Sterling and Moore (2020) from the reconnection site – do not necessarily involve the same open-flux-transport mechanism, but clearly favor an RLO-based coronal heating scenario, and have more specific consequences for each individual models; for example, the importance flux-rope structures to the energetics of the inner heliosphere for Drake et al. (2021), magnetosonic perturbations in Zank et al. (2020), or specific photospheric/chromospheric motions for He et al. (2021b), Sterling and Moore (2020). The model of Ruffolo et al. (2020) suggests a very different scenario, whereby shear-driven instabilities play a crucial role outside of the Alfvén critical zone (where $V_R \gtrsim V_A$), where they would set the properties of the turbulent cascade and change the energy budget by boosting heating and acceleration of slower regions. Finally, in the Alfvénic turbulence/waves scenario, switchbacks result from the evolution of turbulence to very large amplitudes $|\delta\mathbf{B}| \gtrsim |\mathbf{B}_0|$ (Squire et al. 2020; Shoda et al. 2021; Mallet et al. 2021). In turn, given the low plasma $\beta$, this implies that the energy contained in Alfvénic fluctuations is significant even at PSP altitudes (at least in switchback-filled regions), by which point they should already have contributed significantly to heating. Combined with low-coronal observations (e.g., De Pontieu et al. 2007), this is an important constraint on wave-heating models (e.g., Cranmer et al. 2007).

Finally, despite the significant differences between models highlighted above, it is also worth noting some similarities. In particular, features of various models are likely to coexist and/or feed into one another. For example, some of the explosive, *ex situ* scenarios (§4.3.1–4.3.2) propose that such events release AWs, which then clearly ties into the AW/expansion scenario of 4.3.4. Indeed, as pointed out by Magyar et al. (2021b), the subsequent evolution of switchbacks as they propagate in the solar wind cannot be *avoided*, which muddies the *in situ/ex situ* distinction. In this case, the distinction between *in situ* and *ex situ* scenarios would be more related to the relevance of distinct, impulsive events to wave launching, as opposed to slower, quasi-continuous stirring of motions. Similarly, Ruffolo et al. (2020) discuss how waves propagating upwards from the low corona could intermix and contribute to the shear-driven dynamics that form the basis for their model. These interrelationships, and the coexistence of different mechanisms, should be kept in mind moving forward as we attempt to distinguish observationally between different mechanisms.

### 4.4.3 Open Questions and Future Encs

Given their predominance in the solar wind plasma close to the Sun and because each switchback is associated with a positive increase in the bulk kinetic energy of the flow – as they imply a net motion of the centre of mass of the plasma – it is legitimate to consider whether switchbacks play any dynamical role in the acceleration of the flow and its evolution in interplanetary space. Moreover, it is an open question if the kinetic energy and Poynting flux carried by these structures have an impact on the overall energy budget of the wind. To summarize, these are some of the main currently open questions about these structures and their role in the solar wind dynamics:

* Do switchbacks play any role in solar wind acceleration?

* Does energy transported by switchbacks constitute a important possible source for plasma heating during expansion?

* Do switchbacks play an active role in driving and maintaining the turbulent cascade?

* Are switchbacks distinct plasma parcels with different properties than surrounding plasma?

* Do switchbacks continuously decay and reform during expansion?

* Are switchbacks signatures of key processes in the Solar atmosphere and tracers of specific types of solar wind sources? (Open field regions vs. streamer)
* Can switchback-like magnetic-field reversals exist close to the Sun, inside the Alfvén radius?

Answering these questions require taking measurements even closer to the Sun and accumulating more statistics for switchbacks in different types of streams. These should include the fast solar wind, which has been so far seldomly encountered by PSP because of solar minimum and then a particularly flat heliospheric current sheet (HCS; which implies a very slow wind close to the ecliptic).

Crucially, future PSP Encs. will provide the ideal conditions for answering these open questions, as the S/C will approach the solar atmosphere further, likely crossing the Alfvén radius. Further, this phase will coincide with increasing solar activity, making possible to sample coronal hole sources of fast wind directly.

# 5 Solar Wind Sources and Associated Signatures

A major outstanding research question in solar and heliophysics is establishing causal relationships between properties of the solar wind and the source of that same plasma in the solar atmosphere. Indeed, investigating these connections is one of the major science goals of PSP, which aims to "determine the structure and dynamics of the plasma and magnetic fields at the sources of the solar wind" (Science Goal #2; Fox et al. 2016) by making in situ measurements closer to the solar corona than ever before. In this section, we outline the major outcomes, and methods used to relate PSP's measurements to specific origins on the Sun. In §5.1 we review modeling efforts and their capability to identify source regions. In §5.2 we outline how PSP has identified significant contributions to the slow solar wind from coronal hole origins with high alfvénicity. In §5.3 we review PSP's measurements of streams associated with the streamer belt and slow solar wind more similar to 1 AU measurements. In §5.4 we examine PSP's limited exposure to fast solar wind, and the diagnostic information about its coronal origin carried by electron pitch angle distributions (PADs). In §5.5 we recap PSP's measurements of energetic particles associated with solar activity and impulsive events, as well as how they can disentangle magnetic topology and identify pathways by which the Sun's plasma can escape. Finally, in §5.6 we briefly discuss clues to the solar origin of streams in which PSP observes switchbacks and refer the reader to §4 for much more detail.

## 5.1 Modeling and Verifying Connectivity

Association of solar wind sources with specific streams of plasma measured in situ in the inner heliosphere requires establishing a connection between the Sun and S/C along which solar wind flows and evolves. One of the primary tools for this analysis is combined coronal and heliospheric modeling, particularly of the solar and interplanetary magnetic field which typically governs the large scale flow streamlines for the solar wind.

In support of PSP, there has been a broad range of such modeling efforts with goals including making advance predictions to test and improve the models, as well as making detailed connectivity estimates informed by in situ measurements after the fact. The physics contained in coronal/heliospheric models lies on a continuum mediated by computational difficulty ranging from high computational tractability and minimal physics (Potential Field Source Surface [PFSS] models, Altschuler and Newkirk (1969), Schatten et al. (1969), Wang and Sheeley (1992) to comprehensive (but usually still time-independent) fluid plasma
* Can switchback-like magnetic-field reversals exist close to the Sun, inside the Alfvén radius?

Answering these questions require taking measurements even closer to the Sun and accumulating more statistics for switchbacks in different types of streams. These should include the fast solar wind, which has been so far seldomly encountered by PSP because of solar minimum and then a particularly flat heliospheric current sheet (HCS; which implies a very slow wind close to the ecliptic).

Crucially, future PSP Encs. will provide the ideal conditions for answering these open questions, as the S/C will approach the solar atmosphere further, likely crossing the Alfvén radius. Further, this phase will coincide with increasing solar activity, making possible to sample coronal hole sources of fast wind directly.

# 5 Solar Wind Sources and Associated Signatures

A major outstanding research question in solar and heliophysics is establishing causal relationships between properties of the solar wind and the source of that same plasma in the solar atmosphere. Indeed, investigating these connections is one of the major science goals of PSP, which aims to "determine the structure and dynamics of the plasma and magnetic fields at the sources of the solar wind" (Science Goal #2; Fox et al. 2016) by making in situ measurements closer to the solar corona than ever before. In this section, we outline the major outcomes, and methods used to relate PSP's measurements to specific origins on the Sun. In §5.1 we review modeling efforts and their capability to identify source regions. In §5.2 we outline how PSP has identified significant contributions to the slow solar wind from coronal hole origins with high alfvénicity. In §5.3 we review PSP's measurements of streams associated with the streamer belt and slow solar wind more similar to 1 AU measurements. In §5.4 we examine PSP's limited exposure to fast solar wind, and the diagnostic information about its coronal origin carried by electron pitch angle distributions (PADs). In §5.5 we recap PSP's measurements of energetic particles associated with solar activity and impulsive events, as well as how they can disentangle magnetic topology and identify pathways by which the Sun's plasma can escape. Finally, in §5.6 we briefly discuss clues to the solar origin of streams in which PSP observes switchbacks and refer the reader to §4 for much more detail.

## 5.1 Modeling and Verifying Connectivity

Association of solar wind sources with specific streams of plasma measured in situ in the inner heliosphere requires establishing a connection between the Sun and S/C along which solar wind flows and evolves. One of the primary tools for this analysis is combined coronal and heliospheric modeling, particularly of the solar and interplanetary magnetic field which typically governs the large scale flow streamlines for the solar wind.

In support of PSP, there has been a broad range of such modeling efforts with goals including making advance predictions to test and improve the models, as well as making detailed connectivity estimates informed by in situ measurements after the fact. The physics contained in coronal/heliospheric models lies on a continuum mediated by computational difficulty ranging from high computational tractability and minimal physics (Potential Field Source Surface [PFSS] models, Altschuler and Newkirk (1969), Schatten et al. (1969), Wang and Sheeley (1992) to comprehensive (but usually still time-independent) fluid plasma
physics (MHD, e.g., Mikić and Linker 1996; Riley et al. 2012) but requiring longer computational run times. Despite these very different overall model properties, in terms of coronal magnetic structure they often agree very well with each other, especially at solar minimum Riley et al. (2006).

In advance of PSP's first solar Enc. in Nov. 2018, Riley et al. (2019) and van der Holst et al. (2019) both ran MHD simulations. They utilized photospheric observations from the Carrington rotation (CR) prior to the Enc. happening and model parameters which were not informed by any *in situ* measurements. Both studies successfully predicted PSP would lie in negative polarity solar wind during perihelion and cross the HCS shortly after (see Fig. 10). Via field line tracing, Riley et al. (2019) in particular pointed to a series of equatorial coronal holes as the likely sources of this negative polarity and subsequent HCS crossing.

This first source prediction was subsequently confirmed with careful comparison of *in situ* measurements of the heliospheric magnetic field and tuning of model parameters. This was done both with PFSS modeling (Bale et al. 2019; Badman et al. 2020; Panasenco et al. 2020), Wang-Sheeley-Arge (WSA) PFSS + Current Sheet Modeling (Szabo et al. 2020) and MHD modeling (Réville et al. 2020a; Kim et al. 2020; Riley et al. 2021), all pointing to a distinct equatorial coronal hole at perihelion as the dominant solar wind source. As discussed in §5.2 the predominant solar wind at this time was slow but with high alfvénicity. This first Enc. has proved quite unique in how distinctive its source was, with subsequent Encs. typically connecting to polar coronal hole boundaries and a flatter HCS such that PSP trajectory skirts along it much more closely (Kim et al. 2020; Chen et al. 2021a; Riley et al. 2021).

It is worth discussing how these different modeling efforts made comparisons with *in situ* data in order to determine their connectivity. The most common is the timing and heliocentric location of current sheet crossings measured *in situ* which can be compared to the advected polarity inversion line (PIL) predicted by the various models (e.g., Szabo et al. 2020, and Fig. 10). By ensuring a given model predicts when these crossings occur as accurately as possible, the coronal magnetic geometry can be well constrained and provide good evidence that field line tracing through the model is reliable. Further, models can be tuned in order to produce the best agreement possible. This tuning process was used to constrain models using PSP data to more accurately find sources. For example, Panasenco et al. (2020) found evidence that different source surface heights (the primary free parameter of PFSS models) were more appropriate at different times during PSP's first two Encs. implying a non-spherical surface where the coronal field becomes approximately radial, and that a higher source surface height was more appropriate for PSP's second Enc. compared to its first. This procedure can also be used to distinguish between choices of photospheric magnetic field data (e.g., Badman et al. 2020).

Further validation of source estimates for PSP have been made in different ways. For example, if a given source estimate indicates a specific coronal hole, or polar coronal hole extension or boundary, the model can be used to produce contours of the open field and compared with EUV observations of coronal holes to detect if the modeled source is empirically present, and if so if its size and shape are accurately captured (e.g., Lee et al. 2011; Badman et al. 2020). Other *in situ* properties besides magnetic polarity have been compared in novel ways: Rouillard et al. (2020a) showed for PSP's second Enc. a distinct trend in *in situ* density depending on whether the S/C mapped to the streamer belt or outside (see §5.3 for more details). MHD models (e.g., Réville et al. 2020a; Kim et al. 2020; Riley et al. 2021) have also allowed direct timeseries predictions of other *in situ* quantities at the location of PSP which can be compared directly to the measured timeseries. Kinetic physics such as plasma distributions have provided additional clues: Berčič et al. (2020) showed cooler electron strahl
physics (MHD, e.g., Mikić and Linker 1996; Riley et al. 2012) but requiring longer computational run times. Despite these very different overall model properties, in terms of coronal magnetic structure they often agree very well with each other, especially at solar minimum Riley et al. (2006).

In advance of PSP's first solar Enc. in Nov. 2018, Riley et al. (2019) and van der Holst et al. (2019) both ran MHD simulations. They utilized photospheric observations from the Carrington rotation (CR) prior to the Enc. happening and model parameters which were not informed by any *in situ* measurements. Both studies successfully predicted PSP would lie in negative polarity solar wind during perihelion and cross the HCS shortly after (see Fig. 10). Via field line tracing, Riley et al. (2019) in particular pointed to a series of equatorial coronal holes as the likely sources of this negative polarity and subsequent HCS crossing.

This first source prediction was subsequently confirmed with careful comparison of *in situ* measurements of the heliospheric magnetic field and tuning of model parameters. This was done both with PFSS modeling (Bale et al. 2019; Badman et al. 2020; Panasenco et al. 2020), Wang-Sheeley-Arge (WSA) PFSS + Current Sheet Modeling (Szabo et al. 2020) and MHD modeling (Réville et al. 2020a; Kim et al. 2020; Riley et al. 2021), all pointing to a distinct equatorial coronal hole at perihelion as the dominant solar wind source. As discussed in §5.2 the predominant solar wind at this time was slow but with high alfvénicity. This first Enc. has proved quite unique in how distinctive its source was, with subsequent Encs. typically connecting to polar coronal hole boundaries and a flatter HCS such that PSP trajectory skirts along it much more closely (Kim et al. 2020; Chen et al. 2021a; Riley et al. 2021).

It is worth discussing how these different modeling efforts made comparisons with *in situ* data in order to determine their connectivity. The most common is the timing and heliocentric location of current sheet crossings measured *in situ* which can be compared to the advected polarity inversion line (PIL) predicted by the various models (e.g., Szabo et al. 2020, and Fig. 10). By ensuring a given model predicts when these crossings occur as accurately as possible, the coronal magnetic geometry can be well constrained and provide good evidence that field line tracing through the model is reliable. Further, models can be tuned in order to produce the best agreement possible. This tuning process was used to constrain models using PSP data to more accurately find sources. For example, Panasenco et al. (2020) found evidence that different source surface heights (the primary free parameter of PFSS models) were more appropriate at different times during PSP's first two Encs. implying a non-spherical surface where the coronal field becomes approximately radial, and that a higher source surface height was more appropriate for PSP's second Enc. compared to its first. This procedure can also be used to distinguish between choices of photospheric magnetic field data (e.g., Badman et al. 2020).

Further validation of source estimates for PSP have been made in different ways. For example, if a given source estimate indicates a specific coronal hole, or polar coronal hole extension or boundary, the model can be used to produce contours of the open field and compared with EUV observations of coronal holes to detect if the modeled source is empirically present, and if so if its size and shape are accurately captured (e.g., Lee et al. 2011; Badman et al. 2020). Other *in situ* properties besides magnetic polarity have been compared in novel ways: Rouillard et al. (2020a) showed for PSP's second Enc. a distinct trend in *in situ* density depending on whether the S/C mapped to the streamer belt or outside (see §5.3 for more details). MHD models (e.g., Réville et al. 2020a; Kim et al. 2020; Riley et al. 2021) have also allowed direct timeseries predictions of other *in situ* quantities at the location of PSP which can be compared directly to the measured timeseries. Kinetic physics such as plasma distributions have provided additional clues: Berčič et al. (2020) showed cooler electron strahl
<figure><img src="image_12.png" /><figcaption>**Fig. 10** Illustration of mapping procedure and model validation. A PFSS model is run using a source surface height of 2.0 $R_⊙$ and a Global Oscillation Network Group (GONG; Harvey et al. 1988) ZQS magnetogram from 6 Nov. 2018 (the date of the first PSP perihelion). A black solid line shows the resulting PIL. Running across the plot is PSP's first solar Enc. trajectory ballistically mapped to the model outer boundary. The color (red or blue) indicated the magnetic polarity measured *in situ* which compares well to the predicted crossings of the PIL. The resulting mapped field lines are shown as curves connecting PSP's trajectory to the Sun. A background map combining EUV images from the STEREO-A Extreme Ultraviolet Imager (EUVI – 195 Å; Wuelser et al. 2004) and the Advanced Imaging Assembly (AIA – 193 Å; Lemen et al. 2012) on the Solar Dynamic Observatory (SDO; Pesnell et al. 2012) shows the mapped locations correspond to coronal holes (dark regions) implying the locations of open magnetic field in the model are physical. Figure adapted from Badman et al. (2020)</figcaption></figure>

temperatures for solar wind mapping to a larger coronal hole during a fast wind stream, and hotter solar wind mapping to the boundaries of a smaller coronal hole during a slow solar wind stream. This suggests a connection between the strahl temperature and coronal origin (see §5.4 for more details). Stansby et al. (2021a) showed further in *in situ* connections with source type, observing an increase in mass flux (with PSP and Wind data) associated with increasing temperature of the coronal source, including variation across coronal holes and active regions (ARs).

Mapping sources with coronal modeling for PSP's early Encs. has nonetheless highlighted challenges yet to be addressed. The total amount of open flux predicted by modeling to escape the corona has been observed to underestimate that measured *in situ* in the solar wind at 1 AU (Linker et al. 2017), and this disconnect persists at least down 0.13 AU (Badman et al. 2021) suggesting there exist solar wind sources which are not yet captured accurately by modeling. Additionally, due to its orbital plane lying very close to the solar equator, the solar minimum configuration of a near-flat HCS and streamer belt means PSP spends a lot of time skirting the HCS (Chen et al. 2021a) and limits the types of sources that can be sampled. For example, PSP has yet to take a significant sample of fast solar wind from deep inside a coronal hole, instead sampling primarily streamer belt wind and coronal hole boundaries. Finally, connectivity modeling is typically time-static either due to physical model constraints or computational tractability. However, the coronal magnetic field is far from static with processes such as interchange reconnection potentially allowing previously closed structures to contribute to the solar wind (Fisk and Kasper 2020; Viall and Borovsky 2020), as well as disconnection at the tips of the streamer belt (Lavraud et al. 2020; Nindos et al. 2021). Such transient processes are not captured by the static modeling techniques discussed in this section, but have still been probed with PSP particularly in the context of streamer blowouts (SBOs; §5.3) via combining remote observations and *in situ* observations, typically requiring multi-S/C collaboration and minimizing modeling uncertainty. Such collaborations are rapidly becoming more and more possible especially with the
<figure><img src="image_13.png" /><figcaption>**Fig. 10** Illustration of mapping procedure and model validation. A PFSS model is run using a source surface height of 2.0 $R_⊙$ and a Global Oscillation Network Group (GONG; Harvey et al. 1988) ZQS magnetogram from 6 Nov. 2018 (the date of the first PSP perihelion). A black solid line shows the resulting PIL. Running across the plot is PSP's first solar Enc. trajectory ballistically mapped to the model outer boundary. The color (red or blue) indicated the magnetic polarity measured *in situ* which compares well to the predicted crossings of the PIL. The resulting mapped field lines are shown as curves connecting PSP's trajectory to the Sun. A background map combining EUV images from the STEREO-A Extreme Ultraviolet Imager (EUVI – 195 Å; Wuelser et al. 2004) and the Advanced Imaging Assembly (AIA – 193 Å; Lemen et al. 2012) on the Solar Dynamic Observatory (SDO; Pesnell et al. 2012) shows the mapped locations correspond to coronal holes (dark regions) implying the locations of open magnetic field in the model are physical. Figure adapted from Badman et al. (2020)</figcaption></figure>

temperatures for solar wind mapping to a larger coronal hole during a fast wind stream, and hotter solar wind mapping to the boundaries of a smaller coronal hole during a slow solar wind stream. This suggests a connection between the strahl temperature and coronal origin (see §5.4 for more details). Stansby et al. (2021a) showed further in *in situ* connections with source type, observing an increase in mass flux (with PSP and Wind data) associated with increasing temperature of the coronal source, including variation across coronal holes and active regions (ARs).

Mapping sources with coronal modeling for PSP's early Encs. has nonetheless highlighted challenges yet to be addressed. The total amount of open flux predicted by modeling to escape the corona has been observed to underestimate that measured *in situ* in the solar wind at 1 AU (Linker et al. 2017), and this disconnect persists at least down 0.13 AU (Badman et al. 2021) suggesting there exist solar wind sources which are not yet captured accurately by modeling. Additionally, due to its orbital plane lying very close to the solar equator, the solar minimum configuration of a near-flat HCS and streamer belt means PSP spends a lot of time skirting the HCS (Chen et al. 2021a) and limits the types of sources that can be sampled. For example, PSP has yet to take a significant sample of fast solar wind from deep inside a coronal hole, instead sampling primarily streamer belt wind and coronal hole boundaries. Finally, connectivity modeling is typically time-static either due to physical model constraints or computational tractability. However, the coronal magnetic field is far from static with processes such as interchange reconnection potentially allowing previously closed structures to contribute to the solar wind (Fisk and Kasper 2020; Viall and Borovsky 2020), as well as disconnection at the tips of the streamer belt (Lavraud et al. 2020; Nindos et al. 2021). Such transient processes are not captured by the static modeling techniques discussed in this section, but have still been probed with PSP particularly in the context of streamer blowouts (SBOs; §5.3) via combining remote observations and *in situ* observations, typically requiring multi-S/C collaboration and minimizing modeling uncertainty. Such collaborations are rapidly becoming more and more possible especially with the
recent launch of Solar Orbiter (SolO; Müller et al. 2020; Velli et al. 2020), recently yielding for the first time detailed imaging of the outflow of a plasma parcel in the mid corona by SolO followed by near immediate in situ measurements by PSP (Telloni et al. 2021a).

## 5.2 Sources of Slow Alfvénic Solar Wind

PSP's orbit has a very small inclination angle w.r.t. the ecliptic plane. It was therefore not surprising to find that over the first Encs. the solar wind streams were observed, with few exceptions, to have slower velocities than that expected for the high-speed streams (HSSs) typically originating in polar coronal holes around solar minimum. What however has been a surprise is that the slow solar wind streams were seen to have turbulence and fluctuation properties, including the presence of large amplitude folds in the magnetic field, i.e. switchbacks, typical of Alfvénic fluctuations usually associated with HSSs.

Further out from the Sun, the general dichotomy between fast Alfvénic solar wind and slow, non-Alfvénic solar wind (Grappin et al. 1991) is broken by the so-called slow Alfvénic streams, first noticed in the *Helios* data acquired at 0.3 AU (Marsch et al. 1981). That slow wind interval appeared to have much of the same characteristics of the fast wind, including the presence of predominantly outwards Alfvénic fluctuations, except for the overall speed. These were observed at solar maximum, while Parker's observations over the first three years have covered solar minimum and initial appearance of activity of the new solar cycle.

Alfvénic slow wind streams have also been observed at 1 AU (D'Amicis et al. 2011), and been extensively studied in their composition, thermodynamic, and turbulent characteristics (D'Amicis and Bruno 2015; D'Amicis et al. 2019). The results of these investigations point to a similar origin (D'Amicis and Bruno 2015) for fast and Alfvénic slow wind streams. Instances of slow Alfvénic wind at solar minimum were found re-examining the *Helios* data collected in the inner heliosphere (Stansby et al. 2019, 2020; Perrone et al. 2020b), again supporting a similar origin – coronal holes – for fast and slow Alfvénic wind streams.

Reconstruction of the magnetic sources of the wind seen by Parker for the first peri-helion clearly showed the wind origin to be associated with a small isolated coronal hole. Both ballistic backwards projection in conjunction with the PFSS method (Panasenco et al. 2020; Badman et al. 2020) and global MHD models showed PSP connected to a negative-polarity equatorial coronal hole, within which it remained for the entire Enc. (Riley et al. 2019; Réville et al. 2020a). The *in situ* plasma associated with the small equatorial coronal hole was a highly Alfvénic slow wind stream, parts of which were also seen near Earth at L1 (Bale et al. 2019; Panasenco et al. 2020). The relatively high intermittency, low compressibility (Perrone et al. 2020b), increased turbulent energy level (Chen et al. 2020a), and spectral break radial dependence are similar to fast wind (Duan et al. 2020), while particle distribution functions are also more anisotropic than in non-Alfvénic slow wind (Huang et al. 2020a).

Whether Alfvénic slow wind always originates from small isolated or quasi-isolated coronal holes (e.g., narrow equatorward extensions of polar coronal holes), with large expansion factors within the subsonic/supersonic critical point, or whether the boundaries of large, polar coronal holes might also produce Alfvénic slow streams, is still unclear.

There is however one possible implication of the overall high Alfvénicity observed by PSP in the deep inner heliosphere: that all of the solar wind might be born Alfvénic, or rather, that Alfvénic fluctuations be a universal initial condition of solar wind outflow. Whether this is borne out by PSP measurements closer to the Sun remains to be seen.
recent launch of Solar Orbiter (SolO; Müller et al. 2020; Velli et al. 2020), recently yielding for the first time detailed imaging of the outflow of a plasma parcel in the mid corona by SolO followed by near immediate in situ measurements by PSP (Telloni et al. 2021a).

## 5.2 Sources of Slow Alfvénic Solar Wind

PSP's orbit has a very small inclination angle w.r.t. the ecliptic plane. It was therefore not surprising to find that over the first Encs. the solar wind streams were observed, with few exceptions, to have slower velocities than that expected for the high-speed streams (HSSs) typically originating in polar coronal holes around solar minimum. What however has been a surprise is that the slow solar wind streams were seen to have turbulence and fluctuation properties, including the presence of large amplitude folds in the magnetic field, i.e. switchbacks, typical of Alfvénic fluctuations usually associated with HSSs.

Further out from the Sun, the general dichotomy between fast Alfvénic solar wind and slow, non-Alfvénic solar wind (Grappin et al. 1991) is broken by the so-called slow Alfvénic streams, first noticed in the *Helios* data acquired at 0.3 AU (Marsch et al. 1981). That slow wind interval appeared to have much of the same characteristics of the fast wind, including the presence of predominantly outwards Alfvénic fluctuations, except for the overall speed. These were observed at solar maximum, while Parker's observations over the first three years have covered solar minimum and initial appearance of activity of the new solar cycle.

Alfvénic slow wind streams have also been observed at 1 AU (D'Amicis et al. 2011), and been extensively studied in their composition, thermodynamic, and turbulent characteristics (D'Amicis and Bruno 2015; D'Amicis et al. 2019). The results of these investigations point to a similar origin (D'Amicis and Bruno 2015) for fast and Alfvénic slow wind streams. Instances of slow Alfvénic wind at solar minimum were found re-examining the *Helios* data collected in the inner heliosphere (Stansby et al. 2019, 2020; Perrone et al. 2020b), again supporting a similar origin – coronal holes – for fast and slow Alfvénic wind streams.

Reconstruction of the magnetic sources of the wind seen by Parker for the first peri-helion clearly showed the wind origin to be associated with a small isolated coronal hole. Both ballistic backwards projection in conjunction with the PFSS method (Panasenco et al. 2020; Badman et al. 2020) and global MHD models showed PSP connected to a negative-polarity equatorial coronal hole, within which it remained for the entire Enc. (Riley et al. 2019; Réville et al. 2020a). The *in situ* plasma associated with the small equatorial coronal hole was a highly Alfvénic slow wind stream, parts of which were also seen near Earth at L1 (Bale et al. 2019; Panasenco et al. 2020). The relatively high intermittency, low compressibility (Perrone et al. 2020b), increased turbulent energy level (Chen et al. 2020a), and spectral break radial dependence are similar to fast wind (Duan et al. 2020), while particle distribution functions are also more anisotropic than in non-Alfvénic slow wind (Huang et al. 2020a).

Whether Alfvénic slow wind always originates from small isolated or quasi-isolated coronal holes (e.g., narrow equatorward extensions of polar coronal holes), with large expansion factors within the subsonic/supersonic critical point, or whether the boundaries of large, polar coronal holes might also produce Alfvénic slow streams, is still unclear.

There is however one possible implication of the overall high Alfvénicity observed by PSP in the deep inner heliosphere: that all of the solar wind might be born Alfvénic, or rather, that Alfvénic fluctuations be a universal initial condition of solar wind outflow. Whether this is borne out by PSP measurements closer to the Sun remains to be seen.
<figure><img src="image_13.png" /><figcaption>**Fig. 11** A zoomed-in view of a Carrington map built from LASCO-C3 bands of image pixels extracted at 8 $R_⊙$. The PSP path corresponds to the points of magnetic connectivity traced back to the radial distance of the map (8 $R_⊙$). The connectivity is estimated by assuming the magnetic field follows a Parker spiral calculated from the speed of the solar wind measured *in situ* at PSP. The color coding is defined by the density ($N \times r^2$) measured *in situ* by PSP with red corresponding to high densities and blue to low densities. Figure adapted from Rouillard et al. (2020a)</figcaption></figure>

## 5.3 Near Streamer Belt Wind

As already discussed in part in §5.2, the slow solar wind exhibits at least two states. One state has similar properties to the fast wind, it is highly Alfvénic, has low densities and low source temperature (low charge state) and appears to originate from inside coronal holes (see for instance the review by D'Amicis et al. 2021). The other state of the slow wind displays greater variability, higher densities and more elevated source temperatures. The proximity of PSP to the Sun and the extensive range of longitudes scanned by the probe during an Enc. makes it inevitable that at least one of the many S/C (the Solar and Heliospheric Observatory [SOHO; Domingo et al. 1995], STEREO, SDO, & SolO) currently orbiting the Sun will image the solar wind measured *in situ* by PSP. Since coronagraph and heliospheric imagers tend to image plasma located preferably (but not only) in the vicinity of the so-called Thomson sphere (very close to the sky plane for a coronagraph), the connection between a feature observed in an image with its counterpart measured *in situ* is most likely to happen when PSP crosses the Thomson sphere of the imaging instrument. A first study exploited such orbital configurations that occurred during Enc. 2 when PSP crossed the Thompson spheres of the SOHO and STEREO-A imagers (Rouillard et al. 2020a). In this study, the proton speed measured by SWEAP was used to trace back ballistically the source locations of the solar wind to identify the source in coronagraphic observations.

Figure 11 presents, in a latitude versus longitude format, a comparison between the brightness of the solar corona observed by the Large Angle and Spectrometric CORonagraph (LASCO; Brueckner et al. 1995) on SOHO and the density of the solar wind measured *in situ* by PSP and color-coded along its trajectory. The Figure shows that as long as the probe remained inside the bright streamers, the density of the solar wind was high but as soon as it exited the streamers (due to the orbital trajectory of PSP), the solar wind density suddenly dropped by a factor of four but the solar wind speed remained the same around 300 km s⁻¹ (Rouillard et al. 2020a). Griton et al. (2021) exploited numerical models and ultraviolet imaging to show that as PSP exited streamer flows it sampled slow solar wind released from deeper inside an isolated coronal hole. These measurements illustrate nicely the transitions that can occur between two slow solar wind types over a short time period. While switchbacks were observed in both flows, the patches of switchbacks were also different between the two types of slow wind with more intense switchbacks patches measured in the streamer
<figure><img src="image_14.png" /><figcaption>**Fig. 11** A zoomed-in view of a Carrington map built from LASCO-C3 bands of image pixels extracted at 8 $R_⊙$. The PSP path corresponds to the points of magnetic connectivity traced back to the radial distance of the map (8 $R_⊙$). The connectivity is estimated by assuming the magnetic field follows a Parker spiral calculated from the speed of the solar wind measured *in situ* at PSP. The color coding is defined by the density ($N \times r^2$) measured *in situ* by PSP with red corresponding to high densities and blue to low densities. Figure adapted from Rouillard et al. (2020a)</figcaption></figure>

## 5.3 Near Streamer Belt Wind

As already discussed in part in §5.2, the slow solar wind exhibits at least two states. One state has similar properties to the fast wind, it is highly Alfvénic, has low densities and low source temperature (low charge state) and appears to originate from inside coronal holes (see for instance the review by D'Amicis et al. 2021). The other state of the slow wind displays greater variability, higher densities and more elevated source temperatures. The proximity of PSP to the Sun and the extensive range of longitudes scanned by the probe during an Enc. makes it inevitable that at least one of the many S/C (the Solar and Heliospheric Observatory [SOHO; Domingo et al. 1995], STEREO, SDO, & SolO) currently orbiting the Sun will image the solar wind measured *in situ* by PSP. Since coronagraph and heliospheric imagers tend to image plasma located preferably (but not only) in the vicinity of the so-called Thomson sphere (very close to the sky plane for a coronagraph), the connection between a feature observed in an image with its counterpart measured *in situ* is most likely to happen when PSP crosses the Thomson sphere of the imaging instrument. A first study exploited such orbital configurations that occurred during Enc. 2 when PSP crossed the Thompson spheres of the SOHO and STEREO-A imagers (Rouillard et al. 2020a). In this study, the proton speed measured by SWEAP was used to trace back ballistically the source locations of the solar wind to identify the source in coronagraphic observations.

Figure 11 presents, in a latitude versus longitude format, a comparison between the brightness of the solar corona observed by the Large Angle and Spectrometric CORonagraph (LASCO; Brueckner et al. 1995) on SOHO and the density of the solar wind measured *in situ* by PSP and color-coded along its trajectory. The Figure shows that as long as the probe remained inside the bright streamers, the density of the solar wind was high but as soon as it exited the streamers (due to the orbital trajectory of PSP), the solar wind density suddenly dropped by a factor of four but the solar wind speed remained the same around 300 km s⁻¹ (Rouillard et al. 2020a). Griton et al. (2021) exploited numerical models and ultraviolet imaging to show that as PSP exited streamer flows it sampled slow solar wind released from deeper inside an isolated coronal hole. These measurements illustrate nicely the transitions that can occur between two slow solar wind types over a short time period. While switchbacks were observed in both flows, the patches of switchbacks were also different between the two types of slow wind with more intense switchbacks patches measured in the streamer
flows (Rouillard et al. 2020a), this is also seen in the spectral power of switchbacks (Fargette et al. 2021a). Griton et al. (2021) show that both types of solar winds can exhibit very quiet solar wind conditions (with no switchback occurrence). These quiet periods are at odds with theories that relate the formation of the slow wind with a continual reconfiguration of the coronal magnetic field lines due to footpoint exchange, since this should drive strong wind variability continually (e.g., Fisk 1996).

Chen et al. (2021a) also measured a distinct transition between streamer belt and non-streamer belt wind by looking at turbulence properties during the fourth PSP perihelion when the HCS was flat and PSP skirted the boundary for an extended period of time. They associated lower turbulence amplitude, higher magnetic compressibility, a steeper turbulence spectrum, lower Alfvénicity and a lower frequency spectral break with proximity to the HCS, showing that at PSP’s perihelia distances in situ data allows indirect distinction between solar wind sources.

Finally, in addition to steady state streamer belt and HCS connectivity, remote sensing and in situ data on board PSP has also been used to track transient solar phenomena erupting or breaking off from the streamer belt. Korreck et al. (2020) detected the passage of a SBO coronal mass ejection (SBO-CME) during PSP Enc. 1 and via imaging from STEREO-A at 1 AU and coronal modeling with WSA associated it with a specific helmet streamer. Similarly, Lario et al. (2020) associated a SBO with a CME measured at PSP during the second Enc. and via stereographic observations from 1 AU and arrival time analysis modeled the flux rope structure underlying the structure.

## 5.4 Fast Solar Wind Sources

During the first eight Encs. of PSP, there are only very few observations of fast solar wind, e.g., 9 Nov. 2018 and 11 Jan. 2021. Most of the time, PSP was inside the slow wind streams. Thus, exploration of the source of fast wind remains as a future work.

The first observed fast wind interval was included in the study by Berčič et al. (2020), who investigated the relation between the suprathermal solar wind electron population called the strahl and the shape of the electron VDF in the solar corona. Combining PSP and Helios observations they found that the strahl parallel temperature ($T_{s\parallel}$) does not vary with radial distance and is anticorrelated with the solar wind velocity, which indicates that $T_{s\parallel}$ is a good proxy for the electron coronal temperature. Figure 12 shows the evolution of $T_{s\parallel}$ along a part of the first PSP orbit trajectory ballistically projected down to the corona to produce sub-S/C points. PFSS model was used to predict the magnetic connectivity of the sub-S/C points to the solar surface. The observed fast solar wind originates from the equatorial coronal hole (Badman et al. 2020), and is marked by low $T_{s\parallel}$ ($< 75$ eV). These values are in excellent agreement with the coronal hole electron temperatures obtained via the spectroscopy technique (David et al. 1998; Cranmer 2002).

Shi et al. (2021) analyzed data from the first five Encs. of PSP and showed how the Alfvénicity varies with the solar wind speed. Figure 13 shows the statistical result of the normalized cross helicity $\sigma_c$ for waves with periods between 112 and 56 seconds, well inside the inertial range of the MHD turbulence. Although the result may be affected by certain individual wind streams due to the limited volume of data, overall, a positive $\sigma_c - V_f$ correlation is observed, indicating that the faster wind is generally more Alfvénic than the slower wind. We should emphasize that the result is acquired mostly from measurements of the slow solar wind as the fast wind was rarely observed by PSP. Thus, the result implies that even for the slow solar wind, the faster stream is more Alfvénic than the slow stream. This could be a result of the shorter nonlinear evolution for the turbulence, which leads to a decrease
flows (Rouillard et al. 2020a), this is also seen in the spectral power of switchbacks (Fargette et al. 2021a). Griton et al. (2021) show that both types of solar winds can exhibit very quiet solar wind conditions (with no switchback occurrence). These quiet periods are at odds with theories that relate the formation of the slow wind with a continual reconfiguration of the coronal magnetic field lines due to footpoint exchange, since this should drive strong wind variability continually (e.g., Fisk 1996).

Chen et al. (2021a) also measured a distinct transition between streamer belt and non-streamer belt wind by looking at turbulence properties during the fourth PSP perihelion when the HCS was flat and PSP skirted the boundary for an extended period of time. They associated lower turbulence amplitude, higher magnetic compressibility, a steeper turbulence spectrum, lower Alfvénicity and a lower frequency spectral break with proximity to the HCS, showing that at PSP's perihelia distances *in situ* data allows indirect distinction between solar wind sources.

Finally, in addition to steady state streamer belt and HCS connectivity, remote sensing and *in situ* data on board PSP has also been used to track transient solar phenomena erupting or breaking off from the streamer belt. Korreck et al. (2020) detected the passage of a SBO coronal mass ejection (SBO-CME) during PSP Enc. 1 and via imaging from STEREO-A at 1 AU and coronal modeling with WSA associated it with a specific helmet streamer. Similarly, Lario et al. (2020) associated a SBO with a CME measured at PSP during the second Enc. and via stereographic observations from 1 AU and arrival time analysis modeled the flux rope structure underlying the structure.

## 5.4 Fast Solar Wind Sources

During the first eight Encs. of PSP, there are only very few observations of fast solar wind, e.g., 9 Nov. 2018 and 11 Jan. 2021. Most of the time, PSP was inside the slow wind streams. Thus, exploration of the source of fast wind remains as a future work.

The first observed fast wind interval was included in the study by Berčič et al. (2020), who investigated the relation between the suprathermal solar wind electron population called the strahl and the shape of the electron VDF in the solar corona. Combining PSP and Helios observations they found that the strahl parallel temperature ($T_{s\|}$) does not vary with radial distance and is anticorrelated with the solar wind velocity, which indicates that $T_{s\|}$ is a good proxy for the electron coronal temperature. Figure 12 shows the evolution of $T_{s\|}$ along a part of the first PSP orbit trajectory ballistically projected down to the corona to produce sub-S/C points. PFSS model was used to predict the magnetic connectivity of the sub-S/C points to the solar surface. The observed fast solar wind originates from the equatorial coronal hole (Badman et al. 2020), and is marked by low $T_{s\|}$ (< 75 eV). These values are in excellent agreement with the coronal hole electron temperatures obtained via the spectroscopy technique (David et al. 1998; Cranmer 2002).

Shi et al. (2021) analyzed data from the first five Encs. of PSP and showed how the Alfvénicity varies with the solar wind speed. Figure 13 shows the statistical result of the normalized cross helicity $\sigma_c$ for waves with periods between 112 and 56 seconds, well inside the inertial range of the MHD turbulence. Although the result may be affected by certain individual wind streams due to the limited volume of data, overall, a positive $\sigma_c - V_f$ correlation is observed, indicating that the faster wind is generally more Alfvénic than the slower wind. We should emphasize that the result is acquired mostly from measurements of the slow solar wind as the fast wind was rarely observed by PSP. Thus, the result implies that even for the slow solar wind, the faster stream is more Alfvénic than the slow stream. This could be a result of the shorter nonlinear evolution for the turbulence, which leads to a decrease
<figure><img src="image_14.png" /><figcaption>**Fig. 12** The evolution of $T_s$|| with part of the PSP orbit 1 between 30 Oct. 2018, 00:30 UT (Universal Time) and 23 Nov. 2018, 17:30 UT. The PSP trajectory is ballistically projected down to the corona ($2 R_⊙$) to produce sub-S/C points. The colored lines denote the magnetic field lines mapped from the sub-S/C points to the solar surface as predicted by the PFSS model with source surface height $2 R_⊙$, the same as used in Bale et al. (2019) and Badman et al. (2020). The white line shows the PFSS neutral line. The points and magnetic field lines are colored w.r.t. hour-long averages of $T_s$||. The corresponding image of the Sun is a synoptic map of the 193 Å emission synthesized from STEREO/EUVI and SDO/AIA for CR 2210, identical to the one used by Badman et al. (2020) in their Figs. 5 and 9</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>**Fig. 13** Normalized cross helicity $\sigma_c$ of wave periods 112 s–56 s as a function of the radial distance to the Sun $R$ (horizontal axis; $R_S \equiv R_⊙$) and radial speed of the solar wind $V_r$ (vertical axis). The colors of each block represent the median values of the binned data. Text on each block shows the value of the block and the number of data points (bracketed) in the block. Figure adapted from Shi et al. (2021)</figcaption></figure>

of the Alfvénicity, in the faster stream. Panasenco et al. (2020) and Shi et al. (2021) showed that the slow wind originating from the equatorial pseudostreamers is Alfvénic while that originating from the boundary of the polar coronal holes is low-Alfvénic. Thus, this speed-dependence of Alfvénicity could also be related to the different sources of the slow wind streams.

## 5.5 Active Region Sources

The magnetic structure of the corona is important to determining solar wind outflow in at least two different ways, closed coronal field lines providing a geometrical backbone deter-
<figure><img src="image_15.png" /><figcaption>**Fig. 12** The evolution of $T_s$|| with part of the PSP orbit 1 between 30 Oct. 2018, 00:30 UT (Universal Time) and 23 Nov. 2018, 17:30 UT. The PSP trajectory is ballistically projected down to the corona ($2 R_⊙$) to produce sub-S/C points. The colored lines denote the magnetic field lines mapped from the sub-S/C points to the solar surface as predicted by the PFSS model with source surface height $2 R_⊙$, the same as used in Bale et al. (2019) and Badman et al. (2020). The white line shows the PFSS neutral line. The points and magnetic field lines are colored w.r.t. hour-long averages of $T_s$||. The corresponding image of the Sun is a synoptic map of the 193 Å emission synthesized from STEREO/EUVI and SDO/AIA for CR 2210, identical to the one used by Badman et al. (2020) in their Figs. 5 and 9</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>**Fig. 13** Normalized cross helicity $\sigma_c$ of wave periods 112 s–56 s as a function of the radial distance to the Sun $R$ (horizontal axis; $R_S \equiv R_⊙$) and radial speed of the solar wind $V_r$ (vertical axis). The colors of each block represent the median values of the binned data. Text on each block shows the value of the block and the number of data points (bracketed) in the block. Figure adapted from Shi et al. (2021)</figcaption></figure>

of the Alfvénicity, in the faster stream. Panasenco et al. (2020) and Shi et al. (2021) showed that the slow wind originating from the equatorial pseudostreamers is Alfvénic while that originating from the boundary of the polar coronal holes is low-Alfvénic. Thus, this speed-dependence of Alfvénicity could also be related to the different sources of the slow wind streams.

## 5.5 Active Region Sources

The magnetic structure of the corona is important to determining solar wind outflow in at least two different ways, closed coronal field lines providing a geometrical backbone deter-
mining the expansion rate of neighboring field lines, and the dynamics of the boundaries between closed and open fields provides time-dependent heating and acceleration mechanisms, as occurs with emerging ARs.

Emerging ARs reconfigure the local coronal field, leading to the formation of new coronal hole or coronal hole corridors often at there periphery, and depending on the latitude emergence may lead to the formation of large pseudostreamer or reconfiguration of helmet streamers, therefore changing solar wind distributions. Such reconfiguration is also accompanied by radio bursts and energetic particle acceleration, with at least one energetic particle event seen by IS©IS, on 4 Apr. 2019, attributed to this type of process (Leske et al. 2020; Kouloumvakos et al. 2020).

The event seen by PSP was very small, with peak 1 MeV proton intensities of ~0.3 particles cm⁻² sr⁻¹ s⁻¹ MeV⁻¹. Temporal association between particle increases and small brightness surges in the EUV observed by STEREO, which were also accompanied by type III radio emission seen by the Electromagnetic Fields Investigation on PSP, provided evidence that the source of this event was an AR nearly 80° east of the nominal PSP magnetic footprint, suggesting field lines expanding over a wide longitudinal range between the AR in the photosphere and the corona. Studies by (Cattell et al. 2021b; Harra et al. 2021) further studied the ARs from these times with remote sensing and in situ data, including the type III bursts, further associating these escaping electron beams with AR dynamics and open field lines indicated by the type III radiation.

The fractional contribution of ARs to the solar wind is negligible at solar minimum, and typically around 40%–60% at solar maximum, scaling with sunspot number (Stansby et al. 2021b). The latitudinal extent of AR solar wind is highly variable between different solar cycles and varying from a band of about ±30° to ±60° around the equator. As the solar cycle activity increases, PSP is expected to measure more wind associated with ARs. Contemporaneous measurements by multiple instruments and opportunities for quadratures and conjunctions with SolO and STEREO abound, and should shed light into the detailed wind types originating from AR sources.

## 5.6 Switchback Stream Sources

As discussed in previous sections, large amplitude fluctuations with characteristics of large amplitude AWs propagating away from the Sun, are ubiquitous in many solar wind streams. Though such features are most frequently found within fast solar wind streams at solar minimum, there are also episodes of Alfvénic slow wind visible both at solar minimum and maximum at 0.3 AU and beyond (in the Helios and Wind data; D'Amicis et al. 2020, 2021). A remarkable aspect of PSP measurements has been the fact that Alfvénic fluctuations also tend to dominate the slow solar wind in the inner heliosphere. Part and parcel of this turbulent regimes are the switchback patches seen throughout the solar Encs. by PSP, with the possible exception of Enc. 3. As the Probe perihelia get closer to the Sun, there are indications that the clustering of switchbacks into patches remains a prominent feature, though their amplitude decreases w.r.t. the underlying average magnetic field. The sources of such switchback patches appear to be open field coronal hole regions, of which at least a few have been identified as isolated coronal hole or coronal hole equatorial coronal holes (this was the case of the PSP connection to the Sun throughout the first perihelion), while streams originating at boundaries of polar coronal holes, although also permeated by switchbacks, appear to be globally less Alfvénic.

The absence of well-defined patches of switchbacks in measurements at 1 AU or other S/C data, together with the association of patches to scales similar to supergranulation, when
mining the expansion rate of neighboring field lines, and the dynamics of the boundaries between closed and open fields provides time-dependent heating and acceleration mechanisms, as occurs with emerging ARs.

Emerging ARs reconfigure the local coronal field, leading to the formation of new coronal hole or coronal hole corridors often at there periphery, and depending on the latitude emergence may lead to the formation of large pseudostreamer or reconfiguration of helmet streamers, therefore changing solar wind distributions. Such reconfiguration is also accompanied by radio bursts and energetic particle acceleration, with at least one energetic particle event seen by IS©IS, on 4 Apr. 2019, attributed to this type of process (Leske et al. 2020; Kouloumvakos et al. 2020).

The event seen by PSP was very small, with peak 1 MeV proton intensities of ~0.3 particles cm⁻² sr⁻¹ s⁻¹ MeV⁻¹. Temporal association between particle increases and small brightness surges in the EUV observed by STEREO, which were also accompanied by type III radio emission seen by the Electromagnetic Fields Investigation on PSP, provided evidence that the source of this event was an AR nearly 80° east of the nominal PSP magnetic footprint, suggesting field lines expanding over a wide longitudinal range between the AR in the photosphere and the corona. Studies by (Cattell et al. 2021b; Harra et al. 2021) further studied the ARs from these times with remote sensing and in situ data, including the type III bursts, further associating these escaping electron beams with AR dynamics and open field lines indicated by the type III radiation.

The fractional contribution of ARs to the solar wind is negligible at solar minimum, and typically around 40%–60% at solar maximum, scaling with sunspot number (Stansby et al. 2021b). The latitudinal extent of AR solar wind is highly variable between different solar cycles and varying from a band of about ±30° to ±60° around the equator. As the solar cycle activity increases, PSP is expected to measure more wind associated with ARs. Contemporaneous measurements by multiple instruments and opportunities for quadratures and conjunctions with SolO and STEREO abound, and should shed light into the detailed wind types originating from AR sources.

## 5.6 Switchback Stream Sources

As discussed in previous sections, large amplitude fluctuations with characteristics of large amplitude AWs propagating away from the Sun, are ubiquitous in many solar wind streams. Though such features are most frequently found within fast solar wind streams at solar minimum, there are also episodes of Alfvénic slow wind visible both at solar minimum and maximum at 0.3 AU and beyond (in the Helios and Wind data; D'Amicis et al. 2020, 2021). A remarkable aspect of PSP measurements has been the fact that Alfvénic fluctuations also tend to dominate the slow solar wind in the inner heliosphere. Part and parcel of this turbulent regimes are the switchback patches seen throughout the solar Encs. by PSP, with the possible exception of Enc. 3. As the Probe perihelia get closer to the Sun, there are indications that the clustering of switchbacks into patches remains a prominent feature, though their amplitude decreases w.r.t. the underlying average magnetic field. The sources of such switchback patches appear to be open field coronal hole regions, of which at least a few have been identified as isolated coronal hole or coronal hole equatorial coronal holes (this was the case of the PSP connection to the Sun throughout the first perihelion), while streams originating at boundaries of polar coronal holes, although also permeated by switchbacks, appear to be globally less Alfvénic.

The absence of well-defined patches of switchbacks in measurements at 1 AU or other S/C data, together with the association of patches to scales similar to supergranulation, when
projected backwards onto the Sun, are indications that switchback patches are a signature of solar wind source structure. PSP measurements near the Sun provide compelling evidence for the switchback patches being the remnants of magnetic funnels and supergranules (Bale et al. 2021; Fargette et al. 2021b).

# 6 Kinetic Physics and Instabilities in the Young Solar Wind

In addition to the observation of switchbacks, the ubiquity of ion- and electron-scale waves, the deformation of the particle VDF from a isotropic Maxwellian, and the kinetic processes connecting the waves and VDFs has been a topic of focused study. The presence of these waves and departures from thermodynamic equilibrium was not wholly unexpected, given previous inner heliospheric observations by Helios (Marsch 2012), but the observations by PSP at previously unrealized distances has helped to clarify the role they play in the thermodynamics of the young solar wind. In addition, the intensity and large variety of plasma waves in the near-Sun solar wind has offered new insight into the kinetic physics of plasma wave growth.

## 6.1 Ion-Scales Waves & Structures

The prevalence of electromagnetic ion-scale waves in the inner heliosphere was first revealed by PSP during Enc. 1 at 36-54 $R_\odot$ by Bale et al. (2019) and studied in more detail in Bowen et al. (2020b); they implicated that kinetic plasma instabilities may be playing a role in ion-scale wave generation. A statistical study by Bowen et al. (2020d) showed that a radial magnetic field was a favorable condition for these waves, namely that 30%-50% of the circularly polarized waves were present in a quiet, radial magnetic field configuration. However, single-point S/C measurements obscure the ability to answer definitively whether or not the ion-scale waves still exist in non-radial fields, only hidden by turbulent fluctuations perpendicular to the magnetic field. Large-amplitude electrostatic ion-acoustic waves are also frequently observed, and have been conjectured to be driven by ion-ion and ion-electron drift instabilities Mozer et al. (2020, 2021b). These ubiquitously observed ion-scale waves strongly suggest that they play a role in the dynamics of the expanding young solar wind.

The direction of ion-scale wave propagation, however, is ambiguous. The procedure for Doppler-shifting the wave frequencies from the S/C to plasma frame is nontrivial. A complementary analysis of the electric field measurements is required, (see Mozer et al. 2020a, for a discussion of initially calibrated DC and low frequency electric field measurements from FIELDS). These electric field measurements enabled Bowen et al. (2020d) to constrain permissible wave polarizations in the plasma frame by Doppler-shifting the cold plasma dispersion relation and comparing to the S/C frame measurements. They found that a majority of the observed ion-scale waves are propagating away from the Sun, suggesting that both left-handed and right-handed wave polarizations are plausible.

The question of the origin of these waves and their role in cosmic energy flow remains a topic of fervent investigation; c.f. reviews in Matteini et al. (2012), Verscharen et al. (2019). An inquiry of the plasma measurements during these wave storms is a natural one, given that ion VDFs are capable of driving ion-scale waves after sufficient deviation from non-local thermal equilibrium (LTE; Gary 1993). Common examples of such non-LTE features are relatively drifting components, e.g., a secondary proton beam, temperature anisotropies along and transverse to the local magnetic field, and temperature disequilibrium between components. Comprehensive statistical analysis of these VDFs have been performed using
projected backwards onto the Sun, are indications that switchback patches are a signature of solar wind source structure. PSP measurements near the Sun provide compelling evidence for the switchback patches being the remnants of magnetic funnels and supergranules (Bale et al. 2021; Fargette et al. 2021b).

# 6 Kinetic Physics and Instabilities in the Young Solar Wind

In addition to the observation of switchbacks, the ubiquity of ion- and electron-scale waves, the deformation of the particle VDF from a isotropic Maxwellian, and the kinetic processes connecting the waves and VDFs has been a topic of focused study. The presence of these waves and departures from thermodynamic equilibrium was not wholly unexpected, given previous inner heliospheric observations by Helios (Marsch 2012), but the observations by PSP at previously unrealized distances has helped to clarify the role they play in the thermodynamics of the young solar wind. In addition, the intensity and large variety of plasma waves in the near-Sun solar wind has offered new insight into the kinetic physics of plasma wave growth.

## 6.1 Ion-Scales Waves & Structures

The prevalence of electromagnetic ion-scale waves in the inner heliosphere was first revealed by PSP during Enc. 1 at 36-54 $R_\odot$ by Bale et al. (2019) and studied in more detail in Bowen et al. (2020b); they implicated that kinetic plasma instabilities may be playing a role in ion-scale wave generation. A statistical study by Bowen et al. (2020d) showed that a radial magnetic field was a favorable condition for these waves, namely that 30%-50% of the circularly polarized waves were present in a quiet, radial magnetic field configuration. However, single-point S/C measurements obscure the ability to answer definitively whether or not the ion-scale waves still exist in non-radial fields, only hidden by turbulent fluctuations perpendicular to the magnetic field. Large-amplitude electrostatic ion-acoustic waves are also frequently observed, and have been conjectured to be driven by ion-ion and ion-electron drift instabilities Mozer et al. (2020, 2021b). These ubiquitously observed ion-scale waves strongly suggest that they play a role in the dynamics of the expanding young solar wind.

The direction of ion-scale wave propagation, however, is ambiguous. The procedure for Doppler-shifting the wave frequencies from the S/C to plasma frame is nontrivial. A complementary analysis of the electric field measurements is required, (see Mozer et al. 2020a, for a discussion of initially calibrated DC and low frequency electric field measurements from FIELDS). These electric field measurements enabled Bowen et al. (2020d) to constrain permissible wave polarizations in the plasma frame by Doppler-shifting the cold plasma dispersion relation and comparing to the S/C frame measurements. They found that a majority of the observed ion-scale waves are propagating away from the Sun, suggesting that both left-handed and right-handed wave polarizations are plausible.

The question of the origin of these waves and their role in cosmic energy flow remains a topic of fervent investigation; c.f. reviews in Matteini et al. (2012), Verscharen et al. (2019). An inquiry of the plasma measurements during these wave storms is a natural one, given that ion VDFs are capable of driving ion-scale waves after sufficient deviation from non-local thermal equilibrium (LTE; Gary 1993). Common examples of such non-LTE features are relatively drifting components, e.g., a secondary proton beam, temperature anisotropies along and transverse to the local magnetic field, and temperature disequilibrium between components. Comprehensive statistical analysis of these VDFs have been performed using
<figure><img src="image_16.png" /><figcaption>**Fig. 14** Example event on 5 Apr. 2019 (Event #1) featuring a strong correlation between a proton beam and an ion-scale wave storm. Shown is the (a) radial magnetic field component, (b) angle of wave propagation w.r.t. B, (c) wavelet transform of B, (d) perpendicular polarization of B, (e) SPAN-i measured moment of differential energy flux, (f) SPAN-i measured moments of temperature anisotropy. In panels (e) and (d), the white dashed-dotted line represents the local $f_{cp}$. Figure adapted from Verniero et al. (2020)</figcaption></figure>

in situ observations from *Helios* at 0.3 AU (Marsch 2012) and at 1 AU (e.g., see review of *Wind* observations in (Wilson et al. 2021)). Many studies employing linear Vlasov theory combined with the observed non-thermal VDFs have implied that the observed structure can drive instabilities leading to wave growth. The question of what modes may dominate, e.g., right-handed magnetosonic waves or left-handed ion-cyclotron waves, under what conditions remains open, but *PSP* is making progress toward solving this mystery.

During Enc. 2, *PSP* witnessed intense secondary proton beams simultaneous with ion-scale waves at ~36 $R_⊙$, using measurements from both SWEAP and FIELDS (Verniero et al. 2020).

The particle instrument suite, SWEAP is comprised of a Faraday Cup, called Solar Probe Cup (SPC; Case et al. 2020) and top-hat electrostatic analyzers called Solar Probe ANalzers that measures electrons (SPAN-e; Whittlesey et al. 2020) and ions (SPAN-i; Livi et al. 2021). The SPANs are partially obstructed by *PSP*'s heat shield, leading to measurements of partial moments of the solar wind plasma. But, full sky coverage can be leveraged using SPC. The placement of SPAN-i on the S/C was optimal for detecting proton beams, both during initial and ongoing Encs. The time-of-flight capabilities on SPAN-i can separate protons from other minor ions, such as alpha particles. The instrument measures particle VDFs in 3D ($E, θ, φ$) energy-angle phase-space.

These particle VDFs were showcased in Verniero et al. (2020) where they displayed two events featuring the evolution of an intense proton beam simultaneous with ion-scale wave storms. The first of these, shown in Fig. 14, involved left-handed circularly polarized waves parallel propagating in a quiet, nearly radial magnetic field; the frequencies of these waves were near the proton gyrofrequency ($f_{cp}$). Analysis of the FIELDS magnetometer
<figure><img src="image_17.png" /><figcaption>**Fig. 14** Example event on 5 Apr. 2019 (Event #1) featuring a strong correlation between a proton beam and an ion-scale wave storm. Shown is the (a) radial magnetic field component, (b) angle of wave propagation w.r.t. B, (c) wavelet transform of B, (d) perpendicular polarization of B, (e) SPAN-i measured moment of differential energy flux, (f) SPAN-i measured moments of temperature anisotropy. In panels (e) and (d), the white dashed-dotted line represents the local $f_{cp}$. Figure adapted from Verniero et al. (2020)</figcaption></figure>

in situ observations from *Helios* at 0.3 AU (Marsch 2012) and at 1 AU (e.g., see review of *Wind* observations in (Wilson et al. 2021)). Many studies employing linear Vlasov theory combined with the observed non-thermal VDFs have implied that the observed structure can drive instabilities leading to wave growth. The question of what modes may dominate, e.g., right-handed magnetosonic waves or left-handed ion-cyclotron waves, under what conditions remains open, but *PSP* is making progress toward solving this mystery.

During Enc. 2, *PSP* witnessed intense secondary proton beams simultaneous with ion-scale waves at ~36 $R_⊙$, using measurements from both SWEAP and FIELDS (Verniero et al. 2020).

The particle instrument suite, SWEAP is comprised of a Faraday Cup, called Solar Probe Cup (SPC; Case et al. 2020) and top-hat electrostatic analyzers called Solar Probe ANalzers that measures electrons (SPAN-e; Whittlesey et al. 2020) and ions (SPAN-i; Livi et al. 2021). The SPANs are partially obstructed by *PSP*'s heat shield, leading to measurements of partial moments of the solar wind plasma. But, full sky coverage can be leveraged using SPC. The placement of SPAN-i on the S/C was optimal for detecting proton beams, both during initial and ongoing Encs. The time-of-flight capabilities on SPAN-i can separate protons from other minor ions, such as alpha particles. The instrument measures particle VDFs in 3D ($E, θ, φ$) energy-angle phase-space.

These particle VDFs were showcased in Verniero et al. (2020) where they displayed two events featuring the evolution of an intense proton beam simultaneous with ion-scale wave storms. The first of these, shown in Fig. 14, involved left-handed circularly polarized waves parallel propagating in a quiet, nearly radial magnetic field; the frequencies of these waves were near the proton gyrofrequency ($f_{cp}$). Analysis of the FIELDS magnetometer
data shows in Fig. 14a the steady $B_r/|B|$; Fig. 14b shows from MVA the wave traveling nearly parallel to **B**, and Fig. 14d shows the wavelet transform of **B** over a narrow frequency range about the $f_{cp}$, indicated by the white dashed horizontal line; Fig. 14d represents the wave polarization, where blue is left-handed in the S/C frame, and red is right-handed. The SPAN-i moments of differential energy flux is displayed in Fig. 14e, and the temperature anisotropy was extracted from the temperature tensor in Fig. 14f.

The evolution of proton VDFs reported in Verniero et al. (2020) during this event (at the times indicated by the black dashed vertical lines in Fig. 14) are displayed in Fig. 15. The left column represents the proton VDF in 3D phase-space, where each line represents a different energy sweep at different elevation angles. The middle column represents contours of the VDF in SPAN-i instrument coordinates $v_r-v_z$, summed and collapsed onto the $\theta$-plane. The right column represents the VDF in the azimuthal plane, where one can notice the portion of the VDF that is obstructed by the heat shield. During this period of time, the proton core was over 50% in the SPAN-i FOV, and therefore was determined as a suitable event to analyze.

During both wave-particle interaction events described in Verniero et al. (2020), 1D fits were applied to the SPAN-i VDFs and inputted to a kinetic instability solver. Linear Vlasov analysis revealed many wave modes with positive growth rates, and that the proton beam was the main driver of the unstable plasma during these times.

Klein et al. (2021) further investigated the nature of proton-beam driven kinetic instabilities by using 3D fits of the proton beam and core populations during Enc. 4. Using the plasma instability solver, PLUMAGE (Klein et al. 2017), they found significant differences in wave-particle energy transfer when comparing results from modeling the VDF as either one or two components. The differences between the waves predicted by the one- and two-component fits were not universal; in some instances, properly accounting for the beam simply enhanced the growth rate of the instabilities predicted by the one-component model while for other intervals, entirely different sets of waves were predicted to be generated.

During Encs. 4 and 5, PSP observed a series of proton beams in which the proton VDF was strongly broadened in directions perpendicular to the magnetic field, but only at $|v_\| \gtrsim 2-3v_A$, where $v_\|$ is the proton velocity parallel to the magnetic field relative to the peak of the proton VDF. At $|v_\| \lesssim 2-3v_A$, the beam protons' velocities were much more aligned with the magnetic-field direction. The resulting level contours of the proton VDF exhibited a 'hammerhead' shape (Verniero et al. 2022). An example VDF is given in Fig. 16, at the time indicated by the vertical dashed line in Fig. 17. These new complex distributions were quantified by modeling the proton VDF as a sum of three bi-Maxwellians, and using the temperature anisotropy of the third population as a proxy for the high energy asymmetries. In addition, the observations substantiate the need for multi-component proton VDF fitting to more accurately characterize the plasma conditions at kinetic scales, as discussed in Klein et al. (2021).

Verniero et al. (2022) found that these hammerhead distributions tended to occur at the same time as intense, right circularly polarized, plasma waves at wave lengths comparable to the proton inertial length. Moreover, the level contours of the VDF within the hammerhead region aligned with the velocity-space diffusion contours that arise in quasilinear theory when protons resonantly interact with parallel-propagating, right circularly polarized, fast-magnetosonic/whistler (FM/W) waves. These findings suggest that the hammerhead distributions occur when field-aligned proton beams excite FM/W waves and subsequently scatter off these waves. Resonant interactions between protons and parallel-propagating FM/W waves occur only when the protons' parallel velocities exceed $\simeq 2.6 v_A$, consistent with the observation that the hammerheads undergo substantial perpendicular velocity-space diffusion only at parallel velocities $\gtrsim 2.6 v_A$ (Verniero et al. 2022).
data shows in Fig. 14a the steady $B_r/|B|$; Fig. 14b shows from MVA the wave traveling nearly parallel to **B**, and Fig. 14d shows the wavelet transform of **B** over a narrow frequency range about the $f_{cp}$, indicated by the white dashed horizontal line; Fig. 14d represents the wave polarization, where blue is left-handed in the S/C frame, and red is right-handed. The SPAN-i moments of differential energy flux is displayed in Fig. 14e, and the temperature anisotropy was extracted from the temperature tensor in Fig. 14f.

The evolution of proton VDFs reported in Verniero et al. (2020) during this event (at the times indicated by the black dashed vertical lines in Fig. 14) are displayed in Fig. 15. The left column represents the proton VDF in 3D phase-space, where each line represents a different energy sweep at different elevation angles. The middle column represents contours of the VDF in SPAN-i instrument coordinates $v_r-v_z$, summed and collapsed onto the $\theta$-plane. The right column represents the VDF in the azimuthal plane, where one can notice the portion of the VDF that is obstructed by the heat shield. During this period of time, the proton core was over 50% in the SPAN-i FOV, and therefore was determined as a suitable event to analyze.

During both wave-particle interaction events described in Verniero et al. (2020), 1D fits were applied to the SPAN-i VDFs and inputted to a kinetic instability solver. Linear Vlasov analysis revealed many wave modes with positive growth rates, and that the proton beam was the main driver of the unstable plasma during these times.

Klein et al. (2021) further investigated the nature of proton-beam driven kinetic instabilities by using 3D fits of the proton beam and core populations during Enc. 4. Using the plasma instability solver, PLUMAGE (Klein et al. 2017), they found significant differences in wave-particle energy transfer when comparing results from modeling the VDF as either one or two components. The differences between the waves predicted by the one- and two-component fits were not universal; in some instances, properly accounting for the beam simply enhanced the growth rate of the instabilities predicted by the one-component model while for other intervals, entirely different sets of waves were predicted to be generated.

During Encs. 4 and 5, PSP observed a series of proton beams in which the proton VDF was strongly broadened in directions perpendicular to the magnetic field, but only at $|v_\| \gtrsim 2-3v_A$, where $v_\|$ is the proton velocity parallel to the magnetic field relative to the peak of the proton VDF. At $|v_\| \lesssim 2-3v_A$, the beam protons' velocities were much more aligned with the magnetic-field direction. The resulting level contours of the proton VDF exhibited a 'hammerhead' shape (Verniero et al. 2022). An example VDF is given in Fig. 16, at the time indicated by the vertical dashed line in Fig. 17. These new complex distributions were quantified by modeling the proton VDF as a sum of three bi-Maxwellians, and using the temperature anisotropy of the third population as a proxy for the high energy asymmetries. In addition, the observations substantiate the need for multi-component proton VDF fitting to more accurately characterize the plasma conditions at kinetic scales, as discussed in Klein et al. (2021).

Verniero et al. (2022) found that these hammerhead distributions tended to occur at the same time as intense, right circularly polarized, plasma waves at wave lengths comparable to the proton inertial length. Moreover, the level contours of the VDF within the hammerhead region aligned with the velocity-space diffusion contours that arise in quasilinear theory when protons resonantly interact with parallel-propagating, right circularly polarized, fast-magnetosonic/whistler (FM/W) waves. These findings suggest that the hammerhead distributions occur when field-aligned proton beams excite FM/W waves and subsequently scatter off these waves. Resonant interactions between protons and parallel-propagating FM/W waves occur only when the protons' parallel velocities exceed $\simeq 2.6 v_A$, consistent with the observation that the hammerheads undergo substantial perpendicular velocity-space diffusion only at parallel velocities $\gtrsim 2.6 v_A$ (Verniero et al. 2022).
<figure><img src="image_17.png" /><figcaption>**Fig. 15** Beam evolution for times indicated by the dashed black lines in Fig. 14. Left: Proton VDFs, where each line refers to an energy sweep at different elevation angles. Middle: VDF contour elevations that are summed and collapsed onto the θ-plane. Right: VDF contour elevations that are summed and collapsed onto the azimuthal plane. The black arrow represents the magnetic field direction in SPAN-i coordinates, where the head is at the solar wind velocity (measured by SPC) and the length is the Alfvén speed. Figure adapted from Verniero et al. (2020)</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Fig. 15** Beam evolution for times indicated by the dashed black lines in Fig. 14. Left: Proton VDFs, where each line refers to an energy sweep at different elevation angles. Middle: VDF contour elevations that are summed and collapsed onto the θ-plane. Right: VDF contour elevations that are summed and collapsed onto the azimuthal plane. The black arrow represents the magnetic field direction in SPAN-i coordinates, where the head is at the solar wind velocity (measured by SPC) and the length is the Alfvén speed. Figure adapted from Verniero et al. (2020)</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Fig. 16** Example of proton VDF displaying a “hammerhead” feature. The VDF was transformed from the SPAN-i $\theta$-plane to the plasma-frame in magnetic field-aligned coordinates. The black arrow represents the magnetic field, where the head is placed at the solar wind speed and the length is the Alfvén speed. The particles diffuse along predicted contours from quasilinear theory, seen by the dashed black curves. Figure adapted from Verniero et al. (2022)</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>**Fig. 17** The proton VDF displays a ‘hammerhead’ feature throughout this interval of enhanced Right-Handed wave power. The proton VDF at the time indicated by the vertical dashed black line is shown in Fig. 16. Figure adapted from Verniero et al. (2022)</figcaption></figure>

Initial studies of the transfer of energy between the ion-scale waves and the proton distribution were performed in Vech et al. (2021). During an Enc. 3 interval where an ion cyclotron wave (ICW) was observed in the FIELDS magnetometer data and SPC was operating in a mode where it rapidly measures a single energy bin, rather than scanning over the entire range of velocities, the work done by the perpendicular electric field on the measured region of the proton VDF was calculated. The energy transferred between the fields and particles was consistent with the damping of an ICW with a parallel f wave-vector of order the thermal proton gyroradius.
<figure><img src="image_19.png" /><figcaption>**Fig. 16** Example of proton VDF displaying a “hammerhead” feature. The VDF was transformed from the SPAN-i $\theta$-plane to the plasma-frame in magnetic field-aligned coordinates. The black arrow represents the magnetic field, where the head is placed at the solar wind speed and the length is the Alfvén speed. The particles diffuse along predicted contours from quasilinear theory, seen by the dashed black curves. Figure adapted from Verniero et al. (2022)</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>**Fig. 17** The proton VDF displays a ‘hammerhead’ feature throughout this interval of enhanced Right-Handed wave power. The proton VDF at the time indicated by the vertical dashed black line is shown in Fig. 16. Figure adapted from Verniero et al. (2022)</figcaption></figure>

Initial studies of the transfer of energy between the ion-scale waves and the proton distribution were performed in Vech et al. (2021). During an Enc. 3 interval where an ion cyclotron wave (ICW) was observed in the FIELDS magnetometer data and SPC was operating in a mode where it rapidly measures a single energy bin, rather than scanning over the entire range of velocities, the work done by the perpendicular electric field on the measured region of the proton VDF was calculated. The energy transferred between the fields and particles was consistent with the damping of an ICW with a parallel f wave-vector of order the thermal proton gyroradius.
## 6.2 Electron-Scales Waves & Structures

Researchers in the 1970s recognized that the distributions should change dramatically as solar wind electrons propagated away from the Sun (Cuperman and Harten 1971; Hollweg 1974a; Feldman et al. 1975). As satellites sampled regions from ~0.3 AU to outside 5 AU, studies showed that the relative fractions of the field-aligned strahl and quasi-isotropic halo electrons change with radial distance in a manner that is inconsistent with adiabatic motion (Maksimovic et al. 2005; Štverák et al. 2009; Graham et al. 2017). The changes in heat flux, which is carried predominantly by the strahl (Scime et al. 1994; Štverák et al. 2015) are also not consistent with adiabatic expansion. Research assessing the relative roles of Coulomb collisions and wave-particle interactions in these changes has often concluded that wave-particle interactions are necessary (Phillips and Gosling 1990; Scudder and Olbert 1979; Boldyrev and Horaites 2019; Bale et al. 2013). The ambipolar electric field is another mechanism that shapes the electron distributions (Lemaire and Scherer 1973; Scudder 2019).

PSP has provided new insights into electrons in the young solar wind, and the role of waves and the ambipolar electric field in their evolution. Halekas et al. (2020), in a study of the first two Encs., found that radial trends inside ~0.3 AU were mostly consistent with earlier studies. The halo density, however, decreases close to the Sun, resulting in a large increase in the strahl to halo ratio. In addition, unlike what is seen at 1 AU, the core electron temperature is anti-correlated with solar wind speed (Halekas et al. 2020; Maksimovic et al. 2020). The core temperature may thus reflect the coronal source region, as also discussed for the strahl parallel temperature in §4.4 (Berčič et al. 2020). Abraham et al. (2022) confirmed the small halo density, showing that it continued to decrease in measurements closer to the Sun, and also found that the suprathermal population (halo plus strahl) comprised only 1% of the solar wind electrons at the closest distances sampled.

The electron heat flux carried primarily by strahl (Berčič et al. 2020; Halekas et al. 2021b) is also anticorrelated with solar wind speed (Halekas et al. 2020). Closer to the Sun (from 0.125 to 0.25 AU) the normalized electron heat flux is also anti-correlated with beta (Halekas et al. 2021b). This beta dependence is not consistent with a purely collisional scattering mechanism.

The signature of the ambipolar electric field has also been clearly revealed in electron data (Halekas et al. 2021a; Berčič et al. 2021a) as a deficit of electrons moving back towards the Sun. This loss of electrons occurs more than 60% of the time inside 0.2 AU. The angular dependence of the deficit is not consistent with Coulomb scattering, and the deficit disappears in the same radial distances as the increase in the halo. There is also a decrease in the normalized heat flux. Both observations provide additional support for the essential role of waves.

The role of whistler-mode waves in the evolution of solar wind electrons and regulation of heat flux has long been a topic of interest. Instability mechanisms including temperature anisotropy and several heat flux instabilities have been proposed (Gary et al. 1994; Gary and Wang 1996; Vasko et al. 2019). Wave studies near 1 AU utilizing data from *Wind*, *STEREO*, *Cluster* (Escoubet et al. 1997) and the Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon's Interaction (ARTEMIS; Angelopoulos 2011) missions provided evidence for both low amplitude parallel propagating whistlers (Lacombe et al. 2014; Tong et al. 2019) and large amplitude highly oblique waves (Breneman et al. 2010; Cattell et al. 2020).

The Fields instrument on PSP, using waveform capture, spectral, and bandpass filter datasets using both electric fields and search coil magnetic fields, has enabled study of whistler-mode waves over a wide range of distances from the Sun and in association with
## 6.2 Electron-Scales Waves & Structures

Researchers in the 1970s recognized that the distributions should change dramatically as solar wind electrons propagated away from the Sun (Cuperman and Harten 1971; Hollweg 1974a; Feldman et al. 1975). As satellites sampled regions from ~0.3 AU to outside 5 AU, studies showed that the relative fractions of the field-aligned strahl and quasi-isotropic halo electrons change with radial distance in a manner that is inconsistent with adiabatic motion (Maksimovic et al. 2005; Štverák et al. 2009; Graham et al. 2017). The changes in heat flux, which is carried predominantly by the strahl (Scime et al. 1994; Štverák et al. 2015) are also not consistent with adiabatic expansion. Research assessing the relative roles of Coulomb collisions and wave-particle interactions in these changes has often concluded that wave-particle interactions are necessary (Phillips and Gosling 1990; Scudder and Olbert 1979; Boldyrev and Horaites 2019; Bale et al. 2013). The ambipolar electric field is another mechanism that shapes the electron distributions (Lemaire and Scherer 1973; Scudder 2019).

PSP has provided new insights into electrons in the young solar wind, and the role of waves and the ambipolar electric field in their evolution. Halekas et al. (2020), in a study of the first two Encs., found that radial trends inside ~0.3 AU were mostly consistent with earlier studies. The halo density, however, decreases close to the Sun, resulting in a large increase in the strahl to halo ratio. In addition, unlike what is seen at 1 AU, the core electron temperature is anti-correlated with solar wind speed (Halekas et al. 2020; Maksimovic et al. 2020). The core temperature may thus reflect the coronal source region, as also discussed for the strahl parallel temperature in §4.4 (Berčič et al. 2020). Abraham et al. (2022) confirmed the small halo density, showing that it continued to decrease in measurements closer to the Sun, and also found that the suprathermal population (halo plus strahl) comprised only 1% of the solar wind electrons at the closest distances sampled.

The electron heat flux carried primarily by strahl (Berčič et al. 2020; Halekas et al. 2021b) is also anticorrelated with solar wind speed (Halekas et al. 2020). Closer to the Sun (from 0.125 to 0.25 AU) the normalized electron heat flux is also anti-correlated with beta (Halekas et al. 2021b). This beta dependence is not consistent with a purely collisional scattering mechanism.

The signature of the ambipolar electric field has also been clearly revealed in electron data (Halekas et al. 2021a; Berčič et al. 2021a) as a deficit of electrons moving back towards the Sun. This loss of electrons occurs more than 60% of the time inside 0.2 AU. The angular dependence of the deficit is not consistent with Coulomb scattering, and the deficit disappears in the same radial distances as the increase in the halo. There is also a decrease in the normalized heat flux. Both observations provide additional support for the essential role of waves.

The role of whistler-mode waves in the evolution of solar wind electrons and regulation of heat flux has long been a topic of interest. Instability mechanisms including temperature anisotropy and several heat flux instabilities have been proposed (Gary et al. 1994; Gary and Wang 1996; Vasko et al. 2019). Wave studies near 1 AU utilizing data from *Wind*, *STEREO*, *Cluster* (Escoubet et al. 1997) and the Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon's Interaction (ARTEMIS; Angelopoulos 2011) missions provided evidence for both low amplitude parallel propagating whistlers (Lacombe et al. 2014; Tong et al. 2019) and large amplitude highly oblique waves (Breneman et al. 2010; Cattell et al. 2020).

The Fields instrument on PSP, using waveform capture, spectral, and bandpass filter datasets using both electric fields and search coil magnetic fields, has enabled study of whistler-mode waves over a wide range of distances from the Sun and in association with
<figure><img src="image_20.png" /><figcaption>**Fig. 18** Enlargement of the trailing edge of the switchback of Fig. 6. Panel (a) shows the magnetic field from MAG with the same color code as in Fig. 6. Panels (b) and (c) show magnetic and electric field wave perturbations respectively. Panel (d) displays the dynamic spectrum of magnetic field perturbations $B_w$. The dashed curves in panels (d-f) represent the $f_{LH}$ frequency (bottom curve) and 0.1 $f_{ce}$ (upper curve). Panel (e) displays the signed radial component of the Poynting flux. Red colors correspond to a sunward propagation. Panel (f) shows the wave normal angle relative to the direction of the background magnetic field</figcaption></figure>

different large-scale structures. This research, in concert with studies of solar wind electrons, has provided critical new evidence for the role of whistler-mode waves in regulation of electron heat flux and scattering of strahl electrons to produce the halo. Observational papers have motivated a number of theoretical studies to further elucidate the physics (Micera et al. 2020, 2021; Cattell and Vo 2021; Vo et al. 2022).

Enc. 1 waveform data provided the first definitive evidence for the existence of sunward propagating whistler mode waves (Agapitov et al. 2020), an important observation because, if the waves have wavevectors parallel to the background magnetic field, only sunward-propagating waves can interact with the anti-sunward propagating strahl. The whistlers observed near the Sun occur with a range of wave angles from parallel to highly oblique (Agapitov et al. 2020; Cattell et al. 2021c, 2022; Dudok de Wit et al. 2022). Because the oblique whistler waves are elliptically polarized (mixture of left and right hand polarized), oblique waves moving anti-sunward can interact with electrons moving away from the Sun. Particle tracing simulations (Cattell and Vo 2021; Vo et al. 2022) and PIC simulations (Micera et al. 2020, 2021; Roberg-Clark et al. 2019) have revealed details of wave-electron interactions.

Several studies have examined the association of whistlers with large-scale solar wind structures. There is a strong correlation between large amplitude waves and the boundaries of switchbacks (Agapitov et al. 2020), and smaller waves can fill switchbacks (Cattell et al. 2021c). The whistlers are also seen primarily in the slow solar wind (Jagarlamudi et al. 2021; Cattell et al. 2022), as initially observed near 1 AU (Lacombe et al. 2014) and in the recent studies using the *Helios* data between 0.3 to 1 AU (Jagarlamudi et al. 2020). Several studies have found differences in the evolution of the non-thermal electron distributions between the slow and fast wind, suggesting that different scattering mechanisms are active in the fast and slow wind (Pagel et al. 2005; Štverák et al. 2009).

Figure 18 shows a zoom-in of the trailing edge of the switchback displayed in Fig. 6. Figure 18a emphasizes that the local dip in the magnetic field is essentially caused by a decrease of its radial component. This dip coincides with an increase of the ratio between electron plasma frequency ($f_{pe}$) and electron gyrofrequency $f_{ce}$ from 120 to ≈ 500. A polarization
<figure><img src="image_21.png" /><figcaption>**Fig. 18** Enlargement of the trailing edge of the switchback of Fig. 6. Panel (a) shows the magnetic field from MAG with the same color code as in Fig. 6. Panels (b) and (c) show magnetic and electric field wave perturbations respectively. Panel (d) displays the dynamic spectrum of magnetic field perturbations $B_w$. The dashed curves in panels (d-f) represent the $f_{LH}$ frequency (bottom curve) and 0.1 $f_{ce}$ (upper curve). Panel (e) displays the signed radial component of the Poynting flux. Red colors correspond to a sunward propagation. Panel (f) shows the wave normal angle relative to the direction of the background magnetic field</figcaption></figure>

different large-scale structures. This research, in concert with studies of solar wind electrons, has provided critical new evidence for the role of whistler-mode waves in regulation of electron heat flux and scattering of strahl electrons to produce the halo. Observational papers have motivated a number of theoretical studies to further elucidate the physics (Micera et al. 2020, 2021; Cattell and Vo 2021; Vo et al. 2022).

Enc. 1 waveform data provided the first definitive evidence for the existence of sunward propagating whistler mode waves (Agapitov et al. 2020), an important observation because, if the waves have wavevectors parallel to the background magnetic field, only sunward-propagating waves can interact with the anti-sunward propagating strahl. The whistlers observed near the Sun occur with a range of wave angles from parallel to highly oblique (Agapitov et al. 2020; Cattell et al. 2021c, 2022; Dudok de Wit et al. 2022). Because the oblique whistler waves are elliptically polarized (mixture of left and right hand polarized), oblique waves moving anti-sunward can interact with electrons moving away from the Sun. Particle tracing simulations (Cattell and Vo 2021; Vo et al. 2022) and PIC simulations (Micera et al. 2020, 2021; Roberg-Clark et al. 2019) have revealed details of wave-electron interactions.

Several studies have examined the association of whistlers with large-scale solar wind structures. There is a strong correlation between large amplitude waves and the boundaries of switchbacks (Agapitov et al. 2020), and smaller waves can fill switchbacks (Cattell et al. 2021c). The whistlers are also seen primarily in the slow solar wind (Jagarlamudi et al. 2021; Cattell et al. 2022), as initially observed near 1 AU (Lacombe et al. 2014) and in the recent studies using the *Helios* data between 0.3 to 1 AU (Jagarlamudi et al. 2020). Several studies have found differences in the evolution of the non-thermal electron distributions between the slow and fast wind, suggesting that different scattering mechanisms are active in the fast and slow wind (Pagel et al. 2005; Štverák et al. 2009).

Figure 18 shows a zoom-in of the trailing edge of the switchback displayed in Fig. 6. Figure 18a emphasizes that the local dip in the magnetic field is essentially caused by a decrease of its radial component. This dip coincides with an increase of the ratio between electron plasma frequency ($f_{pe}$) and electron gyrofrequency $f_{ce}$ from 120 to ≈ 500. A polarization
analysis reveals a right-handed circular polarization of the magnetic field and an elliptical polarization of the electric field perturbations with a $\pi/2$ phase shift. The dynamic spectrum in Fig. 18d shows a complex inner structure of the wave packet, which consists of a series of bursts. The phase shift of the magnetic and electric field components transverse to the radial direction attest a sunward propagation of the observed waves. The sign of the radial component of the Poynting vector (Fig. 18f) changes from positive (sunward) at high frequencies to negative (anti-sunward) at lower frequencies. The frequencies of these wave packets fall between $f_{LH}$ (lower dashed curve in Figs. 18f and 18g) and one tenth of $f_{ce}$ (upper dashed curve). This suggests that the observed frequency range of the whistler waves is shifted down by the Doppler effect as the whistler phase velocity (300 – 500 km s$^{-1}$) is comparable to that of the plasma bulk velocity. The observed whistlers are found to have a wide range of wave normal angle values from quasi-parallel propagation to quasi-electrostatic propagating close to the resonance cone corresponding to the complex structure of the dynamics spectrum (Fig. 18b). Figure 18h thereby further supports the idea that our complex wave packet consists of a bunch of distinct and narrowband wave bursts. The wave frequency in the solar wind plasma frame, as reconstructed from the Doppler shift and the local parameters of plasma, are found to be in the range of 100 Hz to 350 Hz, which corresponds to 0.2-0.5 $f_{ce}$ (Fig. 18d). Incidentally, the reconstructed wave frequency can be used to accurately calibrate the electric field measurements, and determine the effective length of the electric field antennas, which was found to be approximately 3.5 m to 4.5 m in the 20 Hz to 100 Hz frequency range (Agapitov et al. 2020; Mozer et al. 2020). More details can be found in Agapitov et al. (2020).

The population of such sunward propagating whistlers can efficiently interact with the energetic particles of the solar wind and affect the strahl population, spreading their field-aligned PAD through pitch-angle scattering. For sunward propagating whistlers around 100 Hz to 300 Hz, the resonance conditions occur for electrons with energies from approximately 50 eV to 1 keV. This energy range coincides with that of the observed strahl (Halekas et al. 2020) and potentially leads to efficient scattering of the strahl electrons. Such an interaction can be even more efficient taking into account that some of the observed waves are oblique. For these waves, the effective scattering is strongly enhanced at higher-order resonances (Agapitov et al. 2020; Cattell et al. 2021a), which leads to a regulation of the heat flux as shown by Roberg-Clark et al. (2019), and to an increase in the fraction of the halo distribution with the distance from the Sun.

PSP has provided direct evidence for scattering of strahl into halo by narrowband whistler-mode waves (Agapitov et al. 2020; Cattell et al. 2021a; Jagarlamudi et al. 2021). The increase in halo occurs in the same beta range and radial distance range as the whistlers, consistent with production of halo by whistler scattering. Comparison of waveform capture data and electron distributions from Enc. 1 (Cattell et al. 2021a) showed that the narrowest strahl occurred when there were either no whistlers or very intermittent low amplitude waves, whereas the broadest distributions were associated with intense, long duration waves. Features consistent with an energy dependent scattering mechanism were observed in approximately half the broadened strahl distributions, as was also suggested by features in electrons displaying the signature of the ambipolar field (Halekas et al. 2021a).

In a study of bandpass filtered data from Encs. 1 through 9, Cattell et al. (2022) have shown that the narrowband whistler-mode waves that scatter strahl electrons and regulate heat flux are not observed inside approximately 30 $R_⊙$. Instead, large amplitude electrostatic (up to 200 mV/m) waves in the same frequency range (from the $f_{LH}$ frequency up to a few tenths of $f_{ce}$) are ubiquitous, as shown in Fig. 19. The peak amplitudes of the electrostatic (ES) waves (~220 mV/m) are an order of magnitude larger than those of the
analysis reveals a right-handed circular polarization of the magnetic field and an elliptical polarization of the electric field perturbations with a $\pi/2$ phase shift. The dynamic spectrum in Fig. 18d shows a complex inner structure of the wave packet, which consists of a series of bursts. The phase shift of the magnetic and electric field components transverse to the radial direction attest a sunward propagation of the observed waves. The sign of the radial component of the Poynting vector (Fig. 18f) changes from positive (sunward) at high frequencies to negative (anti-sunward) at lower frequencies. The frequencies of these wave packets fall between $f_{LH}$ (lower dashed curve in Figs. 18f and 18g) and one tenth of $f_{ce}$ (upper dashed curve). This suggests that the observed frequency range of the whistler waves is shifted down by the Doppler effect as the whistler phase velocity (300 – 500 km s$^{-1}$) is comparable to that of the plasma bulk velocity. The observed whistlers are found to have a wide range of wave normal angle values from quasi-parallel propagation to quasi-electrostatic propagating close to the resonance cone corresponding to the complex structure of the dynamics spectrum (Fig. 18b). Figure 18h thereby further supports the idea that our complex wave packet consists of a bunch of distinct and narrowband wave bursts. The wave frequency in the solar wind plasma frame, as reconstructed from the Doppler shift and the local parameters of plasma, are found to be in the range of 100 Hz to 350 Hz, which corresponds to 0.2-0.5 $f_{ce}$ (Fig. 18d). Incidentally, the reconstructed wave frequency can be used to accurately calibrate the electric field measurements, and determine the effective length of the electric field antennas, which was found to be approximately 3.5 m to 4.5 m in the 20 Hz to 100 Hz frequency range (Agapitov et al. 2020; Mozer et al. 2020). More details can be found in Agapitov et al. (2020).

The population of such sunward propagating whistlers can efficiently interact with the energetic particles of the solar wind and affect the strahl population, spreading their field-aligned PAD through pitch-angle scattering. For sunward propagating whistlers around 100 Hz to 300 Hz, the resonance conditions occur for electrons with energies from approximately 50 eV to 1 keV. This energy range coincides with that of the observed strahl (Halekas et al. 2020) and potentially leads to efficient scattering of the strahl electrons. Such an interaction can be even more efficient taking into account that some of the observed waves are oblique. For these waves, the effective scattering is strongly enhanced at higher-order resonances (Agapitov et al. 2020; Cattell et al. 2021a), which leads to a regulation of the heat flux as shown by Roberg-Clark et al. (2019), and to an increase in the fraction of the halo distribution with the distance from the Sun.

PSP has provided direct evidence for scattering of strahl into halo by narrowband whistler-mode waves (Agapitov et al. 2020; Cattell et al. 2021a; Jagarlamudi et al. 2021). The increase in halo occurs in the same beta range and radial distance range as the whistlers, consistent with production of halo by whistler scattering. Comparison of waveform capture data and electron distributions from Enc. 1 (Cattell et al. 2021a) showed that the narrowest strahl occurred when there were either no whistlers or very intermittent low amplitude waves, whereas the broadest distributions were associated with intense, long duration waves. Features consistent with an energy dependent scattering mechanism were observed in approximately half the broadened strahl distributions, as was also suggested by features in electrons displaying the signature of the ambipolar field (Halekas et al. 2021a).

In a study of bandpass filtered data from Encs. 1 through 9, Cattell et al. (2022) have shown that the narrowband whistler-mode waves that scatter strahl electrons and regulate heat flux are not observed inside approximately 30 $R_\odot$. Instead, large amplitude electrostatic (up to 200 mV/m) waves in the same frequency range (from the $f_{LH}$ frequency up to a few tenths of $f_{ce}$) are ubiquitous, as shown in Fig. 19. The peak amplitudes of the electrostatic (ES) waves (~220 mV/m) are an order of magnitude larger than those of the
<figure><img src="image_21.png" /><figcaption>**Fig. 19** Statistics of whistler-mode waves and ES waves identified in bandpass filter data. Left hand column, from top to bottom: the number of BBF samples identified as ES waves versus radial distance, the number of BBF samples identified as whistler-mode waves versus radial distance, and the total number of BBF samples in Enc. 1 through Enc. 9 versus radial distance. The right hand column: the electrostatic wave occurrence rate and the whistler-mode wave occurrence rate, both versus radial distance. Note that the drop off outside $75 R_⊙$ (0.3 AU) is associated with the impact of the decrease in frequency with radial distance on the algorithm used to identify waves. Figure adapted from Cattell et al. (2022)</figcaption></figure>

whistlers (~40 mV/m). Within the same region where whistlers disappear, the deficit of sunward electrons is seen, and the density of halo relative to the total density decreases. The finding that, when the deficit was observed, the normalized heat flux-parallel electron beta relationship was not consistent with the whistler heat flux fan instability is consistent with loss of whistlers. The differences in the functional form of electron distributions due to this deficit very likely result in changes in the instabilities excited (Halekas et al. 2021a; Berčič et al. 2021b).

Theoretical studies have examined how changes in the distributions and background plasma properties might change which modes are destabilized. López et al. (2020) examined dependence on beta and the ratio of the strahl speed to the electron Alfvén speed for different electromagnetic and electrostatic instabilities. This ratio decreases close to the Sun. Other studies (Micera et al. 2021; Roberg-Clark et al. 2019; Schroeder et al. 2021) have concluded that multiple instabilities operate sequentially and/or at different distances from the Sun.

Closer to the Sun, other scattering mechanisms must operate, associated with the large narrowband ES waves and the nonlinear waves. Note that in some cases these ES waves have been identified as ion acoustic waves (Mozer et al. 2021c). Dum (1983) has discussed anomalous transport and heating associated with ES waves in the solar wind. The lack of narrowband whistler-mode waves close to the sun and in regions of either low ($< 1$) or high ($> 10$) parallel electron beta may also be significant for the understanding and modeling the evolution of flare-accelerated electrons, other stellar winds, the interstellar medium, and intra-galaxy cluster medium.
<figure><img src="image_22.png" /><figcaption>**Fig. 19** Statistics of whistler-mode waves and ES waves identified in bandpass filter data. Left hand column, from top to bottom: the number of BBF samples identified as ES waves versus radial distance, the number of BBF samples identified as whistler-mode waves versus radial distance, and the total number of BBF samples in Enc. 1 through Enc. 9 versus radial distance. The right hand column: the electrostatic wave occurrence rate and the whistler-mode wave occurrence rate, both versus radial distance. Note that the drop off outside $75 R_⊙$ (0.3 AU) is associated with the impact of the decrease in frequency with radial distance on the algorithm used to identify waves. Figure adapted from Cattell et al. (2022)</figcaption></figure>

whistlers (~40 mV/m). Within the same region where whistlers disappear, the deficit of sunward electrons is seen, and the density of halo relative to the total density decreases. The finding that, when the deficit was observed, the normalized heat flux-parallel electron beta relationship was not consistent with the whistler heat flux fan instability is consistent with loss of whistlers. The differences in the functional form of electron distributions due to this deficit very likely result in changes in the instabilities excited (Halekas et al. 2021a; Berčič et al. 2021b).

Theoretical studies have examined how changes in the distributions and background plasma properties might change which modes are destabilized. López et al. (2020) examined dependence on beta and the ratio of the strahl speed to the electron Alfvén speed for different electromagnetic and electrostatic instabilities. This ratio decreases close to the Sun. Other studies (Micera et al. 2021; Roberg-Clark et al. 2019; Schroeder et al. 2021) have concluded that multiple instabilities operate sequentially and/or at different distances from the Sun.

Closer to the Sun, other scattering mechanisms must operate, associated with the large narrowband ES waves and the nonlinear waves. Note that in some cases these ES waves have been identified as ion acoustic waves (Mozer et al. 2021c). Dum (1983) has discussed anomalous transport and heating associated with ES waves in the solar wind. The lack of narrowband whistler-mode waves close to the sun and in regions of either low ($< 1$) or high ($> 10$) parallel electron beta may also be significant for the understanding and modeling the evolution of flare-accelerated electrons, other stellar winds, the interstellar medium, and intra-galaxy cluster medium.
<figure><img src="image_22.png" /><figcaption>**Fig. 20** The left-column shows a spectrogram of electric field data, with *f*<sub>ce</sub> indicated by the white line. The near-cyclotron waves are present at the center of the interval, where fluctuations in the ambient magnetic field (b), solar wind velocity (c), plasma density (d), and electron temperature (e) show decreased variability. The right-column shows a high-cadence observation of near-cyclotron waves, where three distinct wave types are identified (A,B,C). Type A was identified as an electron Bernstein wave. Figure adapted from Malaspina et al. (2021b) and Malaspina et al. (2020b)</figcaption></figure>

PSP data has been instrumental in advancing the study of electron-resonant plasma waves other than whistler-mode waves. Larosa et al. (2022) presented the first unambiguous observations of the Langmuir z-mode in the solar wind (Langmuir-slow extraordinary mode) using high frequency magnetic field data. This wave mode is thought to play a key role in the conversion of electron-beam driven Langmuir waves into type III and type II solar radio emission (e.g., Cairns and Layden 2018, and references therein). However, progress understanding the detailed kinetic physics powering this interaction has been slowed by a lack of direct z-mode observations in the solar wind. Z-mode wave occurrence was found to be highly impacted by the presence of solar wind density fluctuations, confirming long-held theoretical assumptions.

PSP data also revealed the presence of unidentified electrostatic plasma waves near fce
in the solar wind (Fig. 20). Malaspina et al. (2020b) showed that these waves occur fre-
quently during solar Encs., but only when fluctuations in the ambient solar wind magnetic
field become exceptionally small. Tigik et al. (2022) identified that a necessary condition
for the existence of these waves is the direction of the ambient solar wind magnetic field
vector. They demonstrated that these waves occur for a preferential range of magnetic field
orientation, and concluded their study by suggesting that these waves may be generated by
S/C interaction with the solar wind. Malaspina et al. (2021a) explored high-cadence ob-
servations of these waves, demonstrating that they are composed of many simultaneously
present modes, one of which was identified as the electron Bernstein mode. The other wave
modes remain inconclusively identified. Shi et al. (2022) and Ma et al. (2021b) explored the
possibility that these waves are created by nonlinear wave-wave interactions. Identifying the
exact wave mode, the origin of these waves near fce, and their impact on the solar wind re-
main areas of active study. PSP data from ever decreasing perihelion distances are expected
to enable new progress.
<figure><img src="image_23.png" /><figcaption>**Fig. 20** The left-column shows a spectrogram of electric field data, with *f*<sub>ce</sub> indicated by the white line. The near-cyclotron waves are present at the center of the interval, where fluctuations in the ambient magnetic field (b), solar wind velocity (c), plasma density (d), and electron temperature (e) show decreased variability. The right-column shows a high-cadence observation of near-cyclotron waves, where three distinct wave types are identified (A,B,C). Type A was identified as an electron Bernstein wave. Figure adapted from Malaspina et al. (2021b) and Malaspina et al. (2020b)</figcaption></figure>

PSP data has been instrumental in advancing the study of electron-resonant plasma waves other than whistler-mode waves. Larosa et al. (2022) presented the first unambiguous observations of the Langmuir z-mode in the solar wind (Langmuir-slow extraordinary mode) using high frequency magnetic field data. This wave mode is thought to play a key role in the conversion of electron-beam driven Langmuir waves into type III and type II solar radio emission (e.g., Cairns and Layden 2018, and references therein). However, progress understanding the detailed kinetic physics powering this interaction has been slowed by a lack of direct z-mode observations in the solar wind. Z-mode wave occurrence was found to be highly impacted by the presence of solar wind density fluctuations, confirming long-held theoretical assumptions.

PSP data also revealed the presence of unidentified electrostatic plasma waves near fce
in the solar wind (Fig. 20). Malaspina et al. (2020b) showed that these waves occur fre-
quently during solar Encs., but only when fluctuations in the ambient solar wind magnetic
field become exceptionally small. Tigik et al. (2022) identified that a necessary condition
for the existence of these waves is the direction of the ambient solar wind magnetic field
vector. They demonstrated that these waves occur for a preferential range of magnetic field
orientation, and concluded their study by suggesting that these waves may be generated by
S/C interaction with the solar wind. Malaspina et al. (2021a) explored high-cadence ob-
servations of these waves, demonstrating that they are composed of many simultaneously
present modes, one of which was identified as the electron Bernstein mode. The other wave
modes remain inconclusively identified. Shi et al. (2022) and Ma et al. (2021b) explored the
possibility that these waves are created by nonlinear wave-wave interactions. Identifying the
exact wave mode, the origin of these waves near fce, and their impact on the solar wind re-
main areas of active study. PSP data from ever decreasing perihelion distances are expected
to enable new progress.
# 7 Turbulence

Turbulence refers to a class of phenomena that characteristically occurs in fluids and plasmas when nonlinear effects are dominant. Nonlinearity creates complexity, involvement of many degrees of freedom and an effective lack of predictability. In contrast, linear effects such as viscous damping or waves in uniform media tend to operate more predictably on just a few coordinates or degrees of freedom. Statistical properties in both the space and time domains are crucial to fully understanding turbulence (Zhou et al. 2004; Matthaeus et al. 2015). The relative independence of spatial and temporal effects in turbulence presents particular challenges to single S/C missions such as PSP. Nevertheless various methods, ranging from Taylor's frozen-in hypothesis (Klein et al. 2015; Chhiber et al. 2019b; Perez et al. 2021) to more elaborate ensemble methods (Bourouaine and Perez 2019; Perez and Bourouaine 2020; Chen et al. 2020a; Chhiber et al. 2021c) have been brought to bear to reveal fundamental properties related to the turbulent dynamics of the newly explored regions of the solar atmosphere. This line of research is of specific importance to the PSP mission in that turbulence is a likely contributor to heating of the corona and the origin of the solar wind — two of the major goals of the PSP mission. In this section we will review the literature related to PSP observations of turbulence that has appeared in the first three years of the mission.

## 7.1 Energy Range and Large-Scale (Correlation Scale) Properties

Turbulence is often described by a cascade process, which in simplest terms describes the transfer of energy across scales from largest to smallest scales. The largest relevant scales act as reservoirs and the smallest scales generally contribute to most of the dissipation of the turbulent fluctuations. The drivers of turbulence are notionally the large “energy-containing eddies” which may be initially populated by a supply of fluctuations at the boundaries, or injection by “stirring” in the interior of the plasma. In the solar wind the dynamics at the photosphere is generally believed to inject a population of fluctuations, usually described as Alfvénic fluctuations. These propagate upwards into the corona triggering subsequent turbulent activity (Matthaeus et al. 1999a; Chandran and Hollweg 2009; van Ballegooijen et al. 2011; Perez and Chandran 2013). However large scale organized shears in magnetic field and velocity field also exist in the solar atmosphere. While these are not initially in a turbulent state, they may become so at a later time, and eventually participate by enhancing the supply of cascading energy. Stream interaction regions (SIRs) are an example of the latter. Still further stirring mechanisms are possible, such as injection of waves due to scattering of reflected particles upstream of shocks, or by newly ionized particles associated with pickup of interstellar neutrals (Pine et al. 2020). We will not be concerned with this latter class of energy injection processes here.

Among the earliest reports from PSP, Chen et al. (2020a) described a number of observations of relevance to the energy range. In particular the large-scale edge of the power-law inertial range (see §5.2) indicates a transition, moving towards large scale, into the energy range. Chen et al. (2020a) reports the presence of a shallower “$1/f$” range at these larger scales, a feature that is familiar from 1 AU observations (Matthaeus and Goldstein 1986). It is important to recognize that in general turbulent theory provides no specific expectation for spectral forms at energy-containing scales, as these may be highly situation dependent. Indeed the implied range of scale at which $1/f$ is observed *in situ* corresponds rather closely to the scales and frequencies at which features are observed in the photospheric magnetic field (Matthaeus et al. 2007b) and in the deep corona (Bemporad et al. 2008). This correspondence strongly hints that the $1/f$ signal is a vestige of dynamical processes very close
# 7 Turbulence

Turbulence refers to a class of phenomena that characteristically occurs in fluids and plasmas when nonlinear effects are dominant. Nonlinearity creates complexity, involvement of many degrees of freedom and an effective lack of predictability. In contrast, linear effects such as viscous damping or waves in uniform media tend to operate more predictably on just a few coordinates or degrees of freedom. Statistical properties in both the space and time domains are crucial to fully understanding turbulence (Zhou et al. 2004; Matthaeus et al. 2015). The relative independence of spatial and temporal effects in turbulence presents particular challenges to single S/C missions such as PSP. Nevertheless various methods, ranging from Taylor's frozen-in hypothesis (Klein et al. 2015; Chhiber et al. 2019b; Perez et al. 2021) to more elaborate ensemble methods (Bourouaine and Perez 2019; Perez and Bourouaine 2020; Chen et al. 2020a; Chhiber et al. 2021c) have been brought to bear to reveal fundamental properties related to the turbulent dynamics of the newly explored regions of the solar atmosphere. This line of research is of specific importance to the PSP mission in that turbulence is a likely contributor to heating of the corona and the origin of the solar wind — two of the major goals of the PSP mission. In this section we will review the literature related to PSP observations of turbulence that has appeared in the first three years of the mission.

## 7.1 Energy Range and Large-Scale (Correlation Scale) Properties

Turbulence is often described by a cascade process, which in simplest terms describes the transfer of energy across scales from largest to smallest scales. The largest relevant scales act as reservoirs and the smallest scales generally contribute to most of the dissipation of the turbulent fluctuations. The drivers of turbulence are notionally the large “energy-containing eddies” which may be initially populated by a supply of fluctuations at the boundaries, or injection by “stirring” in the interior of the plasma. In the solar wind the dynamics at the photosphere is generally believed to inject a population of fluctuations, usually described as Alfvénic fluctuations. These propagate upwards into the corona triggering subsequent turbulent activity (Matthaeus et al. 1999a; Chandran and Hollweg 2009; van Ballegooijen et al. 2011; Perez and Chandran 2013). However large scale organized shears in magnetic field and velocity field also exist in the solar atmosphere. While these are not initially in a turbulent state, they may become so at a later time, and eventually participate by enhancing the supply of cascading energy. Stream interaction regions (SIRs) are an example of the latter. Still further stirring mechanisms are possible, such as injection of waves due to scattering of reflected particles upstream of shocks, or by newly ionized particles associated with pickup of interstellar neutrals (Pine et al. 2020). We will not be concerned with this latter class of energy injection processes here.

Among the earliest reports from PSP, Chen et al. (2020a) described a number of observations of relevance to the energy range. In particular the large-scale edge of the power-law inertial range (see §5.2) indicates a transition, moving towards large scale, into the energy range. Chen et al. (2020a) reports the presence of a shallower “$1/f$” range at these larger scales, a feature that is familiar from 1 AU observations (Matthaeus and Goldstein 1986). It is important to recognize that in general turbulent theory provides no specific expectation for spectral forms at energy-containing scales, as these may be highly situation dependent. Indeed the implied range of scale at which $1/f$ is observed *in situ* corresponds rather closely to the scales and frequencies at which features are observed in the photospheric magnetic field (Matthaeus et al. 2007b) and in the deep corona (Bemporad et al. 2008). This correspondence strongly hints that the $1/f$ signal is a vestige of dynamical processes very close
to the sun, possibly in the dynamo. Still, Chen et al. (2020a) point out that the measured nonlinear times at the break scale between inertial and energy ranges suggest that there is sufficient time in transit for the source region to develop nonlinear correlations at the that scale. This lends some credence to theories (e.g., Velli et al. 1989; Matteini et al. 2018) offering explanation for local dynamical emergence of 1/f signals. This issue remains to be fully elucidated.

An important length scale that describes the energy range is the correlation scale, which is nominally the scale of the energy containing eddies (Wan et al. 2012b). The notion of a unique scale of this kind is elusive, given that a multiplicity of such scales exists, e.g., for MHD and plasmas. Even in incompressible MHD, one deals with one length for each of two Elsasser energies, as well as a separate correlation scale for magnetic field and velocity field fluctuations. Accounting for compressibility, the fluctuations of density (Parashar et al. 2020) also become relevant, and when remote sensing (e.g., radio) techniques are used to probe density fluctuations observed by PSP (Krupar et al. 2020), the notion of effective turbulence scale is introduced as a nominal characteristic scale.

The correlation lengths themselves are formally defined as integrals computed from correlation functions, and are therefore sensitive to energy range properties. But this definition is notoriously sensitive to low frequency power (or length of data intervals; see Isaacs et al. 2015). For this reason, simplified methods for estimating correlation lengths are often adopted. Chen et al. (2020a) examined two of these in PSP data – the so called “1/e” method (see also Parashar et al. 2020) and the break point method alluded to above. As expected based on analytical spectral models (e.g., Matthaeus et al. 2007a), correlation scales based on the break point and on $1/e$ are quite similar.

A number of researchers have suggested that measured correlation scales near PSP perihelia are somewhat shorter than what may be expected based on extrapolations of 1 AU measurements (Cuesta et al. 2020). It is possible that this is partly explained as a geometric effect, noting that the standard Parker magnetic field is close to radial in the inner heliosphere, while it subtends increasing angles relative to radial at larger distances. One approach to explaining these observations is based on a 1D turbulence transport code (Adhikari et al. 2020b) that distinguishes “slab” and “2D” correlations scales, a parameterization of correlation anisotropy (Bieber et al. 1994). Solutions of these equations (Adhikari et al. 2020b) were able to account for shorter correlation lengths seen in selected PSP intervals with nearly radial mean magnetic fields. This represents a partial explanation but leaves open the question of what sets the value of the slab (parallel) correlation scales closer to the sun.

The parallel and perpendicular correlation scales, measured relative to the ambient magnetic field direction, have obvious fundamental importance in parameterizing interplanetary turbulence. These scales also enter into expressions for the decay rates of energy and related quantities in von Karman similarity theory and its extensions (de Karman and Howarth 1938; Wan et al. 2012b). These length scales, or a subset of them, then enter into essentially all macroscopic theories of turbulence decay in the solar wind (Breech et al. 2008; Verdini et al. 2010; van der Holst et al. 2014; Lionello et al. 2014; Adhikari et al. 2017; Usmanov et al. 2018; Chandran and Perez 2019). While the subject is complex and too lengthy for full exposition here, a few words are in order. First, the perpendicular scale may likely be set by the supergranulation scale in the photosphere. A reasonably well accepted number is 35,000 km, although smaller values are sometimes favored. The perpendicular scale is often adopted as a controlling parameter in the cascade, in that the cascade is known to be anisotropic relative to the ambient field direction, and favoring perpendicular spectral transfer (Shebalin et al. 1983; Goldreich and Sridhar 1995; Matthaeus et al. 1999b). The parallel
to the sun, possibly in the dynamo. Still, Chen et al. (2020a) point out that the measured nonlinear times at the break scale between inertial and energy ranges suggest that there is sufficient time in transit for the source region to develop nonlinear correlations at the that scale. This lends some credence to theories (e.g., Velli et al. 1989; Matteini et al. 2018) offering explanation for local dynamical emergence of 1/f signals. This issue remains to be fully elucidated.

An important length scale that describes the energy range is the correlation scale, which is nominally the scale of the energy containing eddies (Wan et al. 2012b). The notion of a unique scale of this kind is elusive, given that a multiplicity of such scales exists, e.g., for MHD and plasmas. Even in incompressible MHD, one deals with one length for each of two Elsasser energies, as well as a separate correlation scale for magnetic field and velocity field fluctuations. Accounting for compressibility, the fluctuations of density (Parashar et al. 2020) also become relevant, and when remote sensing (e.g., radio) techniques are used to probe density fluctuations observed by PSP (Krupar et al. 2020), the notion of effective turbulence scale is introduced as a nominal characteristic scale.

The correlation lengths themselves are formally defined as integrals computed from correlation functions, and are therefore sensitive to energy range properties. But this definition is notoriously sensitive to low frequency power (or length of data intervals; see Isaacs et al. 2015). For this reason, simplified methods for estimating correlation lengths are often adopted. Chen et al. (2020a) examined two of these in PSP data – the so called “1/e” method (see also Parashar et al. 2020) and the break point method alluded to above. As expected based on analytical spectral models (e.g., Matthaeus et al. 2007a), correlation scales based on the break point and on 1/e are quite similar.

A number of researchers have suggested that measured correlation scales near PSP perihelia are somewhat shorter than what may be expected based on extrapolations of 1 AU measurements (Cuesta et al. 2020). It is possible that this is partly explained as a geometric effect, noting that the standard Parker magnetic field is close to radial in the inner heliosphere, while it subtends increasing angles relative to radial at larger distances. One approach to explaining these observations is based on a 1D turbulence transport code (Adhikari et al. 2020b) that distinguishes “slab” and “2D” correlations scales, a parameterization of correlation anisotropy (Bieber et al. 1994). Solutions of these equations (Adhikari et al. 2020b) were able to account for shorter correlation lengths seen in selected PSP intervals with nearly radial mean magnetic fields. This represents a partial explanation but leaves open the question of what sets the value of the slab (parallel) correlation scales closer to the sun.

The parallel and perpendicular correlation scales, measured relative to the ambient magnetic field direction, have obvious fundamental importance in parameterizing interplanetary turbulence. These scales also enter into expressions for the decay rates of energy and related quantities in von Karman similarity theory and its extensions (de Karman and Howarth 1938; Wan et al. 2012b). These length scales, or a subset of them, then enter into essentially all macroscopic theories of turbulence decay in the solar wind (Breech et al. 2008; Verdini et al. 2010; van der Holst et al. 2014; Lionello et al. 2014; Adhikari et al. 2017; Usmanov et al. 2018; Chandran and Perez 2019). While the subject is complex and too lengthy for full exposition here, a few words are in order. First, the perpendicular scale may likely be set by the supergranulation scale in the photosphere. A reasonably well accepted number is 35,000 km, although smaller values are sometimes favored. The perpendicular scale is often adopted as a controlling parameter in the cascade, in that the cascade is known to be anisotropic relative to the ambient field direction, and favoring perpendicular spectral transfer (Shebalin et al. 1983; Goldreich and Sridhar 1995; Matthaeus et al. 1999b). The parallel
correlation scale appears to be less well constrained in general, and may be regulated (at least initially in the photosphere) by the correlation time of magnetic field footpoint motions (see, e.g., Giacalone et al. 2006). Its value at the innermost boundary remains not well determined, even as PSP observations provide ever better determinations at lower perihelia, where the field direction is often radial.

One interesting possibility is that shear driven nonlinear Kelvin Helmholtz-like rollups (Landi et al. 2006; Horbury et al. 2018) drive solar wind fluctuations towards a state of isotropy as reported prior to PSP based on remote sensing observations (DeForest et al. 2016; Russell 1929). Shear induced rollups of this type would tap energy in large scale shear flows, enhancing the energy range fluctuations, and supplementing pre-existing driving of the inertial range (Ruffolo et al. 2020). Such interactions are likely candidates for inducing a mixing, or averaging, between the parallel and perpendicular turbulence length scales in regions of Kelvin-Helmholtz-like rollups (Ruffolo et al. 2020).

In general, multi-orbit PSP observations (Chen et al. 2020a; Chhiber et al. 2021c; Adhikari et al. 2020b) provide better determination of not only length scales but other parameters that characterize the energy containing scales of turbulence. Knowledge of energy range parameters impacts practical issues such as the selection of appropriate times for describing local bulk properties such as mean density, a quantity that enters into computations of cross helicity and other measures of the Alfvénicity in observed fluctuations (Parashar et al. 2020).

Possibly the most impactful consequence of energy range parameters is their potential control over the cascade rate, and therefore control over the plasma dissipation and heating, whatever the details of those processes may be. One approach is to estimate the energy supply into the smaller scales from the energy containing range by examining the evolution of the break point between the $1/f$ range and the inertial range (Wu et al. 2020). This approach involves assumptions about the relationship of the $1/f$ range to the inertial range. Using three orbits of PSP data, these authors evaluated the estimated energy supply rate from the radial break point evolution with the estimated perpendicular proton heating rate, finding a reasonable level of heating in fast and slow wind. Another approach to estimating heating rates in PSP observations Martinović et al. (2020) makes use of approximate connections between heating rate and radial gradient of temperature (Vasquez et al. 2007; Bourouaine and Chandran 2013) along with theoretical estimates from a form of stochastic heating (Chandran et al. 2010). Again, reasonable levels of correspondence are found. Both of these approaches (Wu et al. 2020; Martinović et al. 2020) derive interesting conclusions based in part on assumptions about transport theory of temperature, or transport of turbulent fluctuations. An alternative approach is based entirely on turbulence theory extended to the solar wind plasma and applied locally to PSP data (Bandyopadhyay et al. 2020a). In this case two evaluations are made – an energy range estimate adapted from von Karman decay theory (Wan et al. 2012b) and a third order Yaglom-like law (Politano and Pouquet 1998) applied to the inertial range. Cascade rates about 100 times that observed at 1 AU are deduced. The consistency of the estimates of cascade rates obtained from PSP observations employing these diverse methods suggests a robust interpretation of interplanetary turbulence and the role of the energy containing eddies in exerting control over the cascade.

## 7.2 Inertial Range

During the solar minimum, fast solar wind streams originate near the poles from open magnetic flux tubes within coronal holes, while slow wind streams originate in the streamer belt within a few tens of degrees from the solar equator (McComas et al. 2008). Because plasma
correlation scale appears to be less well constrained in general, and may be regulated (at least initially in the photosphere) by the correlation time of magnetic field footpoint motions (see, e.g., Giacalone et al. 2006). Its value at the innermost boundary remains not well determined, even as PSP observations provide ever better determinations at lower perihelia, where the field direction is often radial.

One interesting possibility is that shear driven nonlinear Kelvin Helmholtz-like rollups (Landi et al. 2006; Horbury et al. 2018) drive solar wind fluctuations towards a state of isotropy as reported prior to PSP based on remote sensing observations (DeForest et al. 2016; Russell 1929). Shear induced rollups of this type would tap energy in large scale shear flows, enhancing the energy range fluctuations, and supplementing pre-existing driving of the inertial range (Ruffolo et al. 2020). Such interactions are likely candidates for inducing a mixing, or averaging, between the parallel and perpendicular turbulence length scales in regions of Kelvin-Helmholtz-like rollups (Ruffolo et al. 2020).

In general, multi-orbit PSP observations (Chen et al. 2020a; Chhiber et al. 2021c; Adhikari et al. 2020b) provide better determination of not only length scales but other parameters that characterize the energy containing scales of turbulence. Knowledge of energy range parameters impacts practical issues such as the selection of appropriate times for describing local bulk properties such as mean density, a quantity that enters into computations of cross helicity and other measures of the Alfvénicity in observed fluctuations (Parashar et al. 2020).

Possibly the most impactful consequence of energy range parameters is their potential control over the cascade rate, and therefore control over the plasma dissipation and heating, whatever the details of those processes may be. One approach is to estimate the energy supply into the smaller scales from the energy containing range by examining the evolution of the break point between the $1/f$ range and the inertial range (Wu et al. 2020). This approach involves assumptions about the relationship of the $1/f$ range to the inertial range. Using three orbits of PSP data, these authors evaluated the estimated energy supply rate from the radial break point evolution with the estimated perpendicular proton heating rate, finding a reasonable level of heating in fast and slow wind. Another approach to estimating heating rates in PSP observations Martinović et al. (2020) makes use of approximate connections between heating rate and radial gradient of temperature (Vasquez et al. 2007; Bourouaine and Chandran 2013) along with theoretical estimates from a form of stochastic heating (Chandran et al. 2010). Again, reasonable levels of correspondence are found. Both of these approaches (Wu et al. 2020; Martinović et al. 2020) derive interesting conclusions based in part on assumptions about transport theory of temperature, or transport of turbulent fluctuations. An alternative approach is based entirely on turbulence theory extended to the solar wind plasma and applied locally to PSP data (Bandyopadhyay et al. 2020a). In this case two evaluations are made – an energy range estimate adapted from von Karman decay theory (Wan et al. 2012b) and a third order Yaglom-like law (Politano and Pouquet 1998) applied to the inertial range. Cascade rates about 100 times that observed at 1 AU are deduced. The consistency of the estimates of cascade rates obtained from PSP observations employing these diverse methods suggests a robust interpretation of interplanetary turbulence and the role of the energy containing eddies in exerting control over the cascade.

## 7.2 Inertial Range

During the solar minimum, fast solar wind streams originate near the poles from open magnetic flux tubes within coronal holes, while slow wind streams originate in the streamer belt within a few tens of degrees from the solar equator (McComas et al. 2008). Because plasma
can easily escape along open flux tubes, fast wind is typically observed to be relatively less dense, more homogeneous and characteristically more Alfvénic than slow streams, which are believed to arise from a number of sources, such as the tip helmet streamers prevalent in ARs (Einaudi et al. 1999; Lapenta and Knoll 2005), opening of coronal loops via interchange reconnection with adjacent open flux tubes (Fisk and Schwadron 2001), or from rapidly expanding coronal holes (Cranmer 2009).

The first two PSP close Encs. with the Sun, which occurred during Nov. 2018 (Enc. 1) and Apr. 2019 (Enc. 2), where not only much closer than any S/C before, but also remained at approximately the same longitude w.r.t. the rotating Sun, allowing PSP to continuously sample a number of solar wind streams rooted in a small equatorial coronal hole (Bale et al. 2019; Kasper et al. 2019). Measurements of velocity and magnetic field during these two Encs. reveal a highly structured and dynamic slow solar wind consisting of a quiet and highly Alfvénic background with frequent impulsive magnetic field polarity reversals, which are associated with so called switchbacks (see also Dudok de Wit et al. 2020; Horbury et al. 2020; McManus et al. 2020). The 30 min averaged trace magnetic spectra for both quiet and switchbacks regions exhibit a dual power-law, with an inertial-range Kolmogorov spectral index of $-5/3$ at high heliocentric distances (as observed in previous observations near 1 AU) and Iroshnikov-Kraichnan index of $-3/2$ near 0.17 AU, consistent with theoretical predictions from MHD turbulence (Chen 2016). These findings indicate that Alfvénic turbulence is already developed at 0.17 AU. Moreover, the radial evolution of the turbulent dissipation rate between 0.17 AU and 0.25 AU, estimated using Politano-Pouquet third order law and the von Karman decay law, increases from $5 \times 10^4$ J kg$^{-1}$s$^{-1}$ at 0.25 AU to $2 \times 10^5$ J kg$^{-1}$s$^{-1}$ at 0.17 AU, which is up to 100 times larger at Perihelion 1 than its measured value at 1 AU (Bandyopadhyay et al. 2020a) and in agreement with some MHD turbulent transport models (Usmanov et al. 2018). Simon and Sahraoui (2021) estimated the energy cascade rate at each scale in the inertial range, based on exact scaling laws derived for isentropic turbulent flows in three particular MHD closures corresponding to incompressible, isothermal and polytropic equations of state, and found the energy cascade rates to be nearly constant in the inertial range at approximately the same value of $2 \times 10^5$ J kg$^{-1}$s$^{-1}$ obtained by (Usmanov et al. 2018) at 0.17 AU, independent of the closure assumption.

Chaston et al. (2020) performed an analysis to decompose PSP measurements from the first two orbits into MHD modes. The analysis used solar wind intervals between switchbacks to reveal the presence of a broad spectrum of shear Alfvén modes, an important fraction of slow modes and a small fraction of fast modes. The analysis of the Poynting flux reveals that while most of the energy is propagating outward from the sun, inversions in the Poynting flux are observed and are consistent with outward-propagating waves along kinked magnetic field lines. These inversions of the energy flux also correlate with the large rotations of the magnetic field. An observed increase of the spectral energy density of inward-propagating waves with increasing frequency suggests back-scattering of outward-propagating waves off of magnetic field reversals and associated inhomogeneities in the background plasma. Wave-mode composition, propagation and polarization within 0.3 AU was also investigated by Zhu et al. (2020) through the Probability Distribution Functions (PDFs) of wave-vectors within 0.3 AU with two main findings: (1) wave-vectors cluster nearly parallel and antiparallel to the local background magnetic field for $kd_i < 0.02$ and shift to nearly perpendicular for $kd_i > 0.02$. The authors also find that outward-propagating AW dominate over all scales and heliocentric distances, the energy fraction of inward and outward slow mode component increases with heliocentric distance, while the corresponding fraction of fast mode decreases.

Chen et al. (2020a) investigated the radial dependency of the trace magnetic field spectra, between 0.17 AU to about 0.6 AU, using MAG data from the FIELDS suite (Bale et al.
can easily escape along open flux tubes, fast wind is typically observed to be relatively less dense, more homogeneous and characteristically more Alfvénic than slow streams, which are believed to arise from a number of sources, such as the tip helmet streamers prevalent in ARs (Einaudi et al. 1999; Lapenta and Knoll 2005), opening of coronal loops via interchange reconnection with adjacent open flux tubes (Fisk and Schwadron 2001), or from rapidly expanding coronal holes (Cranmer 2009).

The first two PSP close Encs. with the Sun, which occurred during Nov. 2018 (Enc. 1) and Apr. 2019 (Enc. 2), where not only much closer than any S/C before, but also remained at approximately the same longitude w.r.t. the rotating Sun, allowing PSP to continuously sample a number of solar wind streams rooted in a small equatorial coronal hole (Bale et al. 2019; Kasper et al. 2019). Measurements of velocity and magnetic field during these two Encs. reveal a highly structured and dynamic slow solar wind consisting of a quiet and highly Alfvénic background with frequent impulsive magnetic field polarity reversals, which are associated with so called switchbacks (see also Dudok de Wit et al. 2020; Horbury et al. 2020; McManus et al. 2020). The 30 min averaged trace magnetic spectra for both quiet and switchbacks regions exhibit a dual power-law, with an inertial-range Kolmogorov spectral index of $-5/3$ at high heliocentric distances (as observed in previous observations near 1 AU) and Iroshnikov-Kraichnan index of $-3/2$ near 0.17 AU, consistent with theoretical predictions from MHD turbulence (Chen 2016). These findings indicate that Alfvénic turbulence is already developed at 0.17 AU. Moreover, the radial evolution of the turbulent dissipation rate between 0.17 AU and 0.25 AU, estimated using Politano-Pouquet third order law and the von Karman decay law, increases from $5 \times 10^4$ J kg$^{-1}$s$^{-1}$ at 0.25 AU to $2 \times 10^5$ J kg$^{-1}$s$^{-1}$ at 0.17 AU, which is up to 100 times larger at Perihelion 1 than its measured value at 1 AU (Bandyopadhyay et al. 2020a) and in agreement with some MHD turbulent transport models (Usmanov et al. 2018). Simon and Sahraoui (2021) estimated the energy cascade rate at each scale in the inertial range, based on exact scaling laws derived for isentropic turbulent flows in three particular MHD closures corresponding to incompressible, isothermal and polytropic equations of state, and found the energy cascade rates to be nearly constant in the inertial range at approximately the same value of $2 \times 10^5$ J kg$^{-1}$s$^{-1}$ obtained by (Usmanov et al. 2018) at 0.17 AU, independent of the closure assumption.

Chaston et al. (2020) performed an analysis to decompose PSP measurements from the first two orbits into MHD modes. The analysis used solar wind intervals between switchbacks to reveal the presence of a broad spectrum of shear Alfvén modes, an important fraction of slow modes and a small fraction of fast modes. The analysis of the Poynting flux reveals that while most of the energy is propagating outward from the sun, inversions in the Poynting flux are observed and are consistent with outward-propagating waves along kinked magnetic field lines. These inversions of the energy flux also correlate with the large rotations of the magnetic field. An observed increase of the spectral energy density of inward-propagating waves with increasing frequency suggests back-scattering of outward-propagating waves off of magnetic field reversals and associated inhomogeneities in the background plasma. Wave-mode composition, propagation and polarization within 0.3 AU was also investigated by Zhu et al. (2020) through the Probability Distribution Functions (PDFs) of wave-vectors within 0.3 AU with two main findings: (1) wave-vectors cluster nearly parallel and antiparallel to the local background magnetic field for $kd_i < 0.02$ and shift to nearly perpendicular for $kd_i > 0.02$. The authors also find that outward-propagating AW dominate over all scales and heliocentric distances, the energy fraction of inward and outward slow mode component increases with heliocentric distance, while the corresponding fraction of fast mode decreases.

Chen et al. (2020a) investigated the radial dependency of the trace magnetic field spectra, between 0.17 AU to about 0.6 AU, using MAG data from the FIELDS suite (Bale et al.
2016) for each 24 h interval during the first two PSP orbits. Their analysis shows that the trace spectra of magnetic fluctuations at each radii consists of a dual power-law, only this time involving the 1/f range followed by an MHD inertial-range with an spectral index varying from approximately -5/3 near 0.6 AU to about -3/2 at perihelion (0.17 AU). Velocity measurements obtained from SWEAP/SPC (Kasper et al. 2016) were used for the 24 h interval around Perihelion 1 to obtain the trace spectra of velocity and Elsasser field fluctuations, all of which show a power law with a spectral index closer to -3/2. The normalized cross-helicity and residual energy, which was also measured for each 24 h interval, shows that the turbulence becomes more imbalanced closer to the Sun, i.e., the dominance of outward-propagating increases with decreasing heliocentric distance. Additional measures of Alfvénicity of velocity and magnetic fluctuations as a function of their scale-size (Parashar et al. 2020) showed that both normalized cross-helicity and the scale-dependent angle between velocity and magnetic field decreases with the scale-size in the inertial-range, as suggested by some MHD turbulence models (Boldyrev 2006; Perez and Boldyrev 2009; Podesta and Bhattacharjee 2010), followed by a sharp decline in the kinetic range, consistent with observations at 1 AU (Parashar et al. 2018). The transition from a spectral index of -5/3 to -3/2 with a concurrent increase in cross helicity is consistent with previous observations at 1 AU in which a spectral index of -3/2 for the magnetic field is prevalent in imbalanced streams (Podesta and Borovsky 2010; Chen et al. 2013; Wicks et al. 2013), as well as consistent with models and simulations of steadily-driven, homogeneous imbalanced Alfvénic turbulence (Perez and Boldyrev 2009; Podesta and Bhattacharjee 2010), and reflection-driven (inhomogeneous) Alfvén turbulence (Perez and Chandran 2013; Chandran and Perez 2019). A similar transition was also found by Alberti et al. (2020), where the Hilbert-Huang Transform (HHT) was used to investigate scaling properties of magnetic-field fluctuations as a function of the heliocentric distance, to show that magnetic fluctuations exhibit multifractal scaling properties far from the sun, with a power spectrum $f^{-5/3}$, while closer to the sun the corresponding scaling becomes monofractal with $f^{-3/2}$ power spectrum. Assuming ballistic propagation, Telloni et al. (2021b) identified two 1.5 h intervals corresponding to the same plasma parcel traveling from 0.1 to 1 AU during the first PSP and SolO radial alignment, and also showed that the solar wind evolved from a highly Alfvénic, less developed turbulent state near the sun to a more fully developed and intermittent state near 1 AU.

Shi et al. (2021) performed a statistical analysis to investigate how the turbulence properties at MHD scales depend on the type of solar wind stream and distance from the sun. Their results show that the spectrum of magnetic field fluctuations steepens with the distance to the Sun while the velocity spectrum remains unchanged. Faster solar wind is found to be more Alfvénic and dominated by outward-propagating waves (imbalanced) and with low residual energy. Energy imbalance (cross helicity) and residual energy decrease with heliocentric distance. Turbulent properties can also vary among different streams with similar speeds, possibly indicating a different origin. For example, slow wind emanating from a small coronal hole has much higher Alfvénicity than a slow wind that originates from the streamer belt. Chen et al. (2021a) investigated the turbulence and acceleration properties of the streamer-belt solar wind, near the HCS, using measurements from PSP's fourth orbit. During this close S/C, the properties of the solar wind from the inbound measurements are substantially different than from the outbound measurements. In the latter, the solar wind was observed to have smaller turbulent amplitudes, higher magnetic compressibility, a steeper magnetic spectrum (closer to -5/3 than to -3/2), lower Alfvénicity and a 1/f break at much smaller frequencies. The transition from a more Alfvénic (inbound) wind to a non-Alfvénic wind occurred at an angular distance of about 4° from the HCS. As opposed to the inbound Alfvénic
2016) for each 24 h interval during the first two PSP orbits. Their analysis shows that the trace spectra of magnetic fluctuations at each radii consists of a dual power-law, only this time involving the 1/f range followed by an MHD inertial-range with an spectral index varying from approximately -5/3 near 0.6 AU to about -3/2 at perihelion (0.17 AU). Velocity measurements obtained from SWEAP/SPC (Kasper et al. 2016) were used for the 24 h interval around Perihelion 1 to obtain the trace spectra of velocity and Elsasser field fluctuations, all of which show a power law with a spectral index closer to -3/2. The normalized cross-helicity and residual energy, which was also measured for each 24 h interval, shows that the turbulence becomes more imbalanced closer to the Sun, i.e., the dominance of outward-propagating increases with decreasing heliocentric distance. Additional measures of Alfvénicity of velocity and magnetic fluctuations as a function of their scale-size (Parashar et al. 2020) showed that both normalized cross-helicity and the scale-dependent angle between velocity and magnetic field decreases with the scale-size in the inertial-range, as suggested by some MHD turbulence models (Boldyrev 2006; Perez and Boldyrev 2009; Podesta and Bhattacharjee 2010), followed by a sharp decline in the kinetic range, consistent with observations at 1 AU (Parashar et al. 2018). The transition from a spectral index of -5/3 to -3/2 with a concurrent increase in cross helicity is consistent with previous observations at 1 AU in which a spectral index of -3/2 for the magnetic field is prevalent in imbalanced streams (Podesta and Borovsky 2010; Chen et al. 2013; Wicks et al. 2013), as well as consistent with models and simulations of steadily-driven, homogeneous imbalanced Alfvénic turbulence (Perez and Boldyrev 2009; Podesta and Bhattacharjee 2010), and reflection-driven (inhomogeneous) Alfvén turbulence (Perez and Chandran 2013; Chandran and Perez 2019). A similar transition was also found by Alberti et al. (2020), where the Hilbert-Huang Transform (HHT) was used to investigate scaling properties of magnetic-field fluctuations as a function of the heliocentric distance, to show that magnetic fluctuations exhibit multifractal scaling properties far from the sun, with a power spectrum $f^{-5/3}$, while closer to the sun the corresponding scaling becomes monofractal with $f^{-3/2}$ power spectrum. Assuming ballistic propagation, Telloni et al. (2021b) identified two 1.5 h intervals corresponding to the same plasma parcel traveling from 0.1 to 1 AU during the first PSP and SoIo radial alignment, and also showed that the solar wind evolved from a highly Alfvénic, less developed turbulent state near the sun to a more fully developed and intermittent state near 1 AU.

Shi et al. (2021) performed a statistical analysis to investigate how the turbulence properties at MHD scales depend on the type of solar wind stream and distance from the sun. Their results show that the spectrum of magnetic field fluctuations steepens with the distance to the Sun while the velocity spectrum remains unchanged. Faster solar wind is found to be more Alfvénic and dominated by outward-propagating waves (imbalanced) and with low residual energy. Energy imbalance (cross helicity) and residual energy decrease with heliocentric distance. Turbulent properties can also vary among different streams with similar speeds, possibly indicating a different origin. For example, slow wind emanating from a small coronal hole has much higher Alfvénicity than a slow wind that originates from the streamer belt. Chen et al. (2021a) investigated the turbulence and acceleration properties of the streamer-belt solar wind, near the HCS, using measurements from PSP's fourth orbit. During this close S/C, the properties of the solar wind from the inbound measurements are substantially different than from the outbound measurements. In the latter, the solar wind was observed to have smaller turbulent amplitudes, higher magnetic compressibility, a steeper magnetic spectrum (closer to -5/3 than to -3/2), lower Alfvénicity and a 1/f break at much smaller frequencies. The transition from a more Alfvénic (inbound) wind to a non-Alfvénic wind occurred at an angular distance of about 4° from the HCS. As opposed to the inbound Alfvénic
wind, in which the measured energy fluxes are consistent with reflection-driven turbulence models (Perez and Chandran 2013; Chandran and Perez 2019), the streamer belt fluxes are significantly lower than those predicted by the same models, suggesting the streamer-belt wind may be subject to additional acceleration mechanisms.

Interpretation of the spectral analysis of temporal signals to investigate scaling laws in the inertial range thus far have relied on the validity of Taylor's Hypothesis (TH). Perez et al. (2021) investigated the applicability of TH in the first four orbits based on a recent model of the space-time correlation function of Alfvénic turbulence (incompressible MHD; Bourouaine and Perez 2018; Perez and Bourouaine 2020). In this model, the temporal decorrelation of the turbulence is dominated by hydrodynamic sweeping under the assumption that the turbulence is strongly anisotropic and Alfvénic. The only parameter in the model that controls the validity of TH is $\epsilon = \delta u_0 / V_\perp$ where $\delta u_0$ is the rms velocity of the large-scale velocity field and $V_\perp$ is the velocity of the S/C in the plasma frame perpendicular to the local field. The spatial energy spectrum of turbulent fluctuations is recovered using conditional statistics based on nearly perpendicular sampling. The analysis is performed on four selected 24h intervals from PSP during the first four perihelia. TH is observed to still be marginally applicable, and both the new analysis and the standard TH assumption lead to similar results. A general prescription to obtain the energy spectrum when TH is violated is summarized and expected to be relevant when PSP get closer to the sun.

Duan et al. (2021) investigated the anisotropy of slow Alfvénic solar wind in the kinetic range from PSP measurements. Magnetic compressibility is consistent with kinetic Alfvén waves (KAW) turbulence at sub-ion scales. A steepened transition range is found between the (MHD) inertial and kinetic ranges in all directions relative to the background magnetic field. Strong power spectrum anisotropy is observed in the kinetic range and a smaller anisotropy in the transition range. Scaling exponents for the power spectrum in the transition range are found to be $\alpha_{t\parallel} = -5.7 \pm 1.0$ and $\alpha_{t\perp} = -3.7 \pm 0.3$, while for the kinetic range the same exponent are $\alpha_{k\parallel} = -3.12 \pm 0.22$ and $\alpha_{k\perp} = -2.57 \pm 0.09$. The wavevector anisotropy in the transition and kinetic ranges follow the scaling $k_\parallel \sim k_\perp^{0.71 \pm 0.17}$ and $k_\perp \sim k_\parallel^{0.38 \pm 0.09}$, respectively.

## 7.3 Kinetic Range, Dissipation, Heating and Implications

In-situ measurements have revealed that the solar wind is not adiabatically cooling, as both the ion and electron temperatures decay at considerably slower rates than the adiabatic cooling rates induced by the radial expansion effect of the solar wind (e.g., Huang et al. 2020a; Maksimovic et al. 2020). Thus, some heating mechanisms must exist in the solar wind. As the solar wind is nearly collisionless, viscosity, resistivity, and thermal conduction are unlikely to contribute much to the heating of the solar wind. Hence, turbulence is believed to be the fundamental process that heats the solar wind plasma. In the MHD inertial range, the turbulence energy cascades from large scales to small scales without dissipation. Near or below the ion kinetic scale, various kinetic processes, such as the wave-particle interaction through cyclotron resonance or Landau damping, and the stochastic heating of the particles, become important. These kinetic processes effectively dissipate the turbulence energy and heat the plasma. As already discussed in §7.1, Wu et al. (2020) show that the estimated energy supply rate at the large scales agrees well with the estimated perpendicular heating rate of the solar wind, implying that turbulence is the major heating source of the solar wind. However, to fully understand how the turbulence energy eventually converts to the internal energy of the plasma, we must analyze the magnetic field and plasma data at and below the ion scales.
wind, in which the measured energy fluxes are consistent with reflection-driven turbulence models (Perez and Chandran 2013; Chandran and Perez 2019), the streamer belt fluxes are significantly lower than those predicted by the same models, suggesting the streamer-belt wind may be subject to additional acceleration mechanisms.

Interpretation of the spectral analysis of temporal signals to investigate scaling laws in the inertial range thus far have relied on the validity of Taylor's Hypothesis (TH). Perez et al. (2021) investigated the applicability of TH in the first four orbits based on a recent model of the space-time correlation function of Alfvénic turbulence (incompressible MHD; Bourouaine and Perez 2018; Perez and Bourouaine 2020). In this model, the temporal decorrelation of the turbulence is dominated by hydrodynamic sweeping under the assumption that the turbulence is strongly anisotropic and Alfvénic. The only parameter in the model that controls the validity of TH is $\epsilon = \delta u_0 / V_\perp$ where $\delta u_0$ is the rms velocity of the large-scale velocity field and $V_\perp$ is the velocity of the S/C in the plasma frame perpendicular to the local field. The spatial energy spectrum of turbulent fluctuations is recovered using conditional statistics based on nearly perpendicular sampling. The analysis is performed on four selected 24h intervals from PSP during the first four perihelia. TH is observed to still be marginally applicable, and both the new analysis and the standard TH assumption lead to similar results. A general prescription to obtain the energy spectrum when TH is violated is summarized and expected to be relevant when PSP get closer to the sun.

Duan et al. (2021) investigated the anisotropy of slow Alfvénic solar wind in the kinetic range from PSP measurements. Magnetic compressibility is consistent with kinetic Alfvén waves (KAW) turbulence at sub-ion scales. A steepened transition range is found between the (MHD) inertial and kinetic ranges in all directions relative to the background magnetic field. Strong power spectrum anisotropy is observed in the kinetic range and a smaller anisotropy in the transition range. Scaling exponents for the power spectrum in the transition range are found to be $\alpha_{t\parallel} = -5.7 \pm 1.0$ and $\alpha_{t\perp} = -3.7 \pm 0.3$, while for the kinetic range the same exponent are $\alpha_{k\parallel} = -3.12 \pm 0.22$ and $\alpha_{k\perp} = -2.57 \pm 0.09$. The wavevector anisotropy in the transition and kinetic ranges follow the scaling $k_\parallel \sim k_\perp^{0.71 \pm 0.17}$ and $k_\perp \sim k_\parallel^{0.38 \pm 0.09}$, respectively.

## 7.3 Kinetic Range, Dissipation, Heating and Implications

In-situ measurements have revealed that the solar wind is not adiabatically cooling, as both the ion and electron temperatures decay at considerably slower rates than the adiabatic cooling rates induced by the radial expansion effect of the solar wind (e.g., Huang et al. 2020a; Maksimovic et al. 2020). Thus, some heating mechanisms must exist in the solar wind. As the solar wind is nearly collisionless, viscosity, resistivity, and thermal conduction are unlikely to contribute much to the heating of the solar wind. Hence, turbulence is believed to be the fundamental process that heats the solar wind plasma. In the MHD inertial range, the turbulence energy cascades from large scales to small scales without dissipation. Near or below the ion kinetic scale, various kinetic processes, such as the wave-particle interaction through cyclotron resonance or Landau damping, and the stochastic heating of the particles, become important. These kinetic processes effectively dissipate the turbulence energy and heat the plasma. As already discussed in §7.1, Wu et al. (2020) show that the estimated energy supply rate at the large scales agrees well with the estimated perpendicular heating rate of the solar wind, implying that turbulence is the major heating source of the solar wind. However, to fully understand how the turbulence energy eventually converts to the internal energy of the plasma, we must analyze the magnetic field and plasma data at and below the ion scales.
<figure><img src="image_23.png" /><figcaption>**Fig. 21 (a,b)** Examples of PSP/FIELDS magnetic field spectra with 3PL (three spectral range continuous power-law fit, blue) and 2PL (two spectral range continuous power-law fit, orange) fits. Vertical lines show 3PL spectral breaks. (c,d) spectral indices for data (black), 3PL (blue) and 2PL fits (orange). Horizontal lines are shown corresponding to spectral indices of −8/3 (teal) and −4 (purple). Top interval has statistically significant spectral steepening, while the bottom interval is sufficiently fit by 2PL. Figure adapted from Bowen et al. (2020c)</figcaption></figure>

Bowen et al. (2020c) analyze data of the MAG and SCM onboard PSP during Enc. 1 when a slow Alfvénic wind originating from an equatorial coronal hole was measured. They show that a very steep transition range in the magnetic field power spectrum with a spectral slope close to −4 is observed around the ion gyroscale ($k_{\perp} \rho_i \sim 1$ where $k_{\perp}$ is the perpendicular wave number and $\rho_i$ is the ion thermal gyroradius) (Fig. 21). This transition range is steeper than both the inertial range ($k_{\perp} \rho_i \ll 1$) and the deep kinetic range ($k_{\perp} \rho_i \gg 1$). Bowen et al. (2020c) estimate that if the steep spectrum corresponds to some dissipation mechanism, then more than 50% of the turbulence energy is dissipated at the ion scale transition range, which is a sufficient energy source for solar wind heating. Duan et al. (2020) conduct a statistical study of the magnetic field spectrum based on PSP data from Enc. 2 and show that the break frequency between the inertial range and the transition range decreases with the radial distance to the Sun and is on the order of the ion cyclotron resonance frequency.

Huang et al. (2020b) find that, in a one-day interval during Enc. 1, the slow wind observed by PSP contains both the right-handed polarized KAWs and the left-handed polarized Alfvén ion cyclotron waves (ACWs) at sub-ion scales. Many previous observations have shown that at 1 AU KAW dominates the turbulence at sub-ion scales (e.g., Sahraoui et al. 2010) and KAW can heat the ions through Landau damping of its parallel electric field. However, the results of (Huang et al. 2020b) imply a possible role of ACWs, at least in the very young solar wind, in heating the ions through cyclotron resonance. Duan et al. (2021), by binning the Enc. 1 data with different **V**–**B** angles, show that the magnetic field spectrum is anisotropic in both the transition range and kinetic range with $k_{\perp} \gg k_{\|}$ and the anisotropy scaling relation between $k_{\perp}$ and $k_{\|}$ is consistent with the critical-balanced KAW model in the sub-ion scales (see §7.2).

Another heating mechanism is the stochastic heating (Chandran et al. 2010), which becomes important when the fluctuation of the magnetic field at the ion gyroscale is large enough such that the magnetic moment of the particles is no longer conserved. Martinović
<figure><img src="image_24.png" /><figcaption>**Fig. 21 (a,b)** Examples of PSP/FIELDS magnetic field spectra with 3PL (three spectral range continuous power-law fit, blue) and 2PL (two spectral range continuous power-law fit, orange) fits. Vertical lines show 3PL spectral breaks. (c,d) spectral indices for data (black), 3PL (blue) and 2PL fits (orange). Horizontal lines are shown corresponding to spectral indices of −8/3 (teal) and −4 (purple). Top interval has statistically significant spectral steepening, while the bottom interval is sufficiently fit by 2PL. Figure adapted from Bowen et al. (2020c)</figcaption></figure>

Bowen et al. (2020c) analyze data of the MAG and SCM onboard PSP during Enc. 1 when a slow Alfvénic wind originating from an equatorial coronal hole was measured. They show that a very steep transition range in the magnetic field power spectrum with a spectral slope close to −4 is observed around the ion gyroscale ($k_{\perp} \rho_i \sim 1$ where $k_{\perp}$ is the perpendicular wave number and $\rho_i$ is the ion thermal gyroradius) (Fig. 21). This transition range is steeper than both the inertial range ($k_{\perp} \rho_i \ll 1$) and the deep kinetic range ($k_{\perp} \rho_i \gg 1$). Bowen et al. (2020c) estimate that if the steep spectrum corresponds to some dissipation mechanism, then more than 50% of the turbulence energy is dissipated at the ion scale transition range, which is a sufficient energy source for solar wind heating. Duan et al. (2020) conduct a statistical study of the magnetic field spectrum based on PSP data from Enc. 2 and show that the break frequency between the inertial range and the transition range decreases with the radial distance to the Sun and is on the order of the ion cyclotron resonance frequency.

Huang et al. (2020b) find that, in a one-day interval during Enc. 1, the slow wind observed by PSP contains both the right-handed polarized KAWs and the left-handed polarized Alfvén ion cyclotron waves (ACWs) at sub-ion scales. Many previous observations have shown that at 1 AU KAW dominates the turbulence at sub-ion scales (e.g., Sahraoui et al. 2010) and KAW can heat the ions through Landau damping of its parallel electric field. However, the results of (Huang et al. 2020b) imply a possible role of ACWs, at least in the very young solar wind, in heating the ions through cyclotron resonance. Duan et al. (2021), by binning the Enc. 1 data with different **V**–**B** angles, show that the magnetic field spectrum is anisotropic in both the transition range and kinetic range with $k_{\perp} \gg k_{\|}$ and the anisotropy scaling relation between $k_{\perp}$ and $k_{\|}$ is consistent with the critical-balanced KAW model in the sub-ion scales (see §7.2).

Another heating mechanism is the stochastic heating (Chandran et al. 2010), which becomes important when the fluctuation of the magnetic field at the ion gyroscale is large enough such that the magnetic moment of the particles is no longer conserved. Martinović
et al. (2020) calculate the stochastic heating rate using data from the first two Encs. and show that the stochastic heating rate $Q_⊥$ decays with the radial distance as $Q_⊥ ∝ r^{-2.5}$. Their result reveals that the stochastic heating may be more important in the solar wind closer to the Sun.

Last, it is known that development of turbulence leads to the formation of intermittency (see §7.4 for more detailed discussions). In plasma turbulence, intermittent structures such as current sheets are generated around the ion kinetic scale. Qudsi et al. (2020) adopt the partial variance of increments (PVI) technique to identify intermittent magnetic structures using PSP data from the first S/C. They show that statistically there is a positive correlation between the ion temperature and the PVI, indicating that the intermittent structures may contribute to the heating of the young solar wind through processes like the magnetic reconnection in the intermittent current sheets.

At the end of this subsection, it is worthwhile to make several comments. First, the Fara-day Cup onboard PSP (SPC) has a flux-angle operation mode, which allows measurements of the ion phase space density fluctuations at a cadence of 293 Hz (Vech et al. 2020). Thus, combination of the flux-angle measurements with the magnetic field data will greatly help us understand the kinetic turbulence. Second, more studies are necessary to understand behaviors of electrons in the turbulence, though direct measurement of the electron-scale fluctuations in the solar wind is difficult with current plasma instruments. Adhikari et al. (2021) show that by distributing the turbulence heating properly among ions and electrons in a turbulence-coupled solar wind model, differential radial evolutions of ion and electron temperatures can be reproduced. However, how and why the turbulence energy is distributed unevenly among ions and electrons are not fully understood yet and need future studies. Third, during the Venus flybys, PSP traveled through Venus's magnetosphere and made high-cadence measurements. Thus, analysis of the turbulence properties around Venus, e.g., inside its magnetosheath (Bowen et al. 2021) will also be helpful in understanding the kinetic turbulence (see §12). Last, Martinović et al. (2021) compare the turbulence properties inside and outside the magnetic switchbacks using the PSP data from the first two Encs. They find that the stochastic heating rates and spectral slopes are similar but other properties such as the intermittency level are different inside and outside the switchbacks, indicating that some processes near the edges of switchbacks, such as the velocity shear, considerably affect the turbulence evolution inside the switchbacks (see §4.2).

## 7.4 Intermittency and Small-scale Structure

In the modern era to turbulence research, intermittency has been established as a fundamental feature of turbulent flows (e.g., Sreenivasan and Antonia 1997). Nonlinearly interacting fluctuations are expected to give rise to structure in space and time, which is characterized by sharp gradients, inhomogeneities, and departures from Gaussian statistics. In a plasma such as the solar wind, such “bursty” or “patchy” structures include current sheets, vortices, and flux tubes. These structures have been associated with enhanced plasma dissipation and heating (Matthaeus et al. 2015), and with acceleration of energetic particles (Tessein et al. 2013). Studies of intermittency may therefore provide insights into dissipation and heating mechanisms active in the weakly-collisional solar wind plasma. Intermittency also has implications for turbulence theory – a familiar example is the evolution of hydrodynamic inertial range theory from the classical Kolmogorov (K41; 1941) theory to the so-called refined similarity hypothesis (Kolmogorov 1962); the former assumed a uniform energy dissipation rate while the latter allowed for fluctuations and inhomogeneities in this fundamental quantity.
et al. (2020) calculate the stochastic heating rate using data from the first two Encs. and show that the stochastic heating rate $Q_⊥$ decays with the radial distance as $Q_⊥ ∝ r^{-2.5}$. Their result reveals that the stochastic heating may be more important in the solar wind closer to the Sun.

Last, it is known that development of turbulence leads to the formation of intermittency (see §7.4 for more detailed discussions). In plasma turbulence, intermittent structures such as current sheets are generated around the ion kinetic scale. Qudsi et al. (2020) adopt the partial variance of increments (PVI) technique to identify intermittent magnetic structures using PSP data from the first S/C. They show that statistically there is a positive correlation between the ion temperature and the PVI, indicating that the intermittent structures may contribute to the heating of the young solar wind through processes like the magnetic reconnection in the intermittent current sheets.

At the end of this subsection, it is worthwhile to make several comments. First, the Fara-day Cup onboard PSP (SPC) has a flux-angle operation mode, which allows measurements of the ion phase space density fluctuations at a cadence of 293 Hz (Vech et al. 2020). Thus, combination of the flux-angle measurements with the magnetic field data will greatly help us understand the kinetic turbulence. Second, more studies are necessary to understand behaviors of electrons in the turbulence, though direct measurement of the electron-scale fluctuations in the solar wind is difficult with current plasma instruments. Adhikari et al. (2021) show that by distributing the turbulence heating properly among ions and electrons in a turbulence-coupled solar wind model, differential radial evolutions of ion and electron temperatures can be reproduced. However, how and why the turbulence energy is distributed unevenly among ions and electrons are not fully understood yet and need future studies. Third, during the Venus flybys, PSP traveled through Venus's magnetosphere and made high-cadence measurements. Thus, analysis of the turbulence properties around Venus, e.g., inside its magnetosheath (Bowen et al. 2021) will also be helpful in understanding the kinetic turbulence (see §12). Last, Martinović et al. (2021) compare the turbulence properties inside and outside the magnetic switchbacks using the PSP data from the first two Encs. They find that the stochastic heating rates and spectral slopes are similar but other properties such as the intermittency level are different inside and outside the switchbacks, indicating that some processes near the edges of switchbacks, such as the velocity shear, considerably affect the turbulence evolution inside the switchbacks (see §4.2).

## 7.4 Intermittency and Small-scale Structure

In the modern era to turbulence research, intermittency has been established as a fundamental feature of turbulent flows (e.g., Sreenivasan and Antonia 1997). Nonlinearly interacting fluctuations are expected to give rise to structure in space and time, which is characterized by sharp gradients, inhomogeneities, and departures from Gaussian statistics. In a plasma such as the solar wind, such “bursty” or “patchy” structures include current sheets, vortices, and flux tubes. These structures have been associated with enhanced plasma dissipation and heating (Matthaeus et al. 2015), and with acceleration of energetic particles (Tessein et al. 2013). Studies of intermittency may therefore provide insights into dissipation and heating mechanisms active in the weakly-collisional solar wind plasma. Intermittency also has implications for turbulence theory – a familiar example is the evolution of hydrodynamic inertial range theory from the classical Kolmogorov (K41; 1941) theory to the so-called refined similarity hypothesis (Kolmogorov 1962); the former assumed a uniform energy dissipation rate while the latter allowed for fluctuations and inhomogeneities in this fundamental quantity.
Standard diagnostics of intermittency in a turbulent field include PDFs of increments, kurtosis (or flatness; fourth-order moment), and structure functions (e.g., Matthaeus et al. 2015). Observational studies tend to focus on the magnetic field due to the availability of higher-quality measurements compared to plasma observations. In well-developed turbulence, one finds that the tails of PDFs of increments become wider (super-Gaussian) and large values of kurtosis are obtained at small scales within the inertial-range. A description in terms of fractality is also employed – monofractality is associated with structure that is non space-filling but lacking a preferred scale (i.e., scale-invariance). In contrast, multifractality also implies non space-filling structure but with at least one preferred scale (Frisch 1995).<fnref n="6" />

Intermittency properties of solar wind turbulence have been extensively studied using observations from several S/C (see, e.g., review by Bruno 2019). High-resolution measurements from the Cluster and the Magnetospheric Multiscale (MMS; Burch 2014) missions have enabled such investigations within the terrestrial magnetosheath as well (e.g., Kiyani et al. 2009; Chhiber et al. 2018), including kinetic-scale studies. PSP's trajectory allows us to extend these studies to the near-Sun environment and to examine the helioradial evolution of intermittency in the inner heliosphere. An advantage offered by PSP is that the observations are not affected by foreshock wave activity that is often found near Earth's magnetosheath (see, e.g., Wan et al. 2012a).

The radial evolution of intermittency in inertial-range magnetic fluctuations measured by PSP was investigated by Alberti et al. (2020), who found monofractal, self-similar scaling at distances below 0.4 AU. At larger distances, a transition to multifractal scaling characteristic of strongly intermittent turbulence was observed (see top panel of Fig. 22). A similar trend was observed by (Telloni et al. 2021b), who used measurements during the first radial alignment of PSP and SolO. Strong intermittency was obtained in SolO observations near 1 AU compared to PSP observations near 0.1 AU, suggesting an evolution from highly Alfvénic and under-developed turbulence to fully-developed turbulence with increasing radial distance. Note that several prior studies have found that inertial-range magnetic turbulence at 1 AU is characterized by multifractal intermittency (Bruno 2019). It is also worth noting (as in §7.1) that PSP observations near the Sun may be statistically biased towards sampling variations in a lag direction that is (quasi-)parallel to the mean magnetic field (Zank et al. 2021; Chhiber et al. 2021c). Future studies could separately examine parallel and perpendicular intervals (e.g., Ruiz et al. 2011), which would clarify the extent to which this geometrical sampling bias affects the measured radial evolution of intermittency.

A comparison of inertial range vs. kinetic-scale intermittency in near-Sun turbulence was carried out by Chhiber et al. (2021a) using the publicly available SCAM data product (Bowen et al. 2020a), which merges MAG and SCM measurements to obtain an optimal signal-to-noise ratio across a wide range of frequencies. They observed multifractal scaling in the inertial range, supported by a steadily increasing kurtosis with decreasing scale down to ~20 $d_i$. The level of intermittency was somewhat weaker in intervals without switchbacks compared to intervals with switchbacks, consistent with PVI-based analyses by Martinović

<footnote n="6">⁶In hydrodynamic turbulence intermittency is often described in terms of the scaling of the structure functions $S_{\ell}^{(p)} \equiv \langle \delta u_{\ell}^{p} \rangle \propto \ell^{p/3+\mu(p)}$, where $\delta u_{\ell} = \hat{\ell} \cdot [u(x+\ell) - u(x)]$ is the longitudinal velocity increment, $\ell$ is a spatial lag, and $(\dots)$ is an appropriate averaging operator. In K41 (homogenous turbulence) the intermittency parameter $\mu(p)$ vanishes. With intermittency one has non-zero $\mu(p)$, and the scaling exponents $\zeta(p) = p/3 + \mu(p)$ can be linear or nonlinear functions of $p$, corresponding to monofractal or multifractal scaling, respectively (Frisch 1995). The scale-dependent kurtosis $\kappa$ can be defined in terms the structure functions: $\kappa(\ell) \equiv S_{\ell}^{(4)}/[S_{\ell}^{(2)}]^2$.</footnote>
Standard diagnostics of intermittency in a turbulent field include PDFs of increments, kurtosis (or flatness; fourth-order moment), and structure functions (e.g., Matthaeus et al. 2015). Observational studies tend to focus on the magnetic field due to the availability of higher-quality measurements compared to plasma observations. In well-developed turbulence, one finds that the tails of PDFs of increments become wider (super-Gaussian) and large values of kurtosis are obtained at small scales within the inertial-range. A description in terms of fractality is also employed – monofractality is associated with structure that is non space-filling but lacking a preferred scale (i.e., scale-invariance). In contrast, multifractality also implies non space-filling structure but with at least one preferred scale (Frisch 1995).<fnref n="6" />

Intermittency properties of solar wind turbulence have been extensively studied using observations from several S/C (see, e.g., review by Bruno 2019). High-resolution measurements from the Cluster and the Magnetospheric Multiscale (MMS; Burch 2014) missions have enabled such investigations within the terrestrial magnetosheath as well (e.g., Kiyani et al. 2009; Chhiber et al. 2018), including kinetic-scale studies. PSP's trajectory allows us to extend these studies to the near-Sun environment and to examine the helioradial evolution of intermittency in the inner heliosphere. An advantage offered by PSP is that the observations are not affected by foreshock wave activity that is often found near Earth's magnetosheath (see, e.g., Wan et al. 2012a).

The radial evolution of intermittency in inertial-range magnetic fluctuations measured by PSP was investigated by Alberti et al. (2020), who found monofractal, self-similar scaling at distances below 0.4 AU. At larger distances, a transition to multifractal scaling characteristic of strongly intermittent turbulence was observed (see top panel of Fig. 22). A similar trend was observed by (Telloni et al. 2021b), who used measurements during the first radial alignment of PSP and SolO. Strong intermittency was obtained in SolO observations near 1 AU compared to PSP observations near 0.1 AU, suggesting an evolution from highly Alfvénic and under-developed turbulence to fully-developed turbulence with increasing radial distance. Note that several prior studies have found that inertial-range magnetic turbulence at 1 AU is characterized by multifractal intermittency (Bruno 2019). It is also worth noting (as in §7.1) that PSP observations near the Sun may be statistically biased towards sampling variations in a lag direction that is (quasi-)parallel to the mean magnetic field (Zank et al. 2021; Chhiber et al. 2021c). Future studies could separately examine parallel and perpendicular intervals (e.g., Ruiz et al. 2011), which would clarify the extent to which this geometrical sampling bias affects the measured radial evolution of intermittency.

A comparison of inertial range vs. kinetic-scale intermittency in near-Sun turbulence was carried out by Chhiber et al. (2021a) using the publicly available SCAM data product (Bowen et al. 2020a), which merges MAG and SCM measurements to obtain an optimal signal-to-noise ratio across a wide range of frequencies. They observed multifractal scaling in the inertial range, supported by a steadily increasing kurtosis with decreasing scale down to ~20 $d_i$. The level of intermittency was somewhat weaker in intervals without switchbacks compared to intervals with switchbacks, consistent with PVI-based analyses by Martinović

<footnote n="6">⁶In hydrodynamic turbulence intermittency is often described in terms of the scaling of the structure functions $S_{\ell}^{(p)} \equiv \langle \delta u_{\ell}^{p} \rangle \propto \ell^{p/3+\mu(p)}$, where $\delta u_{\ell} = \hat{\ell} \cdot [u(x+\ell) - u(x)]$ is the longitudinal velocity increment, $\ell$ is a spatial lag, and $(\dots)$ is an appropriate averaging operator. In K41 (homogenous turbulence) the intermittency parameter $\mu(p)$ vanishes. With intermittency one has non-zero $\mu(p)$, and the scaling exponents $\zeta(p) = p/3 + \mu(p)$ can be linear or nonlinear functions of $p$, corresponding to monofractal or multifractal scaling, respectively (Frisch 1995). The scale-dependent kurtosis $\kappa$ can be defined in terms the structure functions:</footnote>

<footnote>$$ \kappa(\ell) \equiv S_{\ell}^{(4)} / [S_{\ell}^{(2)}]^2 $$</footnote>
<figure><img src="image_24.png" /><figcaption>**Fig. 22** Top: Scaling exponents $ζ_q$ (see text) of the radial magnetic field for different orders $q$, observed by PSP at different helioradii $r$. A transition from monofractal linear scaling to multifractal scaling is observed for $r > 0.4$. Figure adapted from Alberti et al. (2020). Bottom: Scale-dependent kurtosis of the magnetic field, as a function of lag. A transition from a multifractal inertial range to a monofractal kinetic range occurs near $20 d_i$ (Chhiber et al. 2021a)</figcaption></figure>

et al. (2021) (see also §7.5.1). At scales below $20 d_i$, Chhiber et al. (2021a) found that the kurtosis flattened (bottom panel of Fig. 22), and their analysis suggested a monofractal and scale-invariant (but still intermittent and non-Gaussian) kinetic range down to the electron inertial scale, a finding consistent with near-Earth observations (Kiyani et al. 2009) and some kinetic simulations (Wan et al. 2016). From these results, they tentatively infer the existence of a scale-invariant distribution of current sheets between proton and electron scales. The SCAM data product was also used by Bowen et al. (2021) to observe strong intermittency at subproton scales in the Venusian magnetosheath. Perrone et al. (2020a) examined coherent structures at ion scales in intervals with varying switchback activity, observed during PSP's first S/C. Using a wavelet-based approach, they found that current sheets dominated intervals with prominent switchbacks, while wave packets were most common in quiet intervals without significant fluctuations. A mixture of vortex structures and wave packets was observed in periods characterized by strong fluctuations without magnetic reversals.

A series of studies used the PVI approach (Greco et al. 2018) with PSP data to identify intermittent structures and examine associated effects. Chhiber et al. (2020) found that the waiting-time distributions of intermittent magnetic and flow structures followed a power law<fnref n="7" /> for events separated by less than a correlation scale, suggesting a high degree of cor-

<footnote n="7">⁷Waiting times between magnetic switchbacks, which may also be considered intermittent structures, followed power-law distributions as well (Dudok de Wit et al. 2020).</footnote>
<figure><img src="image_25.png" /><figcaption>**Fig. 22** Top: Scaling exponents $\zeta_q$ (see text) of the radial magnetic field for different orders $q$, observed by PSP at different helioradii $r$. A transition from monofractal linear scaling to multifractal scaling is observed for $r > 0.4$. Figure adapted from Alberti et al. (2020). Bottom: Scale-dependent kurtosis of the magnetic field, as a function of lag. A transition from a multifractal inertial range to a monofractal kinetic range occurs near $20 \ d_i$ (Chhiber et al. 2021a)</figcaption></figure>

et al. (2021) (see also §7.5.1). At scales below $20 \ d_i$, Chhiber et al. (2021a) found that the kurtosis flattened (bottom panel of Fig. 22), and their analysis suggested a monofractal and scale-invariant (but still intermittent and non-Gaussian) kinetic range down to the electron inertial scale, a finding consistent with near-Earth observations (Kiyani et al. 2009) and some kinetic simulations (Wan et al. 2016). From these results, they tentatively infer the existence of a scale-invariant distribution of current sheets between proton and electron scales. The SCAM data product was also used by Bowen et al. (2021) to observe strong intermittency at subproton scales in the Venusian magnetosheath. Perrone et al. (2020a) examined coherent structures at ion scales in intervals with varying switchback activity, observed during PSP's first S/C. Using a wavelet-based approach, they found that current sheets dominated intervals with prominent switchbacks, while wave packets were most common in quiet intervals without significant fluctuations. A mixture of vortex structures and wave packets was observed in periods characterized by strong fluctuations without magnetic reversals.

A series of studies used the PVI approach (Greco et al. 2018) with PSP data to identify intermittent structures and examine associated effects. Chhiber et al. (2020) found that the waiting-time distributions of intermittent magnetic and flow structures followed a power law<fnref n="7" /> for events separated by less than a correlation scale, suggesting a high degree of cor-

<footnote n="7">⁷Waiting times between magnetic switchbacks, which may also be considered intermittent structures, followed power-law distributions as well (Dudok de Wit et al. 2020).</footnote>