meter NOAA buoys that were instrumented with Campbell Scientific electric field mills to measure the static electric fields. These data were compared to selected electric field records from the existing on-shore electric field mill suite of 31 sensors at Kennedy Space Center (KSC). CG lightning occurrence times, locations and peak current values for both on-shore and ocean were provided by the U.S. National Lightning Detection Network. The buoy instruments were first evaluated on-shore at the Florida coast, to calibrate field enhancements and to confirm proper behavior of the system in elevated-field environments. The buoys were then moored 20NM and 120NM off the coast of KSC in February (20NM) and August (120NM) 2014. Statistically larger CG peak currents were reported over the deep ocean for first strokes and for subsequent strokes with new contacts points. Storm-related static fields were significantly larger at both oceanic sites, likely due to decreased screening by nearby space charge. Time-evolution of the static field during storm development and propagation indicated weak or missing lower positive charge regions in most storms that initiated over the deep ocean, supporting one mechanism for the observed high peak currents in negative first strokes over the deep ocean. This project also demonstrated the practicality of off-shore electric field measurements for safety-related decision making at KSC.

Electric Fields↗

Design and Development of a 200-kW Turbo-Electric Distributed Propulsion Testbed

There a few NASA funded electric and hybrid electric projects from different NASA Centers, including the NASA Armstrong Flight Research Center (AFRC) (Edwards, California). Each project identifies a specific technology gap that is currently inhibiting the growth and proliferation of relevant technologies in commercial aviation. This paper describes the design and development of a turbo-electric distributed propulsion (TeDP) hardware-in-the-loop (HIL) simulation bench, which is a test bed for discovering turbo-electric control, distributed electric control, power management control, and integration competencies while providing risk mitigation for future turbo-electric flying demonstrators.

propulsion↗

Personal Rotorcraft Design and Performance with Electric Hybridization

Recent and projected improvements for more or all-electric aviation propulsion systems can enable greater personal mobility, while also reducing environmental impact (noise and emissions). However, all-electric energy storage capability is significantly less than present, hydrocarbon-fueled systems. A system study was performed exploring design and performance assuming hybrid propulsion ranging from traditional hydrocarbon-fueled cycles (gasoline Otto and diesel) to all-electric systems using electric motors generators, with batteries for energy storage and load leveling. Study vehicles were a conventional, single-main rotor (SMR) helicopter and an advanced vertical takeoff and landing (VTOL) aircraft. Vehicle capability was limited to two or three people (including pilot or crew); the design range for the VTOL aircraft was set to 150 miles (about one hour total flight). Search and rescue (SAR), loiter, and cruise-dominated missions were chosen to illustrate each vehicle and degree of hybrid propulsion strengths and weaknesses. The traditional, SMR helicopter is a hover-optimized design; electric hybridization was performed assuming a parallel hybrid approach by varying degree of hybridization. Many of the helicopter hybrid propulsion combinations have some mission capabilities that might be effective for short range or on-demand mobility missions. However, even for 30 year technology electrical components, all hybrid propulsion systems studied result in less available fuel, lower maximum range, and reduced hover and loiter duration than the baseline vehicle. Results for the VTOL aircraft were more encouraging. Series hybrid combinations reflective of near-term systems could improve range and loiter duration by 30. Advanced, higher performing series hybrid combinations could double or almost triple the VTOL aircrafts range and loiter duration. Additional details on the study assumptions and work performed are given, as well as suggestions for future study effort.

electric motors↗

The SPACE Computer Code for Analyzing the International Space Station Electrical Power System: Past, Present, and Future

The System Power Analysis for Capability Evaluation (SPACE) computer code was initially developed by NASA in 1988 to assess the Space Station Freedom electric power system and later adapted to support contractor electrical power system capability analyses for the International Space Station (ISS). Over time, the code has supported many efforts such as ISS redesign activities in the early 1990s, assessment of time-phased loads against power system operating limits for future ISS assembly flights (including Certification of Flight Readiness reviews by the ISS program office), and determining the optimum solar array gimbal positions while respecting keep-out zones which minimize both solar array contamination and structural loads. The code has been validated by comparisons with ISS on-orbit data in multiple validation episodes. Recent updates to the code include the incorporation of a Lithium-Ion battery model in addition to the Nickel Hydrogen battery model and modifications to the solar array degradation model to better match on-orbit test results. SPACE has also been extended beyond the ISS to include modeling of the Orion Multi-Purpose Crew Vehicle electrical power system (SPACE-MPCV) and Mars Surface Electrical Power Systems (MSEPS). Portions of SPACE were integrated with a trajectory code to form a Solar Electric Propulsion Simulation (SEPSim), which can be used for analyzing solar electric propulsion missions. In addition, SPACE methods and subroutines have been adapted to a multitude of other projects. This paper summarizes the initial code development and subsequent code utilization in the context of the overall ISS program development and on-orbit operations. Recent updates and results from the code are discussed, including preliminary analyses for the Orion power system.

Electrical Power System↗

Design Study of Double-Sided Axial-Flux Magnetically Geared Motors for Electric Aircraft Applications

Electric aircraft require advances in electric motor drivetrain efficiency, specific power, and reliability. In terms of mass and efficiency, mechanically geared electric motor drivetrains will significantly outperform direct drive electric motor drive trains in most applications. Mechanical gears however have numerous wear and failure modes that can result in increased maintenance and reliability penalties for an aircraft. Magnetic gears are being explored by NASA as a potential alternative to mechanical gears for electric aircraft applications. Magnetic gears have none of the surface contact related wear and failure modes of mechanical gears. Therefore, they potentially pose a high reliability alternative to mechanical gears. Magnetic gears can also share magnetic components with an electric motor in a magnetically geared drivetrain to achieve significant weight savings. In this paper, one possible topology of magnetically geared motor, the double-sided axial flux magnetically geared motor, is studied to quantify its achievable performance. Design study results suggest that the topology can achieve greater than 20 Nm/kg and 97% efficiency at a 100 kW output power.

Magnetic gears↗

Solid-state Architecture Batteries for Enhanced Rechargeability and Safety (SABERS) Beyond Li-Ion: Technology to Enable Sustainable Electric Aviation

All-electric and hybrid electric aerovehicle concepts face numerous technical barriers prior to their introduction into the consumer marketplace in order to meet sustainable aviation goals. One of the primary barriers to overcome is developing an energy dense storage system capable of meeting the rigorous aerospace safety and performance criteria. Additionally, the electric aviation market requires that the batteries be fabricated in a sustainable manner with materials that are readily available and abundant within the U.S. to ensure there are no supply chain issues during manufacturing. The performance metrics to enable electric aviation are at least two times greater than those of electric ground vehicles. Furthermore, inherently non-flammable batteries are essential for safe operation of commercial electric aerovehicles. The SABERS concept proposes a battery that meets the key performance criteria through development of a solid-state architecture battery utilizing high-capacity sulfur-selenium cathode and lithium metal anode. The combination of sulfur and selenium offers a balanced energy-to-power density ratio, which can be tailored to the specific application by altering the stoichiometric ratios of sulfur to selenium. The hybrid cathode has been developed by implementing NASA patented holey graphene technology as a highly conductive, ultra-lightweight electrode scaffold. A solid-state electrolyte has been used as a safe, non-flammable replacement to the highly flammable liquid organic electrolytes currently used in SOA lithium-ion batteries. This solid-state lithium-sulfur/selenium cell will be designed into a serial stacking configuration to enable dense packaging of the battery cells. The serial stacking configuration is termed a bipolar stack, which has the advantages of reducing overall cell weight, simplifying the interfaced connections for the cell, and minimizing the cooling requirements. Lastly, optimization of battery components will occur through a robust and rigorous combination of various computational modeling techniques covering multiple length scales. The expected result will be a fully solid-state battery with operational temperatures up to 150 °C which provides the required energy density, discharge rates, and inherent safety to meet the strict aerospace mission performance criteria. This poster summarizes recent results from battery component optimization to scale-up production of full SABERS pouch cells.

Urban Air Mobility (UAM) Vehicles↗

Analysis of Hybrid Electric Aircraft Operations in the National Airspace System

This paper investigates the fuel burn and flight time impacts of hybrid electric aircraft operating in the National Airspace System. Future scenarios with hybrid electric flights and the same passenger travel capacity between city pairs as a baseline scenario, taken from historical data, were created. Aircraft that serviced select flights in the baseline scenario were replaced with hybrid electric aircraft based on the flight’s range and seat capacity. Additional hybrid electric flights were added to future scenarios when necessary to keep the future scenario passenger capacity equal or greater to that of the baseline scenario. The baseline and future scenarios were simulated in the NAS Digital Twin, a live, virtual, and constructive environment for building and executing simulations of the Nation Airspace System. Results showed that the future scenarios with hybrid electric flights saved fuel burn, but increased flight time. In the future scenarios, the additional hybrid electric flights did not cause any airports to exceed their operational capacity.

Simulation↗

Operating Hybrid Electric Aircraft in the National Airspace System

This paper investigates the fuel burn and flight time impacts of hybrid electric aircraft operating in the National Airspace System. Future scenarios with hybrid electric flights and the same passenger travel capacity between city pairs as a baseline scenario, taken from historical data, were created. Aircraft that serviced select flights in the baseline scenario were replaced with hybrid electric aircraft based on the flight’s range and seat capacity. Additional hybrid electric flights were added to future scenarios when necessary to keep the future scenario passenger capacity equal or greater to that of the baseline scenario. The baseline and future scenarios were simulated in the NAS Digital Twin, a live, virtual, and constructive environment for building and executing simulations of the Nation Airspace System. Results showed that the future scenarios with hybrid electric flights saved fuel burn, but increased flight time. In the future scenarios, the additional hybrid electric flights did not cause any airports to exceed their operational capacity.

hybrid electric aircraft↗

GEOPHYSICS AND SITE CHARACTERIZATION AT THE HANFORD SITE THE SUCCESSFUL USE OF ELECTRICAL RESISTIVITY TO POSITION BOREHOLES TO DEFINE DEEP VADOSE ZONE CONTAMINATION - 11509

Historic boreholes confirmed the presence of nitrate and radionuclide contaminants at various intervals throughout a more than 60 m (200 ft) thick vadose zone, and a 2010 electrical resistivity survey mapped the known contamination and indicated areas of similar contaminants, both laterally and at depth; therefore, electrical resistivity mapping can be used to more accurately locate characterization boreholes. At the Hanford Nuclear Reservation in eastern Washington, production of uranium and plutonium resulted in the planned release of large quantities of contaminated wastewater to unlined excavations (cribs). From 1952 until 1960, the 216-U-8 Crib received approximately 379,000,000 L (100,000,000 gal) of wastewater containing 25,500 kg (56,218 lb) uranium; 1,029,000 kg (1,013 tons) of nitrate; 2.7 Ci of technetium-99; and other fission products including strontium-90 and cesium-137. The 216-U-8 Crib reportedly holds the largest inventory of waste uranium of any crib on the Hanford Site. Electrical resistivity is a geophysical technique capable of identifying contrasting physical properties; specifically, electrically conductive material, relative to resistive native soil, can be mapped in the subsurface. At the 216-U-8 Crib, high nitrate concentrations (from the release of nitric acid [HNO{sub 3}] and associated uranium and other fission products) were detected in 1994 and 2004 boreholes at various depths, such as at the base of the Crib at 9 m (30 ft) below ground surface (bgs) and sporadically to depths in excess of 60 m (200 ft) bgs. These contaminant concentrations were directly correlative with the presence of observed low electrical resistivity responses delineated during the summer 2010 geophysical survey. Based on this correlation and the recently completed mapping of the electrically conductive material, additional boreholes are planned for early 2011 to identify nitrate and radionuclide contamination: (a) throughout the entire vertical length of the vadose zone (i.e., 79 m [260 ft] bgs) within the footprint of the Crib, and (b) 15 to 30 m (50 to 100 ft) east of the Crib footprint, where contaminants are inferred to have migrated through relatively permeable soils. Confirmation of the presence of contamination in historic boreholes correlates well with mapping from the 2010 survey, and serves as a basis to site future characterization boreholes that will likely intersect contamination both laterally and at depth.

54 ENVIRONMENTAL SCIENCES↗

Quantifying Changes in Building Electricity Use, with Application to Demand Response

We present methods for analyzing commercial and industrial facility 15-minute-interval electric load data. These methods allow building managers to better understand their facility's electricity consumption over time and to compare it to other buildings, helping them to ask the right questions to discover opportunities for demand response, energy efficiency, electricity waste elimination, and peak load management. We primarily focus on demand response. Methods discussed include graphical representations of electric load data, a regression-based electricity load model that uses a time-of-week indicator variable and a piecewise linear and continuous outdoor air temperature dependence, and the definition of various parameters that characterize facility electricity loads and demand response behavior. In the future, these methods could be translated into easy-to-use tools for building managers.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Computational Needs for the Next Generation Electric Grid Proceedings

The April 2011 DOE workshop, 'Computational Needs for the Next Generation Electric Grid', was the culmination of a year-long process to bring together some of the Nation's leading researchers and experts to identify computational challenges associated with the operation and planning of the electric power system. The attached papers provide a journey into these experts' insights, highlighting a class of mathematical and computational problems relevant for potential power systems research. While each paper defines a specific problem area, there were several recurrent themes. First, the breadth and depth of power system data has expanded tremendously over the past decade. This provides the potential for new control approaches and operator tools that can enhance system efficiencies and improve reliability. However, the large volume of data poses its own challenges, and could benefit from application of advances in computer networking and architecture, as well as data base structures. Second, the computational complexity of the underlying system problems is growing. Transmitting electricity from clean, domestic energy resources in remote regions to urban consumers, for example, requires broader, regional planning over multi-decade time horizons. Yet, it may also mean operational focus on local solutions and shorter timescales, as reactive power and system dynamics (including fast switching and controls) play an increasingly critical role in achieving stability and ultimately reliability. The expected growth in reliance on variable renewable sources of electricity generation places an exclamation point on both of these observations, and highlights the need for new focus in areas such as stochastic optimization to accommodate the increased uncertainty that is occurring in both planning and operations. Application of research advances in algorithms (especially related to optimization techniques and uncertainty quantification) could accelerate power system software tool performance, i.e. speed to solution, and enhance applicability for new and existing real-time operation and control approaches, as well as large-scale planning analysis. Finally, models are becoming increasingly essential for improved decision-making across the electric system, from resource forecasting to adaptive real-time controls to online dynamics analysis. The importance of data is thus reinforced by their inescapable role in validating, high-fidelity models that lead to deeper system understanding. Traditional boundaries (reflecting geographic, institutional, and market differences) are becoming blurred, and thus, it is increasingly important to address these seams in model formulation and utilization to ensure accuracy in the results and achieve predictability necessary for reliable operations. Each paper also embodies the philosophy that our energy challenges require interdisciplinary solutions - drawing on the latest developments in fields such as mathematics, computation, economics, as well as power systems. In this vein, the workshop should be viewed not as the end product, but the beginning of what DOE seeks to establish as a vibrant, on-going dialogue among these various communities. Bridging communication gaps among these communities will yield opportunities for innovation and advancement. The papers and workshop discussion provide the opportunity to learn from experts on the current state-of-the-art on computational approaches for electric power systems, and where one may focus to accelerate progress. It has been extremely valuable to me as I better understand this space, and consider future programmatic activities. I am confident that you too will enjoy the discussion, and certainly learn from the many experts. I would like to thank the authors of the papers for sharing their perspectives, as well as the paper discussants, session recorders, and participants. The meeting would not have been as successful without your commitment and engagement. I also would like to thank Joe Eto and Bob Thomas for their vision and leadership in bringing together such a well-structured and productive forum.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Physically Realistic Estimates of Electric Water Heater Demand Response Resource

Multiple grid integration studies have examined the value of demand response, including from water heaters, to bulk power systems. Common shortcomings of these studies include physically unrealistic assumptions. For example, studies often assume that all electric water heater load can be shed for up to an hour to provide capacity or contingency service, that all electric water heater load is shiftable, and that round-trip efficiencies for shifting service are 100%. Another issue is that simply summing up estimates of individual water heaters' flexibility bounds, an attractive idea for constructing the MW-scale resources necessary for direct inclusion in grid investment and operational models, can result in significant overestimates of actual resource, because, e.g., a water heater with the ability to reduce load may not be able sustain the reduction for as long as the aggregate model suggests is possible. This presentation demonstrates the impact of estimating the flexibility of electric water heaters with physically realistic models suitable for grid service analysis. Electric water heater flexibility representations are constructed based on ResStock simulations of New England. Specifically, we examine contingency resource (related to capacity, shed, and contingency reserve services) and energy shifting resource from electric resistance and heat pump water heaters. Different estimation methods are compared; and the surrogate models' event responses are validated against events directly simulated in EnergyPlus. We also demonstrate the impact of using electric water heaters for contingency reserves and energy shifting in detailed models of possible future ISO New England power systems.

building energy modeling↗

Multiscale Electricity Modeling for Evaluating Carbon Capture and Sequestration Technologies (MEME-CCS)

This effort employs and adapts a rigorous multiscale electricity modeling platform at the National Renewable Energy Laboratory (NREL) to evaluate carbon capture and sequestration (CCS) and negative emissions technologies (NET) from the ARPA-E FLECCS program. NREL's modeling platform includes the Regional Energy Deployment System (ReEDS) electric sector capacity expansion model, which projects future electricity generation mixes at sub-state-level resolution that are downscaled to the unit-level to enable hourly, zonal or nodal electricity production cost modeling in the PLEXOS model. The ReEDS-PLEXOS modeling suite is well-established for examining electric sector futures with high renewable energy penetrations, energy storage, electrification, and distributed generation. The key advancement proposed herein utilizes collaboration with CCS experts at the University of Wyoming (U.WY) and the FLECCS technology development teams to create innovative methods for representing CCS and NET in the ReEDS and PLEXOS models. Expanded technology options and new operational parameterizations are integrated into these models to allow an unprecedented combination of scope and resolution for exploring the future of CCS and NET. The resulting capabilities permit wide-ranging scenario analysis to assess CCS and NET deployment under alternative scenarios of CO2 prices and competitiveness of flexible CCS and NET technologies. We demonstrate sample deployment and operational outcomes to show how these models are being used to assess the future potential for FLECCS technologies and their impacts on the U.S. electricity system. These products will help an emerging CCS/NET industry in the United States by providing economics-driven guidance to technology developers while informing policy and investment decisions in the public and private sectors.

capacity expansion↗

Carbon pricing, nuclear power and electricity markets

In 2010, the NEA in conjunction with the International Energy Agency produced an analysis of the Projected Costs of Electricity for almost 200 power plants, covering nuclear, fossil fuel and renewable electricity generation. That analysis used lifetime costs to consider the merits of each technology. However, the lifetime cost analysis is less applicable in liberalised markets and does not look specifically at the viewpoint of the private investor. A follow-up NEA assessment of the competitiveness of nuclear energy against coal- and gas-fired generation under carbon pricing has considered just this question. The economic competition in electricity markets is today between nuclear energy and gas-fired power generation, with coal-fired power generation not being competitive as soon as even modest carbon pricing is introduced. Whether nuclear energy or natural gas comes out ahead in their competition depends on a number of assumptions, which, while all entirely reasonable, yield very different outcomes. The analysis in this study has been developed on the basis of daily data from European power markets over the last five-year period. Three different methodologies, a Profit Analysis looking at historic returns over the past five years, an Investment Analysis projecting the conditions of the past five years over the lifetime of plants and a Carbon Tax Analysis (differentiating the Investment Analysis for different carbon prices) look at the issue of competitiveness from different angles. They show that the competitiveness of nuclear energy depends on a number of variables which in different configurations determine whether electricity produced from nuclear power or from CCGTs generates higher profits for its investors. These are overnight costs, financing costs, gas prices, carbon prices, profit margins (or mark-ups), the amount of coal with carbon capture and electricity prices. This paper will present the outcomes of the analysis in the context of a liberalised electricity market, looking at the impact of the seven key variables and provide conclusions on the portfolio that a utility would be advised to maintain, given the need to limit risks but also to move to low carbon power generation. Such portfolio diversification would not only limit financial investor risk, but also a number of non-financial risks (climate change, security of supply, accidents). (authors)

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

ELECTRIC FIELD-ASSISTED DIFFUSION WELDING TO FABRICATE ALLOY 617 COMPACT HEAT EXCHANGERS

Compact heat exchangers are of interest for a number of applications including advanced reactors. Alloy 617 is one of the top candidate materials for the gas-cooled reactor intermediate heat exchanger. Previous endeavors to diffusion weld Alloy 617 utilized hot pressing (HP). It was reported that grain boundary migration across the interface was hindered by extensive precipitation. Bonds of this nature have been observed to reduce the elevated-temperature mechanical properties compared to the wrought-product form. It was hypothesized that the electric current applied during electric-field-assisted sintering (EFAS) can overcome these challenges, resulting in improved diffusion welding (DW). This study investigated DW of Alloy 617 via EFAS. Stacks composed of three sheets that were 20 mm in diameter were welded using EFAS. Specimens were welded with an applied electric current, a pressure of 30 MPa, hold time of 30 min, and temperatures of 1050°C, 1100°C, and 1150°C. DW using HP as the zero-current analog of EFAS was also performed at the most promising EFAS conditions. Results revealed that both the applied electric current and temperature played a key role in precipitation and grain boundary migration in diffusion-welded Alloy 617. Precipitates were observed at the interface of the hot-pressed samples which limited grain boundary migration. Electric current was found to prevent precipitate formation along the interface at 1150°C. The electric current coupled with a temperature of 1150°C during EFAS resulted in significant grain boundary migration across the interface.

36 - MATERIALS SCIENCE↗

On the Debye–Hückel effect of electric screening

The paper considers non-linear self-consistent electric potential equation (Sec. I), due to a cloud made of a single species of electric charges, satisfying a Boltzmann distribution law (Sec. II). Exact solutions are obtained in a simple logarithmic form, in three cases: (Sec. III) spherical radial symmetry; (Sec. IV) plane parallel symmetry; (Sec. V) a special case of azimuthal-cylindrical symmetry. All these solutions, and their transformations (Sec. VI), involve the Debye-Hückel radius; the latter was originally defined from a solution of the linearized self-consistent potential equation. Using an exact solution of the self-consistent potential equation, the distance at which the potential vanishes differs from the Debye-Hückel radius by a factor of √(2). The preceding (Secs. II–VI) simple logarithmic exact solutions of the self-consistent potential equations involve no arbitrary constants, and thus are special or singular integrals not the general integral. The general solution of the self-consistent potential equation is obtained in the plane parallel case (Sec. VII), and it involves two arbitrary constants that can be reduced to one via a translation (Sec. VIII). The plots of dimensionless potential (Figure 1), electric field (Figure 2), charge density (Figure 3), and total charge between ζ and infinity (Figure 4), versus distance normalized to Debye-Hückel radius ζ ≡ z/a, show that (Sec. IX) there is a continuum of solutions, ranging from a charge distribution concentrated inside the Debye-Hückel radius to one spread-out beyond it. The latter case leads to the limiting case of logarithmic potential, and stronger electric field; the former case, of very concentrated charge distribution, leads to a fratricide effect and weaker electric field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

INTERDEPENDENCE OF ELECTRIC DISCHARGE AND MAGNETOROTATIONAL INSTABILITY IN PROTOPLANETARY DISKS

We study how the magnetorotational instability (MRI) in protoplanetary disks is affected by the electric discharge caused by the electric field in the resistive magnetohydrodynamic. We performed three-dimensional shearing box simulations with various values of plasma beta and electrical breakdown models. We find that the MRI is self-sustaining in spite of the high resistivity. The instability gives rise to the large electric field that causes the electrical breakdown, and the breakdown maintains the high degree of ionization required for the instability. The condition for this self-sustained MRI is set by the balance between the energy supply from the shearing motion and the energy consumed by ohmic dissipation. We apply the condition to various disk models and study where the active, self-sustained, and dead zones of MRI are located. In the fiducial minimum-mass solar-nebula model, the newly found sustained zone occupies only a limited volume of the disk. In the late-phase gas-depleted disk models, however, the sustained zone occupies a larger volume of the disk.

79 ASTRONOMY AND ASTROPHYSICS↗