A numerical study of planar discharge motion

Advances in Computational Mathematics, 2019

This paper deals with the numerical solution of an ionization wave propagation in air, described by a coupled set of convection-diffusion-reaction equations and a Poisson equation. The standard three-species and more complex eleven-species models with simple chemistry are formulated. The PDEs are solved by a finite volume method that is theoretically second order in space and time on an unstructured adaptive grid. The upwind scheme and the diamond scheme are used for the discretization of the convective and diffusive fluxes, respectively. The Poisson equation is also discretized by the diamond scheme. The results of both models are compared in details for a test case. The influence of physically pertinent boundary conditions at electrodes is also presented. Finally, we deal with numerical accuracy study of implicit scheme in two variants for simplified standard model. It allows us in the future to compute simultaneously and efficiently a process consisting of short time discharge propagation and long-term after-discharge phase or repetitively pulsed discharge.

Physics of Plasmas, 2005

A numerical model for two-species plasma involving electrons and ions at pressure of 0.1 torr is presented here. The plasma-wall problem is modeled using one-and two-dimensional hydrodynamic equations coupled with Poisson equation. The model utilizes a finite-element algorithm to overcome the stiffness of the resulting plasma-wall equations. The one-dimensional result gives insight into the discharge characteristics including net charge density, electric field, and temporal space-charge sheath evolution. In two dimensions, the plasma formation over a flat plate is investigated for three different cases. The numerical algorithm is first benchmarked with published literature for plasma formed between symmetric electrodes in nitrogen gas. The characteristics of plasma are then analyzed for an infinitesimally thin electrode under dc and rf potentials in the presence of applied magnetic field using argon as a working gas. The magnetic field distorts the streamwise distribution because of a large y-momentum V ϫ B coupling. Finally, the shape effects of the insulator-conductor edge for an electrode with finite thickness have been compared using a 90°shoulder and a 45°chamfer. The 90°chamfer displays a stronger body force created due to plasma in the downward and forward directions.

1993

We present an overview of models of low pressure, non-thermal gas discharges as commonly used in plasma processing. Significant progress has been made in the past decade towards the goal of a self-consistent model of the electrical properties of discharges, whether d.c., r.f. or microwave discharges. These models are based on solutions of the charged particle transport equations coupled with Poisson's equation for the electric field, and provide the space and time distribution of charged particle densities, current densities and electric field or potential. Some of the most sophisticated models also provide the electron and ion velocity distribution functions in the discharge at any point in space or time. It is now possible to describe reasonably accurately the physical properties of a discharge (including the plasma, the electrode regions and the walls) for two-dimensional cylindrical geometries, even for complex electrode configurations involving e.g. a hollow cathode or anode. A survey of the available models is presented here and we illustrate the current state ofthe art by results from one-and two-dimensional models ofd.c., r.f. and transient discharges.

2010

Dielectric Barrier Discharge (DBD) is a discharge phenomenon where a high voltage is applied on at least two electrodes separated by an insulating dielectric material. Dielectric Barrier Discharge plasma actuator has been studied widely in this last decade but mostly the study is focusing on experimental research rather than mathematical modeling. The limitation with studying DBD plasma actuator experimentally is that it does not obtain direct information on the physics of the plasma flow, which is important in determining its efficiency. In this paper, we model the steady fluid model DBD plasma actuator mathematically. The preliminary result of the model are presented and discussed. To initiate the modeling process, the stream-function and vorticity are defined so that the Navier-Stokes momentum equation could be transformed into vorticity equation. The resulting two governing equations, which are vorticity and stream-function equations are solved numerically to obtain the vorticity of the flow in x and y directions. Finite difference method was adopted to discretize both equations and the system of equations is solved by the Gauss-Seidel method. Our numerical solutions show that the applied voltage plays an important role in the model. We found that as the applied voltage increases, the vorticity of the plasma flow also increases.

Spectrochimica Acta Part B: Atomic Spectroscopy, 1989

Ahstract-A two-dimensional computer model has been applied in the simulation of an analytical inductively coupled plasma (ICP) discharge. The temperature and flow fields as well as the electromagnetic field in an argon ICP discharge operated at 40 MHz and 1 kW have been investigated. The results are compared with those obtained with an earlier model.

36th AIAA Plasmadynamics and Lasers Conference, 2005

The hydrodynamic equations of continuity and momentum for electrons and ions along with the electrostatic field equation are solved numerically using a self-consistent finite-element algorithm in the low-pressure, high frequency regime. The plasma formation over a flat plate is investigated for three different cases. The twodimensional numerical algorithm is first benchmarked with published literature for plasma formed between symmetric electrodes in nitrogen gas. Discharge characteristics of plasma for an electrode-insulator configuration are then analyzed under steady and transient conditions using argon as a working gas. The effect of magnetic field on electric potential and charge difference is studied for an infinitesimally thin electrode. The magnetic field distorts the stream-wise distribution because of strong y-momentum v×B coupling. Finally, the shape effects of insulator-conductor edge for an electrode of finite thickness have been compared using a 90 o shoulder and a 45 o chamfer. The 90 o chamfer displays a stronger body force created due to plasma in the downward and forward directions.

IEEE Conference Record - Abstracts. 1996 IEEE International Conference on Plasma Science

For radio-frequency discharges of electronegative gases, one-dimensional equilibrium equations for plasma variables are formulated and the scaling formulae of the plasma variables are derived in terms of the control parameters. The control parameters consist of three parameters: p (pressure), lp (halfsystem length), and P (power) or ne (electron density). The classifications of the operating regions are performed according to the prevailing particle-loss mechanism (recombination-loss-dominated or ion-flux-loss-dominated) and according to the main heating mechanism (ohmic-heating-dominated or stochastic-heating-dominated). The variations of the charged particle densities with pressure and absorbed power are estimated and compared with the results of a particle-in-cell simulation.

The European Physical Journal Applied Physics, 2005

A fluid model has been used in this work to analyze the electric and energetic behavior of a lowpressure DC glow discharge in Ar chosen as a gas test. The governing equations are the first three moments of the Boltzmann transport equations under their complete form without using the classical-drift-diffusion approximation for the momentum transfer equation while the energy conservation equation involves both thermal and drift energies. In the framework of the local energy approximation, the basic data needed more particularly in the collision source terms for both momentum transfer and energy equations are determined from a multi term solution of Boltzmann equation. Due to the strong coupling with electric field obtained from Poisson equation and the high sheath gradients, the transport equations are numerically solved using a powerful Galerkin finite elements method. This model, after a validation from comparison with literature results, is then used to analyze the convective and drift energy effects on the electric discharge characteristics. Present results show a large influence of the convective term in comparison to the driftdiffusion approximation, mainly on the electric field and charged density profiles due to the antagonist effect induced by this term on the electron and ion motion which reinforces the charge space. Present results show also the discharge characteristic changes mainly in the sheath due to the drift energy consideration.

Physics of Plasmas, 2020

This paper develops a general approach to the derivation of the boundary conditions for hydrodynamic equations for charged and neutral plasma components. It includes both a well-known classical case for pure diffusion, and considers the expressions for diffusion and drift together-for an absorbing (neutralizing) wall with partial reflection and the possible emission of plasma components. Some unclear and controversial terms found in the existing literature are clarified. Several examples of applications of the results, which illustrate the properties of boundary conditions for electrons and ions, are calculated and analyzed.

Journal of Computational Physics, 2002

A fully conservative and efficient numerical algorithm is developed for fluid simulations of radio-frequency plasma discharges. Results are presented in one and multiple dimensions for a helium discharge. The algorithm produces accurate results even on fairly coarse grids without the use of numerical dissipation. The proposed electron flux discretization is more accurate and efficient than two of the most commonly used discretizations: low-order upwinding (M. S.