On multipole expansions in the theory of electromagnetic radiation

Bouwkamp, C.J.; Casimir, H. B. G.

doi:10.1016/s0031-8914(54)80068-1

Cited by 111 publications

(65 citation statements)

References 4 publications

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“…2.2) ensure that the surface current vanishes. The magnetic field at the stellar surface is therefore uniquely determined by its radial component Br (Bouwkamp & Casimir 1954), which satisfies…”

Section: Magnetic Dipole Momentmentioning

confidence: 99%

Gravitational radiation from neutron stars deformed by crustal Hall drift

Suvorov

Mastrano

Geppert

2016

Mon. Not. R. Astron. Soc.

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A precondition for the radio emission of pulsars is the existence of strong, small-scale magnetic field structures ('magnetic spots') in the polar cap region. Their creation can proceed via crustal Hall drift out of two qualitatively and quantitatively different initial magnetic field configurations: a field confined completely to the crust and another which penetrates the whole star. The aim of this study is to explore whether these magnetic structures in the crust can deform the star sufficiently to make it an observable source of gravitational waves. We model the evolution of these field configurations, which can develop, within ∼ 10 4 -10 5 yr, magnetic spots with local surface field strengths ∼ 10 14 G maintained over 10 6 yr. Deformations caused by the magnetic forces are calculated. We show that, under favourable initial conditions, a star undergoing crustal Hall drift can have ellipticity ∼ 10 −6 , even with sub-magnetar polar field strengths, after ∼ 10 5 yr. A pulsar rotating at ∼ 10 2 Hz with such is a promising gravitational-wave source candidate. Since such large deformations can be caused only by a particular magnetic field configuration that penetrates the whole star and whose maximum magnetic energy is concentrated in the outer core region, gravitational wave emission observed from radio pulsars can thus inform us about the internal field structures of young neutron stars.

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Section: Magnetic Dipole Momentmentioning

confidence: 99%

Gravitational radiation from neutron stars deformed by crustal Hall drift

Suvorov

Mastrano

Geppert

2016

Mon. Not. R. Astron. Soc.

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“…The integration path is chosen so as to take into account both the homogeneous and inhomogeneous (imaginary values of α) plane waves that propagate back to the glass surface. In addition to the angular spectrum representation, it is also convenient to multipole-expand the fields [34] when solving the Mie scattering problem at each iteration. Each plane-wave component is written in terms of electric ( E ) and magnetic ( M ) Debye potentials:…”

Section: General Formalismmentioning

confidence: 99%

Theory of optical-tweezers forces near a plane interface

et al. 2016

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Optical-tweezers experiments in molecular and cell biology often take place near the surface of the microscope slide that defines the bottom of the sample chamber. There, as elsewhere, force measurements require forcecalibrated tweezers. In bulk, one can calculate the tweezers force from first principles, as recently demonstrated. Near the surface of the microscope slide, this absolute calibration method fails because it does not account for reverberations from the slide of the laser beam scattered by the trapped microsphere. Nor does it account for evanescent waves arising from total internal reflection of wide-angle components of the strongly focused beam. In the present work we account for both of these phenomena. We employ Weyl's angular spectrum representation of spherical waves in terms of real and complex rays and derive a fast-converging recursive series of multiple reflections that describes the reverberations, including also evanescent waves. Numerical simulations for typical setup parameters evaluate these effects on the optical force and trap stiffness, with emphasis on axial trapping. Results are in good agreement with available experimental data. Thus, absolute calibration now applies to all situations encountered in practice.

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“…Similar operator relations in three dimensions have also been discussed in [38][39][40]. Now the field in terms of the basis functions, also called the multipole field, can be expressed in operator form in terms of the function w 0 (ρ) as…”

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confidence: 79%

Heaviside Operational Rules Applicable to Electromagnetic Problems

Lindell¹

2000

PIER

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On multipole expansions in the theory of electromagnetic radiation

Cited by 111 publications

References 4 publications

Gravitational radiation from neutron stars deformed by crustal Hall drift

Gravitational radiation from neutron stars deformed by crustal Hall drift

Theory of optical-tweezers forces near a plane interface

Heaviside Operational Rules Applicable to Electromagnetic Problems

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