a composite magnetic spectrum taken at 1 AU using the ACE and Cluster spacecraft (Kiyani et al., 2015). Fluctuations are organized in different frequency ranges, each with a different power law. The main central part (10−3Hz < f < 10−1Hz) is characterized by a Kolmogorov −5/3 spectral slope; this corresponds to the inertial range of an MHD turbulent cascade that transports energy from large to small scales, as in hydrodynamics turbulence (Bruno & Carbone, 2013).
It should be recalled here that due to the high speed of the solar wind flow compared to the typical velocities associated to the motion of the plasma fluctuations (Taylor hypothesis), time frequencies measured in the spacecraft frame can be interpreted as spatial k‐vectors in the plasma frame. It is then possible to study the 3D distribution of k‐vectors in the inertial range using measurements at different angles with respect to the main field (Horbury et al., 2008; Saur & Bieber, 1999; Wicks et al., 2010); this suggests a quasi‐2D distribution of the power, constituted by very elongated turbulent eddies along the magnetic field and a turbulent cascade that occurs preferentially for k‐vectors perpendicular with respect to the magnetic field.
At larger scales, the spectrum of magnetic fluctuations is often characterized by a shallower slope, close to −1 (Bavassano, Dobrowolny, Mariani et al., 1982; Denskat & Neubauer, 1982); this range, called 1/f, is sometimes considered as the energy reservoir for the turbulent cascade, in analogy with hydrodynamics, although this analogy is not necessarily straightforward (Tu & Marsch, 1995) and more generally, the origin of the 1/f range is still under debate in the community (Chandran, 2018; Matteini et al., 2018; Matthaeus & Goldstein, 1986; Velli et al., 1989; Verdini et al., 2012).
At higher frequencies, around scales corresponding to the typical ion characteristic lengths (ion gyroradius ρi and inertial length di ), the spectrum becomes steeper. This is expected when MHD breaks down, and kinetic physics starts to play a role. Moreover, fluctuations become more compressible at these scales, as a result of the transition from a regime where the electric field is controlled by ideal‐MHD to a Hall‐MHD regime (e.g., Alexandrova et al., 2008; Kiyani et al., 2013; Lacombe et al., 2017). As a consequence, the spectrum of the electric field, which follows that of the magnetic field at large MHD fluid scales, starts to depart at ion scales and display a shallower spectral slope at sub‐ion scale, such that the ratio of electric‐to‐magnetic fluctuations increases linearly with f (Matteini et al., 2017).
At even higher frequencies, approaching electron plasma scales (f: 50–100Hz, corresponding to a few km at 1 AU), the magnetic spectrum of the background turbulence steepens further; see 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
