Numerical double layer solutions with ionisation

Andersson, Dag; Sorensen, J.

doi:10.1088/0022-3727/16/4/020

Cited by 17 publications

(10 citation statements)

References 8 publications

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“…Thus, quasineutrality must first be established on the high potential side, creating a region with E ≈ 0, before an imbalance in the static Langmuir condition implies expansion of the double layer. Previous attempts to model spot onset solved an integral form of Poisson's equation 16,28,29 . In these models, the integral of the charge density within the sheath, including contributions from electron impact ionization, were formulated as a function of the sheath electric field…”

Section: A Anode Spot Onsetmentioning

confidence: 99%

Theory and simulation of anode spots in low pressure plasmas

et al. 2017

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When electrodes are biased above the plasma potential, electrons accelerated through the associated electron sheath can dramatically increase the ionization rate of neutrals near the electrode surface. It has previously been observed that if the ionization rate is great enough, a double layer separates a luminous high-potential plasma attached to the electrode surface (called an anode spot or fireball) from the bulk plasma. Here, results of the first 2D particle-in-cell simulations of anode spot formation are presented along with a theoretical model describing the formation process. It is found that ionization leads to the buildup of an ion-rich layer adjacent to the electrode, forming a narrow potential well near the electrode surface that traps electrons born from ionization. Anode spot onset occurs when a quasineutral region is established in the potential well and the density in this region becomes large enough to violate the steady-state Langmuir condition, which is a balance between electron and ion fluxes across the double layer. A model for steady-state properties of the anode spot is also presented, which predicts values for the anode spot size, double layer potential drop, and form of the sheath at the electrode by considering particle, power, and current balance. These predictions are found to be consistent with the presented simulation and previous experiments.Comment: Submitted to Phys. Plasma

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Section: A Anode Spot Onsetmentioning

confidence: 99%

Theory and simulation of anode spots in low pressure plasmas

et al. 2017

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“…The numerical solution of equation (1) using equation (13) for the recalculation of the concentrations in the matrix gives the algorithm for the simulation of the PSD of precipitates.…”

Section: Resultsmentioning

confidence: 99%

“…In a system with n components there are n-l independent diffusion fluxes. The expression for every independent flux is obtained using the Onsager extension of Fick's law for multi component systems [13]:…”

mentioning

confidence: 99%

“…The components are not independent of each other, and the dependent component can be chosen arbitrarily (it is usually the solvent). The calculation of chemical diffusion coefficients follows the procedure described by Andersson and Agren [13]. In their formulation individual diffusion coefficients D mi are calculated from the atomic mobilities multiplied by the thermodynamic factor, which in tum is computed with the aid of the thermodynamic description of the system.…”

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Prediction of the size distribution of precipitates

Prikhodovsky

2001

Steel Research

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Modelling has proven to be an efficient way of cutting the time and costs associated with the investigation of materials properties. A new mathematical model for the prediction of the particle size distribution of precipitates has been developed. The model allows the description of all stages of the precipitation process: nucleation, growth and Ostwald ripening of particles. The incorporation of existing thermodynamic databases allows the simulation of a formation of dispersed phases in commercial multicomponent alloys. The influence of the model parameters on the final particle size distribution was investigated with the example of NbC formation in austenite. It was shown that the interfacial energy of a particle‐matrix interface has the most significant effect on the final particle arrangement. A pre‐exponential factor, which is the subject of nucleation theories, plays a less significant role in the final particle arrangement.

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“…From this Langmuir condition, it turns out that ionization modifies the sheath profile when the ionization mean-free path is of the order of ͱm i /m e times the sheath thickness ͑provided that the potential jump across the sheath is larger than the ionization potential͒. The transformation of the sheath into a DL was studied numerically by Andersson and Sorensen, 9 and by Cooke and Katz. 10 Both works considered no plasma emission by the contactor and computed the relation between the contactor voltage and the gas density needed to reach the a͒ Electronic mail: ahedo@fmetsia.upm.es TCM.…”

Section: Introductionmentioning

confidence: 99%

Current–voltage response of anodic plasma contactors with external ionization

Ahedo

1996

Physics of Plasmas

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A spherical, steady-state model that considers the combined influence of plasma emission and external ionization of neutral gas on the operation of electron-collecting contactors is presented. Ionization by both Maxwellian and streaming electrons is investigated. A core ͑or quasineutral cloud͒ and a no-core mode are considered and the transition conditions from one to another are derived. The collected current is determined in terms of the main plasma and contactor parameters. The current-voltage response reproduces the ignited regime observed in experiments. The transition to the ignited regime and the transition to the core mode are not equivalent. It is shown that ionization by the electron beam is the main driver of ignition. The Langmuir law for the double layer causes a self-regulation of the core that affects the collection of current and leads to a multiplicity of solutions. Different neutral gas profiles are analyzed. It is uncertain whether ignition is reached when the neutral gas is provided by the contactor exclusively. The appearance of nonmonotonic potential profiles for low plasma emissions is noted.

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Numerical double layer solutions with ionisation

Cited by 17 publications

References 8 publications

Theory and simulation of anode spots in low pressure plasmas

Theory and simulation of anode spots in low pressure plasmas

Prediction of the size distribution of precipitates

Current–voltage response of anodic plasma contactors with external ionization

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