1. Plasma frequency [Blackwell2005] Network analyzer performs frequency sweeps. Look for peak near where you expect $\omega_{pe}$ to be.

2. Electron density [Blackwell2005] Excite a two-stream instability [Blackwell2005]. Introduce a beam of electrons into a cold, unmagnetized plasma to excite a two-stream instability. If the beam is weak enough, the instability peaks at roughly the electron plasma frequency. Since this is effectively another measurement of the plasma frequency, I'm not sure why this is better than the 1st method. Perhaps exciting the instability has a higher signal/noise ratio?

• [Blackwell2005] An improvement over Langmuir probes because contamination of the probe has a larger impact on its measurements than on the PIP.

• [Blackwell2005] recommends “choosing sufficiently shielded coax cables so that the impedance characteristics are not changed as cables are moved around during the experiment. ”
• [Blackwell2005] Nearby objects to the probe reflected radiation
• [Blackwell2005] At frequencies related to certain wavelengths, standing waves can form in the chamber.

• Planar probes
• Spherical probes - leads to a simpler analysis [Blackwell2005]
• Monopole antenna [Bilen1999]

Blackwell2005 discusses a PIP in a cold (cold ions) and unmagnetized plasma using a spherical probes. Provides a derivation of the circuit model (I reproduce part of it below) that captures the impedance of the sheath and the plasma.

Derivation of Eq. 2. Also citing Piel2009.

A calibration is common to remove the impedance of the non-plasma components (coax feedlines, network analyzer, etc).

• [Blackwell2005] does this by attaching a 50ohm load and then a short at the end of the feedline with the other end attached to a network analyzer. “the calibration consists of programming the analyzer to add phase shifts to the value of G to cancel out the phase shift from the cable.”