Quadrupolar contact fields: Theory and applications

Gray, C.G.; Karl, Gabriel; Novikov, V.A.

doi:10.1119/1.3138700

Cited by 9 publications

(13 citation statements)

References 35 publications

(23 reference statements)

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“…40 ͒ For example, the path of the electrostatic field lines for a linear quadrupole in spherical coordinates, can be found in Appendix A of Ref. 37. For the electrostatic case it is much more common for the path of the field lines to be determined in Cartesian coordinates.…”

Section: Discussionmentioning

confidence: 99%

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Equation of the field lines of an axisymmetric multipole with a source surface

Gregory

2011

American Journal of Physics

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Optical spectropolarimeters can be used to produce maps of the surface magnetic fields of stars and hence to determine how stellar magnetic fields vary with stellar mass, rotation rate, and evolutionary stage. In particular, we now can map the surface magnetic fields of forming solar-like stars, which are still contracting under gravity and are surrounded by a disk of gas and dust. Their large scale magnetic fields are almost dipolar on some stars, and there is evidence for many higher order multipole field components on other stars. The availability of new data has renewed interest in incorporating multipolar magnetic fields into models of stellar magnetospheres. I describe the basic properties of axial multipoles of arbitrary degree ᐉ and derive the equation of the field lines in spherical coordinates. The spherical magnetic field components that describe the global stellar field topology are obtained analytically assuming that currents can be neglected in the region exterior to the star, and interior to some fixed spherical equipotential surface. The field components follow from the solution of Laplace's equation for the magnetostatic potential.

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Section: Discussionmentioning

confidence: 99%

“…16 Likewise, the equation for the field lines of a point electric linear multipole can be found in an analogous manner, see for example Appendix A of Ref. 37, either in spherical or Cartesian coordinates. 23,24 We substitute Eqs.…”

Section: Equation Of the Field Linesmentioning

confidence: 99%

Equation of the field lines of an axisymmetric multipole with a source surface

Gregory

2011

American Journal of Physics

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“…A corresponding expression can be derived for the Cartesian form of the non-primitive multipole moment [87,89], and analogous spherical and Cartesian tensor formulae exist for the non-primitive electric multipole moments [87,88].…”

Section: Magnetostatic Expansionmentioning

confidence: 99%

“…The coefficients of contact field terms for ψ, χ and B involve the primitive magnetic multipole moments. An application of contact multipolar fields to lunar magnetism is described in reference [88]. The corresponding electrostatic multipolar contact fields [88], which can be derived using the electric scalar potential since ∇ × E = 0 in the source regions, are mentioned in §Appendix B.…”

Section: The Magnetic Field Componentsmentioning

confidence: 99%

The magnetic fields of forming solar-like stars

Gregory,

Jardine,

Gray

et al. 2010

Preprint

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Magnetic fields play a crucial role at all stages of the formation of low mass stars and planetary systems. In the final stages, in particular, they control the kinematics of in-falling gas from circumstellar discs, and the launching and collimation of spectacular outflows. The magnetic coupling with the disc is thought to influence the rotational evolution of the star, while magnetised stellar winds control the braking of more evolved stars and may influence the migration of planets. Magnetic reconnection events trigger energetic flares which irradiate circumstellar discs with high energy particles that influence the disc chemistry and set the initial conditions for planet formation. However, it is only in the past few years that the current generation of optical spectropolarimeters have allowed the magnetic fields of forming solar-like stars to be probed in unprecedented detail. In order to do justice to the recent extensive observational programs new theoretical models are being developed that incorporate magnetic fields with an observed degree of complexity. In this review we draw together disparate results from the classical electromagnetism, molecular physics/chemistry, and the geophysics literature, and demonstrate how they can be adapted to construct models of the large scale magnetospheres of stars and planets. We conclude by examining how the incorporation of multipolar magnetic fields into new theoretical models will drive future progress in the field through the elucidation of several observational conundrums.

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“…* While the electrical gradients refresh at a very high frequency (>2kHz), an effort can be made to visualize a single electronic rotation responsible for the eventual generation of the QMA's saddle field. 58 It is common practice to describe ionic trajectories in terms of vectors, by convention X and Y describe the ions location relative to the cross-section of the electrode array while Z represents the distance the ion has traveled down the length of the analyzer. To aid in the conceptualization of this electromagnetic phenomenon the X-Y and X-Z influences will be considered separately, also, an attempt will be made to separate the time-dependant (alternating) and time-independent (direct) electronic influences into their principal components.…”

Section: = �mentioning

confidence: 99%

High Resolution Mass Spectrometry (HRMS) Based Investigation of Small Molecule, Bioactive Secondary Metabolites as Probes in the Examination of Bacterial Resistance and Virulence

Scarborough¹

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The widespread availability of antimicrobial chemotherapeutics over the last half of the twentieth century has offered dramatic increases in life expectancy. Unfortunately, many pathogenic agents are exhibiting ever increasing resistance to many frontline antibiotics. New chemotherapeutic agents are urgently needed to combat this threat; this work seeks to illustrate applications in which mass spectrometric techniques may be applied to the investigation of novel, small molecule chemotherapeutics for the treatment of bacterial infections. Chapter 1 contains an introduction to mass spectrometry, as well as an overview of relevant chromatographic techniques. Chapter 2 introduces the bacterium F tularensis and M ulcerans and details the MS based investigation of their secreted virulence factors. Chapter 3 introduces a human pathogen of particular concern, M tuberculosis, and contains a detailed reporting on the MS based investigation of internally synthesized compounds for the treatment of latent Tb. vii TABLE OF CONTENTS CHAPTER 1. INTRODUCTION TO MASS SPECTROMETERY .

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Quadrupolar contact fields: Theory and applications

Cited by 9 publications

References 35 publications

Equation of the field lines of an axisymmetric multipole with a source surface

Equation of the field lines of an axisymmetric multipole with a source surface

The magnetic fields of forming solar-like stars

High Resolution Mass Spectrometry (HRMS) Based Investigation of Small Molecule, Bioactive Secondary Metabolites as Probes in the Examination of Bacterial Resistance and Virulence

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