The Impedance Characteristic of a Spherical Probe in an Isotropic Plasma


  • J. Tarstrup,

  • W. J. Heikkila


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 ∼ 500°K) 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 106 to 107 sec−1. 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.