High-Resolution Measurement of the Turbulent Frequency-Wavenumber Power Spectrum in a Laboratory Magnetosphere

In a laboratory magnetosphere, plasma is confined by a strong dipole magnet, where interchange and entropy mode turbulence can be studied and controlled in near steady-state conditions\footnote{Garnier, \textit{et al.}, \textit{Phys Plasmas}, \textbf{24}, 012506 (2017).}. Whole-plasma imaging shows turbulence dominated by long wavelength modes having chaotic amplitudes and phases\footnote {Grierson, \textit{et al.}, \textit{Phys Plasmas}, \textbf{16}, 055902 (2009).}. Here, we report for the first time, high-resolution measurement of the frequency-wavenumber power spectrum by applying the method of Capon\footnote{Capon, \textit{Proc. IEEE}, \textbf{57}, 1408 (1969).} to simultaneous multi-point measurement of electrostatic entropy modes using an array of floating potential probes. Unlike previously reported measurements in which ensemble correlation between two probes detected only the dominant wavenumber, Capon's ``maximum likelihood method'' uses all available probes to produce a frequency-wavenumber spectrum, showing the existence of modes propagating in \emph{both} electron and ion magnetic drift directions. We also discuss the wider application of this technique to laboratory and magnetospheric plasmas with simultaneous multi-point measurements.