The Impedance Characteristic of a Spherical Probe in an Isotropic Plasma

Abstract

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

Active plasma resonance spectroscopy: eigenfunction solutions in spherical geometry

“…After the orthonormal basis is derived, we have to compute the excitation vector to determine the admittance (15). Based on the specified geometry we are able to calculate the general excitation vector |e n .…”

“…Finally, we have to evaluate the matrix elements of the resolvent. Equation (16) shows that the matrix of the resolvent is equal the inverse of the matrix of the operator iω RF −T C −T D . As an example, we compute the matrix element concerning to the first term in equation ( 49), whereas the eigenvalue representation of the conservative operator T C is used…”

“…Within this class the coupling of a surface wave to the plasma is utilized, which excites resonance modes of frequencies below the electron plasma frequency. A number of different approaches has been reported to provide a deeper understanding of the resonance behavior of the system [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. All of them are based on a fluid dynamical approach and restricted to specific probe designs.…”

Kinetic damping in the spectra of the spherical impedance probe

“…In subsequent years, the RP was intensively investigated both experimentally and theoretically. Many researchers have attempted this task, especially the RP with a spherical electrode [4][5][6][7][8][9][10][11][12][13][14][15]. The theoretical works of the cited papers share a common feature in that the underlying models are based on an electrostatic approximation, but the plasma description is of a different complexity.…”

The planar Multipole Resonance Probe: a functional analytic approach

“…One class of APRS probes excites electrostatic resonances [2][3][4][5][6][7][8][9], which occur below ω pe and can be described by a model of the probeplasma system in an electrostatic approximation. Many approaches to understand these resonance phenomena have been reported [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. They have in common, that their models are based on a fluid dynamical description and they focus only on a specific design of a certain probe.…”