Electrostatic problem for a torus and a disk

Шушкевич, Г. Ч.

doi:10.1134/1.1258698

Cited by 5 publications

(1 citation statement)

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“…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%

Outside localization around a toroidal electrode of a Paul trap

et al. 2020

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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.

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Section: Calculation Of Elecrical Fieldmentioning

confidence: 99%

Outside localization around a toroidal electrode of a Paul trap

et al. 2020

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Computation of Field-Emission Cathode-Based Electron Guns

Егоров

Sheshin

2017

Field Emission Electronics

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Decomposition theorem and Riesz basis for axisymmetric potentials in the right half-plane

Chaabi

Rigat

2015

European Journal of Mathematics

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Abstract. The Weinstein equation with complex coefficients is the equation governing generalized axisymmetric potentials (GASP) which can be written as Lm[u] = ∆u + (m/x) ∂xu = 0, where m ∈ C. We generalize results known for m ∈ R to m ∈ C. We give explicit expressions of fundamental solutions for Weinstein operators and their estimates near singularities, then we prove a Green's formula for GASP in the right half-plane H + for Re m < 1. We establish a new decomposition theorem for the GASP in any annular domains for m ∈ C, which is in fact a generalization of the Bôcher's decomposition theorem. In particular, using bipolar coordinates, we prove for annuli that a family of solutions for GASP equation in terms of associated Legendre functions of first and second kind is complete. For m ∈ C, we show that this family is even a Riesz basis in some non-concentric circular annulus.

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Electrostatic problem for a torus and a disk

Cited by 5 publications

References 0 publications

Outside localization around a toroidal electrode of a Paul trap

Outside localization around a toroidal electrode of a Paul trap

Computation of Field-Emission Cathode-Based Electron Guns

Decomposition theorem and Riesz basis for axisymmetric potentials in the right half-plane

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