Boundary conditions for the electron kinetic equation using expansion techniques

Becker, Markus M.; Grubert, Gordon K.; Loffhagen, Detlef

doi:10.1051/epjap/2010073

Cited by 3 publications

(2 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the past, the system (6) has been solved in two-term approximation [29,30] using the expression (7) with 2 as well as in multiterm approximation considering higher order contributions to the evdf anisotropy [32][33][34][35] to study the behaviour of electrons in prescribed time-dependent as well as stationary electric fields. But the coupled solution (stationary or time-dependent) of the kinetic Equations (6) for electrons, fluid equations for heavy particles and Poisson's equation for the electric field is still an ambitious task and has been achieved for a few discharge situations, only [21,[36][37][38].…”

Section: Kinetic Description Of Electronsmentioning

confidence: 99%

Derivation of Moment Equations for the Theoretical Description of Electrons in Nonthermal Plasmas

Becker¹,

Loffhagen²

2013

APM

View full text Add to dashboard Cite

The derivation of moment equations for the theoretical description of electrons is of interest for modelling of gas discharge plasmas and semiconductor devices. Usually, certain artificial closure assumptions are applied in order to derive a closed system of moment equations from the electron Boltzmann equation. Here, a novel four-moment model for the description of electrons in nonthermal plasmas is derived by an expansion of the electron velocity distribution function in Legendre polynomials. The proposed system of partial differential equations is consistently closed by definition of transport coefficients that are determined by solving the electron Boltzmann equation and are then used in the fluid calculations as function of the mean electron energy. It is shown that the four-moment model can be simplified to a new drift-diffusion approximation for electrons without loss of accuracy, if the characteristic frequency of the electric field alteration in the discharge is small in comparison with the momentum dissipation frequency of the electrons. Results obtained by the proposed fluid models are compared to those of a conventional drift-diffusion approximation as well as to kinetic results using the example of low pressure argon plasmas. It is shown that the results provided by the new approaches are in good agreement with kinetic results and strongly improve the accuracy of fluid descriptions of gas discharges.

show abstract

Section: Kinetic Description Of Electronsmentioning

confidence: 99%

Derivation of Moment Equations for the Theoretical Description of Electrons in Nonthermal Plasmas

Becker¹,

Loffhagen²

2013

APM

View full text Add to dashboard Cite

show abstract

“…Based on such a view, it is thus sufficient to replace the plasma-facing solid by an object with a geometrical boundary and probabilities for electron sticking/reflection, ion neutralization, and secondary electron emission [59]. Within such an approach [228][229][230] it is of course impossible to investigate the plasma-induced modifications of the electronic structure of the solid, which in turn however may strongly affect the probabilities for charge transfer. We consider this to be a particularly severe drawback for the modeling of microdischarges on semiconducting substrates [231,232].…”

Section: A Integrated Modeling Of the Electric Double Layermentioning

confidence: 99%

Towards an integrated modeling of the plasma-solid interface

Bönitz

Filinov

Abraham

et al. 2019

Front. Chem. Sci. Eng.

View full text Add to dashboard Cite

Solids facing a plasma are a common situation in many astrophysical systems and laboratory setups. Moreover, many plasma technology applications rely on the control of the plasma-surface interaction, i.e. of the particle, momentum and energy fluxes across the plasma-solid interface. However, presently often a fundamental understanding of them is missing, so most technological applications are being developed via trial and error. The reason is that the physical processes at the interface of a low-temperature plasma and a solid are extremely complex, involving a large number of elementary processes in the plasma, in the solid as well as fluxes across the interface. An accurate theoretical treatment of these processes is very difficult due to the vastly different system properties on both sides of the interface: quantum versus classical behavior of electrons in the solid and plasma, respectively; as well as the dramatically differing electron densities, length and time scales. Moreover, often the system is far from equilibrium. In the majority of plasma simulations surface processes are either neglected or treated via phenomenological parameters such as sticking coefficients, sputter rates or secondary electron emission coefficients. However, those parameters are known only in some cases and with very limited accuracy. Similarly, while surface physics simulations have often studied the impact of single ions or neutrals, so far, the influence of a plasma medium and correlations between successive impacts have not been taken into account. Such an approach, necessarily neglects the mutual influences between plasma and solid surface and cannot have predictive power.In this paper we discuss in some detail the physical processes a the plasma-solid interface which brings us to the necessity of coupled plasma-solid simulations. We briefly summarize relevant theoretical methods from solid state and surface physics that are suitable to contribute to such an approach and identify four methods. The first are mesoscopic simulations such as kinetic Monte Carlo (KMC) and molecular dynamics (MD) that are able to treat complex processes on large scales but neglect electronic effects. The second are quantum kinetic methods based on the quantum Boltzmann equation that give access to a more accurate treatment of surface processes using simplifying models for the solid. The third approach are ab initio simulations of surface process that are based on density functional theory (DFT) and time-dependent DFT. The fourths are nonequilibrium Green functions that able to treat correlation effects in the material and at the interface. The price for the increased quality is a dramatic increase of computational effort and a restriction to short time and length scales. We conclude that, presently, none of the four methods is capable of providing a complete picture of the processes at the interface. Instead, each of them provides complementary information, and we discuss possible combinations. PACS numbers:

show abstract

Boltzmann equation and Monte Carlo analysis of the electrons in spatially inhomogeneous, bounded plasmas

Grubert¹,

Loffhagen²

2013

J. Phys. D: Appl. Phys.

View full text Add to dashboard Cite

Boundary conditions for the electron kinetic equation using expansion techniques

Abstract: Abstract. The numerical solution of partial differential equations requires suitable boundary conditions.

Cited by 3 publications

References 39 publications

Derivation of Moment Equations for the Theoretical Description of Electrons in Nonthermal Plasmas

Derivation of Moment Equations for the Theoretical Description of Electrons in Nonthermal Plasmas

Towards an integrated modeling of the plasma-solid interface

Boltzmann equation and Monte Carlo analysis of the electrons in spatially inhomogeneous, bounded plasmas

Contact Info

Product

Resources

About