To be more specific, the plasma has a density <5x10^19/m^3 and 10eV temperature.
I was thinking either capacitive probes as, depending on the design, these can work in hotter/denser plasmas than Langmuir probes. They are really just a Langmuir probe without an exposed metallic tip when it comes down to it though, and work on a similar principle.
Also, perhaps millimeter-wave interferometry because when a microwave signal is passed through the plasma, where wave-particle interactions with the electrons cause a phase shift in the signal. The phase shift between this signal and a reference beam path is measured, and density information can be inferred.
