target="_blank" rel="nofollow" href="#ulink_7e1a7fca-4541-53b9-8c55-3c24a58ae30e">Figure 1.14 (right). We will discuss the background turbulence at electron scales in more detail below. Note that at these frequencies whistler wave activity is also sometimes observed, characterized by right‐handed circular polarization very distinct from that of the background turbulence (Kajdič et al., 2016a; Lacombe et al., 2014; O. W. Roberts et al., 2017; Stansby et al., 2016)
Figure 1.14 Top: Typical spectrum of magnetic field fluctuations in the solar wind from Kiyani et al. (2015). Measurements of ACE and Cluster at 1 AU from MHD to electron scales are shown. Doppler‐shifted characteristic scales, such as the correlation length λc and the ion and electron Larmor radii ρi, e are indicated by vertical dashed lines. Bottom: Superposed (more then 100) turbulent spectra of magnetic fluctuations under different plasma conditions from inertial to sub‐electron scales as measured by Cluster (Alexandrova et al., 2012).
(Source: Kiyani et al., 2015.)
1.4.2. Alfvén Waves in the Fast and Slow Winds
At large scales, one of the most distinctive feature is the high degree of correlation between magnetic and velocity fluctuations, suggesting an Alfvénic origin and corresponding to a flux of waves moving away from the Sun (Belcher & Davis, 1971). Even though the spectrum of velocity fluctuations within the inertial range follows a shallower power law, f −3/2, than the one governing magnetic fluctuations (Podesta et al., 2006; C. Salem et al., 2009). Alfvénic fluctuations are ubiquitous in the fast solar wind, where the correlation between velocity and magnetic field is typically very high, especially closer to the Sun. This is not the case in the slow wind, which is more irregular and compressible, and in general it does not display a high level of Alfvénic correlation. However, there are also periods of slow wind that appear highly Alfvénic, suggesting then a common origin as the main fast wind coming from coronal holes (D’Amicis & Bruno, 2015). Consistent with that, all the properties of this Alfvénic slow wind match those of the fast wind, thus reinforcing the idea of a common origin of the plasma (D’Amicis et al., 2018). Interestingly, in situ measurements suggest that a higher fraction of slow solar wind is also Alfvénic closer to the Sun (Stansby et al., 2019); this is an aspect that will benefit from the future explorations of Solar Orbiter and Parker Solar Probe.
Alfvénic streams (fast and slow) always display a 1/f range at large scales (Bavassano, Dobrowolny, Mariani et al., 1982; Denskat & Neubauer, 1982). It has been suggested that these fluctuations originate in the corona (Matthaeus & Goldstein, 1986), could be generated by Alfvén wave reflection in the acceleration region due to strong density gradients (Velli et al., 1989; Verdini et al., 2012), by parametric instability (Chandran, 2018), or be a consequence of a saturation of the wave amplitude (Matteini et al., 2018).
Alfvénic periods in the solar wind are also characterized by a remarkably low plasma and magnetic field compressibility (Matteini et al., 2015). This means that fluctuations in the 1/f range, although large and comparable to the background magnetic field intensity, act mostly like directional changes rather than compressing the field. How this state is achieved is today not fully understood, but it is very well maintained by the plasma during expansion, as confirmed by observations by Ulysses beyond 1 AU. Another consequence of this state is that modulation of the magnetic field also implies (anti‐correlated) local variations of the flow speed. This results in a spiky velocity profile in the fast solar wind (Matteini et al., 2014); the amplitude of the velocity enhancements tracks the Alfvén speed and is then largest close to the Sun. As mentioned earlier, Horbury et al. (2018) have suggested that the Alfvénic spikes observed in fast streams could be signatures of Alfvénic pulses injected by coronal jets surviving in interplanetary space (Karpen et al., 2017; M. A. Roberts et al., 2018). It has been argued that the effect of jets and velocity shears that may develop in the corona could significantly increase the strength of the radial component of the interplanetary magnetic field with radial distance away from the Sun (Lockwood et al., 2009a, 2009b). These kinematic effects could be the source of discrepancy between the open magnetic flux derived from numerical models of the solar corona and the magnetic field measured in situ (Lockwood et al., 2009a).
Below the 1/f range, and at scales smaller than a few hours, a turbulent inertial range is observed in all main fields (magnetic, electric, velocity and density); for example, see the review paper by Alexandrova et al. (2013). In the fast/Alfvénic wind, this corresponds to an almost incompressible MHD cascade, where fluctuations in density are small compared to magnetic and velocity fluctuations. The slow wind typically has a higher level of compressibility, suggesting a mixture of Alfvénic fluctuations and compressible structures, whose weight in the power spectrum also varies as a function of distance. Estimations of the turbulent cascade rate (Coburn et al., 2014; Sorriso‐Valvo et al., 2007) confirm the existence of an energy flux through MHD scales, whose amplitude roughly matches the external energy input needed to explain ion temperature profiles in interplanetary space (Hellinger et al., 2011)
1.4.3. Solar Wind Fluctuations at Kinetic Scales
We now discuss the turbulent fluctuations at the end of the Kolmogorov inertial range and at smaller scales, that is, the kinetic range of the solar wind turbulence, sometimes called the dissipation range by analogy with the usual hydrodynamic (HD) turbulence.
Approaching ion scales (100 km at 1 AU), the MHD approximation is no more valid, and ions and electrons cannot be considered as one fluid. As protons are much heavier than electrons, in the vicinity of the ion inertial length λi , there is a separation into two fluids (Hall‐MHD description). Arriving at the ion Larmor radius scale, ρi , ions should be considered as particles and not a fluid. The corresponding time scale is the ion cyclotron frequency fci . In the vicinity of fci , Alfvén waves become dispersive. In plasma with anisotropic ions, the Alfvén ion cyclotron (AIC) instability generates quasi‐parallel AIC waves, visible in turbulent spectra as bumps or breaks at the vicinity of fci (e.g., L. K. Jian et al., 2014; Lion et al., 2016). The intermittent structures present in the inertial range, have their smallest spatial scales with the strongest gradients. For example, the thickness of the current sheets is observed to be several λi , or the cross section of magnetic vortices is about a few ρi (Perrone et al., 2016, 2017). These small‐scale discontinuities have a distinct Fourier spectrum, f −2, for current sheets and shocks, and f −4 for magnetic vortices (Alexandrova, 2008). Thus, the presence of different phenomena, like ion temperature instabilities (Bale et al., 2009; Hellinger et al., 2006) and the strongest gradients of the intermittent structures, is at the origin of the spectral variability observed in the frequency range covering ion scales∼[0.1,3] Hz (C. W. Smith et al., 2006).
Between ion and electron scales, ∼[3, 30] Hz at 1 AU, one observes another general power‐law behavior of the magnetic spectrum (Alexandrova et al., 2009, 2012; Sahraoui et al., 2013). This suggests a small‐scale turbulent cascade of the electron fluid (e.g., Alexandrova et al., 2008; Schekochihin et al., 2009). This cascade is more compressible than the MHD inertial range (Alexandrova et al., 2008; Hamilton et al., 2008; Kiyani et al., 2013; Leamon et al., 1998; C. S. Salem et al., 2012; Turner et al., 2011). The observed compressibility can be explained by the β ‐dependent compressibility of oblique kinetic Alfvén waves (KAWs; Cerri et al., 2017; Lacombe et al., 2017; C. S. Salem et al., 2012).
In the vicinity of the electron scales (1 km at 1 AU), ions are fully kinetic and electrons start to become kinetic, so no magneto‐fluid motions are