Db Diana Mihailova

The plasma modelling toolkit Plasimo

The Plasimo code is a toolbox that provides support for the numerical simulation of plasma sources of various degrees of equilibrium. It comes with a number of electromagnetic modules, flow solvers, modules for calculating transport coefficients, radiation transport and for the generation of ortho-curvilinear coordinate systems. Plasimo supports transient and steady-state simulations of plasma sources in one-, two and three-dimensional geometries.This paper presents a selection of Plasimos sub-models. A discussion of the physics behind each module is accompanied by notes about the modules capabilities and limitations and by references to original works and papers in which that particular module was used. As such, it provides a good entry point for people who consider using Plasimo?or parts of it?for their simulation needs.

Theoretical Characterization of an Atmospheric Pressure Glow Discharge Used for Analytical Spectrometry

We have investigated the plasma processes in an atmospheric pressure glow discharge (APGD) in He used for analytical spectrometry by means of fluid and Monte Carlo (MC) simulations. Typical results include the potential and electric field distributions in the plasma, the density profiles of the various plasma species throughout the discharge, the mean electron energy, as well as the rates of the various collision processes in the plasma, and the relative importance of the different production and loss rates for the various species. The similarities and differences with low-pressure glow discharges are discussed. The main differences are a very small cathode dark space region and a large positive column as well as the dominant role of molecular ions. Some characteristic features of the APGD, such as the occurrence of the different spatial zones in the discharge, are illustrated, with links to experimental observations.

The complete flux scheme : error analysis and application to plasma simulation

The complete flux scheme (CFS) [J. ten Thije Boonkkamp, M. Anthonissen, The finite volume-complete flux scheme for advection–diffusion–reaction equations, J. Sci. Comput. 46 (1) (2011) 47–70. http://dx.doi.org/10.1007/s10915-010-9388-8] is an extension of the widely used exponential difference scheme for advection–diffusion–reaction equations. In this paper, we provide a rigorous proof that the convergence order of this scheme is 2 for all grid Peclet numbers, whereas that of the exponential difference scheme reduces to 1 for high grid Peclet numbers in the presence of source terms. The performance of both schemes is compared in two case studies: a test problem and a physical model of a parallel-plate glow discharge. The results indicate that the usage of the CFS allows a considerable reduction of the number of grid points that is required to obtain the same accuracy. The MATLAB/Octave source code that has been used in these studies has been made available.

Analytical model of a longitudinal hollow cathode discharge

This paper presents a simple analytical model of a longitudinal hollow cathode discharge used in metal vapour lasers. The model describes the principle relations between the voltage, current, plasma density and axial structure of the discharge. Contrary to standard dc discharges, this discharge does not require electron multiplication in the cathode fall (CF) to produce ions, but rather to satisfy the electron energy balance. A self-sustainment condition is obtained from the energy balance per electron–ion pair. From this, it follows that there is a maximum voltage at which the CF thickness tends to zero and the current density tends asymptotically to infinity. The discharge develops axial non-uniformity and an axial electric field in order to evacuate the created electrons to the anode, such that the characteristic time for transport losses is the same for electrons as for ions. The axial profiles of the current density, plasma density and potential are obtained from the electron continuity equation. It is shown that additional energy absorption from the axial field, similar to electron heating in dc positive columns, modifies the self-sustainment condition and thus leads to a shift in the voltage–current characteristic, depending on the cathode length.

Modelling of an RF plasma shower

A capacitive radiofrequency (RF) discharge at atmospheric pressure is studied by means of a time-dependent, two-dimensional fluid model. The plasma is created in a stationary argon gas flow guided through two perforated electrodes, hence resembling a shower. The inner electrode, the electrode facing the flow entrance, is powered with a frequency of 13.56 MHz, and the outer electrode is grounded. The model solves the mass balance equations for the relevant active species and the electron energy balance equation in conjunction with the Poisson equation for the field sustaining the plasma. The mass balance equations of the active species are calculated using the drift–diffusion–convection approach, thus taking the bulk velocity into account. The velocity field is calculated with the Navier–Stokes module of the Plasimo toolkit. The plasma dynamics is studied in three connected regions; the space between the electrodes, the regions before the powered electrode and the extended region behind the grounded electrode. The effect of the shower holes and the recirculation gas flow on the plasma is examined.

A flexible platform for simulations of sputtering hollow cathode discharges for laser applications

The Plasimo modelling platform, extended with a cathode wall sputtering module is used to study the discharge processes and to optimise the design parameters of a sputtering hollow cathode discharge (HCD). We present Plasimo simulations of a HCD used for laser applications. A time dependent sub-model is used to describe the behaviour of the plasma species. The sputtering yield at the metallic boundaries is calculated using an empirical formula. Copper is chosen as the cathode material and the discharge operates in helium with a small admixture of argon for more efficient sputtering. The optimal conditions for lasing of the infra-red (IR) copper ion line (780.8 nm) that have been determined experimentally are used as input conditions for the simulation model. Calculations are made for various gas mixtures. The observed quantities are compared with the experimental data obtained for the same discharge geometry and operating conditions. The agreement between the measured data and the results from modelling indicates that the main reactions in the model are correctly described. Therefore, it is believed that this model can be used as a design tool in optimizing discharge studies for various applications based on the sputtering of the cathode material.

Geometrical features in longitudinal sputtering hollow cathode discharges for laser applications

Longitudinal sputtering hollow cathode discharge (HCD) used as active medium for lasing is studied by means of numerical modelling. Due to the longitudinal non-uniformities of the discharge, the laser operation could be strongly affected. The non-uniformity of the discharge is mainly influenced by the dimensions of the hollow cathode, in particular by the aspect ratio length/radius. To study the geometrical features, a simulation model for HCDs has been constructed using the Plasimo modelling platform. The model allows in-depth studies of the plasma mechanisms and enables finding the optimum under the working conditions of the HCDs. The model is validated by comparing the results with the experimental observations. The spatial distribution of the plasma density and potential as well as an in-depth discussion of the results and the trends revealed by the model are presented. The proper understanding of the essential geometrical features allowed defining the optimal aspect ratio length/diameter for stable and uniform discharge with high excitation efficiency.

A hollow cathode discharge for laser applications: influence of the cathode length

The influence of the geometry of a longitudinal hollow cathode discharge (HCD) excited in a Cu cathode and He–Ar mixture is studied experimentally and theoretically. Special attention is devoted to the optimization of the HC length to obtain a stable and uniform laser medium with a high excitation efficiency. The influence of the cathode length is demonstrated experimentally by the behaviour of the 780.8 nm Cu ion line. The dependence of the laser power and gain as a function of the cathode length segments is measured. The Plasimo modelling platform is used to construct a model allowing more profound studies of the plasma processes and plasma behaviour under different conditions. Calculations at different cathode lengths are made and typical results such as spatial potential and plasma density distributions are presented and discussed. It is demonstrated that when the cathode length is increased the plasma density at the centre of the cathode decreases and the discharge tends to separate into two independent parts causing axial non-uniformity and reducing the discharge efficiency. The results also suggest that there exist a lower limit of the cathode length. Below this limit an inversion of the axial electric field occurs, which can be regarded as a transition between the conventional and high-voltage HCD under the conditions under study.

Efficient simulation of drift–diffusive discharges: application of the ‘complete flux scheme’

Fluid models have successfully explained the physics of a variety of plasmas. To solve the fluid model, the discretization scheme commonly used is the exponential difference scheme (EDS) (Sharfetter D et al 1969 IEEE Trans. Electron Devices 16 64–77). We present an extension of the EDS, the complete flux scheme (ten Thije Boonkkamp J H M et al 2011 J. Sci. Comput. 46 47–70) and show that for typical glow discharge models it is ten times more accurate.The Peclet number is the key parameter throughout the paper. A new interpretation of this number is presented. It is then used to explain the glow discharge structure and to formulate a necessary condition for the validity of the local field approximation.

Monte Carlo simulation of a sputtering hollow-cathode discharge for laser applications

We report on a kinetic model that computes the electron behaviour in a hollow cathode discharge. It is a part of the PLASIMO toolkit and is based on a Monte-Carlo technique. The model is tested by varying the input parameters and by comparing the output with the output obtained by the freeware Boltzmann equation solver BOLSIG+. The results show that the Monte-Carlo model gives reliable information about the behavior of the electrons in the discharge. The Monte-Carlo module is applied to the case of a hollow cathode discharge for laser applications. Analysis of the output data and its adequateness is done. Future developments of the model are discussed.