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NASA NTRS1991

Determination of the coronal magnetic field from vector magnetograph data

A new algorithm was developed, tested, and applied to determine coronal magnetic fields above solar active regions. The coronal field above NOAA active region AR5747 was successfully estimated on 20 Oct. 1989 from data taken at the Mees Solar Observatory of the Univ. of Hawaii. It was shown that observational data can be used to obtain realistic estimates of coronal magnetic fields. The model has significantly extended the realism with which the coronal magnetic field can be inferred from observations. The understanding of coronal phenomena will be greatly advanced by a reliable technique, such as the one presented, for deducing the detailed spatial structure of the coronal field. The payoff from major current and proposed NASA observational efforts is heavily dependent on the success with which the coronal field can be inferred from vector magnetograms. In particular, the present inability to reliably obtain the coronal field has been a major obstacle to the theoretical advancement of solar flare theory and prediction. The results have shown that the evolutional algorithm can be used to estimate coronal magnetic fields.

Mikic, Zoran↗

NASA NTRS1990

The significance of vector magnetic field measurements

Observations of four flaring solar active regions, obtained during 1980-1986 with the NASA Marshall vector magnetograph (Hagyard et al., 1982 and 1985), are presented graphically and characterized in detail, with reference to nearly simultaneous Big Bear Solar Observatory and USAF ASW H-alpha images. It is shown that the flares occurred where local photospheric magnetic fields differed most from the potential field, with initial brightening on either side of a magnetic-neutral line near the point of maximum angular shear (rather than that of maximum magnetic-field strength, typically 1 kG or greater). Particular emphasis is placed on the fact that these significant nonpotential features were detected only by measuring all three components of the vector magnetic field.

Hagyard, M. J.↗

NASA NTRS1992

Visualization of second order tensor fields and matrix data

We present a study of the visualization of 3-D second order tensor fields and matrix data. The general problem of visualizing unsymmetric real or complex Hermitian second order tensor fields can be reduced to the simultaneous visualization of a real and symmetric second order tensor field and a real vector field. As opposed to the discrete iconic techniques commonly used in multivariate data visualization, the emphasis is on exploiting the mathematical properties of tensor fields in order to facilitate their visualization and to produce a continuous representation of the data. We focus on interactively sensing and exploring real and symmetric second order tensor data by generalizing the vector notion of streamline to the tensor concept of hyperstreamline. We stress the importance of a structural analysis of the data field analogous to the techniques of vector field topology extraction in order to obtain a unique and objective representation of second order tensor fields.

Delmarcelle, Thierry↗

NASA NTRS1999

Which Way Is the Flow?

The line integral convolution (LIC) technique has been known to be an effective tool for depicting flow patterns in a given vector field. There have been many extensions to make it run faster and reveal useful flow information such as velocity magnitude, motion, and direction. There are also extensions to unsteady flows and 3D vector fields. Surprisingly, none of these extensions automatically highlight flow features, which often represent the most important and interesting physical flow phenomena. In this sketch, a method for highlighting flow direction in LIC images is presented. The method gives an intuitive impression of flow direction in the given vector field and automatically reveals saddle points in the flow.

Kao, David↗

NASA NTRS1995

A simple method for verifying the deployment of the TOMS-EP solar arrays

The Total Ozone Mapping Spectrometer-Earth Probe (TOMS-EP) mission relies upon a successful deployment of the spacecraft's solar arrays. Several methods of verification are being employed to ascertain the solar array deployment status, with each requiring differing amounts of data. This paper describes a robust attitude-independent verification method that utilizes telemetry from the coarse Sun sensors (CSS's) and the three-axis magnetometers (TAM's) to determine the solar array deployment status - and it can do so with only a few, not necessarily contiguous, points of data. The method developed assumes that the solar arrays are deployed. Telemetry data from the CSS and TAM are converted to the Sun and magnetic field vectors in spacecraft body coordinates, and the angle between them is calculated. Deployment is indicated if this angle is within a certain error tolerance of the angle between the reference Sun and magnetic field vectors. Although several other methods can indicate a non-deployed state, with this method there is a 70% confidence level in confirming deployment as well as a nearly 100% certainty in confirming a non-deployed state. In addition, the spacecraft attitude (which is not known during the first orbit after launch) is not needed for this algorithm because the angle between the Sun and magnetic field vectors is independent of the spacecraft attitude. This technique can be applied to any spacecraft with a TAM and with CSS's mounted on the solar array(s).

Koppersmith, James R.↗

NASA NTRS2014

First Use of Synoptic Vector Magnetograms for Global Nonlinear, Force-Free Coronal Magnetic Field Models

Context. The magnetic field permeating the solar atmosphere is generally thought to provide the energy for much of the activity seen in the solar corona, such as flares, coronal mass ejections (CMEs), etc. To overcome the unavailability of coronal magnetic field measurements, photospheric magnetic field vector data can be used to reconstruct the coronal field. Currently, there are several modelling techniques being used to calculate three-dimensional field lines into the solar atmosphere. Aims. For the first time, synoptic maps of a photospheric-vector magnetic field synthesized from the vector spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) are used to model the coronal magnetic field and estimate free magnetic energy in the global scale. The free energy (i.e., the energy in excess of the potential field energy) is one of the main indicators used in space weather forecasts to predict the eruptivity of active regions. Methods. We solve the nonlinear force-free field equations using an optimization principle in spherical geometry. The resulting threedimensional magnetic fields are used to estimate the magnetic free energy content E(sub free) = E(sub nlfff) − E(sub pot), which is the difference of the magnetic energies between the nonpotential field and the potential field in the global solar corona. For comparison, we overlay the extrapolated magnetic field lines with the extreme ultraviolet (EUV) observations by the atmospheric imaging assembly (AIA) on board the Solar Dynamics Observatory (SDO). Results. For a single Carrington rotation 2121, we find that the global nonlinear force-free field (NLFFF) magnetic energy density is 10.3% higher than the potential one. Most of this free energy is located in active regions.

Sun: corona↗

NASA NTRS2012

Lightweight, Miniature Inertial Measurement System

A miniature, lighter-weight, and highly accurate inertial navigation system (INS) is coupled with GPS receivers to provide stable and highly accurate positioning, attitude, and inertial measurements while being subjected to highly dynamic maneuvers. In contrast to conventional methods that use extensive, groundbased, real-time tracking and control units that are expensive, large, and require excessive amounts of power to operate, this method focuses on the development of an estimator that makes use of a low-cost, miniature accelerometer array fused with traditional measurement systems and GPS. Through the use of a position tracking estimation algorithm, onboard accelerometers are numerically integrated and transformed using attitude information to obtain an estimate of position in the inertial frame. Position and velocity estimates are subject to drift due to accelerometer sensor bias and high vibration over time, and so require the integration with GPS information using a Kalman filter to provide highly accurate and reliable inertial tracking estimations. The method implemented here uses the local gravitational field vector. Upon determining the location of the local gravitational field vector relative to two consecutive sensors, the orientation of the device may then be estimated, and the attitude determined. Improved attitude estimates further enhance the inertial position estimates. The device can be powered either by batteries, or by the power source onboard its target platforms. A DB9 port provides the I/O to external systems, and the device is designed to be mounted in a waterproof case for all-weather conditions.

Tang, Liang↗

NASA NTRS2011

Probabilistic Path Planning of Montgolfier Balloons in Strong, Uncertain Wind Fields

Lighter-than-air vehicles such as hot-air balloons have been proposed for exploring Saturn s moon Titan, as well as other bodies with significant atmospheres. For these vehicles to navigate effectively, it is critical to incorporate the effects of surrounding wind fields, especially as these winds will likely be strong relative to the control authority of the vehicle. Predictive models of these wind fields are available, and previous research has considered problems of planning paths subject to these predicted forces. However, such previous work has considered the wind fields as known a priori, whereas in practical applications, the actual wind vector field is not known exactly and may deviate significantly from the wind velocities estimated by the model. A probabilistic 3D path-planning algorithm was developed for balloons to use uncertain wind models to generate time-efficient paths. The nominal goal of the algorithm is to determine what altitude and what horizontal actuation, if any is available on the vehicle, to use to reach a particular goal location in the least expected time, utilizing advantageous winds. The solution also enables one to quickly evaluate the expected time-to-goal from any other location and to avoid regions of large uncertainty. This method is designed for balloons in wind fields but may be generalized for any buoyant vehicle operating in a vector field. To prepare the planning problem, the uncertainty in the wind field is modeled. Then, the problem of reaching a particular goal location is formulated as a Markov decision process (MDP) using a discretized space approach. Solving the MDP provides a policy of what actuation option (how much buoyancy change and, if applicable, horizontal actuation) should be selected at any given location to minimize the expected time-to-goal. The results provide expected time-to-goal values from any given location on the globe in addition to the action policy. This stochastic approach can also provide insights not accessible by deterministic methods; for example, one can evaluate variability and risk associated with different scenarios, rather than only viewing the expected outcome.

Wolf, Michael↗

NASA NTRS2011

Fabrication and Test of an Optical Magnetic Mirror

Traditional mirrors at optical wavelengths use thin metalized or dielectric layers of uniform thickness to approximate a perfect electric field boundary condition. The electron gas in such a mirror configuration oscillates in response to the incident photons and subsequently re-emits fields where the propagation and electric field vectors have been inverted and the phase of the incident magnetic field is preserved. We proposed fabrication of sub-wavelength-scale conductive structures that could be used to interact with light at a nano-scale and enable synthesis of the desired perfect magnetic-field boundary condition. In a magnetic mirror, the interaction of light with the nanowires, dielectric layer and ground plate, inverts the magnetic field vector resulting in a zero degree phase shift upon reflection. Geometries such as split ring resonators and sinusoidal conductive strips were shown to demonstrate magnetic mirror behavior in the microwave and then in the visible. Work to design, fabricate and test a magnetic mirror began in 2007 at the NASA Goddard Space Flight Center (GSFC) under an Internal Research and Development (IRAD) award Our initial nanowire geometry was sinusoidal but orthogonally asymmetric in spatial frequency, which allowed clear indications of its behavior by polarization. We report on the fabrication steps and testing of magnetic mirrors using a phase shifting interferometer and the first far-field imaging of an optical magnetic mirror.

Hagopian, John G.↗

NASA NTRSDate not supplied

A Method for Obtaining Surface Flow Vectors and Its Implementation in Interferometric Skin Friction Measurement

A new method was developed to extract surface flow vectors from an oilflow visualization image that has oil streaklines. The method is analogous to the PIV processing where the image is divided into interrogation windows. A representative flow direction is obtained for each interrogation window using image processing with a line-detection algorithm. Repeating the process for the entire image, one can find the surface vector field. The Hough transformation, Radon transformation and Machine Learning were used as line-detection algorithms. The obtained vector field is then postprocessed to filter spurious vectors and to apply smoothing. The method was tested on 2D and 3D models with different flow complexities. The method was able to predict surface flow vectors for all cases tested. The predicted surface flow vectors were used in obtaining the surface skin friction. The successful implementation of the surface flow vectors enables interferometric skin friction measurements on surfaces beneath 3D complex flows. In addition, the surface flow vectors can be superimposed on the oilflow visualization images to better explain the surface flow topology.

Surface flow vectors↗

NASA NTRSDate not supplied

A Method for Obtaining Surface Flow Vectors and Its Implementation in Interferometric Skin Friction Measurement

Surface flow vectors↗

NASA NTRS1971

The equilibrium and stability of the gaseous component of the galaxy, 4

The stability of a self-gravitating, nonrotating, plane-parallel, isothermal gas layer with equipartition magnetic and cosmic ray components, immersed in a rigid isothermal layer of stars, is considered with respect to waves with motions perpendicular to the equilibrium magnetic and gravitational field vectors. The magnetic field and cosmic ray gas hinder gravitational instability and increase the minimum length necessary to produce instability.

Kellman, S. A.↗

NASA NTRS1982

Electron heating within the earth's bow shock

High-temporal-resolution measurements of electron velocity distributions have been obtained for many transits through the earth's bow shock. Within all oblique shocks studied, the maximum of the electron velocity distribution is offset with respect to the ion rest frame parallel to the magnetic field vector and directed downstream. These observations indicate that electron thermalization within the bow shock consists first of a downstream acceleration parallel to the magnetic field vector by the macroscopic shock electric field, followed by beam-driven plasma instabilities.

Feldman, W. C.↗

NASA NTRS1989

Field structure of collapsing wave packets in 3D strong Langmuir turbulence

A simple model is constructed for the electric fields in the collapsing wave packets found in 3D simulations of driven and damped isotropic strong Langmuir turbulence. This model, based on a spherical-harmonic decomposition of the electrostatic potential, accounts for the distribution of wave-packet shapes observed in the simulations, particularly the predominance of oblate wave packets. In contrast with predictions for undamped and undriven subsonic collapse of scalar fields, oblate vector-field wave packets do not flatten during collapse but, instead, remain approximately self-similar and rigid.

Newman, D. L.↗

NASA NTRS2001

Multifunctional Collaborative Modeling and Analysis Methods in Engineering Science

Engineers are challenged to produce better designs in less time and for less cost. Hence, to investigate novel and revolutionary design concepts, accurate, high-fidelity results must be assimilated rapidly into the design, analysis, and simulation process. This assimilation should consider diverse mathematical modeling and multi-discipline interactions necessitated by concepts exploiting advanced materials and structures. Integrated high-fidelity methods with diverse engineering applications provide the enabling technologies to assimilate these high-fidelity, multi-disciplinary results rapidly at an early stage in the design. These integrated methods must be multifunctional, collaborative, and applicable to the general field of engineering science and mechanics. Multifunctional methodologies and analysis procedures are formulated for interfacing diverse subdomain idealizations including multi-fidelity modeling methods and multi-discipline analysis methods. These methods, based on the method of weighted residuals, ensure accurate compatibility of primary and secondary variables across the subdomain interfaces. Methods are developed using diverse mathematical modeling (i.e., finite difference and finite element methods) and multi-fidelity modeling among the subdomains. Several benchmark scalar-field and vector-field problems in engineering science are presented with extensions to multidisciplinary problems. Results for all problems presented are in overall good agreement with the exact analytical solution or the reference numerical solution. Based on the results, the integrated modeling approach using the finite element method for multi-fidelity discretization among the subdomains is identified as most robust. The multiple-method approach is advantageous when interfacing diverse disciplines in which each of the method's strengths are utilized. The multifunctional methodology presented provides an effective mechanism by which domains with diverse idealizations are interfaced. This capability rapidly provides the high-fidelity results needed in the early design phase. Moreover, the capability is applicable to the general field of engineering science and mechanics. Hence, it provides a collaborative capability that accounts for interactions among engineering analysis methods.

Ransom, Jonathan B.↗

NASA NTRS2001

On Multifunctional Collaborative Methods in Engineering Science

Multifunctional methodologies and analysis procedures are formulated for interfacing diverse subdomain idealizations including multi-fidelity modeling methods and multi-discipline analysis methods. These methods, based on the method of weighted residuals, ensure accurate compatibility of primary and secondary variables across the subdomain interfaces. Methods are developed using diverse mathematical modeling (i.e., finite difference and finite element methods) and multi-fidelity modeling among the subdomains. Several benchmark scalar-field and vector-field problems in engineering science are presented with extensions to multidisciplinary problems. Results for all problems presented are in overall good agreement with the exact analytical solution or the reference numerical solution. Based on the results, the integrated modeling approach using the finite element method for multi-fidelity discretization among the subdomains is identified as most robust. The multiple method approach is advantageous when interfacing diverse disciplines in which each of the method's strengths are utilized.

Ransom, Jonathan B.↗

NASA NTRS2018

MAVEN Case Studies of Plasma Dynamics in Low‐Altitude Crustal Magnetic Field at Mars 1: Dayside Ion Spikes Associated With Radial Crustal Magnetic Fields

We report for the first time, simultaneous ion, electron, magnetic field vector and electric field wave measurements made possible by Mars Atmosphere and Volatile EvolutioN, during ion energy flux spikes in low‐altitude radial crustal magnetic fields on the Mars dayside. Observations show energetic electrons and ions (E > 25 eV) precipitating on magnetic field lines assumed as closed. Ions (E < 1.4 keV) display broad velocity distributions toward Mars, showing ions flowing from higher altitude possibly after magnetic reconnection or loss cone filling from pitch angle scattering effects. Precipitating ions (E < 1.4 keV) show nonadiabatic features depending on ion mass and energy and returning ions (E < 1.4 keV) show evidence of conserving the first adiabatic invariant in a mirror field. We observe magnetic field perturbations up to 60 nT, electric field wave amplitudes up to 38 mV/m, and brief periods of peaked electron spectra. At ∼175 km and at times Mars Atmosphere and Volatile EvolutioN is below the mirroring altitude of electrons, we observe mirroring and transverse heating of H+ ions alongside increased electric field wave amplitude fluctuations. It suggests field aligned potential drops result from different mirror altitudes of ions and electrons. Ions E > 1.4 keV (O+) occur as injected accelerated ion beams and ions heated after energization or deceleration. Energy dispersed kilo‐electron‐volt ions suggest a selection effect in radial magnetic fields for lower‐energy Marsward ions, compared to reflection of higher‐energy anti‐Sunward ions. Precipitating kilo‐electron‐volt ions show energy deposition rates of 3.6 ×10(exp -6) W/sq m and sputtering escape rates from precipitating O+ ions of 1.5 ×10(exp 5)/(sq cm.s) and 2.1 ×10(exp 6)/(sq cm.s) are calculated.

Plasma Dynamics↗

DOE OSTI2023

The infinite level normal forms for non-resonant double Hopf singularities

Here, in this paper, we explore hypernormal forms of vector fields that have non-resonant double Hopf singularities with a non-zero radial cubic part. Our primary focus is on investigating the infinite-level normal form classification of this type of singularities. We provide a normal form decomposition in terms of planar-rotating and planar-radial vector fields, which greatly facilitate the pattern recognition and analysis of the corresponding generalized homological maps. Notably, our paper represents the first instance of the normal form classification for general non-resonant double Hopf singularities without structural symmetry.

97 MATHEMATICS AND COMPUTING↗