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Determining the three-dimensional magnetostatic field in current-induced situations has usually involved vector potentials, which can lead to excessive computational times. How such magnetic fields may be determined using scalar potentials is reviewed. It is shown how the heat transfer capability of NASTRAN level 17 was modified to take advantage of the new method.
Cerenkov radiation from charge spiralling in warm plasma under action of infinite magnetostatic field
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.
Magnetostatic sunspot model with twisted field showing radial dependence of azimuthal component
Some ideas in the theoretical study of force-free magnetic fields and magnetostatic fields, which are relevant to the effort of using magnetograph data as inputs to model the quasi-static, large-scale magnetic structures in the solar atmosphere are discussed. Basic physical principles will be emphasized. An attempt will be made to assess what we may learn, physically, from the models based on these ideas. There is prospect for learning useful physics and this ought to be an incentive for intensifying the efforts to improve vector magnetograph technology and to solve the basic radiative-transfer problems encountered in the interpretation of magnetograph raw data.
Electron beam compression with electrostatic and magnetostatic fields
A method of combined use of magnetic vector potential based finite-element (FE) formulations and magnetic scalar potential (MSP) based formulations for computation of three-dimensional magnetostatic fields is introduced. In this method, the curl-component of the magnetic field intensity is computed by a reduced magnetic vector potential. This field intensity forms the basic of a forcing function for a global magnetic scalar potential solution over the entire volume of the region. This method allows one to include iron portions sandwiched in between conductors within partitioned current-carrying subregions. The method is most suited for large-scale global-type 3-D magnetostatic field computations in electrical devices, and in particular rotating electric machinery.
Magnetic nozzles are used in many laboratory experiments in which plasma flows are to be confined, cooled. accelerated, or directed. At present, however, there is no generally accepted theoretical description that explains the phenomena of plasma detachment from an externally-imposed magnetic field. This is an important problem in the field of plasma propulsion, where the ionized gas must detach from the applied, solenoidal magnetic field to realize thrust production. In this paper we simulate a plasma flowing in the presence of an applied magnetic field using a multidimensional numerical simulation tool that includes theoretical models of the various dispersive and dissipative processes present in the plasma. This is an extension of the simulation tool employed in previous work by Sankaran et al. The new tool employs the same formulation of the governing equation set. but retains the axial and radial components of magnetic field and the azimuthal component of velocity that were neglected in other works. We aim to compare the computational results with the various proposed magnetic nozzle detachment theories to develop an understanding of the physical mechanisms that cause detachment. An applied magnetic field topology is obtained using a magnetostatic field solver and this field is superimposed on the time-dependent magnetic field induced in the plasma to provide a self-consistent field description. The applied magnetic field and model geometry match those found in experiments by Kurtki and Okada. We model this geometry because there ts a substantial amount of experimental data that can be compared to our computations, allowing for validation of the model. In addition, comparison of the simulation results with the experimentally obtained plasma parameters will provide insight into the mechanisms that lead to plasma detachment, revealing how the 3 scale with different input parameters.
At present there exists no generally accepted theoretical model that provides a consistent physical explanation of plasma detachment from an externally-imposed magnetic nozzle. To make progress towards that end, simulation of plasma flow in the magnetic nozzle of an arcjet experiment is performed using a multidimensional numerical simulation tool that includes theoretical models of the various dispersive and dissipative processes present in the plasma. This is an extension of the simulation tool employed in previous work by Sankaran et al. The aim is to compare the computational results with various proposed magnetic nozzle detachment theories to develop an understanding of the physical mechanisms that cause detachment. An applied magnetic field topology is obtained using a magnetostatic field solver (see Fig. I), and this field is superimposed on the time-dependent magnetic field induced in the plasma to provide a self-consistent field description. The applied magnetic field and model geometry match those found in experiments by Kuriki and Okada. This geometry is modeled because there is a substantial amount of experimental data that can be compared to the computational results, allowing for validation of the model. In addition, comparison of the simulation results with the experimentally obtained plasma parameters will provide insight into the mechanisms that lead to plasma detachment, revealing how they scale with different input parameters. Further studies will focus on modeling literature experiments both for the purpose of additional code validation and to extract physical insight regarding the mechanisms driving detachment.
Magnetic nozzles are used in many laboratory experiments in which plasma flows are to be confined, cooled, accelerated, or directed. At present, however, there is no generally accepted theoretical description that explains the phenomena of plasma expansion in and detachment from an externally-imposed magnetic field. The latter is an especially important problem in the field of plasma propulsion, where the ionized gas must detach from the applied, solenoidal magnetic field to realize thrust production. In this paper we simulate a plasma flowing in the presence of an applied magnetic field using a multidimensional numerical simulation tool that includes theoretical models of the various dispersive and dissipative processes present in the plasma. This is an extension of the simulation tool employed in previous work by Sankaran et al. The new tool employs the same formulation of the governing equation set, but retains the axial and radial components of magnetic field and the azimuthal component of velocity that were neglected. We aim to compare the computational results with the various proposed magnetic nozzle detachment theories to develop an understanding of the physical mechanisms that cause detachment. An applied magnetic field topology is obtained using a magnetostatic field solver, and this field is superimposed on the time-dependent magnetic field induced in the plasma to provide a self-consistent field description. The applied magnetic field and model geometry match those found in experiments by Kuriki and Okada. 4 A schematic showing the setup used in those experiments is shown. We model this geometry because there is a substantial amount of experimental data that can be compared to our computations, allowing for validation of the model. In addition, comparison of the simulation results with the experimentally obtained plasma parameters will provide insight into the mechanisms that lead to plasma detachment, revealing how they scale with different input parameters.
This paper develops the optical analogy for a general vector field. The optical analogy allows the examination of certain aspects of a vector field that are not otherwise readily accessible. In particular, in the cases of a stationary Eulerian flow v of an ideal fluid and a magnetostatic field B, the vectors v and B have surface loci in common with their curls. The intrinsic discontinuities around local maxima in absolute values of v and B take the form of vortex sheets and current sheets, respectively, the former playing a fundamental role in the development of hydrodyamic turbulence and the latter playing a major role in heating the X-ray coronas of stars and galaxies.
A method of combined use of magnetic vector potential (MVP) based finite element (FE) formulations and magnetic scalar potential (MSP) based FE formulations for computation of three-dimensional (3D) magnetostatic fields is developed. This combined MVP-MSP 3D-FE method leads to considerable reduction by nearly a factor of 3 in the number of unknowns in comparison to the number of unknowns which must be computed in global MVP based FE solutions. This method allows one to incorporate portions of iron cores sandwiched in between coils (conductors) in current-carrying regions. Thus, it greatly simplifies the geometries of current carrying regions (in comparison with the exclusive MSP based methods) in electric machinery applications. A unique feature of this approach is that the global MSP solution is single valued in nature, that is, no branch cut is needed. This is again a superiority over the exclusive MSP based methods. A Newton-Raphson procedure with a concept of an adaptive relaxation factor was developed and successfully used in solving the 3D-FE problem with magnetic material anisotropy and nonlinearity. Accordingly, this combined MVP-MSP 3D-FE method is most suited for solution of large scale global type magnetic field computations in rotating electric machinery with very complex magnetic circuit geometries, as well as nonlinear and anisotropic material properties.
This paper describes the results of application of three well known 3D magnetic vector potential (MVP) based finite element formulations for computation of magnetostatic fields in electrical devices. The three methods were identically applied to three practical examples, the first of which contains only one medium (free space), while the second and third examples contained a mix of free space and iron. The first of these methods is based on the unconstrained curl-curl of the MVP, while the second and third methods are predicated upon constraining the divergence of the MVP 10 zero (Coulomb's Gauge). It was found that the two latter methods cease to give useful and meaningful results when the global solution region contains a mix of media of high and low permeabilities. Furthermore, it was found that their results do not achieve the intended zero constraint on the divergence of the MVP.
A document discusses polymer nano - composite superparamagnetic actuators that were prepared by the addition of organically modified superparamagnetic nanoparticles to the polymer matrix. The nanocomposite films exhibited large deformations under a magnetostatic field with a low loading level of 0.1 wt% in a thermoplastic polyurethane elastomer (TPU) matrix. The maximum actuation deformation of the nanocomposite films increased exponentially with increasing nanoparticle concentration. The cyclic deformation actuation of a high-loading magnetic nanocomposite film was examined in a low magnetic field, and it exhibited excellent reproducibility and controllability. Low-loading TPU nanocomposite films (0.1-2 wt%) were transparent to semitransparent in the visible wavelength range, owing to good dispersion of the magnetic nanoparticles. Magnetoactuation phenomena were also demonstrated in a high-modulus, high-temperature polyimide resin with less mechanical deformation.
Nonaccelerated electron beam envelope trajectory equation reformulated and solved allowing for finite emittance, space charge and self- magnetostatic forces
A special class of magnetostatic equilibria is described, which are mathematically simple and yet sufficiently versatile so as to fit any arbitrary normal magnetic flux prescribed at the photosphere. With these solutions, the corona can be modeled with precisely the same mathematically simple procedure as has previously been done with potential fields. The magnetostatic model predicts, in addition to the coronal magnetic field, the three dimensional coronal density which can be compared with coronagraph observations.
Theoretical transit time of magnetostatic spin waves propagated at microwave frequencies in normally magnetized disk
Magnetostatic model for perpendicular anisotropy in polycrystalline nickel-iron thin films