Electrical field modified by injected space charge in blade-plate configuration

Khaddour, B.; Atten, P.; Coulomb, Jean‐Louis

doi:10.1109/tmag.2006.870974

Cited by 10 publications

(21 citation statements)

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“…In [7] this boundary condition is investigated even further by comparison between direct ionisation criterion and two approximate formulations. Similar FEM-MOC hybrid method is demonstrated in [8], where structured mesh used for MOC is constructed on the basis of electric field lines and equipotential lines and has to be redefined in each iteration. The solution obtained with hybrid method was also used to calculate body force and velocity in [9].…”

Section: Nomenclaturementioning

confidence: 99%

“…To overcome this problem an alternative form of space charge density boundary condition was proposed in [8]: …”

Section: Geometry and Boundary Conditionsmentioning

confidence: 99%

“…The second is the lack of clarity in the matter of proper choice of the value of the coefficient A. In [8] authors suggest that this value should be large which is not clear but justified in their case since they solve the non-dimensional form of governing equations. In present work a slight modification to BC defined by (7) is proposed.…”

Section: Geometry and Boundary Conditionsmentioning

confidence: 99%

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Numerical modeling of body force induced by corona discharge

Gałek

2017

ZN PRz Mechanika

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The paper presents the theoretical basis and results of numerical modeling of corona discharge phenomenon carried out to determine the value of body force that induces the flow of surrounding fluid. The system of two partial differential equations is solved with the values of electric potential ϕ and space charge density ρq as unknowns. The first equation is of Poisson-type with Laplacian acting on the value of potential and source term dependent on space charge density as well as electric permittivity of the medium. The second equation is current continuity equation, where the current density is composed of charge carrier diffusion term and the term describing their drift in electric field. Particular attention was given to the boundary condition of space charge density due to its indirect nature. Geometry of the problem assumes that positive corona discharge takes place on the sharp edge of the blade-shaped anode while flat grounded plate acts as a cathode. Such configuration enables simplified analysis in 2D Cartesian coordinates assuming that the section plane is sufficiently far from the lateral edges of the blade. The system of equations is solved with MOOSE (Multiphysics Object-Oriented Simulation Environment) Framework released in public domain on GNU LGPL license by Idaho National Laboratory. Presented results include 2D distributions of electric potential, electric field strength, space charge density and body force in air surrounding electrodes.

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Section: Nomenclaturementioning

confidence: 99%

“…To overcome this problem an alternative form of space charge density boundary condition was proposed in [8]: …”

Section: Geometry and Boundary Conditionsmentioning

confidence: 99%

Section: Geometry and Boundary Conditionsmentioning

confidence: 99%

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Numerical modeling of body force induced by corona discharge

Gałek

2017

ZN PRz Mechanika

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“…The most frequently used algorithms are the hydrodynamic diffusion-drift model incorporating flux-corrected-transport (FCT) method and particle-in-cell (PIC) method [2][3][4][5][6]. In this paper, we proposed a full finite element approach where the charge transport equations of hydrodynamic diffusion-drift model and the electric field equation were numerically solved in a fully coupled system by using a standard finite element procedure for transient analysis [7][8][9][10][11]. Numerical technique for the hydrodynamic diffusiondrift modeling using charge transport equations is used in various applications such as corona discharge, heat transfer and cooling effect of heavy electric machines [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

FE Analysis of Plasma Discharge and Sheath Characterization in Dry Etching Reactor

Yu¹,

Kim²,

Lee³

et al. 2014

Journal of Electrical Engineering and Technology

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-We present a full finite element analysis for plasma discharge in etching process of semiconductor circuit. The charge transport equations of hydrodynamic diffusion-drift model and the electric field equation were numerically solved in a fully coupled system by using a standard finite element procedure for transient analysis. The proposed method was applied to a real plasma reactor in order to characterize the plasma sheath that is closely related to the yield of the etching process. Throughout the plasma discharge analysis, the base electrode of reactor was tested and modified for improving the uniformity around the wafer edge. The experiment and numerical results were examined along with SEM data of etching quality. The feasibility and usefulness of the proposed method was shown by both numerical and experimental results.

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“…The injection of charge results from the partial discharge in the small region of high field close to the blade edge or to the needle tip. As the size of the bi-ionized zone is very limited compared to the electrode spacing, this zone is usually neglected and its effect taken into account through a law of charge injection [1], [3]. With such a law, it is possible to determine the potential and the charge density numerically.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution and Experimental Test for Corona Discharge Between Blade and Plate

Khaddour¹,

Atten

Coulomb

2007

IEEE Trans. Magn.

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This paper presents a numerical technique to solve the problem of space charge distribution in a blade-plate electrodes system. The coupled equations are: Poisson equation solved by finite element method (FEM) to determine the distributions of potential, and charge conservation equation solved by the method of characteristics (MOC) to obtain the charge density between the two electrodes. The structured mesh is redefined at each step of the iterative scheme. A simplified injection law at the blade is retained; it allows us to obtain solutions which compare very favorably with experimental results concerning the current density distribution at the plate.Index Terms-Electrical field, mesh redefinition, method of characteristics (MOC), space charge effect.

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Electrical field modified by injected space charge in blade-plate configuration

Cited by 10 publications

References 10 publications

Numerical modeling of body force induced by corona discharge

Numerical modeling of body force induced by corona discharge

FE Analysis of Plasma Discharge and Sheath Characterization in Dry Etching Reactor

Numerical Solution and Experimental Test for Corona Discharge Between Blade and Plate

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