Active plasma resonance spectroscopy: Eigenfunction solutions in spherical geometry

Research output: Journal contributionsJournal articlesResearchpeer-review

Authors

The term active plasma resonance spectroscopy 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 ωpe: 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. The mathematical model of an arbitrarily shaped probe-plasma system can be written in an abstract but very compact equation. It contains an appropriate operator, which describes the dynamical behavior and can be split into a conservative and a dissipative part. Based on the cold plasma model, this manuscript provides a solution strategy to determine the electrical admittance of a specific probe-plasma system derived from the abstract dynamical equation. Focusing on probes with a spherical-shaped probe tip the general admittance can be derived analytically. Therefore, the matrix representation of the resolvent of the dynamical operator is determined. This matrix representation is derived by means of the eigenfunctions and eigenvalues of the conservative operator. It can be shown that these eigenvalues 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 established probe designs: the spherical impedance probe and the multipole resonance probe.

Original languageEnglish
Article number065025
JournalPlasma Sources Science and Technology
Volume23
Issue number6
Number of pages10
ISSN0963-0252
DOIs
Publication statusPublished - 01.12.2014
Externally publishedYes

    Research areas

  • Engineering - active plasma resonance spectroscopy, eigenfunctions, eigenvalues, functional analytic, impedance probe, multipole resonance probe, resonance frequencies

Recently viewed

Publications

  1. Material flow analysis between dynamic modelling and life cycle assessment
  2. Collaborative benchmarking of functional-structural root architecture models
  3. Finite element modeling of laser beam welding for residual stress calculation
  4. Internet research differs from research on internet users
  5. Frame-based Data Factorizations
  6. Gerbil – Benchmarking named entity recognition and linking consistently
  7. Introduction to the Design, Implementation, and Management of Digital Government Policies and Strategies Minitrack
  8. Strengthening the transformative impulse while mainstreaming real-world labs: Lessons learned from three years of BaWü-Labs
  9. Learning in the "Third Space"
  10. Introduction: Habitual Action, Automaticity, and Control
  11. Practice and carryover effects when using small interaction devices
  12. Teaching Sustainable Development in a Sensory and Artful Way — Concepts, Methods, and Examples
  13. Unraveling Privacy Concerns in Complex Data Ecosystems with Architectural Thinking
  14. Influence of Mg content in Al alloys on processing characteristics and dynamically recrystallized microstructure of friction surfacing deposits
  15. A Two-Stage Augmented Extended Kalman Filter as an Observer for Sensorless Valve Control in Camless Internal Combustion Engines
  16. Stimulating Computing
  17. Comparison of three methods of length compensation in a parallel kinematic and their equivalence conditions
  18. Introduction
  19. Can a Revision of the Universal Service Scope Result in Substantive Change?
  20. Modeling and simulation of the heterogenous material behavior in thermal-sprayed coatings
  21. Sliding Mode Control of an Inductive Power Transmission System with Maximum Efficiency
  22. Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions
  23. Estimated substitution elasticities of a nested CES production function approach for Germany
  24. Short-arc measurement and fitting based on the bidirectional prediction of observed data
  25. Graph-Based Early-Fusion for Flood Detection
  26. Adaptive Notch Filter in Wavelet Packet Trees
  27. An introduction to sliding mode control for interdisciplinary education
  28. Short and long-term dominance of negative information in shaping public energy perceptions
  29. Deconstructing and reconstructing diversity in client-provider-relationships of social work
  30. Analysis of the relevance of models, influencing factors and the point in time of the forecast on the prediction quality in order-related delivery time determination using machine learning
  31. A Framework for Applying Natural Language Processing in Digital Health Interventions
  32. Vielfalt des Alterns - Differenz oder Integration?
  33. Changing the decision context to enable social learning for climate adaptation
  34. On the Equivalence of Transmission Problems in Nonoverlapping Domain Decomposition Methods for Quasilinear PDEs