The spectral ratio method has some shortcomings, e.g., one has to assume that the transverse fluctuations consist of a slab component and a 2D component only, and that these two components have the same spectral shape over the wavenumber range considered. This is why new techniques have recently been developed to investigate the slab and 2D turbulence. In particular, Horbury et al. (2008) proposed a different approach: a local mean magnetic field can be defined, at any given time and scale, as the convolution between the instantaneous magnetic field B0 and a Gaussian function (normalized to unity) whose width is the scale of interest. Fluctuations at a particular scale and at a range of angles to the local mean magnetic field can be gathered to study the solar wind turbulence in that direction. To obtain an estimate for the component of the turbulence that might provide the largest contribution to the scattering of the electrons, most likely fluctuations with wavevectors nearly parallel to the magnetic field (i.e., the “slab” component) with which the electrons can interact resonantly, we apply the method of wavelet transforms (e.g., Bruno & Telloni 2015). Figure 11 shows the power spectral density of the z-component of the magnetic field during 2002 October 20 as a function of the angle between the orientations of the local mean magnetic field and the sampling direction. The angular distribution of the normalized magnetic helicity spectrum of the magnetic field fluctuations is presented in Figure 12. At wavenumbers around 





 km−1 left- and right-handed polarized magnetic fluctuations, commonly associated with ion cyclotron waves and kinetic Alfvén waves, respectively (Podesta & Gary 2011; Telloni et al. 2015), are clearly resolved in quasi-perpendicular and quasi-parallel directions with respect to the local mean magnetic field. Figure 13 shows the total power spectral density, Pzz(k), of the Bz component computed by means of the wavelet transforms (black curve), which is in good agreement with the spectral density determined with the standard FFT method as described above. The red curve, which makes up ≈50% of the transverse power, shows our estimate for the slab component. It is obtained by integrating the angular distribution of power spectral density of Bz shown in Figure 11, between 0° and 10°, i.e., over the angle range where the magnetic field vector can be considered quasi-parallel to the radial direction. In other words, the slab component is obtained by averaging, at each scale, the power spectral density found at those time instants when the magnetic field and the velocity vectors are, at that particular scale, aligned within 10°. It is worth noting that, since the data points involved in these averages can be very few (in an Alfvénic fast wind, such as the one considered in the present analysis, the magnetic field vector is mostly perpendicular or highly oblique to the velocity vector), the uncertainty related to the averages can be very large. As for the spectral ratio test, the underlying assumption is that Pzz(k) consists of two disjoint parts—a slab component with 





 and a 2D component with 





—and the more the real geometry of the fluctuations deviates from the above, the larger the uncertainty in the amount of the slab component will become. Nevertheless, the above method seems to provide the best estimate of the slab component of the solar wind fluctuations that can be provided by single-spacecraft measurements at the moment (e.g., Chen et al. 2010; Wicks et al. 2010). In the following, we adopt as a working hypothesis that a 50% slab component is responsible for the scattering of the electrons and we neglect effects of the magnetic helicity.
Citation: Telloni et al. 2015
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