Communications regarding a new calculation of the terrestrial magnetic potential
Terrestrial magnetic potential calculations taking into account deviation of earth from spherical shape
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A regularization method for extrapolation of solar potential magnetic fields
The mathematical basis of a Tikhonov regularization method for extrapolating the chromospheric-coronal magnetic field using photospheric vector magnetograms is discussed. The basic techniques show that the Cauchy initial value problem can be formulated for potential magnetic fields. The potential field analysis considers a set of linear, elliptic partial differential equations. It is found that, by introducing an appropriate smoothing of the initial data of the Cauchy potential problem, an approximate Fourier integral solution is found, and an upper bound to the error in the solution is derived. This specific regularization technique, which is a function of magnetograph measurement sensitivities, provides a method to extrapolate the potential magnetic field above an active region into the chromosphere and low corona.
Gary, G. A.↗
Magnetic potential model for the structure of the solar corona for the March 1970 eclipse
Magnetic potential model of solar corona structure for March 1970 eclipse
Schatten, K. H.↗
Report on new calculations of the magnetic potential of the Earth
A procedure to establish better agreement between theoretical and calculated values of the magnetic potential of the Earth is discussed.
Schmidt, A.↗
FMR thermomagnetic studies up to 900 C of lunar soils and potential magnetic analogues
Using a recently developed furnace, ferromagnetic resonance (FMR) thermomagnetic studies up to 900 C were employed to measure the Curie points of the superparamagnetic (SP) and single domain (SD) particles in lunar soils and potential magnetic analogue materials. Based on measured Curie points of 775 C, the SP and SD particles in lunar soils 10084-853, 12070-29, 14161-46, and 67010-4 are essentially pure metallic Fe. Synthetic and terrestrial samples containing magnetite, titanomaghemites, and magnetite-like particles have measured Curie points below 600 C are thus not magnetic analogues of lunar soils.
Morris, R. V.↗
Comparison of heliospheric current sheet structure obtained from potential magnetic field computations and from observed polarization coronal brightness
A comparison is conducted of the structure of the heliospheric current sheet early in sunspot cycle 21 as computed from the observed photospheric magnetic field with a potential field approximation and as inferred from synoptic maps of the observed coronal polarization brightness. On most of the solar rotations compared, the two methods give essentially the same results; the basic shape of the warped current sheet and the amplitude (in solar latitude) of the displacements of the sheet from the solar equator are similar. On one rotation the current sheet computed with the potential field approximation appears to be distorted by a large photospheric region of unbalanced magnetic flux.
Wilcox, J. M.↗
Comparisons of measured and calculated potential magnetic fields
Photospheric line-of-sight and transverse-magnetic-field data obtained, with a vector magnetograph system for an isolated sunspot are described. A study of the linear polarization patterns and of the calculated transverse field lines indicates that the magnetic field of the region is very nearly potential. The H-alpha fibril structures of this region as seen in high-resolution photographs corroborate this conclusion. Consequently, a potential-field calculation is described using the measured line-of-sight fields together with assumed Neumann boundary conditions; both are necessary and sufficient for a unique solution. The computed transverse fields are then compared with the measured transverse fields to verify the potential-field model and assumed boundary values. The implications of these comparisons for the validity of magnetic-field extrapolations using potential theory are discussed.
Hagyard, M. J.↗
Three dimensional magnetic fields in extra high speed modified Lundell alternators computed by a combined vector-scalar magnetic potential finite element method
A 3D finite element (FE) approach was developed and implemented for computation of global magnetic fields in a 14.3 kVA modified Lundell alternator. The essence of the new method is the combined use of magnetic vector and scalar potential formulations in 3D FEs. This approach makes it practical, using state of the art supercomputer resources, to globally analyze magnetic fields and operating performances of rotating machines which have truly 3D magnetic flux patterns. The 3D FE-computed fields and machine inductances as well as various machine performance simulations of the 14.3 kVA machine are presented in this paper and its two companion papers.
Demerdash, N. A.↗
Patterns of potential magnetic field merging sites on the dayside magnetopause
Models of the magnetospheric and magnetosheath magnetic fields are used to determine the relative orientations of these fields at the dayside magnetopause in order to locate potential merging sites. Areas on the magnetopause with different fractional antiparallel components are displayed by contour diagrams for a variety of interplanetary field orientations. For interplanetary fields oriented perpendicular to the solar wind velocity the areas of nearly antiparallel field agree with those obtained by Crooker using simplified representations for the magnetic field geometry. Here, the application of more realistic models gives the locations of areas where any antiparallel component occurs. Potential merging sites for interplanetary fields with radial components are also illustrated. The results suggest that the topology of the magnetosheath and magnetospheric fields provides antiparallel components over a substantial fraction of the magnetopause for most interplanetary field orientations.
Luhmann, J. G.↗
Isothermal magnetostatic atmospheres. II - Similarity solutions with current proportional to the magnetic potential cubed
The paper presents a family of isothermal magnetostatic atmospheres with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry. The distributed current in the model J is directed along the x-axis, where x is the horizontal ignorable coordinate. The current J is taken to be proportional to the cube of the magnetostatic potential A and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. A range of similarity solution examples are displayed depending on the values of the similarity parameters. Each similarity parameter corresponds to a symmetry of the underlying nonlinear elliptic equation for A. The similarity parameters also determine the source currents for the potential field solution of the family. The solutions show the interplay between the gravitational force, the J & B force (B, magnetic field induction) and the gas pressure gradient.
Webb, G. M.↗
Isothermal magnetostatic atmospheres. III - Similarity solutions with current proportional to the magnetic potential squared
A family of isothermal magnetostatic atmospheres with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry is considered. It is assumed that the current (J) is proportional to the square of the magnetostatic potential and falls off exponentially with distance. Results are presented for the contributions of the anisotropic J x B force (where B is the magnetic field induction), the gravitational force, and the gas pressure gradient to the force balance.
Webb, G. M.↗
The evolution of a sheared potential magnetic field in the solar corona
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Karpen, J. T.↗
Global Non-Potential Magnetic Models of the Solar Corona During the March 2015 Eclipse
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Anthony R. Yeates↗
Analysis of superconducting electromagnetic finite elements based on a magnetic vector potential variational principle
Electromagnetic finite elements are extended based on a variational principle that uses the electromagnetic four potential as primary variable. The variational principle is extended to include the ability to predict a nonlinear current distribution within a conductor. The extension of this theory is first done on a normal conductor and tested on two different problems. In both problems, the geometry remains the same, but the material properties are different. The geometry is that of a 1-D infinite wire. The first problem is merely a linear control case used to validate the new theory. The second problem is made up of linear conductors with varying conductivities. Both problems perform well and predict current densities that are accurate to within a few ten thousandths of a percent of the exact values. The fourth potential is then removed, leaving only the magnetic vector potential, and the variational principle is further extended to predict magnetic potentials, magnetic fields, the number of charge carriers, and the current densities within a superconductor. The new element produces good results for the mean magnetic field, the vector potential, and the number of superconducting charge carriers despite a relatively high system condition number. The element did not perform well in predicting the current density. Numerical problems inherent to this formulation are explored and possible remedies to produce better current predicting finite elements are presented.
Schuler, James J.↗
Extra high speed modified Lundell alternator parameters and open/short-circuit characteristics from global 3D-FE magnetic field solutions
The combined magnetic vector potential - magnetic scalar potential method of computation of 3D magnetic fields by finite elements, introduced in a companion paper, is used for global 3D field analysis and machine performance computations under open-circuit and short-circuit conditions for an example 14.3 kVA modified Lundell alternator, whose magnetic field is of intrinsic 3D nature. The computed voltages and currents under these machine test conditions were verified and found to be in very good agreement with corresponding test data. Results of use of this modelling and computation method in the study of a design alteration example, in which the stator stack length of the example alternator is stretched in order to increase voltage and volt-ampere rating, are given here. These results demonstrate the inadequacy of conventional 2D-based design concepts and the imperative of use of this type of 3D magnetic field modelling in the design and investigation of such machines.
Wang, R.↗
Computation of load performance and other parameters of extra high speed modified Lundell alternators from 3D-FE magnetic field solutions
The combined magnetic vector potential - magnetic scalar potential method of computation of 3D magnetic fields by finite elements, introduced in a companion paper, in combination with state modeling in the abc-frame of reference, are used for global 3D magnetic field analysis and machine performance computation under rated load and overload condition in an example 14.3 kVA modified Lundell alternator. The results vividly demonstrate the 3D nature of the magnetic field in such machines, and show how this model can be used as an excellent tool for computation of flux density distributions, armature current and voltage waveform profiles and harmonic contents, as well as computation of torque profiles and ripples. Use of the model in gaining insight into locations of regions in the magnetic circuit with heavy degrees of saturation is demonstrated. Experimental results which correlate well with the simulations of the load case are given.
Wang, R.↗
Magnetic Field Solver
The Magnetic Field Solver computer program calculates the magnetic field generated by a group of collinear, cylindrical axisymmetric electromagnet coils. Given the current flowing in, and the number of turns, axial position, and axial and radial dimensions of each coil, the program calculates matrix coefficients for a finite-difference system of equations that approximates a two-dimensional partial differential equation for the magnetic potential contributed by the coil. The program iteratively solves these finite-difference equations by use of the modified incomplete Cholesky preconditioned-conjugate-gradient method. The total magnetic potential as a function of axial (z) and radial (r) position is then calculated as a sum of the magnetic potentials of the individual coils, using a high-accuracy interpolation scheme. Then the r and z components of the magnetic field as functions of r and z are calculated from the total magnetic potential by use of a high-accuracy finite-difference scheme. Notably, for the finite-difference calculations, the program generates nonuniform two-dimensional computational meshes from nonuniform one-dimensional meshes. Each mesh is generated in such a way as to minimize the numerical error for a benchmark one-dimensional magnetostatic problem.
Ilin, Andrew V.↗
Lunar and Planetary Science XXXV: Mars Geophysics
The titles in this section include: 1) Distribution of Large Visible and Buried Impact Basins on Mars: Comparison with Free-Air Gravity, Crustal Thickness, and Magnetization Models; 2) The Early Thermal and Magnetic State of Terra Cimmeria, Southern Highlands of Mars; 3) Compatible Vector Components of the Magnetic Field of the Martian Crust; 4) Vertical Extrapolation of Mars Magnetic Potentials; 5) Rock Magnetic Fields Shield the Surface of Mars from Harmful Radiation; 6) Loading-induced Stresses near the Martian Hemispheric Dichotomy Boundary; 7) Growth of the Hemispheric Dichotomy and the Cessation of Plate Tectonics on Mars; 8) A Look at the Interior of Mars; 9) Uncertainties on Mars Interior Parameters Deduced from Orientation Parameters Using Different Radio-Links: Analytical Simulations; 10) Refinement of Phobos Ephemeris Using Mars Orbiter Laser Altimetry Radiometry.
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