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Noncoplanar magnetic fields, shock potentials, and ion deflection

A puzzling aspect of the structure of collisionless shock waves concerns the existence of a component of magnetic field that lies out of the coplanarity plane in the transition layer. It is shown that the existence of this component may be understood and its value calculated from a simple expression derived from first principles. The value of this field component may be derived without reference to the transformation properties of the fields or the changes in energy that the ions and electrons undergo on traversing the electrostatic potential of the shock interface.

Jones, Frank C.↗

General design method for 3-dimensional, potential flow fields. Part 2: Computer program DIN3D1 for simple, unbranched ducts

The general design method for three-dimensional, potential, incompressible or subsonic-compressible flow developed in part 1 of this report is applied to the design of simple, unbranched ducts. A computer program, DIN3D1, is developed and five numerical examples are presented: a nozzle, two elbows, an S-duct, and the preliminary design of a side inlet for turbomachines. The two major inputs to the program are the upstream boundary shape and the lateral velocity distribution on the duct wall. As a result of these inputs, boundary conditions are overprescribed and the problem is ill posed. However, it appears that there are degrees of compatibility between these two major inputs and that, for reasonably compatible inputs, satisfactory solutions can be obtained. By not prescribing the shape of the upstream boundary, the problem presumably becomes well posed, but it is not clear how to formulate a practical design method under this circumstance. Nor does it appear desirable, because the designer usually needs to retain control over the upstream (or downstream) boundary shape. The problem is further complicated by the fact that, unlike the two-dimensional case, and irrespective of the upstream boundary shape, some prescribed lateral velocity distributions do not have proper solutions.

Stanitz, J. D.↗

The RHESSI Microflare Height Distribution

We present the first in-depth statistical survey of flare source heights observed by RHESSI. Flares were found using a flare-finding algorithm designed to search the 6-10 keV count-rate when RHESSI's full sensitivity was available in order to find the smallest events (Christe et al., 2008). Between March 2002 and March 2007, a total of 25,006 events were found. Source locations were determined in the 4-10 keV, 10-15 keV, and 15-30 keV energy ranges for each event. In order to extract the height distribution from the observed projected source positions, a forward-fit model was developed with an assumed source height distribution where height is measured from the photosphere. We find that the best flare height distribution is given by g (h) oc exp(-h/lambda) where lambda = 6.1 plus or minus 0.3 Mm is the scale height. A power law height distribution with a negative power law index, gamma = 3.1 plus or minus 0.3 is also consistent with the data. Interpreted as thermal loop top sources, these heights are compared to loops generated by a potential field model (PFSS). The measured flare heights distribution are found to be much steeper than the potential field loop height distribution which may be a signature of the flare energization process.

Christe, P.↗

Variability of the ocean-induced magnetic field predicted at sea surface and at satellite altitudes

Spatial and temporal variability of the magnetic field component induced by ocean circulation is investigated on the basis of a standard thin-shell approximation of electro- and magneto-static equations. Well-known difficulties of numerical solution of the governing equations are resolved by reducing the problem to an equation for the electric field potential,(ef) as opposed to a more conventional approach focused on the vertical jump, (psi), of the magnetic field potential across a combined ocean/ marine-sediment-layer spherical shell. The present formulation permits using more realistic input data on ocean currents and ultimately yields much greater (by at least an order of magnitude) values of the magnetic field at sea surface than predicted in earlier studies. Such large values are comparable to, and in some cases exceed, magnetic field variations caused by lithospheric and ionospheric sources on monthly to interannual timescales. At the 400-km altitude (of CHAMP satellite), the field attains 6 nT. The model predictions show favorable comparisons with some in situ measurements as well as with Challenging Minisatellite Payload (CHAMP) satellite magnetometer data.

ocean induced magnetic field↗

On the effects of grid ill-conditioning in three dimensional finite element vector potential magnetostatic field computations

The effects of finite element grid geometries and associated ill-conditioning were studied in single medium and multi-media (air-iron) three dimensional magnetostatic field computation problems. The sensitivities of these 3D field computations to finite element grid geometries were investigated. It was found that in single medium applications the unconstrained magnetic vector potential curl-curl formulation in conjunction with first order finite elements produce global results which are almost totally insensitive to grid geometries. However, it was found that in multi-media (air-iron) applications first order finite element results are sensitive to grid geometries and consequent elemental shape ill-conditioning. These sensitivities were almost totally eliminated by means of the use of second order finite elements in the field computation algorithms. Practical examples are given in this paper to demonstrate these aspects mentioned above.

Wang, R.↗

Analysis of crustal structure of Venus utilizing residual Line-of-Sight (LOS) gravity acceleration and surface topography data. A trial of global modeling of Venus gravity field using harmonic spline method

To construct Venus' gravity disturbance field (or gravity anomaly) with the spacecraft-observer line of site (LOS) acceleration perturbation data, both a global and a local approach can be used. The global approach, e.g., spherical harmonic coefficients, and the local approach, e.g., the integral operator method, based on geodetic techniques are generally not the same, so that they must be used separately for mapping long wavelength features and short wavelength features. Harmonic spline, as an interpolation and extrapolation technique, is intrinsically flexible to both global and local mapping of a potential field. Theoretically, it preserves the information of the potential field up to the bound by sampling theorem regardless of whether it is global or local mapping, and is never bothered with truncation errors. The improvement of harmonic spline methodology for global mapping is reported. New basis functions, a singular value decomposition (SVD) based modification to Parker & Shure's numerical procedure, and preliminary results are presented.

Fang, Ming↗

The Limit of Free Magnetic Energy in Active Regions

By measuring from active-region magnetograms a proxy of the free energy in the active region fs magnetic field, it has been found previously that (1) there is an abrupt upper limit to the free energy the field can hold that increases with the amount of magnetic field in the active region, the active region fs magnetic flux content, and (2) the free energy is usually near its limit when the field explodes in a CME/flare eruption. That is, explosive active regions are concentrated in a main-sequence path bordering the free-energy ]limit line in (flux content, free-energy proxy) phase space. Here, from measurement of Marshall Space Flight Center vector magnetograms, we find the magnetic condition that underlies the free ]energy limit and the accompanying main sequence of explosive active regions. Using a suitable free ]energy proxy measured from vector magnetograms of 44 active regions, we find that (1) in active regions at and near their free ]energy limit, the ratio of magnetic-shear free energy to the non ]free magnetic energy the potential field would have is approximately 1 in the core field, the field rooted along the neutral line, and (2) this ratio is progressively less in active regions progressively farther below their free ]energy limit. This shows that most active regions in which this core-field energy ratio is much less than 1 cannot be triggered to explode; as this ratio approaches 1, most active regions become capable of exploding; and when this ratio is 1 or greater, most active regions are compelled to explode. From these results we surmise the magnetic condition that determines the free ]energy limit is the ratio of the free magnetic energy to the non-free energy the active region fs field would have were it completely relaxed to its potential ]field configuration, and that this ratio is approximately 1 at the free-energy limit and in the main sequence of explosive active regions.

Moore, Ron↗

Laser velocimeter measurements of the flowfield generated by an advanced counterrotating propeller

Results are presented of an 0.72 regime, with the advance ratio of each rotor set at 2.80. The measured data indicate only a slight influence of the potential field of each front rotor blade on the flowfield upstream of the rotor. The data measured downstream of the front rotor characterize the tip vortices, vortex sheets and potential field nonuniformities generated by the front rotor. The unsteadiness of the flow in the rotating frame of reference of the aft rotor is also illustrated.

Podboy, Gary G.↗

Robot path planning for space-truss assembly

Construction, repair, and maintenance of space-based structures will require extensive planning of operations in order to effectively carry out these tasks. The path planning algorithm described here is a general approach to generating paths that guarantee collision avoidance for a single chain nonredundant or redundant robot. The algorithm uses a graph search of feasible points in position space, followed by a local potential field method that guarantees collision avoidance among objects, structures, and the robot arm as well as conformance to joint limit constraints. This algorithm is novel in its computation of goal attractive potential fields in Cartesian space, and computation of obstacle repulsive fields in robot joint space. These effects are combined to generate robot motion. Computation is efficiently implemented through the computation of the robot arm Jacobian and not the full inverse arm kinematics. These planning algorithms have been implemented and evaluated using existing space-truss designs, and are being integrated into the RPI-CIRSSE Testbed environment.

Muenger, Rolf↗

Effect of the Great Attractor on the cosmic microwave background radiation

A map is presented of the anisotropy Delta T/T in cosmic microwave background (CMB) temperature of our region of the universe as viewed by a distant observer, predicted on the basis of the gravitational potential field. This field is calculated in the vicinity of the Local Group of galaxies from the observed peculiar velocities of galaxies under the assumption that the peculiar motions are induced by gravity. If the cosmological density parameter Omega is one, the gravitational potential field of the Great Attractor and surrounding regions produces a maximum Sachs-Wolfe anisotropy of Delta T/T = (1.7 + or - 0.3) x 10 to the -5th on an angular scale of 1 deg. Doppler and adiabatic contributions to this anisotropy are expected to be somewhat larger. If similar fluctuations in the gravitational potential are present elsewhere in the universe, the anisotropy present when the CMB was last scattered should be visible from the earth and should be detectable in current experiments.

Bertschinger, Edmund↗

Laser velocimeter measurements of the flowfield generated by an advanced counterrotating propeller

Results are presented of an investigation to measure the flowfield generated by an advanced counterrotating pusher propeller model similar to the full-scale Unducted Fan demonstrator engine. A laser Doppler velocimeter was used to measure the velocity field in several planes normal to the centerline of the model at axial stations upstream and downstream of each rotor. During this investigation, blades of the F4/A4 type were installed on the model which was operating in a freestream Mach 0.72 regime, with the advance ratio of each rotor set at 2.80. The measured data indicate only a slight influence of the potential field of each front rotor blade on the flowfield upstream of the rotor. The data measured downstream of the front rotor characterize the tip vortices, vortex sheets and potential field nonuniformities generated by the front rotor. The unsteadiness of the flow in the rotating frame of reference of the aft rotor is also illustrated.

Podboy, Gary G.↗

Work function measurements by the field emission retarding potential method

Using the field emission retarding potential method true work functions have been measured for the following monocrystalline substrates: W(110), W(111), W(100), Nb(100), Ni(100), Cu(100), Ir(110) and Ir(111). The electron elastic and inelastic reflection coefficients from several of these surfaces have also been examined near zero primary beam energy.

Swanson, L. W.↗

Motion planning for a free-flying robot

An investigation is presented of motion planning combining low level control and obstacle avoidance for a free flying robot. This free flying robot is an outgrowth of the concept of an assistant for astronauts on the U.S. Space Station and Shuttle. A motion planner based on the Khatib potential field approach is described. Because of the uncluttered environment in space, it generates a path from representation of known obstacles rather than from a representation of free space. A global planner supplies the low level controller with interim points between the current position and the desired goal position so that the vehicle does not become trapped by local minima, a phenomenon of the potential field approach. Discussion of the feasibility of this system for space applications is presented.

Kaiser, Donald Leo↗

Controlling Herds of Cooperative Robots

A document poses, and suggests a program of research for answering, questions of how to achieve autonomous operation of herds of cooperative robots to be used in exploration and/or colonization of remote planets. In a typical scenario, a flock of mobile sensory robots would be deployed in a previously unexplored region, one of the robots would be designated the leader, and the leader would issue commands to move the robots to different locations or aim sensors at different targets to maximize scientific return. It would be necessary to provide for this hierarchical, cooperative behavior even in the face of such unpredictable factors as terrain obstacles. A potential-fields approach is proposed as a theoretical basis for developing methods of autonomous command and guidance of a herd. A survival-of-the-fittest approach is suggested as a theoretical basis for selection, mutation, and adaptation of a description of (1) the body, joints, sensors, actuators, and control computer of each robot, and (2) the connectivity of each robot with the rest of the herd, such that the herd could be regarded as consisting of a set of artificial creatures that evolve to adapt to a previously unknown environment. A distributed simulation environment has been developed to test the proposed approaches in the Titan environment. One blimp guides three surface sondes via a potential field approach. The results of the simulation demonstrate that the method used for control is feasible, even if significant uncertainty exists in the dynamics and environmental models, and that the control architecture provides the autonomy needed to enable surface science data collection.

Quadrelli, Marco B.↗

The flares of August 1972

Analysis is made of observations of the August, 1972 flares at Big Bear and Tel Aviv, involving monochromatic movies, magnetograms, and spectra. In each flare the observations fit a model of particle acceleration in the chromosphere with emission produced by impart and by heating by the energetic electrons and protons. The region showed twisted flux and high gradients from birth, and flares appear due to strong magnetic shears and gradients across the neutral line produced by sunspot motions. Post flare loops show a strong change from sheared, force-free fields parallel to potential-field-like loops, perpendicular to the neutral line above the surface.

Zirin, H.↗

Measurement of magnetic field aligned potential differences using high resolution conjugate photoelectron energy spectra

Simultaneous high-resolution observations of a distinctive feature in the energy spectrum of conjugate photoelectrons and spacecraft potential relative to the local ionosphere have allowed the net potential difference between magnetic conjugate points at latitudes below the region of low-energy (i.e., lower than 100 eV) auroral electron precipitation to be determined. Measurements made at 300 km from Atmosphere Explorer C show that there is normally no net potential difference between hemispheres in this region, which extended up to invariant latitudes as high as 74 deg. Two types of apparently related anomalous behavior were infrequently observed at high latitudes. During these periods the incident flux of conjugate photoelectrons was either decelerated by about 3 eV or was not detected.

Peterson, W. K.↗

Langmuir probe theory and the problem of anisotropic collection

A more general understanding of Langmuir probe theory by going beyond particular coordinate systems as far as possible was studied. To delineate the role of initial velocities in the problem and to characterize the interaction between the velocity flow field and the electrostatic potential field both of which enter into the determination of particle trajectories are desired. The probe is supposed to be negatively charged throughout and the ensuing region of positive space charge about it differs fundamentally from the plasma region beyond in the sense that the former represents a region in which deterministic trajectories dominate while the lattice is a region dominated by statistical interactions largely controlled by the collisionless stationary Boltzmann equation. A general solution of this Boltzmann equation is given and its relationship to the problem of saturation current density in 3D is elucidated.

Kyrala, A.↗