Method to Characterize Experimentally Linear and Nonlinear Growth of Electrostatic Waves in Low Temperature Plasmas

An experimental method is presented for investigating the spatiotemporal properties of electrostatic waves that induce particle and energy transport in low temperature plasmas (LTP). The technique is based on formulating the evolution of the instabilities in terms of a governing equation for the complex amplitudes of the plasma instabilities. This equation encodes information about the dispersion, linear growth, and wave-wave coupling of the resonant modes in the plasma. A technique that leverages a translating, rotating two-point probe diagnostic is then presented for generating the data necessary regress the governing wave equation. Multiple methods for inferring the wave properties from this data are presented including a technique based on Bayesian regression with conjugate priors. The method is validated against direct numerical simulations of a crossed-field LTP in which numerical probes are employed to simulate the placement of physical probes. The extension of the technique to laboratory plasmas is also discussed.