RF Impedance of a Spherical Probe at High and Low Gas Pressure

ORAL

Abstract

The plasma electron density n$_{eo}$ is most often determined using a Langmuir probe to measure the dc current as a function of the applied dc voltage V$_{dc}$. The dc impedance Z$_{dc}$ varies strongly with V$_{dc}$, and models are needed to relate Z$_{dc}$ to n$_{eo}$. Secondary electron emission, ion collisions, and other effects further complicate the analysis. Alternatively, a variable rf voltage can be applied while holding V$_{dc}$ fixed. As long as the rf voltage is small, the rf impedance Z$_{rf}$ varies with the frequency f but not the amplitude of the voltage, and for a fixed frequency, Z$_{rf}$ depends only on n$_{e}$(r) and the neutral gas density N. In this talk theoretical and experimental results for Z$_{rf}$ are related to n$_{eo}$ for a small spherical probe. At low N, Z$_{rf}$ becomes resistive whenever f equals the local plasma frequency, and both the real and imaginary parts of Z$_{rf}$ peak when f equals the bulk plasma frequency. The peaks make n$_{eo}$ easy to determine, and the resistance at lower frequencies can be used to determine n$_{e}$(r) within the sheath and presheath. At high N, the resistance depends mainly on n$_{eo}$/N, so n$_{eo}$ is again easy to determine. Theoretical and experimental results for several spheres will be compared with Langmuir-probe data at high and low gas pressure.

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Authors

  • R.F. Fernsler

    US Naval Research Laboratory, Plasma Physics Division, US Naval Research Laboratory

  • Paule Maguire

    Department of Chemistry and Physics, Lamar University, Applied Materials, Sandia National Laboratories, Institute for Theoretical Electrical Engineering, Ruhr University Bochum, D-44780 Bochum, Germany, Ecole Polytechnique, France, Assistant Research Professor, University of Saskatchewan, PPPL, University of Saskatchewan, Saskatoon, Canada, Plasma Physics Laboratory, Princeton University, Technische Universiteit Eindhoven, Institut fur Niedertemperatur Plasmaphysik, Old Dominion University, Norfolk, VA 23529, Korea Advanced Institute of Science and Technology \& New York University, Korea Advanced Institute of Science and Technology, St.Petersburg State Politechnical University, St.Petersburg, Russia, Hanyang University, University of Nantes, Eindhoven University of Technology, Universidad Nacional Autonoma de Mexico, Air Force Research Laboratory, Innovative Scientific Solutions, Inc, University of Cambridge, UK, University of Bristol, UK, University Kiel, Germany, INP Greifswald, Germany, KRISS, INP, Greifswald, Germany, Australian National University, Drake University, University of Central Florida, University of Missouri-Rolla, John Carroll University, Indiana University-Purdue University Fort Wayne, University of Southampton, UK and Hong Kong Polytechnic University, University of Nottingham, UK, University of Pittsburgh, Department of Physics, Pittsburgh, PA 15260, Department of Computer Science, Lamar University, Institute of Nuclear Physics, Moscow State University, Russia, Univ. of Houston, Dublin City University, Ireland, West Virginia University, Nagoya Institute of Technology, National University of Ireland, Maynooth, 3M Company, Samsung Electronics, Kyoto University, EM2C, Ecole Centrale, CNRS, Chatenay, France, University of Duisburg-Essen, Ruhr Uni Bochum, LSP, UJF, CNRS, Grenoble, France, Lawrence Berkeley National Laboratory, Tech-X Corporation, Dublin City University, Princeton Plasma Physics Laboratory, Plasma Physics Division, Naval Research Laboratory, The Open University, United Kingdom, Eindhoven University of Technology, The Netherlands, University of Minnesota, Universit\'e Joseph Fourier de Grenoble, France, Nagoya University, Japan, West Virginia University, Physics Department, Morgantown, WV 26506-6315, Dept. of Physics and Astronomy, The Open University, Milton Keynes, UK, Institute for Plasma and Atomic Physics, CPST, Ruhr-University Bochum, Germany, CAMS, Australian National University, Schuster Laboratory, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK, Centre for Antimatter-Matter Studies, Griffith University, ISAS/JAXA, University of Tokyo, Department of Aeronautics and Astronautics, Kyoto University, Kyoto, Japan, University of Texas at Austin, LTM, Grenoble, LSP, Grenoble, CPAT,Toulouse, LPGP, Orsay, France, NRL-NRC Postdoctoral Associate, SFA, Crofton, MD, Center for Plasma Science and Technology CPST, Ruhr University Bochum, D-44780 Bochum, Germany, Department of Physics, University Duisburg-Essen, D-45141 Essen, Germany, LACE, UCBL, CNRS, Lyon, France, LPTP, Ecole Polytechnique, CNRS, Palaiseau, France, Air Force Research Laboratory, Wright-Patterson AFB, OH, UES, INC., Dayton, OH, St. Petersburg State University, St. Petersburg, Russia, Suzuka National College of Technology, Japan, Plasma Research Laboratory, NCPST, Dublin City University, Dublin 9, Ireland, University Greifswald, Germany, Facultad de Ciencias, Universidad Autonoma del Estado de Morelos, Nagoya University, University of Liverpool, United Kingdom, LPTP, Ecole Polytechnique, Palaiseau, France, Laboratory for Optical Physics and Engineering, Dept. of Elec. and Computer Engr., University of Illinois, Laboratory for Optical Physics and Engineering, Dept. of Elect. and Computer Engr., University of Illinois, The Ohio State University (OH), Department of Physics, University of Rajshahi, Rajshahi, Bangladesh, CAMS, Murdoch University, Australia, Drake University, USA, Gothenburg University, University of Wisconsin- Madison, University of Wisconsin-Madison, Physics Dept., Sophia University, Chiyoda-ku, Tokyo 102-855, Japan, ARC Centre for Antimatter-Matter Studies, SoCPES, Flinders University, GPO Box 2100, Adelaide, 5001 Australia, Korea Advanced Institute of Science and Technology / New York University, National Fusion Research Center / Korea Advanced Institute of Science and Technology, Korea Advanced Institute of Science and Technology and Courant Institute-NYU, Institute for Theoretical Electrical Engineering, Ruhr University Bochum, Korea Advanced Institute of Science and Technology / NewYork University, Sandia National Labs, Plasma, Pulsed-Power, and Microwave Lab, Nuclear Engineering and Radiological Sciences Dept., University of Michigan, Varian Semiconductor Equipment Associates, Gloucester, MA, Dominion University, Norfolk, VA, Sheffield Hallam University, GE Global Research, Kintech, University of Nebraska, University of Fribourg, Switzerland, CAMS, Flinders University, Australia, University of Nantes, France, CFD Research Corporation, Huntsville, AL, USA, Research Professor

  • Paule Maguire

    Department of Chemistry and Physics, Lamar University, Applied Materials, Sandia National Laboratories, Institute for Theoretical Electrical Engineering, Ruhr University Bochum, D-44780 Bochum, Germany, Ecole Polytechnique, France, Assistant Research Professor, University of Saskatchewan, PPPL, University of Saskatchewan, Saskatoon, Canada, Plasma Physics Laboratory, Princeton University, Technische Universiteit Eindhoven, Institut fur Niedertemperatur Plasmaphysik, Old Dominion University, Norfolk, VA 23529, Korea Advanced Institute of Science and Technology \& New York University, Korea Advanced Institute of Science and Technology, St.Petersburg State Politechnical University, St.Petersburg, Russia, Hanyang University, University of Nantes, Eindhoven University of Technology, Universidad Nacional Autonoma de Mexico, Air Force Research Laboratory, Innovative Scientific Solutions, Inc, University of Cambridge, UK, University of Bristol, UK, University Kiel, Germany, INP Greifswald, Germany, KRISS, INP, Greifswald, Germany, Australian National University, Drake University, University of Central Florida, University of Missouri-Rolla, John Carroll University, Indiana University-Purdue University Fort Wayne, University of Southampton, UK and Hong Kong Polytechnic University, University of Nottingham, UK, University of Pittsburgh, Department of Physics, Pittsburgh, PA 15260, Department of Computer Science, Lamar University, Institute of Nuclear Physics, Moscow State University, Russia, Univ. of Houston, Dublin City University, Ireland, West Virginia University, Nagoya Institute of Technology, National University of Ireland, Maynooth, 3M Company, Samsung Electronics, Kyoto University, EM2C, Ecole Centrale, CNRS, Chatenay, France, University of Duisburg-Essen, Ruhr Uni Bochum, LSP, UJF, CNRS, Grenoble, France, Lawrence Berkeley National Laboratory, Tech-X Corporation, Dublin City University, Princeton Plasma Physics Laboratory, Plasma Physics Division, Naval Research Laboratory, The Open University, United Kingdom, Eindhoven University of Technology, The Netherlands, University of Minnesota, Universit\'e Joseph Fourier de Grenoble, France, Nagoya University, Japan, West Virginia University, Physics Department, Morgantown, WV 26506-6315, Dept. of Physics and Astronomy, The Open University, Milton Keynes, UK, Institute for Plasma and Atomic Physics, CPST, Ruhr-University Bochum, Germany, CAMS, Australian National University, Schuster Laboratory, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK, Centre for Antimatter-Matter Studies, Griffith University, ISAS/JAXA, University of Tokyo, Department of Aeronautics and Astronautics, Kyoto University, Kyoto, Japan, University of Texas at Austin, LTM, Grenoble, LSP, Grenoble, CPAT,Toulouse, LPGP, Orsay, France, NRL-NRC Postdoctoral Associate, SFA, Crofton, MD, Center for Plasma Science and Technology CPST, Ruhr University Bochum, D-44780 Bochum, Germany, Department of Physics, University Duisburg-Essen, D-45141 Essen, Germany, LACE, UCBL, CNRS, Lyon, France, LPTP, Ecole Polytechnique, CNRS, Palaiseau, France, Air Force Research Laboratory, Wright-Patterson AFB, OH, UES, INC., Dayton, OH, St. Petersburg State University, St. Petersburg, Russia, Suzuka National College of Technology, Japan, Plasma Research Laboratory, NCPST, Dublin City University, Dublin 9, Ireland, University Greifswald, Germany, Facultad de Ciencias, Universidad Autonoma del Estado de Morelos, Nagoya University, University of Liverpool, United Kingdom, LPTP, Ecole Polytechnique, Palaiseau, France, Laboratory for Optical Physics and Engineering, Dept. of Elec. and Computer Engr., University of Illinois, Laboratory for Optical Physics and Engineering, Dept. of Elect. and Computer Engr., University of Illinois, The Ohio State University (OH), Department of Physics, University of Rajshahi, Rajshahi, Bangladesh, CAMS, Murdoch University, Australia, Drake University, USA, Gothenburg University, University of Wisconsin- Madison, University of Wisconsin-Madison, Physics Dept., Sophia University, Chiyoda-ku, Tokyo 102-855, Japan, ARC Centre for Antimatter-Matter Studies, SoCPES, Flinders University, GPO Box 2100, Adelaide, 5001 Australia, Korea Advanced Institute of Science and Technology / New York University, National Fusion Research Center / Korea Advanced Institute of Science and Technology, Korea Advanced Institute of Science and Technology and Courant Institute-NYU, Institute for Theoretical Electrical Engineering, Ruhr University Bochum, Korea Advanced Institute of Science and Technology / NewYork University, Sandia National Labs, Plasma, Pulsed-Power, and Microwave Lab, Nuclear Engineering and Radiological Sciences Dept., University of Michigan, Varian Semiconductor Equipment Associates, Gloucester, MA, Dominion University, Norfolk, VA, Sheffield Hallam University, GE Global Research, Kintech, University of Nebraska, University of Fribourg, Switzerland, CAMS, Flinders University, Australia, University of Nantes, France, CFD Research Corporation, Huntsville, AL, USA, Research Professor

  • Paule Maguire

    Department of Chemistry and Physics, Lamar University, Applied Materials, Sandia National Laboratories, Institute for Theoretical Electrical Engineering, Ruhr University Bochum, D-44780 Bochum, Germany, Ecole Polytechnique, France, Assistant Research Professor, University of Saskatchewan, PPPL, University of Saskatchewan, Saskatoon, Canada, Plasma Physics Laboratory, Princeton University, Technische Universiteit Eindhoven, Institut fur Niedertemperatur Plasmaphysik, Old Dominion University, Norfolk, VA 23529, Korea Advanced Institute of Science and Technology \& New York University, Korea Advanced Institute of Science and Technology, St.Petersburg State Politechnical University, St.Petersburg, Russia, Hanyang University, University of Nantes, Eindhoven University of Technology, Universidad Nacional Autonoma de Mexico, Air Force Research Laboratory, Innovative Scientific Solutions, Inc, University of Cambridge, UK, University of Bristol, UK, University Kiel, Germany, INP Greifswald, Germany, KRISS, INP, Greifswald, Germany, Australian National University, Drake University, University of Central Florida, University of Missouri-Rolla, John Carroll University, Indiana University-Purdue University Fort Wayne, University of Southampton, UK and Hong Kong Polytechnic University, University of Nottingham, UK, University of Pittsburgh, Department of Physics, Pittsburgh, PA 15260, Department of Computer Science, Lamar University, Institute of Nuclear Physics, Moscow State University, Russia, Univ. of Houston, Dublin City University, Ireland, West Virginia University, Nagoya Institute of Technology, National University of Ireland, Maynooth, 3M Company, Samsung Electronics, Kyoto University, EM2C, Ecole Centrale, CNRS, Chatenay, France, University of Duisburg-Essen, Ruhr Uni Bochum, LSP, UJF, CNRS, Grenoble, France, Lawrence Berkeley National Laboratory, Tech-X Corporation, Dublin City University, Princeton Plasma Physics Laboratory, Plasma Physics Division, Naval Research Laboratory, The Open University, United Kingdom, Eindhoven University of Technology, The Netherlands, University of Minnesota, Universit\'e Joseph Fourier de Grenoble, France, Nagoya University, Japan, West Virginia University, Physics Department, Morgantown, WV 26506-6315, Dept. of Physics and Astronomy, The Open University, Milton Keynes, UK, Institute for Plasma and Atomic Physics, CPST, Ruhr-University Bochum, Germany, CAMS, Australian National University, Schuster Laboratory, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK, Centre for Antimatter-Matter Studies, Griffith University, ISAS/JAXA, University of Tokyo, Department of Aeronautics and Astronautics, Kyoto University, Kyoto, Japan, University of Texas at Austin, LTM, Grenoble, LSP, Grenoble, CPAT,Toulouse, LPGP, Orsay, France, NRL-NRC Postdoctoral Associate, SFA, Crofton, MD, Center for Plasma Science and Technology CPST, Ruhr University Bochum, D-44780 Bochum, Germany, Department of Physics, University Duisburg-Essen, D-45141 Essen, Germany, LACE, UCBL, CNRS, Lyon, France, LPTP, Ecole Polytechnique, CNRS, Palaiseau, France, Air Force Research Laboratory, Wright-Patterson AFB, OH, UES, INC., Dayton, OH, St. Petersburg State University, St. Petersburg, Russia, Suzuka National College of Technology, Japan, Plasma Research Laboratory, NCPST, Dublin City University, Dublin 9, Ireland, University Greifswald, Germany, Facultad de Ciencias, Universidad Autonoma del Estado de Morelos, Nagoya University, University of Liverpool, United Kingdom, LPTP, Ecole Polytechnique, Palaiseau, France, Laboratory for Optical Physics and Engineering, Dept. of Elec. and Computer Engr., University of Illinois, Laboratory for Optical Physics and Engineering, Dept. of Elect. and Computer Engr., University of Illinois, The Ohio State University (OH), Department of Physics, University of Rajshahi, Rajshahi, Bangladesh, CAMS, Murdoch University, Australia, Drake University, USA, Gothenburg University, University of Wisconsin- Madison, University of Wisconsin-Madison, Physics Dept., Sophia University, Chiyoda-ku, Tokyo 102-855, Japan, ARC Centre for Antimatter-Matter Studies, SoCPES, Flinders University, GPO Box 2100, Adelaide, 5001 Australia, Korea Advanced Institute of Science and Technology / New York University, National Fusion Research Center / Korea Advanced Institute of Science and Technology, Korea Advanced Institute of Science and Technology and Courant Institute-NYU, Institute for Theoretical Electrical Engineering, Ruhr University Bochum, Korea Advanced Institute of Science and Technology / NewYork University, Sandia National Labs, Plasma, Pulsed-Power, and Microwave Lab, Nuclear Engineering and Radiological Sciences Dept., University of Michigan, Varian Semiconductor Equipment Associates, Gloucester, MA, Dominion University, Norfolk, VA, Sheffield Hallam University, GE Global Research, Kintech, University of Nebraska, University of Fribourg, Switzerland, CAMS, Flinders University, Australia, University of Nantes, France, CFD Research Corporation, Huntsville, AL, USA, Research Professor

  • Paule Maguire

    Department of Chemistry and Physics, Lamar University, Applied Materials, Sandia National Laboratories, Institute for Theoretical Electrical Engineering, Ruhr University Bochum, D-44780 Bochum, Germany, Ecole Polytechnique, France, Assistant Research Professor, University of Saskatchewan, PPPL, University of Saskatchewan, Saskatoon, Canada, Plasma Physics Laboratory, Princeton University, Technische Universiteit Eindhoven, Institut fur Niedertemperatur Plasmaphysik, Old Dominion University, Norfolk, VA 23529, Korea Advanced Institute of Science and Technology \& New York University, Korea Advanced Institute of Science and Technology, St.Petersburg State Politechnical University, St.Petersburg, Russia, Hanyang University, University of Nantes, Eindhoven University of Technology, Universidad Nacional Autonoma de Mexico, Air Force Research Laboratory, Innovative Scientific Solutions, Inc, University of Cambridge, UK, University of Bristol, UK, University Kiel, Germany, INP Greifswald, Germany, KRISS, INP, Greifswald, Germany, Australian National University, Drake University, University of Central Florida, University of Missouri-Rolla, John Carroll University, Indiana University-Purdue University Fort Wayne, University of Southampton, UK and Hong Kong Polytechnic University, University of Nottingham, UK, University of Pittsburgh, Department of Physics, Pittsburgh, PA 15260, Department of Computer Science, Lamar University, Institute of Nuclear Physics, Moscow State University, Russia, Univ. of Houston, Dublin City University, Ireland, West Virginia University, Nagoya Institute of Technology, National University of Ireland, Maynooth, 3M Company, Samsung Electronics, Kyoto University, EM2C, Ecole Centrale, CNRS, Chatenay, France, University of Duisburg-Essen, Ruhr Uni Bochum, LSP, UJF, CNRS, Grenoble, France, Lawrence Berkeley National Laboratory, Tech-X Corporation, Dublin City University, Princeton Plasma Physics Laboratory, Plasma Physics Division, Naval Research Laboratory, The Open University, United Kingdom, Eindhoven University of Technology, The Netherlands, University of Minnesota, Universit\'e Joseph Fourier de Grenoble, France, Nagoya University, Japan, West Virginia University, Physics Department, Morgantown, WV 26506-6315, Dept. of Physics and Astronomy, The Open University, Milton Keynes, UK, Institute for Plasma and Atomic Physics, CPST, Ruhr-University Bochum, Germany, CAMS, Australian National University, Schuster Laboratory, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK, Centre for Antimatter-Matter Studies, Griffith University, ISAS/JAXA, University of Tokyo, Department of Aeronautics and Astronautics, Kyoto University, Kyoto, Japan, University of Texas at Austin, LTM, Grenoble, LSP, Grenoble, CPAT,Toulouse, LPGP, Orsay, France, NRL-NRC Postdoctoral Associate, SFA, Crofton, MD, Center for Plasma Science and Technology CPST, Ruhr University Bochum, D-44780 Bochum, Germany, Department of Physics, University Duisburg-Essen, D-45141 Essen, Germany, LACE, UCBL, CNRS, Lyon, France, LPTP, Ecole Polytechnique, CNRS, Palaiseau, France, Air Force Research Laboratory, Wright-Patterson AFB, OH, UES, INC., Dayton, OH, St. Petersburg State University, St. Petersburg, Russia, Suzuka National College of Technology, Japan, Plasma Research Laboratory, NCPST, Dublin City University, Dublin 9, Ireland, University Greifswald, Germany, Facultad de Ciencias, Universidad Autonoma del Estado de Morelos, Nagoya University, University of Liverpool, United Kingdom, LPTP, Ecole Polytechnique, Palaiseau, France, Laboratory for Optical Physics and Engineering, Dept. of Elec. and Computer Engr., University of Illinois, Laboratory for Optical Physics and Engineering, Dept. of Elect. and Computer Engr., University of Illinois, The Ohio State University (OH), Department of Physics, University of Rajshahi, Rajshahi, Bangladesh, CAMS, Murdoch University, Australia, Drake University, USA, Gothenburg University, University of Wisconsin- Madison, University of Wisconsin-Madison, Physics Dept., Sophia University, Chiyoda-ku, Tokyo 102-855, Japan, ARC Centre for Antimatter-Matter Studies, SoCPES, Flinders University, GPO Box 2100, Adelaide, 5001 Australia, Korea Advanced Institute of Science and Technology / New York University, National Fusion Research Center / Korea Advanced Institute of Science and Technology, Korea Advanced Institute of Science and Technology and Courant Institute-NYU, Institute for Theoretical Electrical Engineering, Ruhr University Bochum, Korea Advanced Institute of Science and Technology / NewYork University, Sandia National Labs, Plasma, Pulsed-Power, and Microwave Lab, Nuclear Engineering and Radiological Sciences Dept., University of Michigan, Varian Semiconductor Equipment Associates, Gloucester, MA, Dominion University, Norfolk, VA, Sheffield Hallam University, GE Global Research, Kintech, University of Nebraska, University of Fribourg, Switzerland, CAMS, Flinders University, Australia, University of Nantes, France, CFD Research Corporation, Huntsville, AL, USA, Research Professor