Electrostatic field of angular-dependent surface electrodes

Salazar, Robert; Bayona-Roa, Camilo; Chaves, Juan Sebastián Solís

doi:10.1140/epjp/s13360-019-00090-3

Cited by 8 publications

(12 citation statements)

References 33 publications

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“…Those SE ion traps are a promising candidates to build ion-trap networks suitable for large-scale quantum processing [1][2][3][4][5][6][7][8]. There are several works describe analytic treatments including the SE in diverse situations : rectangular strip electrode held at constant [9], Ring-shaped SE traps [10,11], and the gapless SE with angular dependent potential [12]. In this document the Hemholtz Descomposition Theorem in combination with the Green's theorem are used to find the vector electric potential of the SE, recovering the Biot-Savart like (BSL) law for the electric field found in Ref.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Electric vector potential formulation in electrostatics: analytical treatment of the gaped surface electrode

2020

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Electric vector potential Θ(r) is a legitimate but rarely used tool to calculate the steady electric field in free-charge regions. Commonly, it is preferred to employ the scalar electric potential Φ(r) rather than Θ(r) in most of the electrostatic problems. However, the electric vector potential formulation can be a viable representation to study certain systems. One of them is the surface electrode SE, a planar finite region A− kept at a fixed electric potential with the rest grounded including a gap of thickness ν between electrodes. In this document we use the Helmholtz Decomposition Theorem and the electric vector potential formulation to provide integral expressions for the surface charge density and the electric field of the SE of arbitrary contour ∂A. We also present an alternative derivation of the result found in [M. Oliveira and J. A. Miranda 2001 Eur. J. Phys. 22 31] for the gapless (ν = 0) surface electrode GSE without invoking any analogy between the GSE and magnetostatics. It is shown that electric vector potential and the electric field of the gapped circular SE at any point can be obtained from an average of the gapless solution on the gap.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Electric vector potential formulation in electrostatics: analytical treatment of the gaped surface electrode

2020

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“…Particularly, the three-dimensional vector field due to a circular-deformed loop with low symmetry. Analytic solutions of the BSL integrals are outstanding for solving steady electric, magnetic or fluid flow problems, as it has been demonstrated in [24,25] by the authors of the present study 3 .…”

Section: Velocitymentioning

confidence: 56%

“…Correspondingly, numerical and expansion solutions for the perfect circular loop have been obtained in [27][28][29]. Also, for the electrostatic analog problem of Surface Electrodes, numerical methods have been applied in [24].…”

Section: Velocitymentioning

confidence: 99%

Expansion formula for the magnetic field of a periodically deformed circular current loop

Salazar¹,

Téllez²,

Bayona-Roa³

2021

Phys. Scr.

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A method is derived to obtain an expansion formula for the magnetic field B(r) generated by a closed planar wire carrying a steady electric current. The parametric equation of the loop is R(φ) = R + Hf (φ), with R the radius of the circle, H ∈ [0, R) the radial deformation amplitude, and f (φ) ∈ [−1, 1] a periodic function. The method is based on the replacement of the 1 r − r ′ 3 factor by an infinite series in terms of Gegenbauer polynomials, as well as the use of the Taylor series. This approach makes it feasible to write B(r) as the circular loop magnetic field contribution plus a sum of powers of H R. Analytic formulas for the magnetic field are obtained from truncated finite expansions outside the neighborhood of the wire. These showed to be computationally less expensive than numerical integration in regions where the dipole approximation is not enough to describe the field properly. Illustrative examples of the magnetic field due to circular wires deformed harmonically are developed in the article, obtaining exact expansion coefficients and accurate descriptions. Error estimates are calculated to identify the regions in R 3 where the analytical expansions perform well. Finally, first-order deformation formulas for the magnetic field are studied for generic even deformation functions f (φ).

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“…For convenience, the potentials of the inner and outer sheets are V o and zero, respectively. This system is commonly referred to as gaped Surface Electrode (SE) Salazar et al, 2019Salazar et al, , 2022Schmied, 2010) and it plays an important role to model the static electric fields in SE ion traps where ion-trap networks including arrays of SE are also promising candidates in quantum processing Seidelin et al, 2006;Daniilidis et al, 2011;Mokhberi et al, 2017;Tao et al, 2018;Van Mourik et al, 2020) The surface electrode also has practical relevance in antenna theory. For instance, when considering a time-varying voltage between the sheets.…”

Section: Introductionmentioning

confidence: 99%

Electric vector potential and the Biot-Savart like law in electrostatics

Salazar

Bayona-Roa²,

Jaramillo

2022

Rev. Acad. Colomb. Cienc. Ex. Fis. Nat.

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A vector potential formulation is shown in this article to compute the electric field of planar surface electrodes. The electric field is derived from from the solution of the Laplace’s equation in the free-charge space. Neumann-boundary conditions must be set on the region between planar metallic sheets as the separation goes to zero. It is shown that the electric field can be written via a Biot Savart- like integral. The strategy enables to generalize the analytical result for its application in the gaped surface electrodes description.

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Electrostatic field of angular-dependent surface electrodes

Cited by 8 publications

References 33 publications

Electric vector potential formulation in electrostatics: analytical treatment of the gaped surface electrode

Electric vector potential formulation in electrostatics: analytical treatment of the gaped surface electrode

Expansion formula for the magnetic field of a periodically deformed circular current loop

Electric vector potential and the Biot-Savart like law in electrostatics

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