# Does Turbulence along the Coronal Current Sheet Drive Ion Cyclotron Waves?

Daniele Telloni National Institute for Astrophysics, Astrophysical Observatory
of Torino, Via Osservatorio 20, I-10025 Pino Torinese, Italy  Gary P. Zank
Center for Space Plasma and Aeronomic Research, University of Alabama in
Huntsville, Huntsville, AL 35805, USA  Department of Space Science, University
of Alabama in Huntsville, Huntsville, AL 35805, USA  Laxman Adhikari Center
for Space Plasma and Aeronomic Research, University of Alabama in Huntsville,
Huntsville, AL 35805, USA  Lingling Zhao Center for Space Plasma and Aeronomic
Research, University of Alabama in Huntsville, Huntsville, AL 35805, USA
Roberto Susino National Institute for Astrophysics, Astrophysical Observatory
of Torino, Via Osservatorio 20, I-10025 Pino Torinese, Italy  Ester Antonucci
National Institute for Astrophysics, Astrophysical Observatory of Torino, Via
Osservatorio 20, I-10025 Pino Torinese, Italy  Silvano Fineschi National
Institute for Astrophysics, Astrophysical Observatory of Torino, Via
Osservatorio 20, I-10025 Pino Torinese, Italy  Marco Stangalini Italian Space
Agency, Via del Politecnico snc, I-00133 Roma, Italy  Catia Grimani University
of Urbino Carlo Bo, Department of Pure and Applied Sciences, Via Santa Chiara
27, I-61029 Urbino, Italy  National Institute for Nuclear Physics, Section in
Florence, Via Bruno Rossi 1, I-50019 Sesto Fiorentino, Italy  Luca Sorriso-
Valvo National Research Council, Institute for the Science and Technology of
Plasmas, Via Amendola 122/D, I-70126 Bari, Italy  Swedish Institute of Space
Physics, Ångström Laboratory, Lägerhyddsvägen 1, SE-751 21 Uppsala, Sweden
Daniel Verscharen Mullard Space Science Laboratory, University College London,
Holmbury St. Mary, RH5 6NT Dorking, UK  Raffaele Marino Université de Lyon,
Centre National de la Recherche Scientifique, École Centrale de Lyon, Institut
National des Sciences Appliquées de Lyon, Université Claude Bernard Lyon 1,
Laboratoire de Mécanique des Fluides et d’Acoustique, F-69134 Écully, France
Silvio Giordano National Institute for Astrophysics, Astrophysical Observatory
of Torino, Via Osservatorio 20, I-10025 Pino Torinese, Italy  Raffaella
D’Amicis National Institute for Astrophysics, Institute for Space Astrophysics
and Planetology, Via del Fosso del Cavaliere 100, I-00133 Roma, Italy  Denise
Perrone Italian Space Agency, Via del Politecnico snc, I-00133 Roma, Italy
Francesco Carbone National Research Council, Institute of Atmospheric
Pollution Research, c/o University of Calabria, I-87036 Rende, Italy
Alessandro Liberatore Jet Propulsion Laboratory, California Institute of
Technology, Pasadena, CA 91109, USA  Roberto Bruno National Institute for
Astrophysics, Institute for Space Astrophysics and Planetology, Via del Fosso
del Cavaliere 100, I-00133 Roma, Italy  Gaetano Zimbardo University of
Calabria, Department of Physics, Ponte Pietro Bucci Cubo 31C, I-87036 Rende,
Italy  Marco Romoli University of Florence, Department of Physics and
Astronomy, Via Giovanni Sansone 1, I-50019 Sesto Fiorentino, Italy  Vincenzo
Andretta National Institute for Astrophysics, Astronomical Observatory of
Capodimonte, Salita Moiariello 16, I-80131 Napoli, Italy  Vania Da Deppo
National Research Council, Institute for Photonics and Nanotechnologies, Via
Trasea 7, I-35131 Padova, Italy  Petr Heinzel Czech Academy of Sciences,
Astronomical Institute, Fričova 298, CZ-25165 Ondřejov, Czechia  John D. Moses
National Aeronautics and Space Administration, Headquarters, Washington, DC
20546, USA  Giampiero Naletto University of Padua, Department of Physics and
Astronomy, Via Francesco Marzolo 8, I-35131 Padova, Italy  Gianalfredo
Nicolini National Institute for Astrophysics, Astrophysical Observatory of
Torino, Via Osservatorio 20, I-10025 Pino Torinese, Italy  Daniele Spadaro
National Institute for Astrophysics, Astrophysical Observatory of Catania, Via
Santa Sofia 78, I-95123 Catania, Italy  Luca Teriaca Max Planck Institute for
Solar System Research, Justus-von-Liebig-Weg 3, D-37077 Göttingen, Germany
Aleksandr Burtovoi National Institute for Astrophysics, Astrophysical
Observatory of Arcetri, Largo Enrico Fermi 5, I-50125 Firenze, Italy  Yara De
Leo Max Planck Institute for Solar System Research, Justus-von-Liebig-Weg 3,
D-37077 Göttingen, Germany  University of Catania, Department of Physics and
Astronomy, Via Santa Sofia 64, I-95123 Catania, Italy  Giovanna Jerse National
Institute for Astrophysics, Astronomical Observatory of Trieste, Località
Basovizza 302, I-34149 Trieste, Italy  Federico Landini National Institute for
Astrophysics, Astrophysical Observatory of Torino, Via Osservatorio 20,
I-10025 Pino Torinese, Italy  Maurizio Pancrazzi National Institute for
Astrophysics, Astrophysical Observatory of Torino, Via Osservatorio 20,
I-10025 Pino Torinese, Italy  Clementina Sasso National Institute for
Astrophysics, Astronomical Observatory of Capodimonte, Salita Moiariello 16,
I-80131 Napoli, Italy  Alessandra Slemer National Research Council, Institute
for Photonics and Nanotechnologies, Via Trasea 7, I-35131 Padova, Italy

###### Abstract

Evidence for the presence of ion cyclotron waves, driven by turbulence, at the
boundaries of the current sheet is reported in this paper. By exploiting the
full potential of the joint observations performed by Parker Solar Probe and
the Metis coronagraph on board Solar Orbiter, local measurements of the solar
wind can be linked with the large-scale structures of the solar corona. The
results suggest that the dynamics of the current sheet layers generates
turbulence, which in turn creates a sufficiently strong temperature anisotropy
to make the solar-wind plasma unstable to anisotropy-driven instabilities such
as the Alfvén ion-cyclotron, mirror-mode, and firehose instabilities. The
study of the polarization state of high-frequency magnetic fluctuations
reveals that ion cyclotron waves are indeed present along the current sheet,
thus linking the magnetic topology of the remotely imaged coronal source
regions with the wave bursts observed in situ. The present results may allow
improvement of state-of-the-art models based on the ion cyclotron mechanism,
providing new insights into the processes involved in coronal heating.

instabilities — magnetohydrodynamics (MHD) — turbulence — waves — Sun: corona
— solar wind

††journal: ApJ

##  1 Introduction

The physical processes that heat the solar corona plasma to temperatures
exceeding one million degrees, thereby driving the solar wind (Hundhausen,
1972), are still strongly debated. Solving this puzzle of the solar physics is
central to the Parker Solar Probe (PSP; Fox et al., 2016) and Solar Orbiter
(SO; Müller et al., 2020) missions. The many models proposed so far to explain
the so-called “coronal heating problem” can be classified into two major
categories, namely alternating current (AC) and direct current (DC) heating
mechanisms. AC/DC models involve energy release by waves/turbulence or
magnetic reconnection events (as nanoflares, Parker, 1972) respectively.
Reviews can be found in Zirker (1993) and Mandrini et al. (2000). On the AC
(wave/turbulence) side, two key mechanisms candidates are Ion Cyclotron Waves
(ICWs) dissipation (Li et al., 1999; Cranmer, 2000; Leamon et al., 2000;
Hollweg & Isenberg, 2002) and low-frequency MagnetoHydroDynamic (MHD)
turbulence dissipation. The latter can further take place either through
nonlinear coupling of a dominant outward Alfvén wave flux with a minority of
inwardly reflected modes (Matthaeus et al., 1999; Verdini et al., 2009, 2010),
or, in the Nearly Incompressible (NI) MHD theory, in the frame of quasi-$2$D
turbulence dynamics generated by the magnetic carpet and advected into the
solar corona where it can then dissipate (Zank et al., 2017, 2018, 2020).
Although recent observational indications seem to point toward the
interpretation in terms of the quasi-$2$D scenario (the reader is referred to
Zank et al., 2021, where the above turbulence models are reviewed and their
predictions tested against PSP observations), there is still no general
consensus on which physical processes drive the deposition of the energy at
small scales, needed to heat the plasma and accelerate the solar wind. Common
to the aforementioned AC classifications, and indeed integral to energy
transport and solar corona heating, are the collisionless field-particle
interactions occurring at scales close to the proton inertial length and
proton gyro-radius. At these scales, the solar wind, which has a fluid-like
behavior in the inertial range of turbulence (see the exhaustive review by
Bruno & Carbone, 2013, and references therein), takes on dispersive kinetic
characteristics (Bale et al., 2005; Howes et al., 2008; Sahraoui et al., 2010;
Alexandrova et al., 2013). Energy is thus transferred from the fluctuating
fields to thermal particle energy, that is, dissipated, resulting in plasma
heating.

PSP measurements compare remarkably well with the quasi-$2$D turbulence model
developed by Zank et al. (2017), both in slow (Adhikari et al., 2020b; Telloni
et al., 2022b) and fast (Adhikari et al., 2020a, 2021) solar wind flows. In
addition, the theoretical predictions based on the NI MHD theory do
satisfactorily match the observed acceleration of coronal outflows to
supersonic (Telloni et al., 2007a, b) and super-Alfvénic (Adhikari et al.,
2022) speeds. Succeeding in reproducing observations of both coronal and
heliospheric plasmas, the NI quasi-$2$D model is thus gaining reputation as a
credible mechanism for solar wind plasma heating and acceleration. On the
other hand, a number of fundamental major issues concerning the ion cyclotron
heating mechanism (see Zank et al., 2021, for more details) seem to rule it
out from playing a relevant role in the interplanetary space plasma heating
processes. A decade of remote-sensing observations of the extended corona with
the UltraViolet Coronagraph Spectrometer (UVCS; Kohl et al., 1995) on board
the SOlar and Heliospheric Observatory (SOHO; Domingo et al., 1995), however,
appear to agree well with a scenario in which ions/atoms are heated by
cyclotron-resonant interaction with high-frequency Alfvén waves (Kohl et al.,
1998; Cranmer et al., 1999b). In particular, the kinetic temperatures of
different coronal ion species were found to vary with their charge-to-mass
$Z/A$ ratio (Cranmer et al., 1999a), as expected for ion cyclotron wave
dissipation, whose rate depends on the local ion gyro-frequency
$\Omega_{i}\propto Z/A$. Similarly, in-situ measurements also strongly
indicate that ICW damping is involved in the energy cascade (Leamon et al.,
1998; Bruno & Trenchi, 2014). Evidence for the presence of ICWs in space
plasmas (He et al., 2011; Podesta & Gary, 2011; Telloni et al., 2015; Bruno &
Telloni, 2015; Luo et al., 2022) when the temperature anisotropy thresholds of
the cyclotron instability are exceeded (Bale et al., 2009; Telloni & Bruno,
2016; Woodham et al., 2019; Telloni et al., 2019) points to ion cyclotron
resonance as a viable energy-conversion mechanism in collisionless plasmas
(Bowen et al., 2022). Alternative heating mechanisms include, for example,
resonant Landau damping of kinetic Alfvén waves (Howes et al., 2018; Chen et
al., 2019; Carbone et al., 2022), and stochastic perpendicular heating of ions
resulting from the violation of the magnetic moment conservation induced by
large-amplitude turbulent fluctuations at ion scales (Chandran et al., 2010;
Martinović et al., 2020). These mechanisms, however, are not discussed here.

In the attempt to reconcile the remote-sensing and in-situ observations in a
unified view of the heating of the coronal plasma and the subsequent
acceleration of the solar wind, local measurements of the coronal regions are
needed. At present, PSP has only occasionally entered the solar corona (Kasper
et al., 2021; Bandyopadhyay et al., 2022; Zank et al., 2022; Zhao et al.,
2022; Marino & Sorriso-Valvo, 2023), although its progressively shrinking
orbits will ensure that the spacecraft spends extended periods immersed in the
coronal plasma. Even then, though, single-spacecraft measurements will provide
only one-point information, precluding a clear understanding of how the global
(magnetic) configuration of coronal sources affects local dynamics and
turbulence properties in space plasmas. It appears thus that remote-sensing
observations of large-scale source regions of the solar wind are of critical
importance to conduct this type of investigations. Correspondingly, these
alone offer only some general, though not conclusive, insights. It follows
that exploiting the synergies between in-situ measurements and remote-sensing
observations and, in particular, the joint PSP – SO observations of the Sun
and its environment, is the most viable approach to answer key questions
concerning the coronal heating. Two companion papers by Telloni et al. (2021,
2022c) can be considered a first attempt to exploit observations of Metis (the
coronagraph aboard SO; Fineschi et al., 2020; Antonucci et al., 2020b) in
combination with in-situ PSP measurements collected while in orbital
quadrature, to link global and local properties of coronal flows and study
their evolution in the transition from sub- to super-Alfvénic wind.

The first Metis observations, performed in $2020$, imaged the solar corona in
its quasi-dipolar magnetic configuration typical of the minimum activity phase
out to $\sim 7$ R⊙, thus allowing the extension of the study of the morphology
and dynamics of the coronal Current Sheet (CS), that originates at the cusp of
the equatorial streamers, beyond the region explored with UVCS and limited to
a heliocentric distance of $5$ R⊙ (see the review by Antonucci et al., 2020a).
In the Metis observations, the initial coronal part of the heliospheric
current sheet, separating opposite polarities of the coronal magnetic field,
is clearly outlined by a slightly warped quasi-equatorial layer, of denser and
slower wind plasma that is undergoing a significant acceleration between $4$
and $5$ R⊙ (Antonucci et al., 2023). These first Metis observations show that
the zone where the slow wind is observed in corona, $\lesssim 30^{\circ}$ in
latitude, is structured as follows: the slowest wind, observed in a layer
$<10^{\circ}$ wide in latitude and associated with the current sheet, is
surrounded by steep velocity gradients, a few degrees wide in latitude,
indicating a transition to slow wind flows characterized by higher velocity
but lower acceleration relative to plasma directly embedded in the current
sheet (Antonucci et al., 2023).

This paper presents evidence on the occurrence of ICWs in the coronal
structures explored by PSP, taking advantage of the SO/Metis – PSP joint
observations of mid-January $2021$. Specifically, the results show that when
PSP flies through the layers of the heliospheric CS remotely imaged by Metis
in its initial coronal stretch, turbulence increases significantly causing the
plasma to depart more from an equilibrium state. A case of local PSP
measurements along the CS, in which a proton cyclotron instability driven by
temperature anisotropy generates ICWs, is shown in the present work. This
combined observation, the first of its kind to be reported, represents a step
forward in understanding how coronal large-scale structures drive and regulate
small-scale fluctuations/waves in the space plasma. This paper first presents
a description of the coordinated SO/Metis – PSP observations (§ 2), then the
methodological approach implemented to link local measurements of the solar
wind to remotely imaged coronal source regions (§ 3), the observation of the
onset of ICWs along the turbulent CS (§ 4), and finally concluding remarks on
the results presented (§ 5).

##  2 SO/Metis – PSP joint observations

From January $14$ through January $17$, $2021$, Metis acquired, with $4$-hour
cadence, $23$ images of the white-light solar corona in an annular Field Of
View (FOV) from $3.5$ to $6.3$ R⊙, which were calibrated in flight according
to De Leo et al. (2023). Figure 1(a) shows the Carrington map (i.e., a
synoptic chart displayed using Carrington coordinates) of the polarized
Brightness (pB) at a distance of $5$ R⊙ above the East limb of the Sun.

Figure 1: Overview of the joint SO/Metis – PSP observations. (a) Carrington
map at $5$ R⊙ from Metis pB observations for the eastern solar limb on which
is superimposed the back-projected trajectory of PSP during the first
(magenta) and second (lime) passage (also labeled). (b) PSP distance as a
function of Carrington longitude in the first (magenta) and second (lime)
crossing of the same POS observed by Metis. (c)–(h) Zoom of the FOV observed
by Metis above the East limb of the Sun in the last $6$ images acquired by the
coronagraph; the apparent position of PSP during the Metis POS crossing is
marked by an open circle (the color code is the same as the previous panels);
the times at which the crossings occur are also reported in the legend; the
extra white x-axis indicates the actual distance of PSP from the Sun.

The coronal CS, namely the initial part of the heliospheric current sheet that
is imaged at coronal level, is clearly visible in the Metis-based Carrington
map around the solar equator as the densest structure. In particular, the dark
orange level line at $2\times 10^{-10}$ B$/$B⊙ (which helps to roughly outline
the CS boundaries) shows the apparent presence of a double structure for
longitudes less than $\sim 132^{\circ}$. As discussed in Telloni et al.
(2021), this is due to two small CS warps extending up to $\sim\pm 10^{\circ}$
in latitude. Due to its retrograde motion relative to the Sun’s rotation, PSP
flies through the Plane Of the Sky (POS) observed by Metis twice (and later to
the Metis observation, see Shi et al., 2021; Telloni et al., 2022c, for a more
extensive discussion on the PSP orbital characteristics). The PSP back-
projected trajectory on the pB Carrington map is shown in Figure 1(a) with
magenta and lime lines, respectively, for the first and second crossing. PSP
collected measurements around the CS, while moving away from the Sun from
$0.11$ to $0.24$ au (Figure 1(b)). The apparent location of PSP with respect
to the CS observed by Metis is shown in Figures 1(c)–(h): during its orbit,
PSP moved in latitude and sampled different portions of the CS.

##  3 Linking PSP measurements to Metis observations of coronal sources

Local solar wind measurements of PSP can thereby be related to the coronal
source structures imaged by Metis. Figure 2 shows some relevant PSP-based MHD
quantities projected onto the Metis pB Carrington map in $1.68^{\circ}$-wide
bins. Specifically, panels (a)–(d) display the direction of the Interplanetary
Magnetic Field (IMF), the proton plasma
$\beta_{\parallel}=\upsilon^{2}_{\mathrm{th}_{\parallel}}/\upsilon^{2}_{\mathrm{A}}$
(where $\upsilon_{\mathrm{th}_{\parallel}}$ and $\upsilon_{\mathrm{A}}$ are
the parallel proton thermal and Alfvén speeds, respectively), the magnetic-
field turbulence amplitude $\delta\mathbf{B}/\langle
B\rangle=\sqrt{\langle|\mathbf{B}(t)-\langle\mathbf{B}\rangle|^{2}\rangle}/\langle
B\rangle$ (where $\langle...\rangle$ indicates time averaging over the typical
fluid scale of $10$ minutes111Note that the results are the same at other
scales in the inertial range.), and the magnetic-field deflection
$z=(1-\cos\alpha)/2$ (where $\alpha$ is the angle between the local and mean
magnetic fields, Dudok de Wit et al., 2020). Magnetic field and plasma data
come from the fluxgate magnetometer and the top-hat electrostatic analyzer of
the FIELDS (Bale et al., 2016) and Solar Wind Electrons Alphas & Protons
(SWEAP; Kasper et al., 2016) instrument suites on board PSP, respectively.

Figure 2: Projection onto the Metis pB Carrington map of the IMF direction
(a), proton plasma $\beta_{\parallel}$ (b), magnetic-field turbulence
amplitude $\delta\mathbf{B}/\langle B\rangle$ (c), and magnetic-field
deflection $z$ (d), estimated from PSP measurements. The topology of the CS as
flown through by PSP is outlined in (a).

PSP measurements of the IMF direction (Figure 2(a)) agree with the topological
structure of the CS imaged by Metis. Specifically, the polarity reversal
(which identifies the CS boundaries) occurs in the proximity of the dark
orange level line that helps to outline the CS edges. Thus, it can be deduced
from PSP observations that the spacecraft, initially outside of the CS (in
blue), first entered the CS at Carrington longitude of about $126^{\circ}$ (in
red), and crossed the CS a second time, exiting it at Carrington longitude of
about $119^{\circ}$. A schematic of the magnetic topology of the CS thus
inferred is illustrated in Figure 2(a). At the double crossing of the CS
(occurring at the “CS layers”, Figure 2(a)), the plasma $\beta_{\parallel}$
increases by an order of magnitude compared with the region outside (Figure
2(b)). This is expected when considering that the current sheet layers
(dominated by opposite parallel magnetic currents) are sites of magnetic
reconnection events, likely related, e.g., to the tearing mode instability
(Priest, 1985; Verneta et al., 1994; Phan et al., 2022), which tends to form
magnetic islands, i.e., small flux ropes, disconnecting from the CS (Zhao et
al., 2021; Réville et al., 2022). At the CS boundaries, the magnetic-field
turbulence also increases (Figure 2(c)), mostly due to the change in field
direction, as indicated by the concurrent increase in the parameter $z$
(Figure 2(d)). Recent analysis of PSP measurements shows that turbulence is
typically reduced in the proximity of the heliospheric CS (see, e.g., Chen et
al., 2021, and references therein). In particular, observations suggest that
closer to the CS (i.e., for angular distance from the CS within $\simeq
4^{\circ}$) fluctuations are similar to non-Alfvénic, slow solar wind (with
steeper and broader power-law spectra, smaller fluctuation amplitude), while
they are closer to Alfvénic, fast wind further away. Zhao et al. (2020, 2021)
presented a detailed analysis of PSP data in the vicinity of the CS,
identifying many magnetic islands, which they argue are consistent with non-
Alfvénic turbulence. These are preferentially located in the vicinity of the
CS. Shi et al. (2022) also report, exploiting MHD simulations complemented by
analysis of in-situ data at $1$ au, the decrease in Alfvénicity of turbulence
around the heliospheric CS. The present observations lie within the angular
range considered as CS in Chen et al. (2021), and therefore show finer details
of the turbulence structure in its boundaries. This result is consistent with
the following scenario. At the CS, the solar wind is slower than typical of
other coronal regions. Nevertheless, the regions along it (i.e., its edges)
are characterized by faster (though still slow) coronal flows and lower wind
acceleration. This is clearly shown by Antonucci et al. (2023). It follows
that the CS layers might be sites of velocity shears. These are also implied
by the magnetic field configuration, the velocity being inversely correlated
with the expansion factor, which is maximum at the CS. Velocity shears are
known to generate turbulence (Stawarz et al., 2016; Sorriso-Valvo et al.,
2019) and deflect the magnetic field (possibly in association with switchback
formation, Ruffolo et al., 2020) through the Kelvin-Helmholtz (KH)
instability. Even without invoking KH-driven magnetic fluctuations, the small-
scale flux ropes disconnected from the CS by magnetic reconnection enhance the
amplitude of the quasi-$2$D MHD turbulence (Zank et al., 2018, 2020).

In order to clarify the correlation between the PSP measurements and the
different regions of the CS crossed by the spacecraft, to provide additional
information, such as the extent of the CS layers, and to support/complement
the results outlined by Figure 2, Figures 3(a)–(d) show profiles of solar wind
speed $V$, magnetic field magnitude $B$ normalized to the square of the
distance $r$ from the Sun222Since $\nabla\cdot\mathbf{B}=0$ the radial
component of the magnetic field, $B_{R}$, clearly scales as $r^{2}$, and as
long as $B_{R}$ is the dominant contributor to $\mathbf{B}$-magnitude as
during these observations, so does $B$., angle between magnetic field vector
and radial direction $\theta_{RB}$, and proton plasma $\beta_{\parallel}$, as
a function of the Carrington longitude range observed in conjunction by PSP
and Metis.

Figure 3: Measurements of flow speed $V$ (a), $r^{2}$-scaled magnetic field
intensity (b), magnetic field-radial direction angle $\theta_{RB}$ (c), and
proton plasma $\beta_{\parallel}$ (d) against Carrington longitude, during the
first (magenta) and second (lime) PSP passage through the POS observed by
Metis. Horizontal lines with different styles schematically depict the
topology of the CS crossed by PSP. The green (orange) shaded area denotes an
interval outside (at the edge) of the CS analyzed in § 4.

As mentioned above, the boundaries of the CS were identified as the regions
around the magnetic field reversal. More specifically, Figure 3(c) clearly
shows that during the first PSP passage, the magnetic field is directed
towards the Sun out to $\sim 126^{\circ}$ Carrington longitude
($\theta_{RB}\sim 180^{\circ}$). Therefrom, the magnetic field shows no
definite direction, fluctuating from inward ($\theta_{RB}\sim 180^{\circ}$) to
outward ($\theta_{RB}\sim 0^{\circ}$) orientation. This is the region of the
CS layer. Similarly, during the second PSP passage, from an initial positive
polarity ($\theta_{RB}\sim 0^{\circ}$), the magnetic field changes direction
for Carrington longitudes less than $\sim 119^{\circ}$, thereby identifying
the second CS layer. It appears evident that at the edges of the CS (marked by
dashed horizontal lines in the panels of Figure 3), the plasma speed, while
remaining slow, undergoes moderate acceleration (Figure 3(a)), albeit more
pronounced during the second crossing (lime line). This might be indicative of
the presence of velocity shears that could explain the onset of greater
turbulence at the CS boundaries. The latter is evident from the larger
amplitude of $B$ fluctuations (Figure 3(b)) as well as the more intense and
numerous magnetic field deflections, shown by the larger fluctuations of the
$\mathbf{B}$ inclination with respect to the sampling direction. Finally,
based on the aforementioned proposed mechanisms, the plasma
$\beta_{\parallel}$ also increases significantly at the CS layers (Figure
3(d)). In addition to helping identify the different portions of the CS, the
longitudinal series also allow for a more accurate estimate of the
longitudinal extent of its boundaries, which turns out to be $3.35^{\circ}$
and $1.67^{\circ}$ wide during the first and second crossing, respectively.

##  4 Onset of ICWs along the turbulent CS

In order to assess whether the increase in turbulence occurring in the plasma
across the CS affects the kinetic properties of the particle velocity
distribution functions, especially regarding the nature of unstable wave-
particle interactions, PSP measurements are plotted in the
$\beta_{\parallel}-T_{\perp}/T_{\parallel}$ plane (where
$T_{\perp}/T_{\parallel}$ is the temperature anisotropy) in Figure 4. The
distribution is compared with different plasma instability thresholds (marked
with different line types) as estimated by Hellinger et al. (2006) for a
maximum growth rate $\gamma=10^{-3}\Omega_{p}$, where $\Omega_{p}$ is the
proton gyro-frequency (see also the comprehensive review by Verscharen et al.,
2019, and references therein).

Figure 4: Scatterplot of the PSP observations in the
$\beta_{\parallel}-T_{\perp}/T_{\parallel}$ plane during the first (a) and
second (b) PSP passage through the POS observed by Metis. The Alfvén ion-
cyclotron, mirror-mode, parallel and oblique firehose instability threshold
curves are displayed as solid, dotted, dashed, and dash-dotted lines,
respectively. The empirical inverse relation by Marsch et al. (2004) is also
shown as a long-dashed line. Black filled symbols refer to regions at the
edges of the CS.

When separating the data points based on the different portions of the CS
crossed by PSP as identified in Figures 2 and 3, two different populations are
distinguishable (though, less evident during the second passage). When inside
or outside the CS (open symbols) PSP data distribute fairly well along the
empirical anti-correlation curve found by Marsch et al. (2004) with Helios
measurements (long-dashed line in Figure 4). Observations corresponding to the
CS layers (black filled symbols) are instead mainly located at larger plasma
$\beta_{\parallel}$. All instability thresholds shown in Figure 4 decrease
with increasing $\beta_{\parallel}$. Therefore, the distribution of the CS
layer data lies closer to the unstable regions of parameter space. Indeed, a
significant portion of the parameter values computed from the data collected
during the second CS crossing (Figure 4(b)) extends beyond the thresholds. As
a result, the plasma along the CS is more likely to be disequilibrated and
thus trigger wave-particle instabilities. Therefore, it can be argued that the
increased turbulence experienced at the CS boundaries, due to either magnetic
reconnection-driven $2$D flux ropes (Zhao et al., 2020, 2021) or KH-
fluctuations (Telloni et al., 2022a), indirectly triggers the Alfvén ion-
cyclotron and the firehose instability via changes of the particle
distributions. These instabilities then transfer energy from the particles
(and thus restore a Maxwellian equilibrium condition) to the electromagnetic
fields, i.e., generating ICWs and fast-mode waves (e.g., Sorriso-Valvo et al.,
2019).

The presence of modes driven by temperature-anisotropy instabilities can in
principle be inferred by identifying in space plasmas the corresponding
polarization properties at the characteristic frequencies. Specifically, the
presence of left-handed circularly polarized ICWs, which result from the
Alfvén ion-cyclotron instability, can be indicated through a strong peak in
the normalized magnetic helicity $\sigma_{m}$ spectrum near the local proton
gyro-frequency (the magnetic helicity can be indeed be used to diagnose the
wave polarization state, Matthaeus & Goldstein, 1982; Matthaeus et al., 1982).
Moreover, the deeper and wider the helicity peak, the more numerous are the
waves (Telloni et al., 2019). Searching for ICWs in the solar wind is,
however, tricky. These are indeed waves with a wavevector parallel to the
magnetic field. This means that any spacecraft can detect this kind of wave
only when sampling solar wind plasma parallel to the mean magnetic field. One-
hour intervals were then selected, inside, outside and along the CS, where the
$\sigma_{m}$ spectrum was calculated, looking for significant peaks around
$\Omega_{p}$. It transpires that on average ICWs are prevalent at the edges of
the CS, but are relatively scarce (about $50$% less abundant) inside or
outside the CS. Examples are given in Figure 5, where the $\sigma_{m}$ spectra
obtained in one-hour intervals, nearly parallel to the magnetic field, outside
the CS (green) and along its boundaries (orange), during the first PSP
trajectory, are shown. These intervals are indicated by shaded areas (with the
same color code) in the longitude series in Figure 3. Note that because the
spacecraft orbital velocity is greater during the first passage (PSP is closer
to the Sun) the range of longitudes spanned in an hour is larger.

Figure 5: Magnetic helicity $\sigma_{m}$ spectra computed outside (green) and
along (orange) the CS when PSP was sampling the nearly parallel solar-wind
magnetic field marked by same-color shaded regions in Figure 3. The
corresponding local proton gyro-frequencies $\Omega_{p}$ are indicated by
color-coded vertical dotted lines. The average Carrington longitude and
sampling angle during both observations are also reported.

Although it should be mentioned that a higher Alfvénic contribution at fluid
scales can also lead to the onset of ICWs (the reader is referred, in this
regard, to Bruno & Telloni, 2015; Telloni et al., 2019) even far from the CS,
the analysis reported here suggests that instabilities, including the ICWs as
shown in the example of Figure 5, are driven along the CS, where turbulent
phenomena, related to either KH instability or magnetic disconnection
processes, are most intense.

A large fraction of the data points lie above the thresholds for the firehose
instabilities (dashed and dash-dotted lines, respectively, in Figure 4).
Although this applies both inside and outside the CS, it occurs mainly along
the CS boundaries (only the core population at the CS layers exceeds the
firehose instability; this is more evident during the first passage). In these
time intervals, the system can drive parallel fast-mode waves with a
polarization opposite from ICWs in the plasma frame (Woodham et al., 2021). A
further in-situ analysis of these fast-mode waves, however, is beyond the
scope of the present work though, which focuses primarily on ICWs, whose
presence is evidenced by Figure 5 and whose importance is related to their
possible contribution in the coronal plasma heating mechanisms discussed in §
1.

##  5 Concluding remarks

The linkage of the temporal pattern of the increased turbulence and ICW burst
with the spatial topology of the coronal structures documented in Figures 1–5
suggests this possible scenario. The large-scale CS layers are source regions
of turbulence (via either KH instability or magnetic reconnection-driven $2$D
flux ropes), which pushes the plasma above the thresholds of instabilities,
which in turn drive small-scale fluctuations/waves and regulate the plasma.
Obviously, these effects are very strong near the Sun, where this is therefore
a very efficient re-shuffling of energy. Moreover, the correlation between the
increased turbulence and ion cyclotron modes is important for connecting
turbulence directly to heating. By estimating the turbulence energy per volume
and adding up the energy in the ion cyclotron modes per unit volume and
further assuming this is dissipated (at a later time) over an ion inertial
time scale, it would indeed be possibile to obtain the heating rate and
estimate the expected temperature. Theoretical work is currently in progress
to test whether the energy released by turbulence and ICWs is sufficient to
heat the plasma to temperatures of a million degrees and accelerate the slow
solar wind along the CS. In addition, it would be worthwhile to undertake a
more comprehensive statistical study of the occurrence of small-scale
fluctuations inside and outside observed CS layers to obtain a better
understanding of the universality of the proposed scenario. It is finally
worth noting that the present results show a link between increased turbulence
along the CS layers and the onset of temperature anisotropy-driven
instabilities, without however proving (but only suggesting) a cause-and-
effect relationship. Causality between increased levels of turbulence and an
increased strength of non-equilibrium plasma features could only be evidenced
through statistical work and a non-linear treatment of the turbulence-plasma
interactions, which is left for future work.

This result shows the tremendous science potential of the Metis coronagraph on
board SO, especially in conjunction with PSP. Indeed, the need for
comparing/combining remote observations of the extended corona with local
measurements of the solar wind acquired by different spacecraft (in
quadrature) emerges clearly, not only to understand how large-scale coronal
dynamics drives the onset of turbulence, waves, and kinetic instabilities, but
also to develop simulation-based numerical experiments and/or theoretical
models that can tackle long-lasting questions such as the coronal heating and
wind acceleration problem.

Solar Orbiter is a space mission of international collaboration between ESA
and NASA, operated by ESA. D.T. was partially supported by the Italian Space
Agency (ASI) under contract 2018-30-HH.0. G.P.Z., L.A., and L.-L.Z.
acknowledge the partial support of a NASA Parker Solar Probe contract
SV4-84017, an NSF EPSCoR RII-Track-1 Cooperative Agreement OIA-2148653, and a
NASA IMAP grant through SUB000313/80GSFC19C0027. L.S.-V. was funded by the
SNSA grants 86/20 and 145/18. D.V. is supported by STFC Ernest Rutherford
Fellowship ST/P003826/1 and STFC Consolidated Grants ST/S000240/1 and
ST/W001004/1. The Metis program is supported by ASI under contracts to the
National Institute for Astrophysics and industrial partners. Metis was built
with hardware contributions from Germany (Bundesministerium für Wirtschaft und
Energie through the Deutsches Zentrum für Luft- und Raumfahrt e.V.), the Czech
Republic (PRODEX) and ESA. The Metis data analyzed in this paper are available
from the PI on request. Parker Solar Probe data was downloaded from the NASA’s
Space Physics Data Facility (https://spdf.gsfc.nasa.gov). This work was
discussed at the ISSI Team “Ion Kinetic Instabilities in the Solar Wind in
Light of Parker Solar Probe and Solar Orbiter Observations” led by L. Ofman
and L. Jian.

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