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 ca p(min), which gives theta(min), the angle between (e) over cap(min) an d the background field B-0. Comparison with theoretical models depends critically on accurate determination of epsilon and theta(min). Howev er, observed fluctuations might not be sets of phase-coherent sine wav es, as implicitly assumed in Fourier analysis, but may consist of seri es of packets whose phase and azimuthal orientation vary randomly. By constructing synthetic nonstationary signals, we find that spectral an alysis of data intervals containing several wave packets systematicall y underestimates theta(min), often by 45 degrees or more, and overesti mates \epsilon\. The problem is caused by fluctuations In the polariza tion ellipse azimuth orientation. We present a minimum variance analys is technique, called wave-step analysis, which requires only a few wav e cycles of data. Tests of the wave-step procedure show that it is val id for signals with bandwidths up to similar to 30% full width at half maximum and is therefore applicable to the majority of proton cyclotr on wave events. Comparison of the wave-step and Fourier analyses for c yclotron wave events confirms that cyclotron wave fluctuations display features characteristic of nonstationary signals. Relative to the wav e-step results, the Fourier results underestimate theta(min), overesti mate \epsilon\, and display the predicted variations of these paramete rs with each other and with azimuth angle fluctuations. The opposite r elationship 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 nonstationari ty. 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 o n timescales shorter than tens of wave periods. Previous analyses repo rted theta(min) less than or equal to 30 degrees, but the wave-step re sults for one linearly polarized event analyzed here show that theta(m in) can be larger than 70 degrees.