The local wavenumber spectrum and its applications in turbulence and noise

This work introduces the concept of the local wavenumber and frequency spectrum, which can be estimated using a pair of spatially fixed, point data sources. The local wavenumber spectrum is shown to be equivalent to the conventional wavenumber and frequency spectrum, which is simply the Fourier transform of the time and space autocorrelation function, if the fluctuation satisfies certain assumptions characteristic of many plasma turbulence theories. Basically, the separate frequency components of the fluctuation must have an approximately sinusoidal spatial dependence with amplitudes and wavenumbers which are slowly varying compared to the mean wavenumber. Comparison of the wavenumber space moments of the two kinds of spectra provides a means of testing the reasonableness of this WKB-type model. Application of the local wavenumber spectrum is demonstrated using data from an RF-excited discharge plasma.