Scale dependence of the variance anisotropy near the proton gyroradius scale: Additional evidence for kinetic Alfvén waves in the solar wind at 1 AU

The kinetic Alfvén wave (KAW) has the property that for _p ∼ 1 the ratio (δB)²/(δB)² approaches zero in the small wave number limit k_p 1 and increases monotonically to values of order unity when k_p ∼ 1, where _p is the thermal proton gyroradius. In this study, the wave number dependence of the ratio (δB)²/(δB)² is used to investigate the existence of KAWs in the solar wind near the proton gyroradius scale k _p = 1. To facilitate comparisons between theory and observations, solar wind measurements of (δB)²/(δB)² are restricted to times when the local mean magnetic field B₀ is nearly perpendicular to the local flow velocity of the solar wind V. The quantity (δB)² is the average magnetic power in the B₀ direction and (δB)² is the average magnetic power in the V × B₀ direction. The analysis of 20 high speed streams in the ecliptic plane near 1AU from 2007 through 2011 consistently yield quantitatively similar results which all show a steady increase in the ratio (δB) ²/(δB)² in the neighborhood of k_p = 1 that is in reasonable agreement with the theory of KAWs derived from the Vlasov-Maxwell dispersion relation. These results are interpreted as evidence for the existence of an axisymmetric spectrum of KAWs in the fast solar wind at wave numbers near k_p = 1 where the energy spectrum of solar wind fluctuations steepens and kinetic physics becomes important.