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At least 1,135 records · Page 63
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NASA NTRS1997

Differential Magnetic Field Shear in an Active Region

The three-dimensional extrapolation of magnetic field lines from a magnetogram obtained at Kitt Peak allows us to understand the global structure of the NOAA active region 6718, as observed in X-rays with the Normal Incidence X-ray Telescope (NIXT) and in Ha with the Multichannel Subtractive Double Pass spectrograph (MSDP) in Meudon on 1991 July 11. This active region was in a quiet stage. Bright X-ray loops connect plages having field strengths of approx. 300 G, while H-alpha fibriles connect penumbrae having strong spot fields to the surrounding network. Small, intense X-ray features in the moat region around a large spot, which could be called X-ray-bright points, are due mainly to the emergence of magnetic flux and merging of these fields with surrounding ones. A set of large-scale, sheared X-ray loops is observed in the central part of the active region. Based on the fit between the observed coronal structure and the field configurations (and assuming a linear force-free field), we propose a differential magnetic field shear model for this active region. The decreasing shear in outer portions of the active region may indicate a continual relaxation of the magnetic field to a lower energy state in the progressively older portions of the AR.

Schmeider, B.↗
NASA NTRS1997

Vertical Tail Buffeting Alleviation Using Piezoelectric Actuators-Some Results of the Actively Controlled Response of Buffet-Affected Tails (ACROBAT) Program

Buffet is an aeroelastic phenomenon associated with high performance aircraft especially those with twin vertical tails. In particular, for the F/A-18 aircraft at high angles of attack, vortices emanating from wing/fuselage leading edge extensions burst, immersing the vertical tails in their wake. The resulting buffet loads on the vertical tails are a concern from fatigue and inspection points of view. Recently, a 1/6-scale F-18 wind-tunnel model was tested in the Transonic Dynamics Tunnel at the NASA Langley Research Center as part of the Actively Controlled Response Of Buffet Affected Tails (ACROBAT) Program to assess the use of active controls in reducing vertical tail buffeting. The starboard vertical tail was equipped with an active rudder and the port vertical tail was equipped with piezoelectric actuators. The tunnel conditions were atmospheric air at Mach 0.10. By using single-input-single-output control laws at gains well below the physical limits of the actuators, the power spectral density of the root strains at the frequency of the first bending mode of the vertical tail was reduced by as much as 60 percent up to angles of attack of 37 degrees. Root mean square (RMS) values of root strain were reduced by as much as 19 percent. The results herein illustrate that buffet alleviation of vertical tails can be accomplished using simple active control of the rudder or piezoelectric actuators. In fact, as demonstrated herein, a fixed gain single input single output control law that commands piezoelectric actuators may be active throughout the high angle-of-attack maneuver without requiring any changes during the maneuver. Future tests are mentioned for accentuating the international interest in this area of research.

Moses, Robert W.↗
NASA NTRS1997

Neutral-Line Magnetic Shear and Enhanced Coronal Heating in Solar Active Regions

By examining the magnetic structure at sites in the bright coronal interiors of active regions that are not flaring but exhibit persistent strong coronal heating, we establish some new characteristics of the magnetic origins of this heating. We have examined the magnetic structure of these sites in five active regions, each of which was well observed by both the Yohkoh SXT and the Marshall Space Flight Center Vector Magnetograph and showed strong shear in its magnetic field along part of at least one neutral line (polarity inversion). Thus, we can assess whether this form of nonpotential field structure in active regions is a characteristic of the enhanced coronal heating and vice versa. From 27 orbits' worth of Yohkoh SXT images of the five active regions, we have obtained a sample of 94 persistently bright coronal features (bright in all images from a given orbit), 40 long (greater than or approximately equals 20,000 km) neutral-line segments having strong magnetic shear throughout (shear angle greater than 45 deg), and 39 long neutral-line segments having weak magnetic shear throughout (shear angle less than 45 deg). From this sample, we find that: (1) all of our persistently bright coronal features are rooted in magnetic fields that are stronger than 150 G; (2) nearly all (95%) of these enhanced coronal features are rooted near neutral lines (closer than 10,000 km); (3) a great majority (80%) of the bright features are rooted near strong-shear portions of neutral lines; (4) a great majority (85%) of long strong-shear segments of neutral lines have persistently bright coronal features rooted near them; (5) a large minority (40%) of long weak-shear segments of neutral lines have persistently bright coronal features rooted near them; and (6) the brightness of a persistently bright Coronal feature often changes greatly over a few hours. From these results, we conclude that most persistent enhanced heating of coronal loops in active regions: (1) requires the presence of a polarity inversion in the magnetic field near at least one of the loop footpoints; (2) is greatly aided by the presence of strong shear in the core magnetic field along that neutral line; and (3) is controlled by some variable process that acts in this magnetic environment. We infer that this variable process is low-lying reconnection accompanying flux cancellation.

Falconer, D. A.↗
NASA NTRS1995

Upper Thermosphere Winds and Temperatures in the Geomagnetic Polar Cap: Solar Cycle, Geomagnetic Activity, and Interplanetary Magnetic Field Dependencies

Ground-based Fabry-Perot interferometers located at Thule, Greenland (76.5 deg. N, 69.0 deg. W, lambda = 86 deg.) and at Sondre Stromfjord, Greenland (67.0 deg. N, 50.9 deg. W, lambda = 74 deg.) have monitored the upper thermospheric (approx. 240-km altitude) neutral wind and temperature over the northern hemisphere geomagnetic polar cap since 1983 and 1985, respectively. The thermospheric observations are obtained by determining the Doppler characteristics of the (OI) 15,867-K (630.0-nm) emission of atomic oxygen. The instruments operate on a routine, automatic, (mostly) untended basis during the winter observing seasons, with data coverage limited only by cloud cover and (occasional) instrument failures. This unique database of geomagnetic polar cap measurements now extends over the complete range of solar activity. We present an analysis of the measurements made between 1985 (near solar minimum) and 1991 (near solar maximum), as part of a long-term study of geomagnetic polar cap thermospheric climatology. The measurements from a total of 902 nights of observations are compared with the predictions of two semiempirical models: the Vector Spherical Harmonic (VSH) model of Killeen et al. (1987) and the Horizontal Wind Model (HWM) of Hedin et al. (1991). The results are also analyzed using calculations of thermospheric momentum forcing terms from the Thermosphere-ionosphere General Circulation Model TGCM) of the National Center for Atmospheric Research (NCAR). The experimental results show that upper thermospheric winds in the geomagnetic polar cap have a fundamental diurnal character, with typical wind speeds of about 200 m/s at solar minimum, rising to up to about 800 m/s at solar maximum, depending on geomagnetic activity level. These winds generally blow in the antisunward direction, but are interrupted by episodes of modified wind velocity and altered direction often associated with changes in the orientation of the Interplanetary Magnetic Field (IMF). The central polar cap (greater than approx. 80 magnetic latitude) antisunward wind speed is found to be a strong function of both solar and geomagnetic activity. The polar cap temperatures show variations in both solar and geomagnetic activity, with temperatures near 800 K for low K(sub p) and F(sub 10.7) and greater than about 2000 K for high K(sub p) and F(sub 10.7). The observed temperatures are significantly greater than those predicted by the mass spectrometer/incoherent scatter model for high activity conditions. Theoretical analysis based on the NCAR TIGCM indicates that the antisunward upper thermospheric winds, driven by upstream ion drag, basically 'coast' across the polar cap. The relatively small changes in wind velocity and direction within the polar cap are induced by a combination of forcing terms of commensurate magnitude, including the nonlinear advection term, the Coriolis term, and the pressure gradient force term. The polar cap thennospheric thermal balance is dominated by horizontal advection, and adiabatic and thermal conduction terms.

Killeen, T. L.↗
NASA NTRS1998

X-Ray Observations of Recurrence of Eruptive Flares and Active Regions

In a study of soft X-ray coronal images obtained with the Yohkoh spacecraft, two eruptive flares with remarkably similar X-ray structures were noted -- most remarkably because the flares occurred at the same solar location (approximately 10 degrees north latitude on the east limb) yet separated in time by three solar rotations. Between the times of the eruptions, the active region responsible for the first flare disappeared from Yohkoh images. An extremely similar X-ray active region replaced it by the third solar rotation. The recurring X-ray active region appearance and recurring flare activity after 86 days suggest that persistent subsurface flux emergence patterns might be responsible, and support previous arguments that 'active longitudes' exist.

Batchelor, David↗
NASA NTRS1997

A Correlation Between Length of Strong-Shear Neutral Lines and Total X-Ray Brightness in Active Regions

From a sample of 7 MSFC vector magnetograms,of active regions and 17 Yohkoh SXT soft X-ray images of these active regions, we have found that the total x-ray brightness of an entire active region is correlated with the total length of neutral lines on which the magnetic field is both strong (less than 250 G) and strongly sheared (shear angle greater than 75 deg) in the same active region. This correlation, if not fortuitous, is additional evidence of the importance of strong-shear strong-field neutral lines to strong heating in active regions.

Falconer, D. A.↗
NASA NTRS1998

Propulsion/ASME Rocket-Based Combined Cycle Activities in the Advanced Space Transportation Program Office

NASA's Office Of Aeronautics and Space Transportation Technology (OASTT) has establish three major coals. "The Three Pillars for Success". The Advanced Space Transportation Program Office (ASTP) at the NASA's Marshall Space Flight Center in Huntsville,Ala. focuses on future space transportation technologies under the "Access to Space" pillar. The Advanced Reusable Technologies (ART) Project, part of ASTP, focuses on the reusable technologies beyond those being pursued by X-33. The main activity over the past two and a half years has been on advancing the rocket-based combined cycle (RBCC) technologies. In June of last year, activities for reusable launch vehicle (RLV) airframe and propulsion technologies were initiated. These activities focus primarily on those technologies that support the year 2000 decision to determine the path this country will take for Space Shuttle and RLV. In February of this year, additional technology efforts in the reusable technologies were awarded. The RBCC effort that was completed early this year was the initial step leading to flight demonstrations of the technology for space launch vehicle propulsion. Aerojet, Boeing-Rocketdyne and Pratt & Whitney were selected for a two-year period to design, build and ground test their RBCC engine concepts. In addition, ASTROX, Pennsylvania State University (PSU) and University of Alabama in Huntsville also conducted supporting activities. The activity included ground testing of components (e.g., injectors, thrusters, ejectors and inlets) and integrated flowpaths. An area that has caused a large amount of difficulty in the testing efforts is the means of initiating the rocket combustion process. All three of the prime contractors above were using silane (SiH4) for ignition of the thrusters. This follows from the successful use of silane in the NASP program for scramjet ignition. However, difficulties were immediately encountered when silane (an 80/20 mixture of hydrogen/silane) was used for rocket ignition.

Hueter, Uwe↗
NASA NTRS1999

An Assessment of Magnetic Conditions for Strong Coronal Heating in Solar Active Regions by Comparing Observed Loops with Computed Potential Field Lines

We report further results on the magnetic origins of coronal heating found from registering coronal images with photospheric vector magnetograms. For two complementary active regions, we use computed potential field lines to examine the global non-potentiality of bright extended coronal loops and the three-dimensional structure of the magnetic field at their feet, and assess the role of these magnetic conditions in the strong coronal heating in these loops. The two active regions are complementary, in that one is globally potential and the other is globally nonpotential, while each is predominantly bipolar, and each has an island of included polarity in its trailing polarity domain. We find the following: (1) The brightest main-arch loops of the globally potential active region are brighter than the brightest main- arch loops of the globally strongly nonpotential active region. (2) In each active region, only a few of the mainarch magnetic loops are strongly heated, and these are all rooted near the island. (3) The end of each main-arch bright loop apparently bifurcates above the island, so that it embraces the island and the magnetic null above the island. (4) At any one time, there are other main-arch magnetic loops that embrace the island in the same manner as do the bright loops but that are not selected for strong coronal heating. (5) There is continual microflaring in sheared core fields around the island, but the main-arch bright loops show little response to these microflares. From these observational and modeling results we draw the following conclusions: (1) The heating of the main-arch bright loops arises mainly from conditions at the island end of these loops and not from their global non-potentiality. (2) There is, at most, only a loose coupling between the coronal heating in the bright loops of the main arch and the coronal heating in the sheared core fields at their feet, although in both the heating is driven by conditions/events in and around the island. (3) The main-arch bright loops are likely to be heated via reconnection driven at the magnetic null over the island. The details of how and where (along the null line) the reconnection is driven determine which of the split-end loops are selected for strong heating. (4) The null does not appear to be directly involved in the heating of the sheared core fields or in the heating of an extended loop rooted in the island. Rather, these all appear to be heated by microflares in the sheared core field.

Gary, G. A.↗
NASA NTRS2000

Active Combustion Control for Aircraft Gas Turbine Engines

Lean-burning combustors are susceptible to combustion instabilities. Additionally, due to non-uniformities in the fuel-air mixing and in the combustion process, there typically exist hot areas in the combustor exit plane. These hot areas limit the operating temperature at the turbine inlet and thus constrain performance and efficiency. Finally, it is necessary to optimize the fuel-air ratio and flame temperature throughout the combustor to minimize the production of pollutants. In recent years, there has been considerable activity addressing Active Combustion Control. NASA Glenn Research Center's Active Combustion Control Technology effort aims to demonstrate active control in a realistic environment relevant to aircraft engines. Analysis and experiments are tied to aircraft gas turbine combustors. Considerable progress has been shown in demonstrating technologies for Combustion Instability Control, Pattern Factor Control, and Emissions Minimizing Control. Future plans are to advance the maturity of active combustion control technology to eventual demonstration in an engine environment.

DeLaat, John C.↗
NASA NTRS2000

KDD Services at the Goddard Earth Sciences Distributed Active Archive Center

NASA's Goddard Earth Sciences Distributed Active Archive Center (GES DAAC) processes, stores and distributes earth science data from a variety of remote sensing satellites. End users of the data range from instrument scientists to global change and climate researchers to federal agencies and foreign governments. Many of these users apply data mining techniques to large volumes of data (up to 1 TB) received from the GES DAAC. However, rapid advances in processing power are enabling increases in data processing that are outpacing tape drive performance and network capacity. As a result, the proportion of data that can be distributed to users continues to decrease. As mitigation, we are migrating more data mining and mining preparation activities into the data center in order to reduce the data volume that needs to be distributed and to offer the users a more useful and manageable product. This migration of activities faces a number of technical and human-factor challenges. As data reduction and mining algorithms are normally quite specific to the user's research needs, the user's algorithm must be integrated virtually unchanged into the archive environment. Also, the archive itself is busy with everyday data archive and distribution activities and cannot be dedicated to, or even impacted by, the mining activities. Therefore, we schedule KDD 'campaigns' (similar to reprocessing campaigns), during which we schedule a wholesale retrieval of specific data products, offering users the opportunity to extract information from the data being retrieved during the campaign.

Lynnes, Christopher↗
NASA NTRS2001

Space-Based Astronomy: An Educator Guide with Activities for Science, Mathematics, and Technology Education

If you go to the country, far from city lights, you can see about 3,000 stars on a clear night. If your eyes were bigger, you could see many more stars. With a pair of binoculars, an optical device that effectively enlarges the pupil of your eye by about 30 times, the number of stars you can see increases to the tens of thousands. With a medium-sized telescope with a light-collecting mirror 30 centimeters in diameter, you can see hundreds of thousands of stars. With a large observatory telescope, millions of stars become visible. This curriculum guide uses hands-on activities to help students and teachers understand the significance of space-based astronomy--astronomical observations made from outer space. It is not intended to serve as a curriculum. Instead, teachers should select activities from this guide that support and extend existing study. The guide contains few of the traditional activities found in many astronomy guides such as constellation studies, lunar phases, and planetary orbits. It tells, rather, the story of why it is important to observe celestial objects from outer space and how to study the entire electromagnetic spectrum. Teachers are encouraged to adapt these activities for the particular needs of their students. When selected activities from this guide are used in conjunction with traditional astronomy curricula, students benefit from a more complete experience.

Vogt, Gregory L.↗
NASA NTRS2000

Operations Assessment of Launch Vehicle Architectures using Activity Based Cost Models

The growing emphasis on affordability for space transportation systems requires the assessment of new space vehicles for all life cycle activities, from design and development, through manufacturing and operations. This paper addresses the operational assessment of launch vehicles, focusing on modeling the ground support requirements of a vehicle architecture, and estimating the resulting costs and flight rate. This paper proposes the use of Activity Based Costing (ABC) modeling for this assessment. The model uses expert knowledge to determine the activities, the activity times and the activity costs based on vehicle design characteristics. The approach provides several advantages to current approaches to vehicle architecture assessment including easier validation and allowing vehicle designers to understand the cost and cycle time drivers.

Ruiz-Torres, Alex J.↗
NASA NTRS1999

Measurements of Active-Region Global Nonpotentiality for Prediction of Coronal Mass Ejections

We introduce two quantitative measures of the global nonpotentiality of predominantly bipolar active regions and explore their usefulness as indicators of whether an active region is likely to produce coronal mass ejections. The two measures, length of strong-field strong-shear main neutral line (L (sub ss)) and global net current (I (sub N)), are obtained directly from vector magnetograms of the regions. From Marshall Space Flight Center vector magnetograms and Yohkoh Soft X-ray Telescope coronal X-ray images of four active regions, we find that (1) L (sub ss) and I (sub N) are each a useful indicator of an active region's likely CME (Coronal Mass Ejections) productivity, (2) L (sub ss) and I (sub N) may be more reliable predictors of the CME productivity of active regions than is the presence or absence of sigmoidal structure in X-ray images of the regions, and (3) L (sub ss) and I (sub N) may have threshold values above which CME production is likely and below which CME production is unlikely.

Falconer, D. A.↗
NASA NTRS2000

Design of the Active Elevon Rotor for Low Vibration

Helicopter fuselages vibrate more than desired, and traditional solutions have limited effectiveness and can impose an appreciable weight penalty. Alternative methods of combating high vibration, including Higher Harmonic Control (HHC) via harmonic swashplate motion and Individual Blade Control (IBC) via active pitch links, have been studied for several decades. HHC via an on-blade control surface was tested in 1977 on a full scale rotor using a secondary active swashplate and a mechanical control system. Recent smart material advances have prompted new research into the use of on-blade control concepts. Recent analytical studies have indicated that the use of on-blade control surfaces produces vibration reduction comparable to swashplate-based HHC but for less power. Furthermore, smart materials (such as piezoceramics) have been shown to provide sufficient control authority for preliminary rotor experiments. These experiments were initially performed at small scale for reduced tip speeds. More recent experiments have been conducted at or near full tip speeds, and a full-scale active rotor is under development by Boeing with Eurocopter et al. pursuing a similarly advanced full-scale implementation. The US Army Aeroflightdynamics Directorate has undertaken a new research program called the Active Elevon Rotor (AER) Focus Demo. This program includes the design, fabrication, and wind. tunnel testing of a four-bladed, 12.96 ft diameter rotor with one or two on-blade elevons per blade. The rotor, which will be Mach scaled, will use 2-5/rev elevon motion for closed-loop control and :will be tested in late 2001. The primary goal of the AER Focus Demo is the reduction of vibratory hub loads by 80% and the reduction of vibratory blade structural loads. A secondary goal is the reduction of rotor power. The third priority is the measurement and possible reduction of Blade Vortex Interaction (BVI) noise. The present study is focused on elevon effectiveness, that is, the elevon's ability to reduce all six components of the nonrotating 4/rev hub loads. Some design parameters have been kept fixed in this study, while others have been varied to determine their influence - on elevon effectiveness. The fixed parameters include all blade structural properties except for torsion stiffness; the varied parameters include torsion stiffness, elevon aerodynamic location, and the number and individual authority of elevon aerodynamic surfaces. This paper describes the preliminary design process being used for the AER, and describes and quantifies the emerging active rotor characteristics.

Fulton, Mark V.↗
NASA NTRS2001

Solar Activity Forecasting for use in Orbit Prediction

Orbital prediction for satellites in low Earth orbit (LEO) or low planetary orbit depends strongly on exospheric densities. Solar activity forecasting is important in orbital prediction, as the solar UV and EUV inflate the upper atmospheric layers of the Earth and planets, forming the exosphere in which satellites orbit. Geomagnetic effects also relate to solar activity. Because of the complex and ephemeral nature of solar activity, with different cycles varying in strength by more than 100%, many different forecasting techniques have been utilized. The methods range from purely numerical techniques (essentially curve fitting) to numerous oddball schemes, as well as a small subset, called 'Precursor techniques.' The situation can be puzzling, owing to the numerous methodologies involved, somewhat akin to the numerous ether theories near the turn of the last century. Nevertheless, the Precursor techniques alone have a physical basis, namely dynamo theory, which provides a physical explanation for why this subset seems to work. I discuss this solar cycle's predictions, as well as the Sun's observed activity. I also discuss the SODA (Solar Dynamo Amplitude) index, which provides the user with the ability to track the Sun's hidden, interior dynamo magnetic fields. As a result, one may then update solar activity predictions continuously, by monitoring the solar magnetic fields as they change throughout the solar cycle. This paper ends by providing a glimpse into what the next solar cycle (#24) portends.

Schatten, Kenneth↗
NASA NTRS2000

NASA's Future Active Remote Sensing Missing for Earth Science

Since the beginning of space remote sensing of the earth, there has been a natural progression widening the range of electromagnetic radiation used to sense the earth, and slowly, steadily increasing the spatial, spectral, and radiometric resolution of the measurements. There has also been a somewhat slower trend toward active measurements across the electromagnetic spectrum, motivated in part by increased resolution, but also by the ability to make new measurements. Active microwave instruments have been used to measure ocean topography, to study the land surface. and to study rainfall from space. Future NASA active microwave missions may add detail to the topographical studies, sense soil moisture, and better characterize the cryosphere. Only recently have active optical instruments been flown in space by NASA; however, there are currently several missions in development which will sense the earth with lasers and many more conceptual active optical missions which address the priorities of NASA's earth science program. Missions are under development to investigate the structure of the terrestrial vegetation canopy, to characterize the earth's ice caps, and to study clouds and aerosols. Future NASA missions may measure tropospheric vector winds and make vastly improved measurements of the chemical components of the earth's atmosphere.

Hartley, Jonathan B.↗
NASA NTRS2000

Physiologic Responses Produced by Active and Passive Personal Cooling Vests

Personal thermoregulatory systems which provide chest cooling are used in the industrial and aerospace environments to alleviate thermal stress. However, little information is available regarding the physiologic and circulatory changes produced by routine operation of these systems. The objectives of this study were to document and compare the subjects' response to three cooling vests in their recommended configurations. The Life Enhancement Tech (LET) lightweight active cooling vest with cap, the MicroClimate Systems Change of Phase garment (MCS), and the Steele Vest were each used to cool the chest regions of 12 male and 8 female Healthy subjects (21 to 69 yr.) in this study. The subjects, seated in an upright position at normal room temperature (approx. 22 C), were tested for 60 min. with one of the cooling garments. The LET active garment had an initial coolant fluid inlet temperature of 60 F, and was ramped down to 50 F. Oral, right and left ear canal temperatures were logged manually every 5 min. Arm, leg, chest and rectal temperatures; heart rate; and respiration were recorded continuously on a U.F.I., Inc. Biolog ambulatory monitor. For men, all three vests had similar, significant cooling effects. Decreases in the average rectal temperature, oral temperature, and ear canal temperatures were approximately 0.2 C, 0.2 C and 0.1 C, respectively. In contrast to the men, the female subjects wearing the MCS and Steel vests had similar cooling responses in which the core temperature remained elevated and oral and ear canal temperatures did not drop. The LET active garment cooled most of the female subjects in this study; rectal, oral and ear temperature decreased about 0.2 C, 0.3 C and 0.3 C, respectively. These results show that the garment configurations tested do not elicit a similar thermal response in all subjects. A gender difference is evident. The LET active garment configuration was most effective in decreasing temperatures of the female subjects; the MCS vest was least effective. For male subjects, the three vests appear to be more nearly equivalent. The active garment system under study included a cooling cap, which may account for some of the difference in response.

Ku, Yu-Tsuan E.↗
NASA NTRS2001

Correlation of the CME Productivity of Solar Active Regions with Measures of their Global Nonpotentiality from Vector Magnetograms: Baseline Results

From conventional magnetograms and chromospheric and coronal images, it is known qualitatively that the fastest coronal mass ejections (CMEs) are magnetic explosions from sunspot active regions in which the magnetic field is globally strongly sheared and twisted from its minimum-energy potential configuration. In this paper, we present measurements from active-region vector magnetograms that begin to quantify the dependence of the CME productivity of an active region on the global nonpotentiality of its magnetic field. From each of 17 magnetograms of 12 bipolar active regions, we obtain a measure of the size of the active region (the magnetic flux content, phi) and three different measures of the global nonpotentiality (L(sub SS), the length of strong-shear, strong-field main neutral line; I(sub N), the net electric current arching from one polarity to the other; and alpha = muI(subN/phi), a flux-normalized measure of the field twist).

Falconer, David A.↗