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At least 145 records · Page 8

An active homopolar magnetic bearing with high temperature superconductor (HTS) coils and ferromagnetic cores

A proof-of-feasibility demonstration showed that high temperature superconductor (HTS) coils can be used in a high-load, active magnetic bearing in liquid nitrogen. A homopolar radial bearing with commercially wound HTS (Bi 2223) bias and control coils produced over 200 lb (890 N) radial load capacity (measured non-rotating) and supported a shaft to 14000 rpm. The goal was to show that HTS coils can operate stably with ferromagnetic cores in a feedback controlled system at a current density similar to that in Cu in liquid nitrogen. Design compromises permitted use of circular coils with rectangular cross section. Conductor improvements will eventually permit coil shape optimization, higher current density and higher bearing load capacity. The bias coil, wound with non-twisted, multifilament HTS conductor, required negligible power to carry its direct current. The control coils were wound with monofilament HTS sheathed in Ag. These dissipated negligible power for direct current (i.e. for steady radial load components). When an alternating current (AC) was added, the AC component dissipated power which increased rapidly with frequency and quadratically with AC amplitude. In fact at frequencies above about 2 hz, the effective resistance of the control coil conductor actually exceeds that of the silver which is in electrical parallel with the oxide superconductor. This is at least qualitatively understandable in the context of a Bean-type model of flux and current penetration into a Type II superconductor. Fortunately the dynamic currents required for bearing stability are of small amplitude. These results show that while twisted multifilament conductor is not needed for stable levitation, twisted multifilaments will be required to reduce control power for sizable dynamic loads, such as those due to unbalance.

Brown, G. V.↗

Impedance Controlled Twisted String Actuators for Tensegrity Robots

We are developing impedance controlled twisted string actuators (TSA) for use in tensegrity robots, as an alternative to traditional spooled cable actuation. Tensegrity robots are composed of continuous tension and discontinuous compression elements, with no rigid joints between elements, which give them unique force distribution properties. The use of tensegrity robots is strongly motivated by biological examples, and they are capable of locomotion and manipulation by changing lengths of their continuous network of tensional elements, which is also the primary pathways for load transfer through the structure. TSA show the potential to address some of the unique engineering challenges faced by tensegrity structures, and provide unique qualities well suited to an actively controlled tension system, such as compact, light-weight mechanical structures, inherent compliance, variable gearing'', and the ability to transmit high forces with a very low input torque. The inherent variable compliance of impedance control is essential for tensegrity robots to move through and manipulate the environment, and is a natural match to the unique qualities of TSA. This paper briefly introduces the tensegrity robots in the NASA Ames Intelligent Robotics Group and an overview of their future application to space planetary exploration. Then the effectiveness and robustness of TSA are verified through the performance of impedance control modes.

Park, In-Won↗

The 2006-2007 Active Phase of Anomalous X-Ray Pulsar 4U 0142+61: Radiative and Timing Changes, Bursts,and Burst Spectral Features

After at least 6 years of quiescence, Anomalous X-ray Pulsar (AXP) 4U 0142+61 entered an active phase in 2006 March that lasted several months and included six X-ray bursts as well as many changes in the persistent X-ray emission. The bursts, the first seen from this AXP in > 11 years of Rossi X-ray Timing Explorer monitoring, all occurred in the interval between 2006 April 6 and 2007 February 7. The burst durations ranged from 0.4 - 1.8 x 10(exp 3) s. The first five burst spectra are well modeled by blackbodies, with temperatures kT approx 2 - 9 keV. However, the sixth burst had a complicated spectrum that is well characterized by a blackbody plus two emission features whose amplitude varied throughout the burst. The most prominent feature was at 14.0 keV. Upon entry into the active phase the pulsar showed a significant change in pulse morphology and a likely timing glitch. The glitch had a total frequency jump of (1.9+/-0.4) x 10(exp -7) Hz, which recovered with a decay time of 17+/-2 days by more than the initial jump, implying a net spin-down of the pulsar. Within the framework of the magnetar model, the net spin-down of the star could be explained by regions of the superfluid that rotate. slower than the rest. The bursts, flux enhancements, and pulse morphology changes can be explained as arising from crustal deformations due to stresses imposed by the highly twisted internal magnetic field. However, unlike other AXP outbursts, we cannot account for a major twist being implanted in the magnetosphere.

Gavriil, Fotis P.↗

A Model for Solar Polar Jets

We propose a model for the jetting activity that is commonly observed in the Sun's corona, especially in the open-field regions of polar coronal holes. Magnetic reconnection is the process driving the jets and a relevant magnetic configuration is the well-known null point and fan separatrix topology. The primary challenge in explaining the observations is that reconnection must occur in a short-duration energetic burst rather than quasi-continuously as is implied by the observations of long-lived structures in coronal holes, such as polar plumes, for example. The key idea underlying our model for jets is that reconnection is forbidden for an axisymmetric null-point topology. Consequently, by imposing a twisting motion that maintains the axisymmetry, magnetic stress can be built up to large levels until an ideal instability breaks the symmetry and leads to an explosive release of energy via reconnection. Using 3D MHD simulations we demonstrate that this mechanism does produce jets with high speed and mass, driven by nonlinear Alfven waves. We discuss the implications of our results for observations of the solar corona.

Pariat, E.↗

A CME-Producing Solar Eruption from the Interior of an Emerging Bipolar Active Region

In a negative-polarity coronal hole, magnetic flux emergence, seen by the Solar Dynamics Observatory's {SDO) Helioseismic Magnetic lmager (HMI), begins at approximately 19:00 UT on March 3, 2016. The emerged magnetic field produced sunspots, which NOAA numbered 12514 two days later. The emerging magnetic field is largely bipolar with the opposite-polarity fluxes spreading apart overall, but there is simultaneously some convergence and cancellation of opposite-polarity flux at the polarity inversion line (PIL) inside the emerging bipole. In the first fifteen hours after emergence onset, three obvious eruptions occur, observed in the coronal EUV images from SDO's Atmospheric Imaging Assembly (AIA). The first two erupt from separate segments of the external PIL between the emerging positve-polarity flux and the extant surrounding negative-polarity flux, with the exploding magnetic field being prepared and triggered by flux cancellation at the external PIL. The emerging bipole shows obvious overall left-handed shear and/or twist in its magnetic field. The focus of th is poster is the third and largest eruption, which comes from inside the emerging bipole and blows it open to produce a CME observed by SOHO/LASCO. That eruption is preceded by flux cancellation at the emerging bipole's interior PIL, cancellation that plausibly builds a sheared and twisted flux rope above the interior PIL and finally triggers the blow-out eruption of the flux rope via photospheric-convection•driven slow tether-cutting reconnection of the legs of the sheared core field, low above the interior PIL, as proposed by van Ballegooijen & Martens (1989) and Moore & Roumeliotis (1992). The production of this eruption is a (perhaps rare) counterexample to solar eruptions that result from external collisional shearing between opposite polarities from two distinct emerging and/or emerged bipoles (Chintzoglou et al. 2019).

Adams, M. L.↗

Speed of CMEs and the Magnetic Non-Potentiality of Their Source ARs

Most fast coronal mass ejections (CMEs) originate from solar active regions (ARs). Non-potentiality of ARs is expected to determine the speed and size of CMEs in the outer corona. Several other unexplored parameters might be important as well. To find out the correlation between the initial speed of CMEs and the non-potentiality of source ARs, we associated over a hundred of CMEs with source ARs via their co-produced flares. The speed of the CMEs are collected from the SOHO LASCO CME catalog. We have used vector magnetograms obtained mainly with HMI/SDO, also with Hinode (SOT/SP) when available within an hour of a CME occurrence, to evaluate various magnetic non-potentiality parameters, e.g. magnetic free-energy proxies, computed magnetic free energy, twist, shear angle, signed shear angle etc. We have also included several other parameters e.g. total unsigned flux, net current, magnetic area of ARs, area of sunspots, to investigate their correlation, if any, with the initial speeds of CMEs. Our preliminary results show that the ARs with larger non-potentiality and area mostly produce fast CMEs but they can also produce slower ones. The ARs with lesser non-potentiality and area generally produce only slower CMEs, however, there are a few exceptions. The total unsigned flux correlate with the non-potentiality parameters and area of ARs but some ARs with large unsigned flux are also found to be least non-potential. A more detailed analysis is underway.

Tiwari, Sanjiv K.↗

A Hinode-IRIS HOP for Searching for Possible Solar Jet Sources for Switchbacks Observed in the Near-Sun Solar Wind by the Parker Solar Probe (PSP)

The Parker Solar Probe (PSP) detects “switchback” magnetic structures in the near-Sun solar wind. A candidate for the source of these is solar coronal jets. Recent studies show that coronal jets are frequently made by eruptions of small-filament-carrying flux ropes, or mini filament flux-rope eruptions, that can inject a magnetic twist wave onto high-reaching ambient magnetic field(Sterling et al. 2015; Moore et al 2015).That is, many coronal jets evidently result from the eruption of a small-scale flux rope of twisted field that holds a mini filament of chromospheric-temperature plasma. The erupting flux rope reconnects with ambient far-reaching field, ejecting both reconnection-heated plasma and cool filament plasma (forming the multi-temperature jet spire), and transferring its twist onto the far-reaching field via a mechanism proposed by Shibata & Uchida(1986).If the far-reaching field opens into the heliosphere, it is plausible that the twist propagates out into the solar wind, possibly appearing as a switchback in the magnetic field in the solar wind (Sterling & Moore 2020).As part of the "Connecting Heliophysics Observatories and Models with PSP" (CHOMP)investigation led by Pete Riley and funded by NASA’s Heliophysics System Observatory Connect (HSOC) Program, we are currently We are currently running a joint Hinode-IRIS HOP, HOP 410, for coordinated observations of the Sun during times of PSP perihelia. An output from this study is a series of soft X-ray movies from Hinode/XRT. If PSP sees a strong switchback during any of its front-side or partly-front-side perihelia, we will examine the corresponding XRT movies to see whether exceptional jet activity occurred at the expected time and location of the potential source of the switchback on the Sun. This work is supported by the NASA HSOC and HGI programs, and by the MSFC Hinode project.

Alphonse C Sterling↗

Observations of photospheric magnetic fields and shear flows in flaring active regions

Horizontal flows in the photosphere and subsurface convection zone move the footpoints of coronal magnetic field lines. Magnetic energy to power flares can be stored in the corona if the flows drive the fields far from the potential configuration. Videodisk movies were shown with 0.5 to 1 arcsecond resolution of the following simultaneous observations: green continuum, longitudinal magnetogram, Fe I 5576 A line center (mid-photosphere), H alpha wings, and H alpha line center. The movies show a 90 x 90 arcsecond field of view of an active region at S29, W11. When viewed at speeds of a few thousand times real-time, the photospheric movies clearly show the active region fields being distorted by a remarkable combination of systematic flows and small eruptions of new flux. Magnetic bipoles are emerging over a large area, and the polarities are systematically flowing apart. The horizontal flows were mapped in detail from the continuum movies, and these may be used to predict the future evolution of the region. The horizontal flows are not discernable in H alpha. The H alpha movies strongly suggest reconnection processes in the fibrils joining opposite polarities. When viewed in combination with the magnetic movies, the cause for this evolution is apparent: opposite polarity fields collide and partially cancel, and the fibrils reconnect above the surface. This type of reconnection, driven by subphotospheric flows, complicates the chromospheric and coronal fields, causing visible braiding and twisting of the fibrils. Some of the transient emission events in the fibrils and adjacent plage may also be related.

Tarbell, T.↗

Preliminary Assessment of Optimal Longitudinal-Mode Control for Drag Reduction through Distributed Aeroelastic Shaping

The emergence of advanced lightweight materials is resulting in a new generation of lighter, flexible, more-efficient airframes that are enabling concepts for active aeroelastic wing-shape control to achieve greater flight efficiency and increased safety margins. These elastically shaped aircraft concepts require non-traditional methods for large-scale multi-objective flight control that simultaneously seek to gain aerodynamic efficiency in terms of drag reduction while performing traditional command-tracking tasks as part of a complete guidance and navigation solution. This paper presents results from a preliminary study of a notional multi-objective control law for an aeroelastic flexible-wing aircraft controlled through distributed continuous leading and trailing edge control surface actuators. This preliminary study develops and analyzes a multi-objective control law derived from optimal linear quadratic methods on a longitudinal vehicle dynamics model with coupled aeroelastic dynamics. The controller tracks commanded attack-angle while minimizing drag and controlling wing twist and bend. This paper presents an overview of the elastic aircraft concept, outlines the coupled vehicle model, presents the preliminary control law formulation and implementation, presents results from simulation, provides analysis, and concludes by identifying possible future areas for research

aeroelastic↗

Sensory-Feedback Exoskeletal Arm Controller

An electromechanical exoskeletal arm apparatus has been designed for use in controlling a remote robotic manipulator arm. The apparatus, called a force-feedback exoskeleton arm master (F-EAM) is comfortable to wear and easy to don and doff. It provides control signals from the wearer s arm to a robot arm or a computer simulator (e.g., a virtual-reality system); it also provides force and torque feedback from sensors on the robot arm or from the computer simulator to the wearer s arm. The F-EAM enables the wearer to make the robot arm gently touch objects and finely manipulate them without exerting excessive forces. The F-EAM features a lightweight design in which the motors and gear heads that generate force and torque feedback are made smaller than they ordinarily would be: this is achieved by driving the motors to power levels greater than would ordinarily be used in order to obtain higher torques, and by providing active liquid cooling of the motors to prevent overheating at the high drive levels. The F-EAM (see figure) includes an assembly that resembles a backpack and is worn like a backpack, plus an exoskeletal arm mechanism. The FEAM has five degrees of freedom (DOFs) that correspond to those of the human arm: 1. The first DOF is that of the side-to-side rotation of the upper arm about the shoulder (rotation about axis 1). The reflected torque for this DOF is provided by motor 1 via drum 1 and a planar four-bar linkage. 2. The second DOF is that of the up-and-down rotation of the arm about the shoulder. The reflected torque for this DOF is provided by motor 2 via drum 2. 3. The third DOF is that of twisting of the upper arm about its longitudinal axis. This DOF is implemented in a cable remote-center mechanism (CRCM). The reflected torque for this DOF is provided by motor 3, which drives the upper-arm cuff and the mechanism below it. A bladder inflatable by gas or liquid is placed between the cuff and the wearer s upper arm to compensate for misalignment between the exoskeletal mechanism and the shoulder. 4. The fourth DOF is that of flexion and extension of the elbow. The reflected torque for this DOF is provided by motor 4 and drum 4, which are mounted on a bracket that can slide longitudinally by a pin-and-slot engagement with the upper-arm cuff to compensate for slight variations in the position of the kinematic center of the elbow. Attached to drum 4 is an adapter plate to which is attached a CRCM for the lower arm. 5. The lower-arm CRCM implements the fifth DOF, which is the twist of the forearm about its longitudinal axis. Motor 5 provides the reflected torque for this DOF by driving the lower-arm cuff. A rod transmits twist and torsion between the lower-arm cuff and the hand cuff. With this system, the motion of the wearer s joints and the reflected torques applied to these joints can be measured and controlled in a relatively simple manner. This is because the anthropomorphic design of the mechanism imitates the kinematics of the human arm, eliminating the need for kinematic conversion of joint-torque and joint-angle data.

An, Bin↗

Design of a Propeller with Global Minimum Torque

Academia, industry, and Government are actively working towards a future where dozens of small to large Unmanned Aerial Systems (UAS) are present within urban environments. In this environment, high noise pollution and inefficiencies have the potential to render these new technologies impractical due to public annoyance and nonacceptance. This study aims to design and analyze a novel propeller design for minimum global torque using an optimization algorithm to find the full three dimensional solution of maximum efficiency. This resulted in a 𝐶 𝑙 distribution defining the global minimum torque solution for propeller design which corresponded with moving as much lift inboard as possible and reducing lift rapidly at the blade tip. The novel propeller (dubbed "Prandtl" propeller) was then compared with the current gold standard in propeller design, a minimum induced loss (MIL) propeller, which had all the same geometric properties except for blade twist and produced the same amount of thrust at the same advance ratio. The results of multiple iterations of Prandtl propellers showed an increase in efficiency of 2.0-3.3% for the Prandtl blade when compared to the equivalent MIL blade. A potential added benefit of this blade design is lower noise generation due to the lower lift loading at the tip reducing the large shear layer intensity which is the point source of noise in propellers. Two major breakthroughs for enabling widespread use of UAS in urban environments are noise reduction and vehicle efficiency, and this new propeller design has the potential to provide both.

Propeller↗

Design of a Propeller with Global Minimum Torque

Academia, industry, and Government are actively working towards a future where dozens of small to large Unmanned Aerial Systems (UAS) are present within urban environments. In this environment, high noise pollution and inefficiencies have the potential to render these new technologies impractical due to public annoyance and nonacceptance. This study aims to design and analyze a novel propeller design for minimum global torque using an optimization algorithm to find the full three dimensional solution of maximum efficiency. This resulted in a 𝐶 𝑙 distribution defining the global minimum torque solution for propeller design which corresponded with moving as much lift inboard as possible and reducing lift rapidly at the blade tip. The novel propeller (dubbed "Prandtl" propeller) was then compared with the current gold standard in propeller design, a minimum induced loss (MIL) propeller, which had all the same geometric properties except for blade twist and produced the same amount of thrust at the same advance ratio. The results of multiple iterations of Prandtl propellers showed an increase in efficiency of 2.0-3.3% for the Prandtl blade when compared to the equivalent MIL blade. A potential added benefit of this blade design is lower noise generation due to the lower lift loading at the tip reducing the large shear layer intensity which is the point source of noise in propellers. Two major breakthroughs for enabling widespread use of UAS in urban environments are noise reduction and vehicle efficiency, and this new propeller design has the potential to provide both.

Propeller↗

Simulations of Solar Jets Confined by Coronal Loops

Coronal jets are collimated, dynamic events that occur over a broad range of spatial scales in the solar corona. In the open magnetic field of coronal holes, jets form quasi-radial spires that can extend far out into the heliosphere, while in closed-field regions the jet outflows are confined to the corona. We explore the application of the embedded-bipole model to jets occurring in closed coronal loops. In this model, magnetic free energy is injected slowly by footpoint motions that introduce twist within the closed dome of the jet source region, and is released rapidly by the onset of an ideal kink-like instability. Two length scales characterize the system: the width (N) of the jet source region and the footpoint separation (L) of the coronal loop that envelops the jet source. We find that both the conditions for initiation and the subsequent dynamics are highly sensitive to the ratio L/N. The longest-lasting and most energetic jets occur along long coronal loops with large L/N ratios, and share many of the features of open-field jets, while smaller L/N ratios produce shorter-duration, less energetic jets that are affected by reflections from the far-loop footpoint. We quantify the transition between these behaviors and show that our model replicates key qualitative and quantitative aspects of both quiet Sun and active-region loop jets. We also find that there connection between the closed dome and surrounding coronal loop is very extensive: the cumulative reconnected flux at least matches the total flux beneath the dome for small L/N, and is more than double that value for large L/N.

Wyper, P. F.↗

Technical activities of the configuration aeroelasticity branch

A number of recent technical activities of the Configuration Aeroelasticity Branch of the NASA Langley Research Center are discussed in detail. The information on the research branch is compiled in twelve separate papers. The first of these topics is a summary of the purpose of the branch, including a full description of the branch and its associated projects and program efforts. The next ten papers cover specific projects and are as follows: Experimental transonic flutter characteristics of supersonic cruise configurations; Aeroelastic effects of spoiler surfaces mounted on a low aspect ratio rectangular wing; Planform curvature effects on flutter of 56 degree swept wing determined in Transonic Dynamics Tunnel (TDT); An introduction to rotorcraft testing in TDT; Rotorcraft vibration reduction research at the TDT; A preliminary study to determine the effects of tip geometry on the flutter of aft swept wings; Aeroelastic models program; NACA 0012 pressure model and test plan; Investigation of the use of extension twist coupling in composite rotor blades; and Improved finite element methods for rotorcraft structures. The final paper describes the primary facility operation by the branch, the Langley TDT.

Cole, Stanley R.↗

Shock Location Dominated Transonic Flight Loads on the Active Aeroelastic Wing

During several Active Aeroelastic Wing research flights, the shadow of the over-wing shock could be observed because of natural lighting conditions. As the plane accelerated, the shock location moved aft, and as the shadow passed the aileron and trailing-edge flap hinge lines, their associated hinge moments were substantially affected. The observation of the dominant effect of shock location on aft control surface hinge moments led to this investigation. This report investigates the effect of over-wing shock location on wing loads through flight-measured data and analytical predictions. Wing-root and wing-fold bending moment and torque and leading- and trailing-edge hinge moments have been measured in flight using calibrated strain gages. These same loads have been predicted using a computational fluid dynamics code called the Euler Navier-Stokes Three Dimensional Aeroelastic Code. The computational fluid dynamics study was based on the elastically deformed shape estimated by a twist model, which in turn was derived from in-flight-measured wing deflections provided by a flight deflection measurement system. During level transonic flight, the shock location dominated the wing trailing-edge control surface hinge moments. The computational fluid dynamics analysis based on the shape provided by the flight deflection measurement system produced very similar results and substantially correlated with the measured loads data.

Lokos, William A.↗

A Parametric Study of Erupting Flux Rope Rotation: Modeling the 'Cartwheel CME' on 9 April 2008

The rotation of erupting filaments in the solar corona is addressed through a parametric simulation study of unstable, rotating flux ropes in bipolar force-free initial equilibrium. The Lorentz force due to the external shear-field component and the relaxation of tension in the twisted field are the major contributors to the rotation in this model, while reconnection with the ambient field is of minor importance, due to the field's simple structure. In the low-beta corona, the rotation is not guided by the changing orientation of the vertical field component's polarity inversion line with height. The model yields strong initial rotations which saturate in the corona and differ qualitatively from the profile of rotation vs. height obtained in a recent simulation of an eruption without preexisting flux rope. Both major mechanisms writhe the flux rope axis, converting part of the initial twist helicity, and produce rotation profiles which, to a large part, are very similar within a range of shear-twist combinations. A difference lies in the tendency of twist-driven rotation to saturate at lower heights than shear-driven rotation. For parameters characteristic of the source regions of erupting filaments and coronal mass ejections, the shear field is found to be the dominant origin of rotations in the corona and to be required if the rotation reaches angles of order 90 degrees and higher; it dominates even if the twist exceeds the threshold of the helical kink instability. The contributions by shear and twist to the total rotation can be disentangled in the analysis of observations if the rotation and rise profiles are simultaneously compared with model calculations. The resulting twist estimate allows one to judge whether the helical kink instability occurred. This is demonstrated for the erupting prominence in the "Cartwheel CME" on 9 April 2008, which has shown a rotation of approximately 115 deg. up to a height of 1.5 Solar R above the photosphere. Out of a range of initial equilibria which include strongly kink-unstable (Phi = 5 pi), weakly kink-unstable (Phi = 3.5 pi), and kink-stable (Phi = 2.5 pi) configurations, only the evolution of the weakly kink-unstable flux rope matches the observations in their entirety.

initiation and propagation↗

Orion Touchdown Heading Control

At touchdown Orion must be aligned so that the crew person's feet are forward in the direction of the horizontal velocity. To ensure that this requirement is met active heading control is being implemented on the Orion crew module. This technique reduces probability of roll-over during splashdown, assures axial loads on the crew at touchdown, and alleviates structural requirements on impact allowing for a light-weight structural design. On-board sensors are used to measure current vehicle orientation and horizontal velocity used in generation of the heading error signal. Linear velocity measured by the IMU drifts while under parachutes due to wind gusts and has to be corrected by GPS; this makes GPS critical for successful landing. Jet fire logic is achieved by use of a phase-plane and commands are realized by using roll jets from the reaction control system (RCS); using pre existing hardware eliminates additional hardware and structural requirements. Touchdown performance is measured by an orientation envelope that was co-developed with structures so that the performance requirements overlap adding system redundancy. Heading control also introduces new difficulties to be addressed such as parachute line twist torque as well as increasing vehicle sensitivity to wind shifts and sea states. Solving these difficulties requires added complexity to flight software as well as increasing the propellant required to achieve successful touchdown. while offering promising results, the criticality of GPS along with a significant propellant cost raises questions on the effectiveness of using touchdown heading control.

Kane, Mark A.↗

Energy buildup in sheared force-free magnetic fields

Photospheric displacement of the footpoints of solar magnetic field lines results in shearing and twisting of the field, and consequently in the buildup of electric currents and magnetic free energy in the corona. The sudden release of this free energy may be the origin of eruptive events like coronal mass ejections, prominence eruptions, and flares. An important question is whether such an energy release may be accompanied by the opening of magnetic field lines that were previously closed, for such open field lines can provide a route for matter frozen into the field to escape the sun altogether. This paper presents the results of numerical calculations showing that opening of the magnetic field is permitted energetically, in that it is possible to build up more free energy in a sheared, closed, force-free magnetic field than is in a related magnetic configuration having both closed and open field lines. Whether or not the closed force-free field attains enough energy to become partially open depends on the form of the shear profile; the results presented compare the energy buildup for different shear profiles. Implications for solar activity are discussed briefly.

Wolfson, Richard↗