FIELD OF AN ALTERNATING MAGNETIC DIPOLE ON THE SURFACE OF A LAYERED EARTH

Geophysics ◽  
1959 ◽  
Vol 24 (1) ◽  
pp. 77-88 ◽  
Author(s):  
Louis B. Slichter ◽  
Leon Knopoff
Keyword(s):  
Magnetic Field ◽  
Layer Thickness ◽  
Magnetic Dipole ◽  
Layered Earth ◽  
Induced Field ◽  
Conductivity Parameter ◽  
The Magnetic Field

The magnetic field near a vertical alternating magnetic dipole on the surface of a layered earth is computed for points on the surface. In the layer the dimensionless conductivity parameter is assumed to take the values 0, [Formula: see text], 1, and 4; in the homogeneous substratum, this parameter is assigned the values 0, [Formula: see text], 1, 4, and infinity. The induced field is computed at distances from the source [Formula: see text], 1, 2, 4, 8, and 16 times the layer thickness.

INDUCTIVE SOUNDING OF A LAYERED EARTH WITH A HORIZONTAL MAGNETIC DIPOLE

Geophysics ◽  
1970 ◽  
Vol 35 (4) ◽  
pp. 660-703 ◽  
Author(s):  
Abhijit Dey ◽  
Stanley H. Ward
Keyword(s):  
Magnetic Field ◽  
Magnetic Dipole ◽  
Complete Solution ◽  
Vertical Component ◽  
Static Approximation ◽  
Phase Measurements ◽  
Layered Earth ◽  
Electric And Magnetic Fields ◽  
Earth Structures ◽  
The Magnetic Field

A complete solution of the boundary value problem of a horizontal magnetic dipole over homogeneous and n‐layered half‐spaces is outlined. Quasi‐static expressions for the electric and magnetic fields have been obtained and a comparison of the complete solution with the quasi‐static approximation in practical frequency ranges is made. An analysis of the phases and amplitudes of the magnetic field components and of the polarization parameters of the magnetic field reveals that the phase of the vertical component of the magnetic field and the ellipticity of the magnetic field polarization ellipse are the most sensitive indicators of layering. Amplitude measurements are, in general, less effective than phase measurements for resolution of layered earth structures. Results from both parametric and geometric modes of sounding have been studied in detail for a number of two‐ and three‐layered models of varying thicknesses and conductivity contrasts. Deduction of layering for different thicknesses of the top layer from the measurements of [Formula: see text] and polarization parameters, seems relatively easier when the underlying layer is more conductive than the top layer. For models in which the underlying layer is less conductive than the top layer, the phases of both [Formula: see text] and wave tilt are more diagnostic of changes in layer parameters.

scholarly journals Magnetohydrodynamic simulations of a Uranus-at-equinox type rotating magnetosphere

2020 ◽  
Vol 633 ◽  
pp. A87 ◽  
Author(s):  
L. Griton ◽  
F. Pantellini
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Supersonic Flow ◽  
Magnetic Dipole ◽  
Stellar Wind ◽  
Rotation Axis ◽  
Spin Axis ◽  
Mhd Equations ◽  
Field Lines ◽  
The Magnetic Field

Context. As proven by measurements at Uranus and Neptune, the magnetic dipole axis and planetary spin axis can be off by a large angle exceeding 45°. The magnetosphere of such an (exo-)planet is highly variable over a one-day period and it does potentially exhibit a complex magnetic tail structure. The dynamics and shape of rotating magnetospheres do obviously depend on the planet’s characteristics but also, and very substantially, on the orientation of the planetary spin axis with respect to the impinging, generally highly supersonic, stellar wind. Aims. On its orbit around the Sun, the orientation of Uranus’ spin axis with respect to the solar wind changes from quasi-perpendicular (solstice) to quasi-parallel (equinox). In this paper, we simulate the magnetosphere of a fictitious Uranus-like planet plunged in a supersonic plasma (the stellar wind) at equinox. A simulation with zero wind velocity is also presented in order to help disentangle the effects of the rotation from the effects of the supersonic wind in the structuring of the planetary magnetic tail. Methods. The ideal magnetohydrodynamic (MHD) equations in conservative form are integrated on a structured spherical grid using the Message-Passing Interface-Adaptive Mesh Refinement Versatile Advection Code (MPI-AMRVAC). In order to limit diffusivity at grid level, we used background and residual decomposition of the magnetic field. The magnetic field is thus made of the sum of a prescribed time-dependent background field B0(t) and a residual field B1(t) computed by the code. In our simulations, B0(t) is essentially made of a rigidly rotating potential dipole field. Results. The first simulation shows that, while plunged in a non-magnetised plasma, a magnetic dipole rotating about an axis oriented at 90° with respect to itself does naturally accelerate the plasma away from the dipole around the rotation axis. The acceleration occurs over a spatial scale of the order of the Alfvénic co-rotation scale r*. During the acceleration, the dipole lines become stretched and twisted. The observed asymptotic fluid velocities are of the order of the phase speed of the fast MHD mode. In two simulations where the surrounding non-magnetised plasma was chosen to move at supersonic speed perpendicularly to the rotation axis (a situation that is reminiscent of Uranus in the solar wind at equinox), the lines of each hemisphere are symmetrically twisted and stretched as before. However, they are also bent by the supersonic flow, thus forming a magnetic tail of interlaced field lines of opposite polarity. Similarly to the case with no wind, the interlaced field lines and the attached plasma are accelerated by the rotation and also by the transfer of kinetic energy flux from the surrounding supersonic flow. The tailwards fluid velocity increases asymptotically towards the externally imposed flow velocity, or wind. In one more simulation, a transverse magnetic field, to both the spin axis and flow direction, was added to the impinging flow so that magnetic reconnection could occur between the dipole anchored field lines and the impinging field lines. No major difference with respect to the no-magnetised flow case is observed, except that the tailwards acceleration occurs in two steps and is slightly more efficient. In order to emphasise the effect of rotation, we only address the case of a fast-rotating planet where the co-rotation scale r* is of the order of the planetary counter-flow magnetopause stand-off distance rm. For Uranus, r*≫ rm and the effects of rotation are only visible at large tailwards distances r ≫ rm.

scholarly journals He-Abnormal Stars

1993 ◽  
Vol 138 ◽  
pp. 394-404 ◽  
Author(s):  
Kurt Hunger ◽  
Detlev Groote
Keyword(s):  
Magnetic Field ◽  
Magnetic Dipole ◽  
Stellar Wind ◽  
Effective Magnetic Field ◽  
Physical Conditions ◽  
Phase Variations ◽  
Axes Of Symmetry ◽  
The Magnetic Field

AbstractThe He-rich variable HD 37479 has 2 axes of symmetry, one characterized by the depletion of metals, and one by the enrichment of He. The former is oriented along the axis of the magnetic dipole, while the latter is off set by some 45°. The 2 axes represent 2 different modes of diffusion, the first one being controlled solely by the magnetic field, irrespective of wind, the second one being due to stellar wind that is controlled by the magnetic field and intertial forces. It has been attempted to formulate simple physical conditions that allow to determine the diffusion regions on the surface. It is shown that the resulting surface map can well reproduce the observed phase variations of the equivalent widths of HeI 4471, of UV resonance lines of C IV and Si IV, and the effective magnetic field.

The effect of a strongly stratified layer in the upper part of Mercury’s core on its magnetic field

2020 ◽  
Author(s):  
Patrick Kolhey ◽  
Daniel Heyner ◽  
Johannes Wicht ◽  
Karl-Heinz Glassmeier
Keyword(s):  
Magnetic Field ◽  
Dipole Moment ◽  
Magnetic Dipole ◽  
Magnetic Dipole Moment ◽  
Rotation Axis ◽  
Outer Core ◽  
Magnetic Field Generation ◽  
Fluid Core ◽  
Planetary Magnetic Fields ◽  
The Magnetic Field

<p>In the 1970’s the flybys of NASA’s Mariner 10 spacecraft confirmed the existence of an internally generated magnetic field at Mercury. The measurements taken during its flybys already revealed, that Mercury‘s magnetic field is unique along other planetary magnetic fields, since the magnetic dipole moment of ~190 nT ∙ R<sub>M</sub><sup>3 </sup>is very weak, e.g. compared to Earth’s magnetic dipole moment. The following MESSENGER mission from NASA investigated Mercury and its magnetic field more precisely and exposed additional interesting properties about the planet’s magnetic field. The tilt of its dipole component is less than 1°, which indicates a strong alignment of the field along the planet’s rotation axis. Additionally the measurement showed that the magnetic field equator is shifted roughly 0.2 ∙ R<sub>M</sub> towards north compared to Mercury‘s actual geographic equator.</p><p>Since its discovery Mercury‘s magnetic field has puzzled the community and modelling the dynamo process inside the planet’s interior is still a challenging task. Adapting the typical control parameters and the geometry in the models of the geodynamo for Mercury does not lead to the observed field morphology and strength. Therefore new non-Earth-like models were developed over the past decades trying to match Mercury’s peculiar magnetic field. One promising model suggests a stably stratified layer on the upper part of Mercury’s core. Such a layer divides the fluid core in a convecting part and a non-convecting part, where the magnetic field generation is mainly inhibited. As a consequence the magnetic field inside the outer core is damped very efficiently passing through the stably stratified layer by a so-called skin effect. Additionally, the non-axisymmetric parts of the magnetic field are vanishing, too, such that a dipole dominated magnetic is left at the planet’s surface.</p><p>In this study we present new direct numerical simulations of the magnetohydrodynamical dynamo problem which include a stably stratified layer on top of the outer core. We explore a wide parameter range, varying mainly the Rayleigh and Ekman number in the model under the aspect of a strong stratification of the stable layer. We show which conditions are necessary to produce a Mercury-like magnetic field and give a inside about the planets interior structure.</p>

Simulation Research on the Magnetic Field of the Positioning Permanent Magnet for MEMS inside Human Body Based on Ansoft

2014 ◽  
Vol 596 ◽  
pp. 67-71
Author(s):  
Xiu Quan Liu ◽  
Yan Hong Li
Keyword(s):  
Magnetic Field ◽  
Permanent Magnet ◽  
Magnetic Dipole ◽  
Human Body ◽  
Magnetic Induction ◽  
Dipole Model ◽  
Magnetization Direction ◽  
Simulation Research ◽  
Magnetic Induction Intensity ◽  
The Magnetic Field

the magnetic dipole model of the cylindrical permanent magnet was introduced. Then, based on Ansoft software, the simulation model of the cylindrical permanent magnet was established, and the influence of some parameters, such as the height, radius and magnetization direction on the magnetic induction intensity ,were studied; at the same time, under these two models the calculation was compared, the result shows the the magnetic dipole model is applied on condition that distance is nine times greater than the cylindrical permanent magnet size.

scholarly journals Scattering of Fermions by a Magnetic Dipole Field

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sergiu Hategan ◽  
Cosmin Crucean
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Differential Cross Section ◽  
Magnetic Dipole ◽  
Cross Section ◽  
Differential Cross ◽  
Coulomb Scattering ◽  
Minkowski Space Time ◽  
Magnetic Dipole Field ◽  
The Magnetic Field

Abstract In this paper we study the problem of fermions scattering by the field of a magnetic dipole in Minkowski space-time. The amplitude and differential cross section for scattering of massive fermions are obtained using the exact solution of the Dirac equation written in the helicity basis. We found that the most probable transitions are those that scatter the fermions perpendicular to the direction of the magnetic field and we consider only the transverse momenta in our analysis. The differential cross section behavior in terms of scattering angle and energy is graphically analysed and we perform a comparative study with the Coulomb scattering.

Magnetosphere of Hot Jupiter HD209458b and transit absorption in lines related to the upper atmosphere

2021 ◽  
Author(s):  
Ildar Shaikhislamov ◽  
Maxim Khodachenko ◽  
Ilya Miroshnichenko ◽  
Marina Rumenskikh ◽  
Artem Berezutsky
Keyword(s):  
Magnetic Field ◽  
Magnetic Dipole ◽  
Stellar Wind ◽  
Mass Loss Rate ◽  
Spectral Lines ◽  
Upper Atmosphere ◽  
Russian Science ◽  
Mhd Simulations ◽  
The Magnetic Field ◽  
Hot Jupiter

<p>Using the global 3D multi-fluid HD and its extension to MHD we simulated the measured HD209458b transit absorption depths at the FUV lines, and at the NIR line (10830 Å) of metastable helium HeI(2<sup>3</sup>S) triplet, paying attention to possible change of the absorption profiles due to the presence of planetary intrinsic magnetic field. As continuation of our previous studies of HD209458b (<em>Shaikhislamov et al. 2018, 2020</em>), the inclusion of the HeI(2<sup>3</sup>S) line into consideration and the comparison with corresponding measurements allows to constrain the helium abundance by He/H ~ 0.02, and stellar XUV flux at 1 a.u. by <em>F</em><sub>XUV </sub>~10 erg cm<sup>2</sup> s<sup>-1</sup> at 1 a.u. For the first time, we studied the influence of the planetary dipole magnetic field with a model which self-consistently describes the generation of the escaping upper atmospheric flow of a magnetized hot Jupiter, formation of magnetosphere and its interaction with the stellar wind. We simulated the absorption in the most of spectral lines for which measurements have been made. MHD simulations have shown that the planetary magnetic dipole moment µ<sub>P</sub> = 0.61 of the Jovian value, which produces the magnetic field equatorial surface value of 1 G, profoundly changes the character of the escaping planetary upper atmosphere. The total mass loss rate in this case is reduced by 2 times, as compared to the non-magnetized planet. In particular, we see the formation of the dead- and the wind- zones around the planet with the different character of plasma motion there. The 3D MHD modelling also confirmed the previous 2D MHD simulations result of <em>Khodachenko et al (2015) </em>that the escaping PW forms a thin magnetodisk in the equatorial region around the planet. The significantly reduced velocity of PW at the low altitudes around the planet, and especially at the night side, results in the stronger photo-ionization of species and significantly lower densities of the corresponding absorbing elements. Altogether, the reduced velocities and lower densities result in significant decrease of the absorption at Lyα (HI), OI, and CII lines, though the absorption at HeI(2<sup>3</sup>S) line remains nearly the same.</p> <p>As it was shown in our previous papers, the dense and fast stellar wind, interacting with the escaping upper atmosphere of HD209458b, generates sufficient amount of Energetic Neutral Atoms (ENAs) to produce significant absorption in the high-velocity blue wing of the Lyα line. However, according to the performed 3D MHD modelling reported here, the planetary magnetic dipole field with the equatorial surface value of B<sub>p</sub>=1 G prevents the formation of ENAs, especially in the trailing tail. This effect opens a possibility to constrain the range of planetary magnetic field values for the evaporating hot Jupiters and warm Neptunes in the stellar-planetary systems where sufficiently strong SW is expected.</p> <p>The presented results fitted to the available measurements indicate that the magnetic field of HD209458b should be at least an order of magnitude less than that of the Jupiter. This conclusion agrees with the previous estimates, based on more simplified models (e.g., <em>Kislyakova et al. 2014</em>) and much less observational data, when only Lyα absorption was considered. We believe that the application of 3D MHD models simulating the escape of upper atmospheres of hot exoplanets and the related transits at the available for measurement spectral lines, sensitive to the dynamics of planetary plasma affected by the MF, opens a way for probing and quantifying of exoplanetary magnetic fields and sheds more light on their nature.</p> <p>This work was supported by grant № 18-12-00080 of the Russian Science Foundation and grant № 075-15-2020-780 of the Russian Ministry of Education and Science.</p> <p> </p> <p>Khodachenko, M.L., Shaikhislamov, I.F., Lammer, H., et al., 2015, ApJ, 813, 50.</p> <p>Shaikhislamov, I. F., Khodachenko, M. L., Lammer, H., et al., 2018, ApJ, 866(1), 47.</p> <p>Shaikhislamov, I. F., Khodachenko, M. L., Lammer, et al., 2020, MNRAS, 491(3), 3435-3447</p>

The external and internal magnetic fields of Titan: Cassini observations

2020 ◽  
Author(s):  
Hanying Wei ◽  
Christopher Russell ◽  
Yingjuan Ma ◽  
Michele Dougherty
Keyword(s):  
Magnetic Field ◽  
Solar Wind Plasma ◽  
Internal Field ◽  
Lower Atmosphere ◽  
Field Pattern ◽  
Conductive Layer ◽  
Induced Field ◽  
External Sources ◽  
Field Lines ◽  
The Magnetic Field

<p>Titan has a thick atmosphere, the top of which is ionized and interacts with its plasma environment, i.e. usually the Saturnian magnetospheric plasma, but occasionally the magnetosheath or even the solar wind plasma. When the upstream plasma flow encounters Titan, the plasma slows down and diverts around Titan, and the magnetic field slowly diffuses into Titan’s ionosphere and induces currents in the ionosphere. The resulting magnetic field pattern is that, in the upstream of Titan, field lines drape around it, and in the downstream, the field lines stretch tail-like. Gradually these external fields penetrate into the lower atmosphere and the interior of Titan, and induce currents in any conductive layer if a conductive layer does indeed exist in Titan’s interior. This internally induced current acts to exclude the penetrated field. Both the internally induced field and the externally induced ionospheric field have strength and orientation variable with certain time scales because they are responses to the penetrated external field. The Cassini observations are a sum of fields from both internal and external sources. In this paper, we review the low altitude observations from all Cassini Titan flybys and examine the different behaviors of the external and internal fields, which ultimately provide an upper limit to Titan’s internal field leading to indications for Titan’s interior.</p>

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