Using Capon's method to measure the Turbulent Frequency-Wavenumber Power Spectrum in a Laboratory Magnetosphere

Capon's ``maximum likelihood method'' computes a high-resolution frequency-wavenumber power spectrum from simultaneous multi-point measurements\footnote{Capon, \textit{Proc. IEEE}, \textbf{57}, 1408 (1969).}. We apply this analysis to an array of floating potential probes in a laboratory magnetosphere. %exhibiting turbulence dominated by long wavelength modes that have chaotic amplitudes and phases\footnote {Grierson, \textit{et al.}, \textit{Phys Plasmas}, \textbf{16}, 055902 (2009).}. A levitated dipole magnet confines plasma and enables the study of interchange and entropy mode turbulence in near steady-state conditions\footnote{Garnier, \textit{et al.}, \textit{Phys Plasmas}, \textbf{24}, 012506 (2017).}. We report a high-resolution measurement of the frequency-wavenumber power spectrum using Capon's analysis. An error analysis to numerically evaluate optimal parameters such as probe number and distribution through synthetic test data is included, and we present a geometrically intuitive derivation with a view to wider application of this technique for other plasma experiments.