Electrostatic field of a thin, unclosed spherical shell and a torus

Шушкевич, Г. Ч.

doi:10.1134/1.1259067

Cited by 5 publications

(6 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Spatial distribution of a potential formed by a Paul trap is described by the solution of Dirichlet problem with boundary conditions [23]. Widely implemented model solution that describes the field distribution inside the trap is given by the following homogeneous second-order polynomial [24]: 0 .…”

Section: Calculation Of Elecrical Fieldmentioning

confidence: 99%

“…We consider a surface of the toroidal electrode as equipotential one, thus the following boundary conditions must be satisfied: Laplace equation in toroidal coordinate system has the following form [25]: After applying the standard separation of variables [23,25,26], the final solution reads: where P n−1/2 and Q n−1/2 are Legendre polynomials of the first and second kind, respectively. Now consider independently the field of the end-cap electrodes.…”

Section: Calculation Of Elecrical Fieldmentioning

confidence: 99%

See 1 more Smart Citation

Outside localization around a toroidal electrode of a Paul trap

et al. 2020

View full text Add to dashboard Cite

Here we describe and experimentally confirm the localization of charged microparticles outside the area of a radio-frequency Paul trap. We consider the nonlinear effective potential formed by the trap, treating the field independently for different electrodes of the trap. To approach the proposed model to reality, we also consider the nonlinear effects originating from the viscousity of surrounding medium. Proposed approach allows to conduct an analytical description of the effective potential and define quasi-equilibrium points both inside and outside the trap. Predictions of the proposed model are in full compliance with obtained experimental results.

show abstract

Section: Calculation Of Elecrical Fieldmentioning

confidence: 99%

Section: Calculation Of Elecrical Fieldmentioning

confidence: 99%

Outside localization around a toroidal electrode of a Paul trap

et al. 2020

View full text Add to dashboard Cite

show abstract

“…Both c m n (x) and s m n (x)/(x + 1)(x) are degree n polynomials in x. The corresponding integral expressions for Ψ mv n are given in operator form by applying (17) and (18) to the integral expression for Ψ mc 0 (14) and Ψ ms 1 (16). However, explicit evaluations of these derivatives do not appear to reveal any simple patterns.…”

Section: Toroidal Coordinates and Harmonicsmentioning

confidence: 99%

“…But the series relationships between spherical and toroidal harmonics are more complex and virtually unknown in the literature, exept for the low degrees: toroidal harmonics of degree zero, corresponding to the potential of rings of sinusoidal charge distributions, are known as series of spherical harmonics, and spherical harmonics corresponding to point charges and dipoles are known as series of toroidal harmonics. The relationships for all degrees and orders have been derived in a Russian paper from 1983 [16], although this does not appear to be well known except for one other paper [17], which analysed the electrostatic interaction between a conducting torus and a partial spherical shell -they used the relationships to construct what is effectively the T -matrix for the conducting torus (eq. ( 32)), expressed on a spherical basis, as part of the kernel of an integral equation.…”

Section: Introductionmentioning

confidence: 99%

Electrostatic T-matrix for a torus on bases of toroidal and spherical harmonics

Majic

2019

Journal of Quantitative Spectroscopy and Radiative Transfer

View full text Add to dashboard Cite

Semi-analytic expressions for the static limit of the T -matrix for electromagnetic scattering are derived for a circular torus, expressed in bases of both toroidal and spherical harmonics. The scattering problem for an arbitrary static excitation is solved using toroidal harmonics and the extended boundary condition method to obtain analytic expressions for auxiliary Q and P -matrices, from which the T -matrix is given by their division. By applying the basis transformations between toroidal and spherical harmonics, the quasi-static limit of the T -matrix block for electric multipole coupling is obtained. For the toroidal geometry there are two similar T -matrices on a spherical basis, for computing the scattered field both near the origin and in the far field. Static limits of the optical cross-sections are computed, and analytic expressions for the limit of a thin ring are derived.

show abstract

“…For example toroidal harmonics of degree zero, corresponding to the potential of rings of sinusoidal charge distributions, are known as series of spherical harmonics, and spherical harmonics corresponding to point charges and dipoles are known as series of toroidal harmonics. The relationships for all degrees and orders have been derived in a Russian paper from 1983 [105], although this does not appear to be well known except for one other paper [106], which analyzed the electrostatic interaction between a conducting torus and a partial spherical shell -they used the relationships to construct what is effectively the T-matrix for the conducting torus (their equation 32), expressed on a spherical basis, as part of the kernel of an integral equation. We begin by investigating properties of toroidal harmonics including deriving new expressions for their source distributions.…”

Section: Chapter 7 Electrostatic T-matrices For the Torusmentioning

confidence: 99%

Electrostatic images and T-matrices for simple geometries

Majic¹

View full text Add to dashboard Cite

<p>This thesis is concerned with electrostatic boundary problems and how their solutions behave depending on the chosen basis of harmonic functions and the location of the fundamental singularities of the potential. The first part deals with the method of images for simple geometries where the exact nature of the image/fundamental singularity is unknown; essentially a study of analytic continuation for Laplace's equation in 3 dimensions. For the sphere, spheroid and cylinder, new deductions are made on the location of the images of point charges and their linear or surface charge densities, by using different harmonic series solutions that reveal the image. The second part looks for analytic expressions for the T-matrix for electromagnetic scattering of simple objects in the low frequency limit. In this formalism the incident and scattered fields are expanded on an orthogonal basis such as spherical harmonics, and the T-matrix is the transformation between the coefficients of these series, providing the general solution of any electromagnetic scattering problem by a given particle at a given wavelength. For the spheroid, bispherical system and torus, the natural basis of harmonic functions for the geometry of the scatterer are used to determine T-matrix expressed in that basis, which is then transformed onto a basis of canonical spherical harmonics via the linear relationships between different bases of harmonic functions.</p>

show abstract

Electrostatic field of a thin, unclosed spherical shell and a torus

Cited by 5 publications

References 2 publications

Outside localization around a toroidal electrode of a Paul trap

Outside localization around a toroidal electrode of a Paul trap

Electrostatic T-matrix for a torus on bases of toroidal and spherical harmonics

Electrostatic images and T-matrices for simple geometries

Contact Info

Product

Resources

About