Temporal limits of a rapidly swept Langmuir probe

Abstract

The finite, electrostatically achievable, temporal resolution of plasma properties from a turbulent discharge is limited by an array of effects wherein the theory of Langmuir probes breaks down. Formulations for the particle transit time, sheath formation time, plasma-probe resonance, polarization current, sheath capacitance, stray capacitance, and mutual capacitance effects are all evaluated for time-resolved operation of a Langmuir probe. The resulting time scales serve to place a theoretical bound on the maximum rate of a rapidly swept Langmuir probe as analyzed with typical thin-sheath collisionless probe theory. For plasma typical to the plume of a Hall effect thruster [xenon plasma, ne=(1–1000)×10+15 m−3, and Te=1–20 eV], upper limits of 0.01–70 kHz are observed for a noncapacitive compensated Langmuir probe. With a high-speed dual Langmuir probe (HDLP) (a regular probe plus a null compensation probe), the upper probing frequency limits are increased to 0.04–11 MHz limited by sheath capacitance in the far and near field, and polarization effects for closer internal measurements. For a typical tokamak edge plasma (with HDLP), the thermally equilibrated hotter species (typically Te≈Ti≈10 to 20 eV) and lighter ions together lend higher limiting rates of ion transit, sheath formation, and sheath capacitance effects (in excess of 20 MHz), but the fully magnetized plasma complicates the collected probe current, limiting the allowable sweep rate to <1 MHz (for a magnetic field of 2 T). Thus we find that the upper rate of Langmuir probe sweeping is in the low megahertz range for both electric thruster and fusion plasma device diagnostics.