Planar Resonance Probe in a Free Molecular Arc-Heated Flowing Plasma

Abstract

A shift in the measured frequency position of the current minimum drawn by a resonance probe near the plasma frequency is shown to be caused by a difference in ion and electron directed velocities in a lowdensity arc-heated wind tunnel.In a uniform stationary plasma a resonance probe draws a minimum current at the plasma frequency if (v c /vp )2«1, where Vp is the plasma frequency and Vc is the electron-neutral collision frequency.l.2 However, in a free molecular flowing plasma in which the electron and ion directed velocities Vand V+ are not equal, the frequency position of the minimum current drawn to a planar probe is shifted even if (v c/vp )2«1 unless none of the directed particles impinge on the probe surface. The frequency shift in this case is given bywhere w= 211"v, Vm is the frequency at the mmlmum current, m is the electron mass, e is the electron charge, and Eo is the magnitude of the alternating electric field in the plasma. The derivation of (1) is based on impedance calculations and follows Ref. 1 from this journal closely. The plasma impedance can be written aswhere C p is the plasma capacitance and the specific impedance Z= flu. E is the dielectric constant and 1 f 1 = 1; u is the conductivity inwhere E= Eo exp(iwt) and the second term is the displacement current. The first term in Eq. (3) is based on the Langevin equation with no magnetic field, m{d[V-(t) J/dt} +mvc V-(t) = -eEo exp(iwt). (4) From Eq. (4) one obtains by integration V-(t) = -(elm) [1/ (vc+iw) JEo exp(iwt) +C, (5)