RF Admittance Measurements of a Slotted‐Sphere Antenna Immersed in a Plasma

Waletzko, J. A.; Bekefi, G.

doi:10.1002/rds196725489

Cited by 16 publications

(11 citation statements)

References 7 publications

(17 reference statements)

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“…Above f• a finite real part shows energy losses caused by the radiation of electrostatic waves. The qualitative agreement of Fejer's work with experiments [e.g., Davies, 1966;Waletzko and Bekefi, 1967;Heikkila et al, 1968] is remarkable, in view of the crude nature of the model. During the next few years the fluid theory was improved in a number of ways.…”

Section: Theorysupporting

confidence: 53%

The Impedance Characteristic of a Spherical Probe in an Isotropic Plasma

Tarstrup¹,

Heikkila²

1972

Radio Science

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An experimental investigation of the impedance characteristic of a spherical plasma probe has been carried out for a quantitative assessment of theoretical work, and of hydrodynamic or fluid theory in particular. A stable, low temperature (T ~ 500øK) plasma was produced in nitrogen by a cold cathode discharge, with a plasma frequency of the order of 15 MHz and with an electron collision frequency in the range of 100 to 107 sec-•. The probe consisted of two hemispheres, one serving as a guard to eliminate the effects of the, connecting leads; this geometry provided an almost purely radial electric field over the test hemisphere. Probe diameters ranged from 7 to 20 mm ( 10 to 30 Debye lengths). Hydrodynamic probe theory was tested against the experimental results for the specific cases corresponding to the probe at floating potential and at space potential. Good agreement was obtained for both the real and imaginary parts. The real part of the impedance shows a peak near the plasma frequency, a small shift being explicable in terms of realistic sheath profiles. Electron density can thus be deduced rather accurately, and electron temperature approximately, on the basis of hydrodynamic theory. Accurate values of the electron-neutral collision frequency were also obtained for plasmas where the collision frequency was larger than 0.4 times the radian plasma frequency. At lower pressures the presence of collisionless or Landau damping was clearly established, and the more accurate kinetic theory is necessary to explain the experimental results. 493 494 TARSTRUP AND HEIKKILA SPHERICAL PROBE IMPEDANCE 495

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Section: Theorysupporting

confidence: 53%

The Impedance Characteristic of a Spherical Probe in an Isotropic Plasma

Tarstrup¹,

Heikkila²

1972

Radio Science

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“…Following the functional analytic approach, we have to expand the admittance Y 1n by means of a complete orthonormal basis {l} of the Hilbert space. Introducing the corresponding completeness relation twice into equation (7) yields…”

Section: Probe Response In Functional Analytic Descriptionmentioning

confidence: 99%

Influence of kinetic effects on the spectrum of a parallel electrode probe

Oberrath

Brinkmann

2016

Plasma Sources Sci. Technol.

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Active Plasma Resonance Spectroscopy (APRS) denotes a class of diagnostic techniques which utilize the natural ability of plasmas to resonate on or near the electron plasma frequency ω pe . One particular class of APRS can be described in an abstract notation based on functional analytic methods in electrostatic approximation. These methods allow for a general solution of the kinetic model in arbitrary geometry. This solution is given as the response function of the probe-plasma system and is defined by the resolvent of an appropriate dynamical operator. The general response predicts an additional damping due to kinetic effects. This manuscript provides the derivation of an explicit response function of the kinetic APRS model in a simple geometry. Therefore, the resolvent is determined by its matrix representation based on an expansion in orthogonal basis functions. This allows to compute an approximated response function. The resulting spectra show clearly a stronger damping due to kinetic effects.

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“…In the course of the last fifty years, many variants of APRS have been proposed [3][4][5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

“…In the presence of plasma these resonances are shifted, and a qualitative analysis -based on the dispersion relation ω 2 = c 2 k 2 +ω 2 pe of an electromagnetic wave in a homogeneous plasmapredicts that the shift of the squared frequency ∆ω 2 = ω 2 − ω 2 0 is proportional to the local electron density n e . Electrostatic techniques [7][8][9][10][11][12][13][14], in contrast, excite surface wave modes which vanish at zero plasma density. In this case, the dispersion relation ω 2 = s k ω 2 pe of a long electrostatic surface wave propagating along a homogeneous plasma boundary sheath of thickness s before a conductor suggests that the squared resonance frequency ω 2 itself is proportional to the local electron density.…”

Section: Introductionmentioning

confidence: 99%

Active plasma resonance spectroscopy: a kinetic functional analytic description

Oberrath¹,

Brinkmann²

2014

Plasma Sources Sci. Technol.

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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 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.

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RF Admittance Measurements of a Slotted‐Sphere Antenna Immersed in a Plasma

Cited by 16 publications

References 7 publications

The Impedance Characteristic of a Spherical Probe in an Isotropic Plasma

The Impedance Characteristic of a Spherical Probe in an Isotropic Plasma

Influence of kinetic effects on the spectrum of a parallel electrode probe

Active plasma resonance spectroscopy: a kinetic functional analytic description

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