arXiv subjects

Ralf Peter Brinkmann

Publications and source records attributed to Ralf Peter Brinkmann.

33 records · Page 2Linked to original sources

arXiv2020

Theoretical investigation of a miniature microwave driven plasma jet

Microwave and radio frequency driven plasmas jets play an important role in many technical applications. They are usually operated in a capacitive mode known as E-mode. As a new plasma source the MMWICP (Miniature Micro Wave ICP) has been proposed, a small scale plasma jet with inductive coupling based on a specially designed resonator that acts as an LC-resonance circuit. This work presents a theoretical model of the new device, based on a series representation of the electromagnetic field in the resonator and the volume integrated (global) model for the loss processes within the plasma. An infinite number of modes can be found ordered by the azimuthal wave number m. These modes essentially determine the electromagnetic behavior of the system and differ from ordinary cavity modes. The mode m=0 can be identified with the inductive mode and is called H-mode, the mode m=1 is the capacitive mode and is called E-mode. Both modes refer to different operating regimes, which are separated by different values of the plasma parameters. In a second step the matching network and its characteristics are taken into account in order to find stable equilibrium points and possible hysteresis effects. As main result, the feasibility of inductive power coupling for the MMWICP resonator is shown.

physics.plasm-ph↗

arXiv2019

Electron power absorption in low pressure capacitively coupled electronegative oxygen radio frequency plasmas

A thorough understanding of the energy transfer mechanism from the electric field to electrons is of utmost importance for optimization and control of different plasma sources and processes. This mechanism, called electron power absorption, involves complex electron dynamics in electronegative capacitively coupled plasmas (CCPs) at low pressures, that are still not fully understood. Therefore, we present a spatio-temporally resolved analysis of electron power absorption in low pressure oxygen CCPs based on the momentum balance equation derived from the Boltzmann equation. Data are obtained from 1d3v Particle-In-Cell / Monte Carlo Collision simulations. In contrast to conventional theoretical models, which predict 'stochastic/collisionless heating' to be important at low pressure, we observe the dominance of Ohmic power absorption. In addition, there is an attenuation of ambipolar power absorption at low pressures due to the strong electronegativity, and the presence of electropositive edge regions in the discharge, which cause a high degree of temporal symmetry of the electron temperature within the RF period.

physics.plasm-ph↗

arXiv2016

A global model of cylindrical and coaxial surface-wave discharges

A volume-averaged global model is developed to investigate surface-wave discharges inside either cylindrical or coaxial structures. The neutral and ion wall flux is self-consistently estimated based on a simplified analytical description both for electropositive and electronegative plasmas. The simulation results are compared with experimental data from various discharge setups of either argon or oxygen, measured or obtained from literature, for a continuous and a pulse-modulated power input. A good agreement is observed between the simulations and the measurements. The calculations show that the wall flux often substantially contributes to the net loss rates of the individual species.

physics.plasm-ph↗

arXiv2015

Analytic model of the energy distribution function for highly energetic electrons in magnetron plasmas

This paper analyzes a situation which is common for magnetized technical plasmas such as dc magnetron discharges and HiPIMS systems, where secondary electrons enter the plasma after being accelerated in the cathode fall and encounter a nearly uniform bulk. An analytic calculation of the distribution function of hot electrons is presented; these are described as an initially monoenergetic beam that slows down by Coulomb collisions with a Maxwellian distribution of bulk (cold) electrons, and by inelastic collisions with neutrals. Although this analytical solution is based on a steady-state assumption, a comparison of the characteristic time-scales suggests that it may be applicable to a variety of practical time-dependent discharges, and it may be used to introduce kinetic effects into models based on the hypothesis of Maxwellian electrons. The results are verified for parameters appropriate to HiPIMS discharges, by means of time-dependent and fully-kinetic numerical calculations.

physics.plasm-ph↗

arXiv2014

Active plasma resonance spectroscopy: Eigenfunction solutions in spherical geometry

The term Active Plasma Resonance Spectroscopy (APRS) denotes a class of related techniques which utilize, for diagnostic purposes, the natural ability of plasmas to resonate on or near the electron plasma frequency: A radio frequent signal (in the GHz range) is coupled into the plasma via an antenna or probe, the spectral response is recorded, and a mathematical model is used to determine plasma parameters like the electron density or the electron temperature. Based on the cold plasma model, this manuscript provides the general analytic expression of the electrical admittance of a spherical shaped probe immersed into a plasma. It is derived from the matrix representation of an appropriate operator, which describes the dynamical behavior of the probe-plasma system. This dynamical operator can be split into a conservative operator and a dissipative operator. It can be shown that the eigenvalues of the conservative operator represent the resonance frequencies of the probe-plasma system which are simply connected to the electron density. As an example, the result is applied to the spherical impedance probe and the multipole resonance probe.

physics.plasm-ph↗

arXiv2014

Continuum and Kinetic Simulations of the Neutral Gas Flow in an Industrial Physical Vapor Deposition Reactor

Magnetron sputtering used for physical vapor deposition processes often requires gas pressures well below 1 Pa. Under these conditions the gas flow in the reactor is usually determined by a Knudsen number of about one, i.e., a transition regime between the hydrodynamic and the rarefied gas regime. In the first, the gas flow is well described by the Navier-Stokes equations, while in the second a kinetic approach via the Boltzmann equation is necessary. In this paper the neutral gas flow of argon and molecular nitrogen gas inside an industrial scale plasma reactor was simulated using both a fluid model and a fully kinetic Direct Simulation Monte Carlo model. By comparing both model results the validity of the fluid model was checked. Although in both models a Maxwell-Boltzmann energy distribution of the neutral particles is the natural outcome, the results of the gas flow differ significantly. The fluid model description breaks down, due to the inappropriate assumption of a fluid continuum. This is due to exclusion of non-local effects in the multi dimensional velocity space, as well as invalid gas/wall interactions. Only the kinetic model is able to provide an accurate physical description of the gas flow in the transition regime. Our analysis is completed with a brief investigation of different definitions of the local Knudsen number. We conclude that the most decisive parameter - the spatial length scale L - has to be very careful chosen in order to obtain a reasonable estimate of the gas flow regime.

physics.comp-ph↗

arXiv2014

Ion energy distribution functions behind the sheaths of magnetized and non magnetized radio frequency discharges

The effect of a magnetic field on the characteristics of capacitively coupled radio frequency discharges is investigated and found to be substantial. A one-dimensional particle-in-cell simulation shows that geometrically symmetric discharges can be asymmetrized by applying a spatially inhomogeneous magnetic field. This effect is similar to the recently discovered electrical asymmetry effect. Both effects act independently, they can work in the same direction or compensate each other. Also the ion energy distribution functions at the electrodes are strongly affected by the magnetic field, although only indirectly. The field influences not the dynamics of the sheath itself but rather its operating conditions, i.e., the ion flux through it and voltage drop across it. To support this interpretation, the particle-in-cell results are compared with the outcome of the recently proposed ensemble-in-spacetime algorithm. Although that scheme resolves only the sheath and neglects magnetization, it is able to reproduce the ion energy distribution functions with very good accuracy, regardless of whether the discharge is magnetized or not.

physics.plasm-ph↗

arXiv2014

Active plasma resonance spectroscopy: A kinetic functional analytic description

The term "Active Plasma Resonance Spectroscopy" (APRS) denotes a class of related techniques which utilize, for diagnostic purposes, the natural ability of plasmas to resonate on or near the electron plasma frequency $ω_{\rm pe}$: A radio frequent signal (in the GHz range) is coupled into the plasma via an antenna or probe, the spectral response is recorded, and a mathematical model is used to determine plasma parameters like the electron density or the electron temperature. This manuscript provides a kinetic description of APRS valid for all pressures and probe geometries. Subject of the description is the interaction of the probe with the plasma of its influence domain. In a first step, the kinetic free energy of that domain is established which has a definite time derivative with respect to the RF power. In the absence of RF excitation, it assumes the properties of a Lyapunov functional; its minimum provides the stable equilibrium of the plasma-probe system. Equipped with a scalar product motivated by the second variation of the free energy, the set of all perturbations of the equilibrium forms a Hilbert space. The dynamics of the perturbations can be cast in an evolution equation in that space. The spectral response function of the plasma-probe system consists of matrix elements of the resolvent of the dynamical operator. An interpretation in terms of an equivalent electric circuit model is given and the residual broadening of the spectrum in the collisionless regime is explained.

physics.plasm-ph↗

arXiv2013

Active plasma resonance spectroscopy: A functional analytic description

The term "Active Plasma Resonance Spectroscopy" refers to a class of diagnostic methods which employ the ability of plasmas to resonate on or near the plasma frequency. The basic idea dates back to the early days of discharge physics: An signal in the GHz range is coupled to the plasma via an electrical probe; the spectral response is recorded, and then evaluated with a mathematical model to obtain information on the electron density and other plasma parameters. In recent years, the concept has found renewed interest as a basis of industry compatible plasma diagnostics. This paper analyzes the diagnostics technique in terms of a general description based on functional analytic (or Hilbert Space) methods which hold for arbitrary probe geometries. It is shown that the response function of the plasma-probe system can be expressed as a matrix element of the resolvent of an appropriately defined dynamical operator. A specialization of the formalism for a symmetric probe desing is given, as well as an interpreation in terms of a lumped circuit model consisting of series resonators. We present ideas for an optimized probe design based on geometric and electrical symmetry.

physics.plasm-ph↗

arXiv2012

Simulations of electromagnetic effects in high frequency capacitively coupled discharges using the Darwin approximation

The Darwin approximation is investigated for its possible use in simulation of electromagnetic effects in large size, high frequency capacitively coupled discharges. The approximation is utilized within the framework of two different fluid models which are applied to typical cases showing pronounced standing wave and skin effects. With the first model it is demonstrated that Darwin approximation is valid for treatment of such effects in the range of parameters under consideration. The second approach, a reduced nonlinear Darwin approximation-based model, shows that the electromagnetic phenomena persist in a more realistic setting. The Darwin approximation offers a simple and efficient way of carrying out electromagnetic simulations as it removes the Courant condition plaguing explicit electromagnetic algorithms and can be implemented as a straightforward modification of electrostatic algorithms. The algorithm described here avoids iterative schemes needed for the divergence cleaning and represents a fast and efficient solver, which can be used in fluid and kinetic models for self-consistent description of technical plasmas exhibiting certain electromagnetic activity.

physics.plasm-ph↗

arXiv2011

Self-pulsing of a micro thin cathode discharge

Microplasmas operated at atmospheric pressure show a number of peculiar dynamic phenomena. One of these phenomena is self-pulsing, which is characterized by intrinsic pulsing behavior of a DC driven plasma discharge. This work focuses on the numerical simulation of self-pulsing in a micro thin cathode discharge operated in atmospheric pressure argon. By means of a hybrid plasma model we show self-pulsing of the discharge in the expected MHz frequency range and described its actual origin.

physics.plasm-ph↗

arXiv2011

Ionization wave propagation on a micro cavity plasma array

Microcavity plasma arrays of inverse pyramidal cavities have been fabricated in p-Si wafers. Each cavity acts as a microscopic dielectric barrier discharge. Operated at atmospheric pressure in argon and excited with high voltage at about 10 kHz, each cavity develops a localized microplasma. Experiments have shown a strong interaction of individual cavities, leading to the propagation of wave-like optical emission structures along the surface of the array. This phenomenon is numerically investigated using computer simulation. The observed ionization wave propagates with a speed of about 5 km/s, which agrees well the experimental findings. It is found that the wave propagation is due to sequential contributions of a drift of electrons followed by drift of ions between cavities seeded by photoemission of electrons by the plasma in adjacent cavities.

physics.plasm-ph↗

arXiv2011

Numerical study of secondary electron emission in a coaxial radio-frequency driven plasma jet at atmospheric pressure

In this work we investigate a numerical model of a coaxial RF-driven plasma jet operated at atmospheric pressure. Due to the cylindrical symmetry an adequate 2-D representation of the otherwise 3-dimensional structure is used. A helium-oxygen chemistry reaction scheme is applied. We study the effect of secondary electrons emitted at the inner electrode as well as the inserted dielectric tube and discuss their impact on the discharge behavior. We conclude that a proper choice of materials can improve the desired mode of operation of such plasma jets in terms of materials and surface processing.

physics.plasm-ph↗

arXiv2011

Spatially resolved simulation of a radio frequency driven micro atmospheric pressure plasma jet and its effluent

Radio frequency driven plasma jets are frequently employed as efficient plasma sources for surface modification and other processes at atmospheric pressure. The radio-frequency driven micro atmospheric pressure plasma jet ($μ$APPJ) is a particular variant of that concept whose geometry allows direct optical access. In this work, the characteristics of the $μ$APPJ operated with a helium-oxygen mixture and its interaction with a helium environment are studied by numerical simulation. The density and temperature of the electrons, as well as the concentration of all reactive species are studied both in the jet itself and in its effluent. It is found that the effluent is essentially free of charge carriers but contains a substantial amount of activated oxygen (O, O$_3$ and O$_2(^1Δ)$). The simulation results are verified by comparison with experimental data.

physics.plasm-ph↗

arXiv2011

Fine-sorting One-dimensional Particle-In-Cell Algorithm with Monte-Carlo Collisions on a Graphics Processing Unit

Particle-in-cell (PIC) simulations with Monte-Carlo collisions are used in plasma science to explore a variety of kinetic effects. One major problem is the long run-time of such simulations. Even on modern computer systems, PIC codes take a considerable amount of time for convergence. Most of the computations can be massively parallelized, since particles behave independently of each other within one time step. Current graphics processing units (GPUs) offer an attractive means for execution of the parallelized code. In this contribution we show a one-dimensional PIC code running on Nvidia GPUs using the CUDA environment. A distinctive feature of the code is that size of the cells that the code uses to sort the particles with respect to their coordinates is comparable to size of the grid cells used for discretization of the electric field. Hence, we call the corresponding algorithm "fine-sorting". Implementation details and optimization of the code are discussed and the speed-up compared to classical CPU approaches is computed.

physics.plasm-ph↗