Vector spherical harmonics and their application to magnetostatics

Barrera, Rubén G.; Estévez, Gentil A.; Giraldo, J

doi:10.1088/0143-0807/6/4/014

Cited by 179 publications

(159 citation statements)

References 7 publications

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“…The wave electric field inside the filament is obtained by substituting (31), (32), and (33) into the right-hand side of (27), and using (20) and (21) for the eikonal e ik.r . The Dirac delta functions simplify the integrals with respect to k ρ and k z .…”

Section: Electromagnetic Fields Inside the Filamentmentioning

confidence: 99%

“…Since the vector cylinder functions form a complete set [19,20], and are solutions of the vector Helmholtz equation, the electric field of the scattered wave can be written, in general, as a linear sum of the entire set of vector cylinder functions. Thus,…”

Section: Electric Fields Of the Scattered Wavesmentioning

confidence: 99%

“…However, they form a complete set [19,20] -a property that is important for constructing the electromagnetic fields of the scattered waves.…”

Section: Appendix B Vector Cylinder Functionsmentioning

confidence: 99%

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Scattering of radio frequency waves by cylindrical density filaments in tokamak plasmas

Ram

Hizanidis

2016

Physics of Plasmas

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In tokamak fusion plasmas, coherent fluctuations in the form of blobs or filaments are routinely observed in the scrape-off layer. Radio frequency (RF) electromagnetic waves, excited by antenna structures placed near the wall of a tokamak, have to propagate through the scrape-off layer before reaching the core of the plasma. While the effect of fluctuations on the properties of RF waves has not been quantified experimentally, it is of interest to carry out a theoretical study to determine if fluctuations can affect the propagation characteristics of RF waves. Usually, the difference between the plasma density inside the filament and the background plasma density is sizable; the ratio of the density difference to the background density being of order one. Generally, this precludes the use of geometrical optics in determining the effect of fluctuations since the relevant ratio has to be much less than one; typically, of the order of 10% or less. In this paper, a full-wave, analytical model is developed for the scattering of a RF plane wave by a cylindrical plasma filament. It is assumed that the plasma inside and outside the filament is cold and uniform, and that the major axis of the filament is aligned along the toroidal magnetic field. The ratio of the density inside the filament to the density of the background plasma is not restricted. The theoretical framework applies to the scattering of any cold plasma wave. In order to satisfy the boundary conditions at the interface between the filament and the background plasma, the electromagnetic fields inside and outside the filament need to have the same k ∥ , the wave vector parallel to the ambient magnetic field, as the incident plane wave. Consequently, in contrast to the scattering of a RF wave by a spherical blob [A. K. Ram, K. Hizanidis, and Y. Kominis, Phys. Plasmas 20, 056110-1-056110-10 (2013)], the scattering by a field-aligned filament does not broaden the k ∥ spectrum. However, the filament induces side-scattering leading to surface waves, and can also couple some power to the cold plasma wave different from the incident wave. The changes induced by a filament in the propagation of electron cyclotron waves and lower hybrid waves are illustrated by numerical results displaying the properties of the Poynting vector. The Poynting flux in the wake of the filament, and directed towards the core of the plasma, develops a spatial structure due to diffraction and shadowing. Thus, the fluctuations affect the uniformity of power flow into the plasma.

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Section: Electromagnetic Fields Inside the Filamentmentioning

confidence: 99%

Section: Electric Fields Of the Scattered Wavesmentioning

confidence: 99%

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Scattering of radio frequency waves by cylindrical density filaments in tokamak plasmas

Ram

Hizanidis

2016

Physics of Plasmas

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“…With vector fields on the 2-sphere, it is not consistent to expand the components of the vector separately in spherical harmonics [20], e.g.…”

Section: Eigenvalues and Eigenstates On The 2-spherementioning

confidence: 99%

Deconstruction of the Maldacena–Núñez compactification

Andrews

Dorey

2006

Nuclear Physics B

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We demonstrate a classical equivalence between the large-N limit of the Higgsed N = 1 * SUSY U (N ) Yang-Mills theory and the MaldacenaNúñez twisted compactification of a six dimensional gauge theory on a two-sphere. A direct comparison of the actions and spectra of the two theories reveals them to be identical. We also propose a gauge theory limit which should describe the corresponding spherical compactification of Little String Theory.

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“…On a unit sphere, the vector spherical harmonics Y lm , lm , and lm are forming a complete orthogonal basis [55], with …”

Section: Appendix A: Single Particlesmentioning

confidence: 99%

How to calculate the pole expansion of the optical scattering matrix from the resonant states

Weiß

Muljarov

2018

Phys. Rev. B

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We present a formulation for the pole expansion of the scattering matrix of open optical resonators, in which the pole contributions are expressed solely in terms of the resonant states, their wave numbers, and their electromagnetic fields. Particularly, our approach provides an accurate description of the optical scattering matrix without the requirement of a fit for the pole contributions, or the restriction to geometries, or systems with low Ohmic losses. Hence, it is possible to derive the analytic dependence of the scattering matrix on the wave number with low computational effort, which allows for avoiding the artificial frequency discretization of conventional frequency-domain solvers of Maxwell's equations and for finding the optical far-and near-field response based on the physically meaningful resonant states. This is demonstrated for three test systems, including a chiral arrangement of nanoantennas, for which we calculate the absorption and the circular dichroism.

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Vector spherical harmonics and their application to magnetostatics

Cited by 179 publications

References 7 publications

Scattering of radio frequency waves by cylindrical density filaments in tokamak plasmas

Scattering of radio frequency waves by cylindrical density filaments in tokamak plasmas

Deconstruction of the Maldacena–Núñez compactification

How to calculate the pole expansion of the optical scattering matrix from the resonant states

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