I have made my own reactor system that i am operating at around 600e-3 mbar. I also made my own single Langmuir probe using tungsten wire of diameter 0.2mm. I have a supply that can give potential from -60 to 60 Dc source for plasma potential and the gap between the electrodes is about 50mm. Whenever i supply plasma potential i cannot observe probe current(tried both in mA and micro ampere range).
I have used the attached image from M. Konuma for my circuit as reference.
EDIT: Actually i did try to measure current using a resistor of about 10 ohm resistance in between probe and the DC supply of -60 to +60. I used galvanometer of micrometer range and digital multi meter in Milli ampere range. Probe voltage is applied between probe tip and ground. One of the possible problem might be due to low density of plasma as Johannes said since the plasma intensity is low. Also there might be other issues yet to be found.