Active plasma resonance spectroscopy: a kinetic functional analytic description

Oberrath, Jens; Brinkmann, R. P.

doi:10.1088/0963-0252/23/4/045006

Cited by 22 publications

(54 citation statements)

References 42 publications

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“…It consists of two half-spherical electrodes E 1/2 of radius R − d, which are surrounded by a dielectric D of thickness d. Applying RF voltages U 1/2 at the electrodes, which are phase shifted by 180 • , the plasma will be dynamically disturbed in the surrounding of the probe. This perturbed plasma P united with the dielectric is defined as the influence region of the probe V = P ∪ D. In the general kinetic model of [41] an interface F between the perturbed and unperturbed plasma is defined, which is treated in this manuscript as a grounded spherical surface at a large distance R ∞ on the length scale of the Debye length λ D (Theoretically it is located in an infinite distance. ).…”

Section: Kinetische Analyse Der Multipol-resonanz-sondementioning

confidence: 99%

“…The analysis of the study of [40] can be generalized in a full kinetic description and yields an abstract kinetic model of electrostatic resonances valid for all pressures [41]. The main result of this model is similar to the result of the fluid model, which is: for any possible probe design, the spectral response of the probe-plasma system can be expressed as a matrix element of the resolvent of the dynamical operator.…”

Section: Introductionmentioning

confidence: 96%

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The spherical multipole resonance probe: kinetic damping in its spectrum

Oberrath¹

2020

Plasma Sources Sci. Technol.

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The multipole resonance probe is one of the recently developed measurement devices to measure plasma parameter like electron density and temperature based on the concept of active plasma resonance spectroscopy. The dynamical interaction between the probe and the plasma in electrostatic, kinetic description can be modeled in an abstract notation based on functional analytic methods.These methods provide the opportunity to derive a general solution, which is given as the response function of the probe-plasma system. It is defined by the matrix elements of the resolvent of an appropriate dynamical operator. Based on the general solution a residual damping for vanishing pressure can be predicted and can only be explained by kinetic effects. Within this manuscript an explicit response function of the multipole resonance probe is derived. Therefore, the resolvent is determined by its algebraic representation based on an expansion in orthogonal basis functions. This allows to compute an approximated response function and its corresponding spectra, which show additional damping due to kinetic effects.

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Section: Kinetische Analyse Der Multipol-resonanz-sondementioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

The spherical multipole resonance probe: kinetic damping in its spectrum

Oberrath¹

2020

Plasma Sources Sci. Technol.

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“…The derivation is presented in the Appendix A). Equation (21) shows, that the inner potential Φ λκ k of a basis function is zero for all λ = 0 = κ. The same holds for the inner potential Φ λ κ k if λ = 0 = κ .…”

Section: Explicit Expansion Of the Inner Admittancementioning

confidence: 99%

Kinetic damping in the spectra of the spherical impedance probe

Oberrath¹

2018

Plasma Sources Sci. Technol.

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The impedance probe is a measurement device to measure plasma parameter like electron density.It consists of one electrode connected to a network analyzer via a coaxial cable and is immersed into a plasma. A bias potential superposed with an alternating potential is applied to the electrode and the response of the plasma is measured. Its dynamical interaction with the plasma in electrostatic, kinetic description can be modeled in an abstract notation based on functional analytic methods.These methods provide the opportunity to derive a general solution, which is given as the response function of the probe-plasma system. It is defined by the matrix elements of the resolvent of an appropriate dynamical operator. Based on the general solution a residual damping for vanishing pressure can be predicted and can only be explained by kinetic effects. Within this manuscript an explicit response function of the spherical impedance probe is derived. Therefore, the resolvent is determined by its algebraic representation based on an expansion in orthogonal basis functions. This allows to compute an approximated response function and its corresponding spectra. These spectra show additional damping due to kinetic effects and are in good agreement with former kinetically determined spectra.

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“…We deal with the following model, which is a linearized and normalized kinetic equation, based on the Boltzmann equation [109], and is given as …”

Section: Modellingmentioning

confidence: 99%

“…Such a response allows to see the natural ability of plasmas, which is the resonance on or near the plasma frequency. The model equation of such a process is a Boltzmann equation, we deal with a linearization and obtain a linear kinetic equation, see [109], which can be applied with linear splitting methods.…”

Section: Introductionmentioning

confidence: 99%

Engineering Applications

Geiser

2015

Multicomponent and Multiscale Systems

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In this chapter, we discuss the different engineering applications related to multicomponent and multiscale models, that occur in different categories (microscopic, mesoscopic and macroscopic). As we have described in the Introduction on p. xxv. That such models can be used as basic model to couple to more complicate models, describing materials, interfaces, etc., see Rosso and de Baas (Review of materials modelling: what makes a material function? Let me compute the ways, 2014, [1]).We deal with the following engineering applications with the two classified multiscaling approaches, see also the Introduction on p. xxv and in Fig. 5.1:• Different time-or spatial scales of same model (mono model or basic model).• Linking of different models (different models or multimodel).One of the main contributions to link the different scales and models together are the coupling techniques. In our motivation, such coupling of different time-and spatial scales or coupling of different models, need the suggested methods, e.g. multiscale methods, multicomponent methods, that allow a data transfer between the different scales and models. Such methods, we have introduced in the previous sections and now, we will close the gap between the theoretical discussions of methods and their applications to engineering problems. In such a stage, we have to adapt the numerical schemes with respect to the real-life properties and we obtain truly working multiscale approaches, that we solve the engineering complexities, see [1].Based on the real-life applications, we could study such helpful coupling of different scales or different models. Therefore, we overcome the gap of the recent problem in linking different scales of complicated engineering models in the industrial applications. Multiscale Methods for Langevin-Like EquationsAbstract In this section, we discuss multiscale methods, that solve Langevin-like equations, see [2]. The underlying ideas are to split into a deterministic and stochastic part of the Langevin equation, see [3]. The splitting methods are based on additive and iterative schemes, which are discussed with respect of their benefits and drawbacks, see [4]. We are motivated to reduce computational time for Coulomb collisions in plasma done in particle simulations. We extend splitting schemes, which are well-known in deterministic applications, to stochastic applications and modify the methods with respect to the stochastic terms. Such an idea allows to solve the multiscale behaviour of the coarse deterministic and fine stochastic timescales in an adequate computational time. Introduction of the ProblemIn the underlying problem, we are motivated to develop fast algorithms to solve the Coulomb collisions in plasma simulations, see [5].Recently in the literature, we can find two main ideas to deal with the Coulomb collisions in particle simulations. Here we have the following two ideas:• Binary algorithm: Particles in a finite cell selected into binary pairs. The collision is computed by the scattered velocities by an ...

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Active plasma resonance spectroscopy: a kinetic functional analytic description

Cited by 22 publications

References 42 publications

The spherical multipole resonance probe: kinetic damping in its spectrum

The spherical multipole resonance probe: kinetic damping in its spectrum

Kinetic damping in the spectra of the spherical impedance probe

Engineering Applications

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