On determining polarization characteristics of ion cyclotron wave magnetic field fluctuations

Polarization characteristics of magnetospheric proton cyclotron waves should provide definitive tests of mechanisms for wave propagation and growth. Previous studies used Fourier spectral analysis to determine the ellipticity epsilon and the minimum variance direction (e) over cap(min), which gives theta(min), the angle between (e) over cap(min) and the background field B-0. Comparison with theoretical models depends critically on accurate determination of epsilon and theta(min). However, observed fluctuations might not be sets of phase-coherent sine waves, as implicitly assumed in Fourier analysis, but may consist of series of packets whose phase and azimuthal orientation vary randomly. By constructing synthetic nonstationary signals, we find that spectral analysis of data intervals containing several wave packets systematically underestimates theta(min), often by 45 degrees or more, and overestimates \epsilon\. The problem is caused by fluctuations In the polarization ellipse azimuth orientation. We present a minimum variance analysis technique, called wave-step analysis, which requires only a few wave cycles of data. Tests of the wave-step procedure show that it is valid for signals with bandwidths up to similar to 30% full width at half maximum and is therefore applicable to the majority of proton cyclotron wave events. Comparison of the wave-step and Fourier analyses for cyclotron wave events confirms that cyclotron wave fluctuations display features characteristic of nonstationary signals. Relative to the wave-step results, the Fourier results underestimate theta(min), overestimate \epsilon\, and display the predicted variations of these parameters with each other and with azimuth angle fluctuations. The opposite relationship between Fourier and wave-step theta(min) should result if the signals were too broadbanded for the wave-step algorithm. Thus the theta(min) results provide an unambiguous indication of nonstationarity. Time windows of 30 s proved to be too long for analysis of similar to 0.5 Hz signals, indicating that analysis needs to be carried out on timescales shorter than tens of wave periods. Previous analyses reported theta(min) less than or equal to 30 degrees, but the wave-step results for one linearly polarized event analyzed here show that theta(min) can be larger than 70 degrees.