  Hairpin probes measure electron density in plasmas where other techniques are
unsuitable. Previous hairpins were constructed as a quarter-wave resonant
structure typically made from a folded piece of wire. The present work conducts
the hairpin measurement in high electron density, up to approximately 10^12 /
cm3, corresponding to a plasma frequency of about 9 GHz. A series of four
probes is described, together with an easily reproducible implementation of the
associated microwave electronics using commercial off the shelf components that
are inexpensive compared to the network analyzer that is typically required.
Measuring higher densities requires increasing the resonant frequency, but we
were unable to accurately fabricate the required quarter wavelength structure
on the scale of 4 mm. Toward this end we explore operating a larger
quarter-wavelength structure at its 3d harmonic (3/4 resonator). Correction
coefficients are described for both the plasma sheath effect and the wire
coating. Measurements are taken in Argon at pressures below 20 mTorr. Results
are compared with Langmuir probe measurements.
