Equipotential transformation from multipole systems to dipole systems

1987 ◽  
Vol 414 (1847) ◽  
pp. 359-369
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Spherical Harmonic ◽  
Magnetic Moments ◽  
Numerical Comparison ◽  
Magnetic Dipoles ◽  
Planetary Magnetic Fields ◽  
Vector Sum ◽  
Planetary Magnetic Field ◽  
Good Agreement

The paper shows that a planetary magnetic field expressed in the conventional form of a spherical harmonic expanson can be completely represented by the vector sum of fields produced by a set of magnetic dipoles with different magnetic moments, tilted from the planetary spin axis and offset from the planetary centre by different amounts. For convenience, the transformation from multipole systems to dipole systems is restricted to that from multipoles up to octupole to five dipoles. The scalar equipotential transformation analytically results in 24 equations; these can be subsequently solved for the 24 adjustable parameters in dipole systems with the predetermined ‘main dipole’. The numerical comparison of the jovian magnetic field between the jovian O 4 and the five-dipole models reveals a very good agreement with the subtle details. It is obvious that this type of transformation would open up the simplest practical way to simulate planetary magnetic fields with the dipole patterns.

scholarly journals Planetary Magnetic Fields and Habitability in Super Earths

2018 ◽  
Vol 27 (1) ◽  
pp. 183-231 ◽  
Author(s):  
Pablo Cuartas-Restrepo
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Scaling Laws ◽  
Thermal Evolution ◽  
Solid Core ◽  
Direct Influence ◽  
Physical Processes ◽  
Planetary Magnetic Fields ◽  
Planetary Magnetic Field ◽  
Planetary Dynamos

Abstract This work seeks to summarize some special aspects of a type of exoplanets known as super-Earths (SE), and the direct influence of these aspects in their habitability. Physical processes like the internal thermal evolution and the generation of a protective Planetary Magnetic Field (PMF) are directly related with habitability. Other aspects such as rotation and the formation of a solid core are fundamental when analyzing the possibilities that a SE would have to be habitable. This work analyzes the fundamental theoretical aspects on which the models of thermal evolution and the scaling laws of the planetary dynamos are based. These theoretical aspects allow to develop models of the magnetic evolution of the planets and the role played by the PMF in the protection of the atmosphere and the habitability of the planet.

scholarly journals On the influence of magnetic fields in neutral planetary wakes

2016 ◽  
Vol 12 (S328) ◽  
pp. 192-197
Author(s):  
C. Villarreal D’Angelo ◽  
M. Schneiter ◽  
A. Esquivel
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Radiation Pressure ◽  
Stellar Wind ◽  
Magnetic Moments ◽  
Radiative Processes ◽  
Planetary Magnetic Fields ◽  
Stellar Magnetic Fields

AbstractWe present a 3D magnetohydrodynamic study of the effect that stellar and planetary magnetic fields have on the calculated Lyα absorption during the planetary transit, employing parameters that resemble the exoplanet HD209458b. We assume a dipolar magnetic field for both the star and the planet, and use the Parker solution to initialize the stellar wind. We also consider the radiative processes and the radiation pressure.We use the numerical MHD code Guacho to run several models varying the values of the planetary and stellar magnetic moments within the range reported in the literature.We found that the presence of magnetic fields influences the escaping neutral planetary material spreading the absorption Lyα line for large stellar magnetic fields.

scholarly journals PLANETARY MAGNETIC FIELD AND GRAVITY IN THE SOLAR SYSTEM

2017 ◽  
Vol 5 (9) ◽  
pp. 145-151
Author(s):  
Samir A Hamouda ◽  
Eman A. Alsslam Alfadeel ◽  
Mohamed Belhasan Mohamed
Keyword(s):  
Magnetic Field ◽  
Solar System ◽  
Magnetic Fields ◽  
Difficult Problem ◽  
Planetary Scale ◽  
Scale Models ◽  
Planetary Magnetic Fields ◽  
Solar System Bodies ◽  
Planetary Magnetic Field ◽  
The Universe

Gravity plays a major role in the planetary formation and the development of the solar system. Gravity attraction is the essence of a power that holds and governs the universe; it makes the planets in the solar system revolve around the sun and the moons around their planets. Magnetic fields are also an important phenomenon in the solar system and beyond. Their causes are complex and have a variety of effects on their surroundings; they have become a critical tool for the exploration of solar system bodies. However, the study of the mechanisms of planets formation in the solar system is a difficult problem made more so by the inability to construct planetary-scale models for laboratory study. However, understanding the nature of the matter comprising the Solar System is crucial for understanding the mechanism that generates planetary magnetic fields and planetary gravity. In this study, a brief history about the development of planetary gravity is presented. Some data about the physical properties of planets in the solar system are presented and discussed. However, much work is still needed before the planetary gravity and planetary magnetic field processes are fully understood and full advantage be taken of the implications of both phenomena  observations.

Effect of Magnetic Fields on the Resistance and Microstructure of Al-Cu Alloy during Solidification Processing

2011 ◽  
Vol 287-290 ◽  
pp. 2916-2920
Author(s):  
Chun Yan Ban ◽  
Peng Qian ◽  
Xu Zhang ◽  
Qi Xian Ba ◽  
Jian Zhong Cui
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Turning Points ◽  
Probe Method ◽  
Solidification Processing ◽  
Ac Magnetic Field ◽  
Dc Magnetic Field ◽  
Cu Alloy ◽  
The Difference ◽  
Good Agreement

The resistance of Al-21%Cu alloy under no magnetic field, DC magnetic field and AC magnetic field from liquid to solid was measured by a four-probe method. The difference of resistance versus temperature curves (R-T curves) was analyzed. It is found that the R-T curves of Al-21%Cu alloy are monotone decreasing and have two obvious turning points. Under DC magnetic field, the liquidus and solidus temperatures of the alloy both decrease, while under AC magnetic field, the liquidus and solidus temperatures both increase. There is a good agreement between the microstructure of quenching sample and R-T curves. The mechanism of the effect of magnetic fields was discussed.

scholarly journals Reducing the influence of interference of spacecraft magnetic field on magnetic measurements

2019 ◽  
Vol 18 (2) ◽  
pp. 33-40
Author(s):  
A. M. Beznyakov ◽  
I. S. Guriev ◽  
I. P. Ryzhova
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Support Systems ◽  
Magnetic Measurements ◽  
Magnetic Moments ◽  
Navigation Support

The article presents constructive ways of reducing the influence of magnetic interference from spacecraft, due to its own magnetic fields, on the on-board magnetic measurements, as well as reducing the resulting magnetic moments. Well-known methods of removing magnetometer sensors from the locations of the most powerful sources of magnetic fields of a spacecraft, in particular, using extendable booms, are considered. In addition, methods for reducing the influence of spacecraft self- magnetic fields on the onboard magnetometric navigation support systems using known closed and proposed hemispherical ferromagnetic shields are considered

Static magnetic fields in vacuum

2018 ◽  
Author(s):  
J. Pierrus
Keyword(s):  
Magnetic Field ◽  
Problem Solving ◽  
Magnetic Fields ◽  
Vector Potential ◽  
Scalar Potential ◽  
Multipole Expansion ◽  
Magnetic Vector Potential ◽  
Magnetic Dipoles ◽  
Static Magnetic Fields ◽  
The Magnetic Field

Wherever possible, an attempt has been made to structure this chapter along similar lines to Chapter 2 (its electrostatic counterpart). Maxwell’s magnetostatic equations are derived from Ampere’s experimental law of force. These results, along with the Biot–Savart law, are then used to determine the magnetic field B arising from various stationary current distributions. The magnetic vector potential A emerges naturally during our discussion, and it features prominently in questions throughout the remainder of this book. Also mentioned is the magnetic scalar potential. Although of lesser theoretical significance than the vector potential, the magnetic scalar potential can sometimes be an effective problem-solving device. Some examples of this are provided. This chapter concludes by making a multipole expansion of A and introducing the magnetic multipole moments of a bounded distribution of stationary currents. Several applications involving magnetic dipoles and magnetic quadrupoles are given.

scholarly journals Connecting magnetic fields from sub-galactic scale to clusters of galaxies and beyond with cosmological MHD simulations

2015 ◽  
Vol 11 (A29B) ◽  
pp. 699-699
Author(s):  
Klaus Dolag ◽  
Alexander M. Beck ◽  
Alexander Arth
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Heat Transport ◽  
Galaxy Clusters ◽  
Large Scale ◽  
High Redshift ◽  
Galactic Halos ◽  
Rotation Measure ◽  
The Magnetic Field ◽  
Good Agreement

AbstractUsing the MHD version of Gadget3 (Stasyszyn, Dolag & Beck 2013) and a model for the seeding of magnetic fields by supernovae (SN), we performed simulations of the evolution of the magnetic fields in galaxy clusters and study their effects on the heat transport within the intra cluster medium (ICM). This mechanism – where SN explosions during the assembly of galaxies provide magnetic seed fields – has been shown to reproduce the magnetic field in Milky Way-like galactic halos (Beck et al. 2013). The build up of the magnetic field at redshifts before z = 5 and the accordingly predicted rotation measure evolution are also in good agreement with current observations. Such magnetic fields present at high redshift are then transported out of the forming protogalaxies into the large-scale structure and pollute the ICM (in a similar fashion to metals transport). Here, complex velocity patterns, driven by the formation process of cosmic structures are further amplifying and distributing the magnetic fields. In galaxy clusters, the magnetic fields therefore get amplified to the observed μG level and produce the observed amplitude of rotation measures of several hundreds of rad/m2. We also demonstrate that heat conduction in such turbulent fields on average is equivalent to a suppression factor around 1/20th of the classical Spitzer value and in contrast to classical, isotropic heat transport leads to temperature structures within the ICM compatible with observations (Arth et al. 2014).

scholarly journals Mathematical foundation of Capon's method for planetary magnetic field analysis

2020 ◽  
Vol 9 (2) ◽  
pp. 471-481
Author(s):  
Simon Toepfer ◽  
Yasuhito Narita ◽  
Daniel Heyner ◽  
Patrick Kolhey ◽  
Uwe Motschmann
Keyword(s):  
Magnetic Field ◽  
Field Studies ◽  
Multipole Expansion ◽  
Minimum Variance ◽  
Field Analysis ◽  
Analysis Tool ◽  
Data Set ◽  
Magnetic Field Analysis ◽  
Planetary Magnetic Fields ◽  
Planetary Magnetic Field

Abstract. Minimum variance distortionless projection, the so-called Capon method, serves as a powerful and robust data analysis tool when working on various kinds of ill-posed inverse problems. The method has not only successfully been applied to multipoint wave and turbulence studies in the context of space plasma physics, but it is also currently being considered as a technique to perform the multipole expansion of planetary magnetic fields from a limited data set, such as Mercury's magnetic field analysis. The practical application and limits of the Capon method are discussed in a rigorous fashion by formulating its linear algebraic derivation in view of planetary magnetic field studies. Furthermore, the optimization of Capon's method by making use of diagonal loading is considered.

Performance Evaluation of an MR-Compatible Rotating Anode X-Ray Tube

2013 ◽  
Author(s):  
Mihye Shin ◽  
Prasheel Lillaney ◽  
Waldo Hinshaw ◽  
Rebecca Fahrig
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Magnetic Moments ◽  
X Ray ◽  
Close Proximity ◽  
Motor Design ◽  
Design Requirements ◽  
And Performance ◽  
The Magnetic Field ◽  
Lorentz Force Law

The key technical innovation needed for close proximity hybrid x-ray/MR (XMR) imaging systems is a new rotating anode x-ray tube motor that can operate in the presence of strong magnetic fields. In order for the new motor design to be optimized between conflicting design requirements, we implemented a numerical model for evaluating the dynamics of the motor. The model predicts the amount of produced torque, rotation speed, and time to accelerate based on the Lorentz force law; the motor is accelerated by the interaction between the magnetic moments of the motor wire loops and an external magnetic field. It also includes an empirical model of bearing friction and electromagnetic force from the magnetic field. Our proposed computational model is validated by experiments using several different magnitudes of external magnetic fields, which averagely shows an agreement within 0.5 % error during acceleration. We are using this model to improve the efficiency and performance of future iterations of the x-ray tube motor.

Capon’s method for planetary magnetic field analysis 

2021 ◽  
Author(s):  
Simon Töpfer ◽  
Yasuhito Narita ◽  
Daniel Heyner ◽  
Patrick Kolhey ◽  
Uwe Motschmann
Keyword(s):  
Magnetic Field ◽  
Field Studies ◽  
Multipole Expansion ◽  
Minimum Variance ◽  
Field Analysis ◽  
Analysis Tool ◽  
Data Set ◽  
Magnetic Field Analysis ◽  
Planetary Magnetic Fields ◽  
Planetary Magnetic Field

<p>Minimum variance distortionless projection, the so-called Capon method, serves as a powerful and robust data analysis tool when working on various kinds of ill-posed inverse problems. The method has not only successfully been applied to multipoint wave and turbulence studies in the context of seismics and space plasma physics, but it is also currently being considered as a technique to perform the multipole expansion of planetary magnetic fields from a limited data set, such as Mercury’s magnetic field analysis. The mathematical foundations and the practical application of the Capon method are discussed in a rigorous fashion by extending its linear algebraic derivation in view of planetary magnetic field studies. Furthermore, the optimization of Capon’s method by making use of diagonal loading is considered.</p>

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