# Solar wind interaction with a comet: evolution, variability, and implication

C. Götz European Space Agency, ESTEC, The Netherlands J. Deca Laboratory for
Atmospheric and Space Physics (LASP), University of Colorado Boulder, Boulder,
Colorado 80303, USA. K. Mandt Johns Hopkins Applied Physics Laboratory,
Laurel, MD, USA M. Volwerk Space Research Institute, Austrian Academy of
Sciences, Graz, Austria

###### Abstract

  * Once a cometary plasma cloud has been created through ionisation of the cometary neutrals, it presents an obstacle to the solar wind and the magnetic field within it. The acceleration and incorporation of the cometary plasma by the solar wind is a complex process that shapes the cometary plasma environment and is responsible for the creation of boundaries such as a bow shock and diamagnetic cavity boundary. It also gives rise to waves and electric fields which in turn contribute to the acceleration of the plasma. This chapter aims to provide an overview of how the solar wind is modified by the presence of the cometary plasma, and how the cometary plasma is incorporated into the solar wind. We will also discuss models and techniques widely used in the investigation of the plasma environment in the context of recent findings by _Rosetta_. In particular, this chapter highlights the richness of the processes and regions within this environment and how processes on small scales can shape boundaries on large scales. It has been fifteen years since the last book on Comets was published and since then we have made great advances in the field of cometary research. But many open questions remain which are listed and discussed with particular emphasis on how to advance the field of cometary plasma science through future space missions.

Keywords:

  1. 5

Magnetic Field; Draping; Magnetotail; Magnetic Reconnection; Plasma
Boundaries;

##  1 Introduction

In the preceding chapter, the reader is introduced to the sources and losses
of the plasma at a comet. In the following, we will describe what happens to
the cometary plasma cloud as it interacts with the solar wind.

Several works have summarized and reviewed the extensive work done in the
field of cometary plasma environments since the 1980s with the first
artificial comet experiments and the 1P/Halley flyby. The reader is for
example referred to summaries by _Gombosi_ (2015) for an overview or _Szegö et
al._ (2000) for the details of the physics in these plasmas. Most new
discoveries since the last book (Comets II, _Combi et al._ , 2004) was
written, are due to the European Space Agency’s _Rosetta_ mission, we
therefore highlight some peculiarities of this mission here. The spacecraft
arrived at comet 67P/Churyumov-Gerasimenko (67P) in August 2014 and explored
the plasma environment for over two years until end of mission at the end of
September 2016. This is in stark contrast to all previous missions to comets
that were equipped with plasma instruments, which were all single flybys with
different closest approach distances (for more details see Chapter 6). The
particular advantage of the long lasting rendezvous is that the observations
cover a large range of activity levels. This allows us to study the cometary
environment and its interaction with the solar wind at different stages and
observe how the increase and decrease in gas production rate and consequently
the cometary ion density affects the solar wind. Rosetta also covered much
lower activity levels than other missions to comets and therefore expands our
knowledge significantly. On the other hand, this means that comparisons with
previous results always need to take into account the different situation and
are usually non-trivial.

_Rosetta’s_ instruments were able to measure the magnetic field vector, the
plasma density, the electron temperature, the ion energy distribution with
mass resolution and the electron energy distribution. For a few days in
November 2014, data by the lander Philae were available for two-point
measurements of the magnetic field. For more details, the reader is referred
to the documentation for the Rosetta Plasma Consortium
(RPC)111https://www.cosmos.esa.int/web/psa/rosetta. There, one can also find
an extensive list of available data products and the limits and error sources
associated with them.

Figure 1: Top: Gas production rate of comet 67P derived from in-situ
measurments using the Haser model (red) and averaged gas production rate from
a DSMC model (blue). Middle: heliocentric distance of comet 67P (red) and
cometocentric distance of _Rosetta_ at 67P (blue). The dayside excursion in
October 2015 and the nightside excursion in April 2015 went out to $1500\,$km
and $1000\,$km respectively. Bottom: solar wind dynamic pressure at 67P
derived from Earth based data and a Tao model (_Tao et al._ , 2005).

As already described in Chapter 16, the primary source of the plasma at the
comet is the neutral gas that is produced by the sublimation of the ices on
the comet’s surface. Processes like photoionisation, charge exchange, and
electron impact ionisation produce ions and electrons from those neutrals. The
resulting ion coma can extend millions of kilometres from the nucleus,
interacting with the plasma and magnetic field of the solar wind in which it
mostly resides. This forms the plasma environment of the comet.

As comet 67P journeys through the solar system, the heliocentric distance
decreases and increases and therefore the gas production rate increases and
decreases as well. This is shown in the top and middle panels of Fig. 1. At
the same time, the solar wind parameters change as well. The bottom panel of
Fig. 1 shows the estimated dynamic pressure of the solar wind at 67P from a
model to illustrate this. The closer the comet is to the Sun the higher the
solar wind density (and therefore the dynamic pressure) and magnetic field
strength. On shorter timescales such as days and hours, solar wind transients
like Corotating Interaction Regions (CIRs) and Interplanetary Coronal Mass
Ejections (ICMEs) can also cause the solar wind parameters to change
significantly. Unfortunately, no solar wind monitor was included in the
_Rosetta_ mission and models need to suffice to infer the solar wind
parameters at the comet. They usually utilise some sort of propagation model
and either observations of the Sun or in-situ measurements at other solar
system locations to estimate the solar wind conditions with spatial and
temporal uncertainties. This is one of the major drawbacks of a single-
spacecraft mission and should be taken into consideration for future missions
(_Götz et al._ , 2019).

Therefore, depending on the gas production rate and solar wind conditions, the
comet influenced plasma environment may extend from as little as $100\,$km up
to millions of km from the nucleus. As a consequence, the collisionality of
the plasma, the gyroradii of the particles within it and the presence of
different electron and ion populations also vary significantly and
systematically over time.

In the following, the reader is given an overview of the solar wind – comet
interaction, starting with a description of the induced cometosphere, the
magnetic field structure near the comet and in the comet plasma tail, followed
by a list of the boundaries that form. At the end, various wave phenomena are
discussed.

##  2 Induced Cometosphere

###  2.1 Introduction

Whereas the cometary environment might appear quite uneventful near aphelion,
as a comet travels closer to the Sun, the increasing availability of neutral
gas leads to the formation of a coma, and dust and plasma tails. Observations
of the latter phenomena revealed the existence of the solar wind and the
interplanetary magnetic field (_Biermann et al._ , 1967). Important is the
realisation that the presence of neutral gas in the solar wind leads to mass-
loaded plasmas of various natures (_Szegö et al._ , 2000; _Gombosi_ , 2015).
One such example is an induced cometosphere, a term analogous to a
magnetosphere at planets, that forms when the magnetized solar wind plasma
interacts with the cometary plasma environment (_Goetz et al._ , 2021a).

Mass-loading describes the process whereby slow, heavy ions like water,
carbondioxide or oxygen are accelerated and incorporated into the fast solar
wind flow. It is therefore an energy and momentum exchange process between
different plasma populations (_Galeev et al._ , 1985; _Huddleston et al._ ,
1993). What distinguishes the cometary neutral environment from that of e.g.
Venus or Mars, is the lack of significant gravitational acceleration of the
central body: while Venus and Mars have an atmosphere that is for the most
part gravitationally bound to the planet, the neutral exosphere of a comet is
radially expanding into space without much gravitational influence. As a
consequence, neutral gas can be ionised anywhere in the environment, even
millions of km upstream of the source body. This then gives a size of the
cometosphere which is dependent on the outgassing and ionisation conditions.
For example, the first signatures of a cometosphere at comet 1P/Halley at
about 1 AU, which had a gas production rate of $Q=10^{30}\,$s-1 and a water
photoionisation rate of $\nu_{H_{2}O}=10^{-6}\,$s-1, were found at $2\times
10^{6}\,$km upstream of the nucleus (_Neubauer et al._ , 1986). On the other
end of the scale, we find that the cometosphere at comet 67P at 3.4 AU only
expands about $10^{2}\,$km at a gas production rate of $4\times 10^{25}\,$s-1
and a water photoionisation rate of $0.5\times 10^{-7}\,$s-1 (_Richter et al._
, 2015). This impressive difference in scale of four orders of magnitude
demonstrates the richness of the cometary plasma environment. Many of the
processes and structures in the cometary plasma environment depend on the
scale size, and therefore the outgassing rate of the comet, which is why it is
useful to talk about different activity stages of a comet. Following _Goetz et
al._ (2021a), we will use the following definition: weakly active for
$Q<10^{26}\,$s-1, intermediately active for $10^{26}\leq Q<5\times
10^{27}\,$s-1, and strongly active for $Q\geq 5\times 10^{27}\,$s-1. These
values are useful guidelines, but should not be taken too strictly, as the
transition between stages is smooth.

In addition to the outgassing rate, the state of the solar wind plasma is an
important parameter shaping the cometosphere. Fig. 1, bottom panel, shows the
solar wind dynamic pressure at comet 67P over two years, at different
heliocentric distances. The closer the comet is to the Sun, the higher the
dynamic pressure $\rho v_{SW}^{2}$, because the density $\rho$ decreases
approximately as $r_{h}^{-2}$, where $r_{h}$ is the heliocentric distance. The
interplanetary magnetic field magnitude is also higher closer to the Sun, so
that, as a comet follows its orbit, the solar wind parameters vary on
timescales of weeks to months due to the heliocentric distance change. Without
knowing the exact solar wind conditions that a comet encounters, it is
difficult (but not impossible!) to distinguish between intrinsic changes of
the plasma environment and changes due to external triggers. The large
timescale changes are therefore usually absorbed in the definitions of the
comet’s activity stages, as they happen on the same timescale. The shorter
timescales are then discussed on a case by case basis.

While most of this chapter will concern itself with the interaction of
different plasma populations with each other, the solar wind can also interact
with the nucleus directly. This is only possible if the activity of the
nucleus is negligible, because if there is a significant atmosphere, the solar
wind will not be able to reach the nucleus. Solar wind sputtering causes dust
particles to be freed from the nucleus. This process is useful to investigate
surface composition without having a surface probe, but so far only comet 67P
was suitable to observe sputtering (_Wurz et al._ , 2015). There, silicon was
the most abundant species, with traces of sodium, calcium and potassium all
detected at 67P. Models showed that indeed the observed signal was due to
sputtering, not gas or dust release due to thermal input into the surface. The
ratio of sodium-to-potassium was of the same order as that of the lunar
surface, the solar system and meteorites.

###  2.2 Shaping the induced cometosphere

When intercepting comet 67P at about 3.5 AU ($Q\simeq 10^{26}\,$s-1), the
_Rosetta_ plasma instruments reported the first signatures of a plasma
environment significantly affected by cometary matter at a few hundreds of km
from the cometary nucleus (_Clark et al._ , 2015; _Yang et al._ , 2016). At
this time, the outgassing rate of 67P was estimated to be four orders of
magnitude smaller than comet 1P/Halley’s outgassing rate (_Combi and Feldman_
, 1993; _Hansen et al._ , 2016). Hence, even during its weakly outgassing
phases, 67P was actively mass-loading the solar wind plasma and maintaining an
induced cometosphere (_Nilsson et al._ , 2015; _Richter et al._ , 2015; _Deca
et al._ , 2017).

####  2.2.1 Plasma sources and sinks

Fundamentally, there are two populations of particles that contribute to
shaping the near-cometary environment, or better, the induced cometosphere:
the incoming solar wind plasma and the radially-expanding neutral gas coma
that is ionised through a variety of processes, such as photo-ionization,
charge exchange, and electron-impact ionization (see Chapter 16).

67P’s neutral coma consists primarily of $H_{2}O$, $CO_{2}$, $CO$ and $O_{2}$
(see Chapter 16). Historically, the Haser model, which assumes a spherically-
symmetric homogeneous outgassing for each species at a constant neutral radial
velocity, has been applied to estimate the production rates of cometary
volatiles (_Haser_ , 1957). While the model can include different species and
loss through ionisation, a reasonable approximation of the overall, momentary
gas production rate Q can be obtained by

$Q=4\pi n_{n}u_{n}r^{2},$ (1)

where $n_{n}$ is the local, measured neutral density, $u_{n}$ is the neutral
velocity of $500-1000\,$m/s and $r$ is the cometocentric distance of the
measurement point. Within a couple of km of the comet a more accurate model
should be used, but for the distances covered by _Rosetta_ during most of its
mission, this approximation is reasonable to disentangle the effects of the
radial variation of the trajectory from that of the temporal variation.

_Rosetta’s_ advanced instruments were able to capture for the first time the
details of the non-uniform time-varying volatile distribution in which the
cometary nucleus is embedded (_Marshall et al._ , 2019). The complexity of the
latter is caused by the rotation and orbital motion of the comet. In other
words, _Rosetta’s_ high temporal and spatial resolution measurements allowed
to develop an accurate shape model that allows solar illumination and
shadowing effects to be taken into account to predict the evolution of the
production rates as a function of heliocentric distance (_Bieler et al._ ,
2016; _Fougere et al._ , 2016, 2016; _Hansen et al._ , 2016).

The cometary plasma density is determined by a continuous interplay of five
main processes. (1) When a neutral molecule absorbs sunlight, a positive ion
and photoelectron may be created. Photoelectrons are believed to be a
significant contributor to the warm electron population (see below). (2) At
larger heliocentric distances/lower outgassing rates, accelerated solar wind
electrons (see Sect. 2.2.3) lead to elevated electron-impact ionisation rates,
because the electron ionisation thresholds for most cometary species are
significantly higher than the typical local photoelectron energies (_Itikawa
and Mason_ , 2005; _Bodewits et al._ , 2016; _Deca et al._ , 2017; _Heritier
et al._ , 2018; _Divin et al._ , 2020). (3) At very large cometocentric
distances, fast and light solar wind H+ and He2+ ions may capture electrons
from slow heavy neutral species through charge-exchange (_Fuselier et al._ ,
1991; _Bodewits et al._ , 2004; _Simon Wedlund et al._ , 2019b). Although this
process does not produce any net ionisation, momentum is transferred from the
fast solar wind ions to the slow neutral coma and mass-loads the cometary
environment (_Simon Wedlund et al._ , 2017). (4) Fast solar wind ions that
impact cometary neutrals can provide an additional source of charged particles
to the cometary plasma density. (5) Finally, the primary process causing a
loss of plasma in the induced cometosphere is electron-ion dissociative
recombination. When the plasma number density is sufficiently high and
contains cold electrons, ions and electrons can merge back together and with
the excess energy create a neutral fragment (see also Chapter 16 and _Simon
Wedlund et al._ , 2019a).

####  2.2.2 Ion Dynamics

Figure 2: Sketch of the bulk ion motion at an intermediately active comet. The
Sun is to the left. The solar wind protons (red) are deflected to conserve
momentum as the locally produced H2O+ (purple) is accelerated along the solar
wind convective electric field $E_{\text{conv}}$. Pick up ions (dark blue)
that were produced far upstream eventually take over the role of the solar
wind protons in the flow towards the comet. Within the solar wind ion cavity,
the convective electric field is shielded. Within this region, the locally
produced water ions (light blue) expand radially and are eventually
accelerated and picked up by various processes (electric fields, wave-particle
interaction). Adapted from _Nilsson et al._ (2020).

In previous books on cometary plasma processes, the discussion on the
behaviour of ions was often based on a (single-)fluid dynamics approach. This
had two reasons: 1. simulations in an MHD regime were the predominant
simulation method, as hybrid and fully kinetic simulations required
computational resources out of reach of the previous generations of
supercomputers, and 2. for the comets visited until then, a fluid dynamics
approach was in reasonable agreement with the measurements (partially because
fine-scale particle dynamics could not be resolved by the onboard
instruments). However, even then it was clear that weakly active comets
necessitate a different approach, because ratios between the relevant plasma
scales are different from more active comets. A useful parameter that
highlights these differences is the particle gyroradius:

$r_{g}=\frac{mv_{\perp}}{\left|q\right|B},$ (2)

where $m$ and $q$ are the particle mass and charge, $B$ is the magnetic field
strength and $v_{\perp}$ is the particle velocity component that is
perpendicular to the field. For $B=5\,$nT and a water group ion with a
relative velocity to the magnetic field of $400\,$km/s, this results in a
gyroradius of $\sim 15000\,$km. Compared to the scale size of comet
1P/Halley’s interaction region ($2\times 10^{6}\,$km) this is small and thus
gyroradius effects on the large scale structure of the environment should be
negligible. On the other hand, the interaction region at 67P only extends
$100\,$km (at low activity) to $\sim 7000\,$km (high activity) and thus the
cometary ion gyroradius is larger and cannot be neglected.

These gyroradius effects are observable in the data collected by _Rosetta’s_
instruments. As was speculated in the last book, the cometary ions are
virtually at rest in the comet’s frame of reference, which means they move at
$-v_{sw}$ in the solar wind frame. Therefore, they are subject to the solar
wind convective electric field:

$\vec{E}_{\text{conv}}=-\vec{v}_{\text{sw}}\times\vec{B}$ (3)

and are accelerated along the field. This is illustrated in Fig. 2 by the
purple arrows. _Rubin et al._ (2014) showed that these gyroradius effects can
be modelled reasonably well with a hybrid as well as a multi-fluid MHD
approach. The inclusion of the cometary ions as a separate fluid was shown to
be a good method to simulate the large scale gyroradius structures, expanding
the applicability of the MHD models. If all cometary ions are moving in one
direction, momentum conservation dictates that the solar wind ions have to
move in the opposite direction, they are deflected away from the comet-Sun
line. This has been observed at low activity at 67P as well as in the
artifical comet experiments, AMPTE (_Coates et al._ , 2015; _Behar et al._ ,
2016b). This in turn modifies the plasma flow, as the addition of the heavy
cometary ions leads to a reduction in overall flow velocity. Incoming solar
wind ions are thus faster than the bulk flow and start to gyrate in the
magnetic field, similar to the cometary ions. This leads to an additional
component to the solar wind ion deflection that can add up to $180^{\circ}$ in
the denser part of the coma, where the magnetic field is higher. In effect
this means that under certain outgassing conditions, solar wind ions can flow
Sunward (see also blue and red boxes in Fig. 10). At this point, the solar
wind ions are so deflected, that they cannot flow towards the inner coma
anymore (red arrow in Fig. 2). This is the approximate position of the solar
wind ion cavity. Within that region, no solar wind ions can be observed (see
Sect. 3). In the aftermath of the Halley flybys, the region outside of the
solar wind ion cavity was often referred to as the cometosheath, i.e. the
region where cometary and solar wind ions are mixed and flow around the inner
coma (_Mandt et al._ , 2016).

For any investigation of the ion flow pattern (as e.g. shown in Fig. 2) at low
gas production rates, or far from the nucleus, it can be advantageous to
transform the data into a Cometocentric Solar Electric (CSE) coordinate
system. In this system the comet is at the origin, and the x-axis points
toward the Sun. The y-axis is aligned with the solar wind convective electric
field and the z-axis completes the triad.

Ignoring the electron dynamics for now (see section 2.2.3), an ion plasma flow
towards the nucleus remains, as also evidenced by the presence of an
interplanetary magnetic field inside the solar wind ion cavity. This means
that accelerated (pick-up) cometary ions must have taken over the role of the
solar wind ions in this flow. Indeed, observations show two distinct
populations of cometary ions at this stage (_Berčič et al._ , 2018): one
accelerated population flowing approximately anti-Sunward (dark blue arrows in
Fig. 2) and a radially expanding, slow moving population (blue locally
produced H2O+ in Fig. 2). This flow pattern is consistently observed in the
innermost coma, where accelerated ions are often observed in pulses, while the
slower, radially expanding population is ubiquitous. An open question remains:
How do the kinetic aspects of the ion dynamics around a low-to-medium activity
comet continuously evolve towards this more fluid-like behaviour at high
outgassing activity, close to the Sun? And, related, what is the speed of the
bulk of those low energy ions accelerated near the nucleus? What is the role
of the ambipolar, polarisation and Hall-electric field for these acceleration
processes?

This transfer of energy and momentum from the solar wind to the cometary ions
can also be surveyed in terms of momentum flux. The momentum flux in a
cometary environment is the sum of the momentum flux of the cometary ions,
solar wind ions, electron pressure and magnetic pressure. The higher the gas
production rate (and the solar wind dynamic pressure) the higher the total
momentum flux measured by the ion instruments. From recent observations it
becomes clear that the electron pressure gradient is the dominant source of
momentum at all activity levels, except those that are very high (close to
perihelion of 67P). While the solar wind ions carry some momentum into the
coma at low activity, this momentum is taken up by the cometary ions within
the solar wind ion cavity (_Williamson et al._ , 2020). This indicates an
efficient momentum and energy transfer from the solar wind ions to the pick-up
cometary ions via the convective electric field.

Within the inner coma, the solar wind convective electric field is not present
anymore, instead other fields such as an ambipolar or a polarization electric
field gain importance and lead to more complicated flow patterns (_Nilsson et
al._ , 2018; _Gunell et al._ , 2019; _Deca et al._ , 2019). Close to the
nucleus, where collisions are important, the dynamics of the ions are coupled
to the radially expanding neutral molecules (_Nicolaou et al._ , 2017; _Berčič
et al._ , 2018; _Nilsson et al._ , 2020). Closer to the Sun, more complex flow
patterns were observed around the diamagnetic cavity as collisional effects
become important in a greater area of the interaction region. In general,
simulations and observations show that the accelerated ions have a flow
pattern that guides them around the diamagnetic cavity most of the time, but
in some instances the accelerated ions can go through the boundary and flow
tailward also within the diamagnetic cavity (_Masunaga et al._ , 2019).

####  2.2.3 A four-fluid coupled system

Close to the nucleus of comet 67P, _Rosetta’s_ Langmuir probe measured a 1/r
decay of the plasma density with cometocentric distance (_Edberg et al._ ,
2015; _Galand et al._ , 2016). Consequently, it indicates that the ratio
between the cometary and solar wind plasma density, and by extension the full
set of plasma parameters throughout 67P’s plasma environment, continuously
changes within a comet’s plasma interaction region (_Nilsson et al._ , 2017;
_Eriksson et al._ , 2017; _Berčič et al._ , 2018). In other words, the global
configuration of the induced cometosphere is driven by changes in the locally
dominating physical processes and the relative ratios of the local plasma
scales, such as the electron/ion-neutral collisional mean-free-path and the
inertial lengths of the plasma species. A variety of permanent and transient
boundaries can be defined (Sect. 3 and _Mandt et al._ , 2016). In addition,
(the existence of) these boundaries evolve(s) with heliocentric distance, or
better, with the activity regime of the comet.

During weakly outgassing regimes, i.e., well before a bow shock or diamagnetic
cavity forms upstream of the cometary nucleus, ionization of the outflowing
neutral gas from the nucleus compresses the incoming solar wind. A magnetic
pileup region forms and the magnetic field lines drape around the nucleus (see
Sect. 2.4 and _Koenders et al._ , 2013, 2015, 2016a; _Behar et al._ , 2016a,
b; _Volwerk et al._ , 2016).

Figure 3: Illustration of the four-fluid coupled system, including various
isovolumes that indicate the significant components of a Generalised Ohm’s
law. See text for details. Figure adapted from (_Deca et al._ , 2019).

In addition to section 2.2.2, here we include the electron dynamics. The
discussion is based on several fully kinetic particle-in-cell simulations that
model self-consistently four plasma populations: solar wind protons and
electrons, cometary water ions and cometary electrons (_Deca et al._ , 2017,
2019; _Sishtla et al._ , 2019; _Divin et al._ , 2020). Assuming a
collisionless plasma, the dynamical interaction that determines the general
structure of the induced cometosphere during the weakly outgassing phases can
be interpreted as a four-fluid coupled system, where the solar wind electrons
move to neutralize the cometary ions, and the cometary electrons organize
themselves to neutralize the solar wind ions (illustrated in Fig. 3) (_Deca et
al._ , 2017). More precisely, ions of cometary origin accelerate along the
local solar wind convective electric field in the cross-magnetic field
direction, whereas electrons of cometary origin are initially accelerated in
the opposite direction. This results in a net (Hall) current that locally
decouples the solar wind protons and electrons as the solar wind plasma
becomes more and more massloaded by cometary ions. It is important to note
that the convective electric field carries an opposite sign in the solar wind
and cometary ion reference frame and transfers momentum between the two
species. As the solar wind protons are deflected and not any longer frozen-in,
the interplanetary magnetic field is carried close to the comet through the
solar wind (and cometary) electrons. Note that a crucial component of the
mechanism described above is provided by the electron dynamics. One of the
revelations of the _Rosetta_ mission and subsequent numerical modelling is
that key interaction mechanisms based on fluid concepts, such as momentum and
energy transfer between the solar wind and cometary plasma can be explained by
including self-consistently the electron dynamics. For example, the deflection
of cometary electrons creates the electron current that induces the magnetic
pileup region as the incoming solar wind is compressed (_Deca et al._ , 2019).
Figure 3 presents an overview of the four-fluid behaviour of the solar wind
interaction with a weakly outgassing comet.

Although modelling both the electron and ion species is a necessity to unveil
the interaction discussed above, less complete approaches (from an electron
point-of-view) often present different benefits. For example, more complex
ion-interaction models can be implemented as less computational resources are
needed when keeping the electron populations as a massless charge-neutralising
fluid as it is done in a hybrid approach (_Simon Wedlund et al._ , 2019a;
_Koenders et al._ , 2016a; _Alho et al._ , 2020). This has the advantage of
reducing simulation time while retaining the ion kinetics. To resolve larger
interaction regions, simulate longer time scales and for parameter studies
that require a short turnover time, a multi-fluid approach can be useful (e.g.
_Huang et al._ , 2018). However, this comes at the cost of losing the electron
and ion kinetics and many small scale structures. Compared to fully kinetic
treatments, hybrid and multi-fluid (Hall-) MHD models often assume a a
suitable electron closure relation combined with a generalised Ohm’s law (GOL)
to approximate the electric field in the system (_Huang et al._ , 2018; _Deca
et al._ , 2019):

$\mathbf{E}=-(\mathbf{u}_{\rm
i}\times\mathbf{B})+\frac{1}{en}(\mathbf{j}\times\mathbf{B})-\frac{1}{en}\nabla\cdot\mathbf{\Pi}_{\rm
e}+\frac{m_{e}}{e}\nabla\cdot(\mathbf{u}_{e}\mathbf{u}_{e}),$ (4)

where $e$ and $m_{e}$ are the electron electric charge and mass, respectively,
$\mathbf{B}$ the magnetic field, $\mathbf{u}_{\rm i}$ the ion mean velocity,
$\mathbf{j}$ the current density, $n$ the plasma total number density defined
as the sum of the solar wind and cometary densities, $n=n_{\rm sw}+n_{\rm c}$
and $\mathbf{\Pi}_{\rm e}$ the electron pressure tensor derived from the
electron momentum equation. The various terms decompose the total electric
field in (from left to right) the convective electric field, the Hall electric
field, the ambipolar electric field and the contribution associated with the
electron inertia. Using the results from their fully kinetic model, _Deca et
al._ (2019) were able to compute the various contributions using the output
particle data from the simulation, in this way identifying where an isotropic
single-electron fluid Ohm’s law approximation can be adopted, and where it
cannot. To illustrate, Figure 3 includes various isovolumes that indicate the
regions where specific terms of the GOL described above are significant.
Consistent with _Rosetta_ ’s measurements, they conclude that near the nucleus
the electron pressure gradient is dominant, and that at spatial scales smaller
than the ion plasma scales the total electric field is primarily a combination
of the solar wind convective electric field and the ambipolar electric field.
Interestingly, throughout most of the region the electron inertial term was
found negligible. This also implies that multi-fluid and hybrid simulations
with an electron pressure equation are valid most of the time, except when a
distinction between electron populations is necessary. While cometary missions
and simulations have helped us understand the complex interplay of these four
fluids to a greater degree, the exact plasma distribution with respect to
cometocentric distance (in 3D), and how it varies in time is still unclear. In
addition, it remains to be investigated what role the (quiet) solar wind
dynamics (e.g. turbulence) play in the inner coma dynamics, where the plasma
is shielded from direct influence of solar wind variation, but could be
affected indirectly, via pick-up ion dynamics.

####  2.2.4 Electron populations and the ambipolar electric field

The electron distributions observed in the inner coma of 67P can be traced
back to two main categories: cometary electrons and solar wind electrons. The
cometary electron population originates from ionising neutral molecules of
cometary origin through solar extreme ultraviolet radiation (photoelectrons;
_Vigren and Galand_ , 2013) or secondary particle processes as described above
(_Simon Wedlund et al._ , 2017; _Heritier et al._ , 2018). The undisturbed
solar wind electron population typically consists of a thermal core (E $<$ 50
eV) and a suprathermal tail (70 $<$ E $<$ 1000 eV) (_Pierrard et al._ , 2016).

A variety of physical mechanisms in the cometary plasma environment can affect
both these source populations, such as ambipolar electric fields (_Madanian et
al._ , 2016; _Deca et al._ , 2019; _Divin et al._ , 2020), adiabatic
compression and expansion (_Nemeth et al._ , 2016; _Broiles et al._ , 2016;
_Deca et al._ , 2019; _Madanian et al._ , 2020), collisional cooling
(_Engelhardt et al._ , 2018a) and wave-particle interactions (_Goldstein et
al._ , 2019; _Lavorenti et al._ , 2021).

In reality, it is not feasible to tell apart which group an electron belongs
to without additional information, e.g., from numerical modelling. Most
generally, three distinct electron populations were observed: a warm (5-10
eV), cold (0.01-1 eV) and hot (or suprathermal) population (few 10s to 100
eV).

In order to understand the origins of these three distinct populations, we
need to have a closer look at the electromagnetic environment surrounding the
cometary nucleus. Whereas ionisation of the cometary gas results in electrons
that have thermal speeds on the order of $\rm 1000\,km\,s^{-1}$ (_Vigren and
Galand_ , 2013), the much heavier ion counterparts tend to retain the speed of
their parent neutral molecule (typically on the order of $\rm 1\,km\,s^{-1}$).
A strong electron pressure gradient forms, which results in a potential well
and ambipolar electric field that surrounds the cometary nucleus (_Madanian et
al._ , 2016; _Deca et al._ , 2019; _Divin et al._ , 2020). Note that efficient
electron cooling during high outgassing phases may neutralize the ambipolar
electric field component, such as was the case for the _Giotto_ flyby of comet
1P/Halley (_Gan and Cravens_ , 1990), but the importance of the ambipolar
electric field for low-activity comets has been one of the most intriguing
discoveries of the _Rosetta_ mission. For example, _Galand et al._ (2020)
found that this acceleration of the electrons in an ambipolar field can
produce EUV emissions, similar to those associated to auroral emissions at
other solar system bodies.

The ambipolar electric field and its associated potential well can temporarily
trap cometary electrons and accelerate solar wind electrons near the cometary
nucleus, leading to the observed warm and hot electron populations (_Deca et
al._ , 2017). Studying the trajectories of trapped electrons in the ambipolar
potential well surrounding the nucleus, a clear boundary in velocity space can
be defined that separates temporarily trapped cometary electrons from passing
solar wind electrons (_Sishtla et al._ , 2019). It shows that electrons may
stay much longer in the region of dense neutral gas around the nucleus than
previously believed, which may also lead to increased cooling of electrons in
non-collisionless plasma regimes (_Engelhardt et al._ , 2018a; _Divin et al._
, 2020). Using fully kinetic particle-in-cell simulations it was found that
cometary electrons exhibit an apparent isotropic and almost isothermal
behaviour, whereas the solar wind electrons, on the other hand, exhibit an
anisotropic and apparent polytropic behaviour (_Deca et al._ , 2019). In
addition, at a few tens of kilometres from the nucleus, the electron sensor
observed a highly variable bi-Maxwellian electron distribution with energies
ranging from tens up to several hundred eV (_Clark et al._ , 2015), consistent
with a dense warm and a rarefied hot electron population (_Madanian et al._ ,
2016; _Deca et al._ , 2017). _Broiles et al._ (2016) constrained the kappa
values of the warm population ranging from 10-1000, suggesting the warm
electrons are near-thermal equilibrium (consistent with _Deca et al._ 2019),
whereas values between 1-10 were found for the hot electron component. The
warm population showed a 1/r density dependence up to about 900 km from the
nucleus and a $r^{-0.7}$ dependence farther out (_Edberg et al._ , 2015;
_Myllys et al._ , 2019), where $r$ is the cometocentric distance. In addition,
_Myllys et al._ (2019) corroborated on a $1/r^{2}$ dependence with density for
the hot electrons.

Taking into account the radial cometocentric dependence of the warm
population, both the warm and hot components manifest an increase in density
with decreasing heliocentric distance, consistent with the observed increase
in neutral gas density and photoionisation frequency. The density of the warm
and hot population increased from about 30 to 100 $\rm cm^{-3}$ and 0.1 to 3
$\rm cm^{-3}$ between 3.5 and 1.3 AU, respectively. The hot electron
population showed a 33% increase in temperature with heliocentric distance,
whereas the warm population seemed not affected by the latter parameter.
_Myllys et al._ (2019) concluded as well that the ambipolar acceleration
process could only explain part of the observed hot electron distribution,
suggesting that part of the population may have its origin in the already
accelerated suprathermal component of the solar wind electron distribution
(_Broiles et al._ , 2016).

Quite intriguingly, the accelerated hot electron population was found to be
correlated with Far-UV emissions observed near comet 67P, showing for the
first time that cometary aurora can be driven by the interaction of the solar
wind with the local environment (_Galand et al._ , 2016).

Figure 4: Distribution of $\rm T_{h}/T_{c}$ versus $\rm n_{h}/n_{tot}$ (left)
and of the electron temperatures versus the electron densities (right)
estimated at the _Rosetta_ orbiter locations in the cometary plasma of comet
67P from January to September 2016 (570 000 samples), where the subscripts
$h$, $c$ and $tot$ indicate hot cold and total, respectively. Colors
correspond to the number of responses (the colour map is logarithmically
scaled in both panels). Figure adapted from _Wattieaux et al._ (2020).

Although _Giotto_ could not directly measure cold electrons, it was assumed
that the dense inner coma of 1P/Halley could efficiently cool electrons
through collisions with the neutral gas (_Feldman et al._ , 1975; _Ip and
Mendis_ , 1975; _Eberhardt and Krankowsky_ , 1995). Electron cooling is
thought to be most efficient within the electron exobase (or collisionopause,
see Chapter 16). However, _Rosetta’s_ Langmuir Probe and Mutual Impedance
Probe instruments detected cold electron signatures significantly outside the
electron exobase, suggesting that once cooled in the inner coma, there is no
mechanism that is able to reheat cold electrons when they travel away from the
nucleus (_Eriksson et al._ , 2017). At this point, it is not known what
processes contribute to cooling newborn, warm electrons. The cold electron
temperature observed ranged between 0.05 to 0.3 eV (_Wattieaux et al._ ,
2020). In addition, cold electrons measurements were only significant in
regions dominated by (warm) cometary plasma (Figure 4). It was shown that
there is a clear correlation between electron cooling and the observations of
the diamagnetic cavity, suggesting that both have to be in close proximity
(_Henri et al._ , 2017; _Odelstad et al._ , 2018). Finally, cold electrons
have as of yet not been observed without the presence of a significant warm
electron population (_Eriksson et al._ , 2017; _Myllys et al._ , 2019; _Gilet
et al._ , 2020; _Wattieaux et al._ , 2020). So far it is unclear what the
energy distribution of electrons below the spacecraft potential is.

####  2.2.5 Cometary outbursts

Up to here, we have focussed on a steady-state solar wind plasma interaction
with the cometary environment. Throughout the _Rosetta_ mission, however, at
least one internal outburst was detected that significantly affected the near-
cometary plasma environment (_Grün et al._ , 2016). During the outburst, the
neutral density doubled, but interestingly, the plasma density quadrupled,
which was attributed to an increased efficiency of the electron impact
ionisation process as well as more efficient ion-neutral coupling in the
denser neutral gas which reduces the ionisation length scales (_Hajra et al._
, 2017). _Rosetta_ also measured locally a decreased suprathermal electron
flux and solar wind ion density, as well as a reconfigured magnetic field and
a change in the singing comet wave activity (see Sect. 4 and _Breuillard et
al._ , 2019).

###  2.3 External drivers to the induced cometosphere

Figure 5: The daily averaged electron differential flux as measured by
_Rosetta_ ’s Ion and Electron Spectrometer. The spectrum from 1 August 2014
shows a typical solar wind type electron flux. The spectrum from 2 October
2014 and 23 October 2014 show a typical quiet and ICME-impacted electron flux
profile near the comet, respectively.

Above we discussed the major internal processes that shape the near-cometary
plasma environment. Solar wind (SW) transients, flares, CIRs, and ICMEs, on
the other hand, are external drivers to the induced cometosphere. Transient
phenomena change the solar wind parameters on relatively short time scales
and, as a result, have the potential to significantly reconfigure/disturb the
near-cometary plasma environment. The effects can be extremely variable and
differ from event to event, depending on the strength and type of the
transient and the heliocentric location and outgassing rate of the comet.
Nevertheless, several characteristics can be identified that are consistently
observed for specific classes of transient phenomena.

Solar flares are short-lived and temporarily increase the local extreme-
ultraviolet flux. However, during the weakly outgassing stages of a comet,
photoionisation is only a minor contributing plasma source. During the
strongly outgassing stages, on the other hand, the induced cometosphere is
inherently very variable even without external drivers. As a result, solar
flares are not observed to significantly disturb the plasma interactions that
shape the induced cometosphere (_Edberg et al._ , 2019).

CIRs, on the other hand, spiral outward in the solar system and are often
accompanied by a forward shock at their leading edge (and a reverse shock at
the trailing edge, _Balogh et al._ , 1999). This has been observed to lead to
an increase in the local solar wind velocity, proton and cometary plasma
density, temperature, magnetic field strength, and suprathermal (hot) electron
flux (_Edberg et al._ , 2016b; _Hajra et al._ , 2018). The latter results in
an increased electron-impact ionisation rate, which, on its turn, may become
the largest contributor to the total plasma density, rather than increased
compression or acceleration due to the ion pickup process (_Galand et al._ ,
2016; _Heritier et al._ , 2018; _Hajra et al._ , 2018). The magnetic
compression resulting from the CIR impact on the induced cometosphere, on the
other hand, is responsible for the local increase in proton density and
magnetic field strength.

Specific for 67P, _Hajra et al._ (2018) observed greater increases on the
southern (summer) hemisphere of the comet versus its northern (winter)
hemisphere. The effects of CIRs are typically observed for about 24h, with
clear signatures of the forward and reverse shock wave visible even in the
coma region. Langmuir waves can be excited near the forward and reverse shocks
of a CIR in the solar wind, where electrons can be accelerated such that they
counterstream in the solar wind flow (_Pierrard et al._ , 2016). Locally
generated Langmuir waves have been observed during times of CIR (and ICME)
interaction with the cometary environment, indicating that backstreaming
electrons exist even in the coma of the comet. However, the exact mechanism
that causes the electrons to backstream along the field lines from the shock
interface is not yet understood (_Myllys et al._ , 2021).

ICMEs comprise the most variable class of external drivers to the induced
cometosphere. However, they tend to accelerate most within 1 AU, after which
they gradually decelerate travelling outward into the solar system (_Zhao et
al._ , 2017). Their interaction with the cometosphere can be characterised by
an increase in magnetic field and plasma density, an increase in energetic
electron flux (e.g. Figure 5), and a rapid (Forbush) decrease in the observed
galactic cosmic ray intensity (_Witasse et al._ , 2017). ICMEs may also merge
with other transients and form more complex structures (_Witasse et al._ ,
2017; _Wellbrock et al._ , 2018). Although the _Rosetta_ spacecraft was not
often in an ideal position to characterise the impacts of ICMEs throughout the
induced cometosphere, an ICME impact detected close to perihelion lead at 170
km from the cometary nucleus to the highest magnetic field strength
($300\,$nT) measured through the mission (_Goetz et al._ , 2018).

###  2.4 Magnetic Field Pile-up

Figure 6: An illustration of the large scale magnetic field at a comet,
including processes in the tail. The Solar wind with the IMF approaches from
the left. The magnetic field lines are shown in green, and a heliospheric
current sheet is marked by the black dashed line. In the near comet tail there
are spiralling magnetic field waves in orange. A possible reconnection region
in the tail produces plasma density enhancements (blue) that travel towards
and away form the reconnection region. For further information and scale sizes
see text.

The interaction of the interplanetary magnetic field (IMF, sometimes also
referred to as the heliospheric magnetic field) carried by the solar wind and
an outgassing comet leads to the formation of an induced magnetosphere with
magnetic field pile-up and field line draping, an overview of which is shown
in Figure 6. This happens as soon as the comet gets active, usually when it
enters Jupiter’s orbit, i.e. $\sim 5$ au radial distance from the Sun. The
convective electric field of the solar wind will accelerate the new-born
cometary ions, and these start to gyrate around the magnetic field lines. This
is called ion pick-up or mass-loading of the solar wind. As most of the
earlier work on cometary magnetospheres is discussed in _Ip_ (2004), this
section will mainly concentrate on work after 2004.

Because of conservation of momentum the mass-loaded solar wind will have to
decelerate. _Biermann et al._ (1967) presented a simple 1-D MHD model of this
solar wind - comet interaction by combining the continuity, momentum and
energy equations. The solar wind velocity $u_{\rm x}(x)$ is in the
$x$-direction and the IMF $B_{\rm y}$ is in the $y$-direction. This results in
a solar wind velocity:

$\displaystyle u_{\rm x}(x)=\left(2(f+1)(M(x)+\rho_{\infty}u_{\infty})\right)$
$\displaystyle\left[(f+2)\rho_{\infty}u_{\infty}^{2}\pm\sqrt{(f+2)\rho_{\infty}^{2}u_{\infty}^{4}-4(f+1)(M(x)+\rho_{\infty}u_{\infty})\rho_{\infty}u_{\infty}^{3}}\right],$
(5)

where $\rho_{\infty}$ and $u_{\infty}$ are the undisturbed solar wind density
and velocity, $f$ is the number of degrees of freedom of the ions, and $M(x)$
is the mass source. Using e.g. the _Haser_ (1957) model for cometary
outgassing one can solve the continuity equation for the magnetic flux, which
leads to $B_{\rm y}(x)\rightarrow\infty$ at the location where the bow shock
is formed. This can be solved by adding cooling of the plasma through charge
exchange processes, to obtain finite field strengths downstream of the bow
shock (for details see _Galeev et al._ , 1985; _Goetz et al._ , 2017).
However, there are some limiting assumptions to this model: the solar wind
magnetic field should be perpendicular to the plasma flow direction (but is in
reality on average at the Parker spiral angle); single fluid MHD is assumed
(although the ion gyro radius can be larger than the interaction region); and
the model is only valid on the Sun-Comet line. Nevertheless, a comparison of
the modeled magnetic field and the measured field at comet 67P gives
reasonable agreement (_Goetz et al._ , 2017).

###  2.5 Magnetic Field Draping

Figure 7: Two-dimensional histograms of the cone angle of the magnetic field
along the _Rosetta_ orbit for the outbound (left) and inbound (right) leg. The
green lines show the cone angles for the Parker spirals. The two white
vertical lines show the interval during which the ICME interaction took place.
From _Volwerk et al._ (2019).

The above described 1D model delivers the magnetic field strength in the
subsolar cometary environment, but does not describe the full structure of the
induced magnetosphere. Therefore it needs to be expanded with a second radial
dimension, perpendicular to the comet-Sun line. This results in the magnetic
field line being draped around the active nucleus as was first described by
_Alfvén_ (1957). Through the finite conductivity, the magnetic field will
diffuse through the plasma cloud around the nucleus, thereby avoiding another
magnetic catastrophy, i.e. an infinite magnetic field strength. The IMF,
however, varies in direction and the radial component of the magnetic field
changes sign regularly. Thereby, differently directed magnetic field can be
draped around the active nucleus. When the diffusion speed through the plasma
is smaller than the flow velocity of the mass-loaded solar wind, a layering of
differently directed magnetic field will be created upstream of the comet,
which is referred to as “nested draping.” This phenomenon was first observed
at comet 1P/Halley during the flybys of _VEGA 1_ (_Riedler et al._ , 1986) and
_Giotto_ (_Raeder et al._ , 1987). The boundaries between these different
magnetic field directions will have to support current sheets. Indeed, during
the early phase of _Rosetta_ , during the unbound pyramidal orbits, many
rotations of the field were found with a minimum magnetic field strength and a
maximum in electron density in the centre of the rotation (_Volwerk et al._ ,
2017). Again, this would argue for nested draping of the IMF if this were a
“snapshot” flyby like _Giotto_. However, _Rosetta_ moves at a speed of only a
few meters per second, which needs a different interpretation. On the other
hand, if the diffusion speed is fast enough, no such pile-up will occur, apart
from a regular increase of the magnetic field strength created by the mass-
loading and slowing down of the solar wind.

Another situation occurred at comet 67P, during the dayside excursion by
_Rosetta_. The spacecraft took an upstream excursion of $\sim 20$ days up to a
distance of $\sim 1500$ km from the nucleus. In order to find nested draping,
_Volwerk et al._ (2019) determined the cone angle of the magnetic field,
defined as:

$\displaystyle\theta_{\rm
co}=\tan^{-1}\left\\{\frac{\sqrt{B_{y}^{2}+B_{z}^{2}}}{B_{x}}\right\\},$ (6)

where $\theta_{\rm co}=0^{\circ}$ is purely sunward directed field and
$\theta_{\rm co}=180^{\circ}$ purely anti-sunward222$B_{x}$, $B_{y}$, and
$B_{z}$ are defined in a CSEQ coordinate system, with the nucleus in the
origin, $\vec{e}_{x}$ points to the Sun, $\vec{e}_{z}$ is parallel to the
Solar rotational axis, and $\vec{e}_{y}$ completes the right handed system. .
Indeed, regions of differently directed magnetic field were found, but when
the spacecraft returned back after apo-apsis, a region was entered that did
not exist during the outbound leg, see Fig. 7. This indicates that the draping
moves faster towards the nucleus than the spacecraft is moving, which is not
difficult as _Rosetta_ moved at $\sim 1\,$m/s. The authors called this
“dynamic draping.” The question of how dynamic and nested field line draping
are related is still open, as there is either a snapshot observation by a fast
moving flyby or there is only a local long-term observation by an orbiting
spacecraft. A multi-spacecraft mission could allow us to get a better grip on
this problem: different trajectories could be flown, like it is planned for
the upcoming Comet Interceptor mission (_Snodgrass and Jones_ , 2019).

Lately, _Delva et al._ (2014) re-investigated the Vega-1 magnetometer data
taken during the flyby of comet 1P/Halley, to study the magnetic pile-up
boundary (MPB) and the draping pattern of the magnetic field. The MPB is the
boundary between the cometosheath (where there is no draping) and the pile-up
region (where there is strong draping). In order to study the draping, an
electromagnetic reference frame was calculated from the abberated
cometocentric coordinate system, in which $x_{\rm IMF}$ is along ${\bf v}_{\rm
SW}$ and the new $y_{\rm IMF}$-axis direction is given by $-{\bf v}_{\rm
SW}\times{\bf B}_{\rm IMF}$. The draping is then studied by the relationship
between $B_{\rm x,IMF}$ and $B_{\rm rad}$ the field component pointing
radially away from the cometary nucleus. There should be a strong negative
correlation between the two variables if the spacecraft is inside the MPB.

One effect has not been taken into account in this discussion, and that is
conservation of momentum related to the pick-up process through the
acceleration of the heavy cometary ions. The newly-created ions are
accelerated by the convective electric field of the solar wind. Through
Newton’s second law, this action will need an opposite reaction, and thus the
solar wind ions will have to move in the direction opposite to the convective
electric field (see also Sect. 2). As the IMF is frozen into the solar wind
plasma flow, this will result in the magnetic field draping in this direction.
_Broiles et al._ (2015) first showed that indeed the solar wind and pick-up
ions moved in opposite directions, and the magnetic field draping effect was
shown for 28 March 2015 (low to medium activity), when _Rosetta_ had a closest
approach of $\sim 15$ km (see e.g. Fig. 5 in _Koenders et al._ , 2016a). This
effect starts to become very important when the pick-up density starts to
become similar to the solar wind density.

The comet-solar wind interaction has influence on the structure of the induced
cometary magnetosphere. This influence can be used to obtain information about
the solar wind for missions, like _Rosetta_ , that do not have easy access to
the undisturbed solar wind. Indeed, the interaction of a ICME and CIR with
comet 67P, on 3 July 2015, led to the unprecedented high magnetic field
strength of almost 300 nT measured by _Rosetta’s_ magnetometer (_Goetz et al._
, 2018). But not only such extreme field measurements are necessary, _Timar et
al._ (2019) derived a proxy by using the magnetic pressure just outside of the
boundary of the diamagnetic cavity. Assuming that the magnetic pressure in the
induced magnetosphere needs to balance the dynamic pressure of the solar wind,
they found a good correlation between the proxy and the propagated solar wind
from the Earth to the comet.

###  2.6 Ion/Plasma/Magnetotail

The most notable structure of a comet is its tail, or rather tails: the dust
tail curved along the comet’s orbit; and the ion tail which points almost
radially away from the Sun. Historically, the cometary tails were categorized
by _Bredikhin_ (1879) into three types: type I - a straight tail pointing away
from the Sun (the ion/plasma tail) and types II and III - tails curved towards
the orbit of the comet (the dust tails) with type II consisting of medium-
heavy elements and type III consisting of heavy metals. With the available new
observations, this classification is no longer valid. The following sections
will focus on the plasma tail itself, but there is also some evidence that the
interaction of a comet with the solar wind can affect the dust tail through
Lorentz force acceleration of the charged dust particles (e.g. _Kramer et al._
, 2014; _Price et al._ , 2019).

####  2.6.1 Remote sensing of the plasma tail

Remote sensing, for example with ground-based observations of comets, gives a
large-scale view of the ion tail, which, because of its large extent cannot be
studied by spacecraft missions. These observations give insight in the
structure and the dynamics of the tail. However, as we know that the cometary
tail is created through the interaction of the solar wind and IMF,
observations of the tail can also provide information about the ambient plasma
(i.e. the solar wind) conditions.

Photometric observations of comet 1P/Halley in 1986 showed many structures in
the tail. _Brandt_ (1982) already talked about rays, streams, kinks, knots,
helices, condensations and disconnection events. _Saito et al._ (1986) added
arcades in the collection of structures. _Mozhenkov and Vaisberg_ (2017)
studied the large scale structure of more than 1500 photographs of comets to
categorize two different plasma tail types: double structures – two bright
diverging rays from the coma, and outflow – single large scale thin tail . The
double structure is assumed to be created by a line-of-sight effect of a
cylindrical distribution of plasma in the tail created by mass loading of the
solar wind. The outflow tails are posited to be created by outflow of plasma
from the coma driven by the dynamic pressure of the solar wind, similar to
Martian ionospheric plasma outflow (_Lundin_ , 2011).

####  2.6.2 Structure of the tail

_Biermann_ (1951) and _Alfvén_ (1957) laid the foundations for the generation
of the ion tail, through mass loading and field line draping described above.
On 11 September 1986, the first evidence for this magnetic field draping in
the comet’s magnetotail was established through observations by the
International Cometary Explorer (ICE) spacecraft. It passed comet
21P/Giacobini-Zinner at the downstream side, crossing the induced magnetotail
(_Smith et al._ , 1986; _Slavin et al._ , 1986b).

Assuming that the IMF is always perpendicular to the comet-Sun line is not
realistic, although it makes the modeling easier. However, the IMF
statistically follows the Parker spiral (_Parker_ , 1958) and thus arrives at
the comet at an angle, making the draping pattern asymmetric (_Volwerk et al._
, 2014), as also observed at Venus (_Delva et al._ , 2017).

Sometimes chance encouters with cometary tails by spacecraft happen, such as
in the case of Ulysses traversing comet Hyakutake’s (C/1996 B2) ion tail
(_Jones et al._ , 2000). It was detected at a distance of more than 3.8 au
from its nucleus and had a diameter of at least 7 million km.

It took 30 years for a planned investigation of a cometary tail. In the period
from 24 March until 10 April 2016 _Rosetta_ was sent on a tail excursion. In
this case the spacecraft moved up to only $\sim 1000$ km from the nucleus so
the very near-region was studied. _Volwerk et al._ (2018) looked at the
draping of the field, the cone-angle $\theta_{\rm co}$ was calculated, and the
distribution peaked between $60^{\circ}$ and $80^{\circ}$. This means that the
“draped” magnetic field is more cross tail than along the Sun-comet-line as
one would expect. This direction of the magnetic field is most-likely caused
by the deflected solar wind magnetic field (_Koenders et al._ , 2016a) as
discussed above, which is transported to the downstream side of the comet.
Eventually the field stretches out to the more regular tail structure.

There is a non-radial component to the orientation of the plasma tail, as it
will be abberated through the motion of the comet itself. The plasma tail will
make an angle $\epsilon$, with the radial direction to the Sun given by:

$\displaystyle\epsilon\approx\tan^{-1}\left\\{\frac{|V_{\rm
c}sin(\gamma)|}{|V_{\rm sw}|}\right\\}$ (7)

where $V_{\rm c}$ is the cometary orbital velocity, $\gamma$ is the angle
between $V_{\rm c}$ and the anti-solar radial direction and $V_{\rm sw}$ is
the radial component of the solar wind (_Mendis_ , 2007), where typical values
are at $\epsilon<6^{\circ}$.

It was found that ion tails often show acceleration of condensations (i.e.
bright blobs of plasma in the tail), which exceed the gravitational pull of
the Sun by 1 to 2 orders of magnitude. _Öpik_ (1964) used _Bobrovnikoff_
(1930)’s observations of comet 1P/Halley from 1910, to show that the usage of
a correct coordinate system leads to better esitmates of the acceleration, as
sometimes values $>1000$ were published. The general acceptance was that the
acceleration was caused by radiation pressure (see, e.g. _Wurm_ , 1943).

####  2.6.3 Plasma acceleration

One of the open questions in (cometary) tail physics is how fast the plasma is
accelerated. Knots are bright patches of plasma that are created by
disconnection events in the tail. Studies by _Niedner_ (1981), _Saito et al._
(1987), _Rauer and Jockers_ (1993), _Kinoshita et al._ (1996) and _Buffington
et al._ (2008) gave a broad range of velocities of these knots varying from 20
to 100 km/s. Acceleration of the knots were measured as 21 cm/s2 (_Niedner_ ,
1981) and 17 cm/s2 (_Saito et al._ , 1987).

_Yagi et al._ (2015) used the Subaru Telescope on Mauna Kea to observe the
tail of comet C/2013 R1 (Lovejoy) and study the short time behaviour through
short exposures, and thereby were able to determine the initial velocity of
the knots to be between 20 and 25 km/s. This is smaller than the earlier
studies, but there the initial velocity was determined by interpolation and
may be inaccurate. There are reasons why the initial velocity can differ, e.g.
the radial distance from the Sun or the heliospheric latitude. Significant
changes in the width of the tail were also found over a time scale of 7
minutes, which makes high-time resolution imaging of cometary tails a
necessity to understand the influence of solar wind variations on the tail.

####  2.6.4 Waves and oscillations

An interesting effect was found at distances $\geq 500$ km from the nucleus of
comet 67P/Churyumov-Gerasimenko. _Volwerk et al._ (2018) calculated the clock
angle, defined as:

$\displaystyle\phi_{\rm cl}=\tan^{-1}\left\\{\frac{B_{\rm z}}{B_{\rm
y}}\right\\}.$ (8)

The unwrapped clock angle showed a continuously increasing angle $\phi_{\rm
cl}$, even when the spacecraft turns around at apoapsis and moves in the
opposite direction. This was interpreted as a traveling rotational wave along
the magnetic field. The angular frequency of this wave whilst _Rosetta_ moved
outbound(inbound) was $\omega_{\rm h}\approx 5.65$($5.83)^{\circ}$/h, and the
spacecraft speed was $v_{\rm ros}\approx 1.3(3)$ m/s. Assuming _Rosetta_
observed a Doppler shifted wave, a phase velocity for the wave was determined
at $v_{\rm h}\approx 136$ m/s. With an average magnetic field of $B_{\rm
m}\approx 10$ nT, this velocity does not correspond any known specific
velocity, nor does the frequency correspond to any gyro frequency.

_Nisticò et al._ (2018) studied oscillations of cometary tails to investigate
the interaction of the solar wind with a cometary plasma tail, especially for
Sun grazing comets. Thereby, insight can be obtained in the solar wind
conditions. Using images of comets Encke and ISON by the STEREO-a/HI-2
telescope they found oscillations of the two cometary plasma tails, which they
interpreted as so called “vortex shedding” (see e.g. _Johnson et al._ , 2004).
Modeling the tail as a driven and damped harmonic oscillator, the authors
obtained information about the local solar wind velocity. Indeed,
_Ramanjooloo_ (2014) makes a case that ion tails can be used to investigate
the the inner structure of the whole heliosphere. This opens a new window in
solar wind studies from historical and contemporary observations (see e.g.
_Ramanjooloo and Jones_ , 2022)

Tail dynamics, such as waves, kinks, detachments and including cometary ion
rays, need to be studied through well-planned campaigns, not in the least
because of the enormous size of a cometary tail. What actually causes
detachments, what accelerates the condensations in the tail, what drives the
kinks? To answer these questions, detailed in-situ observations, combined with
ground observation campaigns are necessary.

####  2.6.5 Historical solar wind

Historical observations of cometary tails can also be used to investigate the
historic solar wind conditions. One interesting historic period is the so-
called Maunder Minimum (1645 - 1715). _Gulyaev_ (2015) studied drawings of
cometary plasma tails (type I tails) made during the Maunder Minimum. More
than 20 comets were observed during that time, including comet 1P/Halley. The
presence of plasma tails is directly related to the presence of a solar wind.
_Gulyaev_ (2015) states that, in principle it should be possible to obtain the
solar wind velocity by looking at shifts of individual features in consecutive
drawings, however these are very hard to distinguish.

_Zolotova et al._ (2018) studied descriptions of comets from the eleventh to
the eighteenth century, but found from colour descriptions that mainly dust
tails were described. Using the determination of the aberration $\epsilon$ as
determined by (_Bredikhin_ , 1879) an average value of $\sim 10^{\circ}$ was
found, also indicating that mainly dust tails were seen, because the plasma
tail is much less intense and thus more difficult to observe with the unaided
eye. _Zolotova et al._ (2018) concludes that probably the first identification
of a plasma tail was done for the great comet C/1769 P1. However, _Hayakawa et
al._ (2021) discuss three cases, earlier than 1769, in which historical
sources talk about two tails at comets C/1577 V1, and 1P/Halley in both the
years 760 and 837. Comparing these descriptions with simulations of the
cometary tails showed that it was indeed plausible that the plasma tail was
observed already centuries before 1769. Indeed, _Silverman and Limor_ (2021)
show that observations of the great comet of 1577 is clearly described as
having two tails in various sources.

####  2.6.6 Sounding the plasma tail

_Iju et al._ (2015) used distant radio sources and scintillation of the signal
to determine the electron density in the tail of comet C/2021 S1 ISON. This
interplanetary scintillation method has been regularly used to obtain the
electron density in the solar wind and its structures such as ICMEs (_Hewish
et al._ , 1964; _Gapper et al._ , 1982). This effect was first seen in a
cometary tail (C/1973 E1 Kohoutek) by _Ananthakrishnan et al._ (1975), and
_Lee_ (1976) used that signal to estimate the electron density fluctuations in
the tail with a value of $\Delta N_{e}\approx 80$ cm-3.

Using five consecutive nights, 13 - 17 November 2013, _Iju et al._ (2015)
obtained scintillation measurements of one radio source through the cometary
tail, from which they could derive the local electron density. There were no
ICMEs passing through the field of view on 13, 16 and 17 November, but the
electron density was determined for all nights. Normally, the number density
increases towards the centre of the cometary tail (see e.g. _Meyer-Vernet et
al._ , 1986), however what was measured was that the electron density
increased as the radio source moved towards the edge of the cometary tail.
This increase is thought to be created by an outburst of the comet (_Combi et
al._ , 2014) or by turbulence on the boundary between the tail and the solar
wind.

Figure 8: Overview of large scale boundaries observed by spacecraft at comets,
not to scale. The gray arrow indicates the boundaries covered by Rosetta.
Credit: E. Behar, adapted from _Goetz et al._ (2021a).

###  2.7 Induced Magnetospheric Activity

A notable feature of comets are the near-linear regions of enhanced brightness
emerging from the coma around the nucleaus, which bend backwards towards the
tail (e.g., _Wurm_ , 1963). These are so-called cometary or ion rays
(_Eddington_ , 1910; _Rahe_ , 1968). Attempts to understand the physics of ray
formation did not start until _Alfvén_ (1957)’s paper on tail formation, which
explains the bend-back of the rays, however, not the brightness variations.
Observations of comet Morehouse, 1P/Halley and others showed that the rays are
most likely created by ionization of H2O, CO and CO2 close to the nucleus,
which happens in a discontinuous way (_Rahe and Donn_ , 1969). Abrupt currents
closing through the “head” of the comet, generated by tail reconnection (see
Sect. 2.8), can act as an extra source for ionization in the coma. _Wolff et
al._ (1985) also considered cometary rays to be channeled outflow of cometary
ions along magnetic flux tubes. However, flux tubes entering the cometary
ionosphere through the Kelvin-Helmholtz instability on the ionopause 3. _Ip_
(1994) expanded on this model by positing that modification of the electron
heat conduction is cause for variations along the flux tubes.

Estimates for the tail magnetic field strength were performed by _Ip and
Mendis_ (1975), who derived a magnetic field of $\geq 100\gamma$ (now nT) for
comet C/1973 E1 Kohoutek, which is similar to the field measured at comet
21P/Giacobini-Zinner (_Slavin et al._ , 1986b) and around 67P (_Goetz et al._
, 2017). This value was determined through observations of a helical structure
that moved down the cometary tail (_Hyder et al._ , 1974). Assuming that this
wave moves at the Alfvén velocity, and that it was created by a kink-mode
instability, _Hyder et al._ (1974) came up with a necessary tail current of
$I\approx 2\times 10^{7}$ A, which was later adjusted by _Ip and Mendis_
(1975) to $I\approx 2\times 10^{6}$ A.

Similar helical waves were also observed in the tails of comets C/1973 E1
Kohoutek, C/1908 R1 Morehouse and C/1956 R1 Arend-Roland by _Ershkovich and
Heller_ (1977). These authors modeled the tail as a cylinder, which is
separated from the solar wind by tangential discontinuities. They determined
the dispersion relation for helical waves for an ideal compressible plasma,
and for typical parameters the phase velocity of these waves was found to be
close to the Alfvén velocity. The authors conclude that the origin of the
waves lies in the Kelvin-Helmholtz instability.

Interest in tail currents was generated through the temporal variations in the
observed brightness, e.g. in CO+ close to the nucleus (_Wurm_ , 1961) and the
cometary rays. _Ip and Mendis_ (1976) discussed how the folding of the
cometary rays generates a strong tail field through accumulation of magnetic
flux. Flux conservation leads to a field strength $B_{\rm t}$ of the tail:

$B_{\rm t}\approx\frac{B_{0}v_{\rm s}t_{\rm f}}{h_{\rm t}},$ (9)

where $B_{0}\approx 5$ nT and $v_{\rm s}\approx 300$ km/s are the solar wind
magnetic field and velocity and $h_{\rm t}\approx 5\times 10^{4}$ km is the
half-width of the tail. These assumptions lead to rather strong magnetic
fields, $B_{\rm t}\approx 1500$ nT, but it was realised that this folding
leads to, similar as in Earth’s magnetotail, two regions of oppositely
directed magnetic field, as in the model by _Alfvén_ (1957). Between these two
lobes there needs to be a cross-tail current sheet, given by Ampère’s law:

$\displaystyle\nabla\times{\bf B}=\mu_{0}{\bf
J}+\frac{1}{c^{2}}\frac{\partial{\bf E}}{\partial t}.$ (10)

_Ip_ (1979) assumed that (part) of this current can suddenly be channeled
through the cometary atmosphere by a process to avoid a magnetic catastrophy.
This could happen in a similar way as in Earth’s magnetotail during a substorm
(_Boström_ , 1974). This current will then flow along the field lines towards
the coma, and can be used to increase the ionization rate near the nucleus.

_Israelevich and Ershkovich_ (2014) studied the magnetotails of Titan, Venus
and comet 1P/Halley. Using the _Giotto_ flyby, they showed that the magnetic
tension of the draped magnetic field lines, given by $T=({\bf
B}\cdot\nabla){\bf B}$ is always pointing tailward because of the specific
geometry of the field. A mean tension of $T\ \approx 1600\ {\rm nT}^{2}/R_{\rm
dc}$, with $R_{\rm dc}=4000$ km, the radius of the diamagnetic cavity. With
$B\approx 80$ nT they estimate a curvature radius of the field lines of
$R_{\rm c}\approx 4R_{\rm dc}$. This is important for tail detachment events
discussed below.

The connection between the solar wind and the folding of cometary ion rays was
clearly shown by _Degroote et al._ (2008), studying ion rays at comet C/2004
Q2 Machholz. They combinined telescopic U-band observations with SOHO solar
wind measurements and suggested that the ion rays were formed and folded back
through a sudden change of the solar wind from slow to fast.

###  2.8 Magnetic Reconnection

The presence of oppositely directed magnetic field throughout the induced
cometary magnetosphere, in the nested/dynamic draping upstream and the two
lobes downstream of the nuclues gives rise to the assumption that reconnection
events should be ubiquitous.

As mentioned in Sect. 2.5 changing directions of the IMF over time leads to a
nested draping of magnetic field around the outgassing nucleus. The rotations
of the magnetic field create current sheets, which can be observed when high-
enough resolution data are available (see, e.g., _Volwerk et al._ , 2017).
These current sheets are usually the location where reconnection will occur.

There was much less nested draping observed by VEGA 1 (see e.g., _Volwerk et
al._ , 2014, figure 3), and inside the coma the plasma instrument did not
measure any solar wind ions (see Sect. 3.4). But near closest approach the
plasma instrument showed bursts of 100 - 1000 eV ions over a period of 5
minutes. _Verigin et al._ (1987) showed the magnetic topology of the site at
which the bursts were observed and proposed a reconnection region, which
accelerates the ions.

_Kirsch et al._ (1989) showed that during the magnetic field rotations there
is a peak in field-aligned high-energy ions and a drop in the low-energy ions.
They calculated the energy of the ions assuming that they are accelerated over
50000 km through reconnection and found a maximum energy of $E_{\rm i}\approx
22$ keV, but this is well below the observed energies of 97 - 145 keV.

These are indirect indications that magnetic reconnection could be taking
place in the nested draping region, and only a multi-probe mission could give
a more precise answer. However, one should also realise the reconnection rate,
as determined by _Sweet_ (1956) and _Parker_ (1957) is probaly very much
reduced because of the high plasma densities in the coma. The rate is
proportional to $1/\sqrt{\rho}$, where $\rho$ is the plasma density, for slow
reconnection, and $\propto 1/\ln S$ for fast reconnection (_Petschek_ , 1964),
where $S$ is the Lundquist (or magnetic Reynolds) number.

The magnetic field measurements by ICE showed a clear draping pattern of the
magnetic field around the comet, reminiscent of the Earth’s magnetotail. The
spacecraft passed through two regions of oppositely directed field, which were
separated by a current sheet of $\sim 200$ km thickness (_Slavin et al._ ,
1986a, b). The current density was determined by _McComas et al._ (1987) and
with that the ${\bf J}\times{\bf B}$-force was calculated, which was negative,
re-accelerating the plasma tailward. Such a magnetotail, comparable with
Earth’s, will experience instabilities driven by external (e.g. by the solar
wind) forces or internally through e.g. flux accumulation. These instabilities
can give rise to magnetic reconnection and in the most drastic version a tail
disconnection event can take place (e.g. _Niedner and Brandt_ , 1978)

Solar wind sector boundaries interact with a comet’s induced magnetosphere, as
well as other structures such as ICMEs (see e.g., _Möstl et al._ , 2014), will
influence the magnetospheric activity. _Vourlidas et al._ (2007) studied comet
2P/Encke interacting with an ICME using STEREO-A’s SECCHI HI-1 instrument. As
an ICME passes over the comet, part of the tail is disconnected and
transported away by the solar wind. After the tail disconnetion, the
magnetotail slowly grows again to “full length.”

To further study tail detachment events one has to turn to numerical
simulations to model the interaction of a cometary tail and the solar wind and
its structures. _Jia et al._ (2009) modeled the tail detachment event of comet
2P/Encke. This interaction was modeled with an MHD code, which showed that a
sudden $180^{\circ}$ rotation of the IMF caused a reconnection event at the
upstream side of the comet. As the model was based on only a single species of
ions, the speed of the evolution was slower than observed. A change to
multiple ion species, cometary and solar wind ions, might improve the
agreement with the observations. Also, this model only looks at one type of
ICME-tail interaction.

Comet 153/Ikeya-Zhang experienced multiple interactions with ICMEs (_Jones and
Brandt_ , 2004). These interactions showed evidence of possible shocks
travelling along the length of the tail, which created a disruption and a
disconnection of part of the tail.

_Edberg et al._ (2016b) found that with the CIR interaction (see Sect. 2.3)
there was a sudden reduction in the piled-up magnetic field, combined with an
increase in energetic electrons. This could be evidence a tail disconnection
event the comet’s ionospheric response.

Similarly, there was an interaction with an ICME (see Sect. 2.3), which
compressed the magnetophere (_Edberg et al._ , 2016a). Large spikes on the
magnetic field data were observed and these were assumed to be created through
reconnection of the magnetic field lines of the ICME with the draped field
lines around the nucleus. Due to the lack of plasma tail observations for 67P,
it is not clear whether this interaction led to a tail disconnection event,
and it need not have done.

Even though IMF reversals, through whatever means (sector boundaries, ICMEs,
CIRs), or shocks can generate tail disconnection events, there is not a one-
to-one correlation between the two. _Delva et al._ (1991) used the data from
the VEGA 1/2 for the period of 1 December 1985 to 1 May 1986 (which includes
the flybys at 6 and 9 March 1986 of comet 1P/Halley) and disconnection events
observed by ground-based observatories. The authors correlated the crossing of
sector boundaries of the solar wind with tail disconnection events. If changes
in the solar wind (_Jockers_ , 1985) generate day-side reconnection (_Niedner
and Brandt_ , 1978), then one should find a good correlation. In all, _Delva
et al._ (1991) determined that 50% of the events showed a correlation between
sector boundary crossing and tail disconnection. The authors also state that
density enhancements in the solar wind are connected to events in the tail.

The first direct observation of an ICME interacting with a comet (but not the
first one published in the literature) was done with the Solar Mass Ejection
Imager (SMEI) looking at comet C/2001 Q4 (NEAT) in 2004 (_Kuchar et al._ ,
2008). The ICME first created a kink in the tail, which moved anti-sunward,
which developed into knots. This seems to be a general behaviour, as seen in a
handful of other events. The generation of the knots, evidence for the
disruption of the tail, can result from various effects like shocks or
polarity reversals of the magnetic field in the ICME.

Comparison of events at comet C/2001 Q4 (NEAT) with those of comet C/2002 T7
(LINEAR), and tracing them back along the Parker spiral shows that these occur
preferably when the comet is near the heliospheric current sheet (_Kuchar et
al._ , 2008). _Brandt et al._ (1999) and _Brandt and Snow_ (2000) also
concluded this effect using observations of comets 1P/Halley, 122P/de Vico,
C/1996 B2 Hyakutake, and C/1995 O1 Hale-Bopp.

_Li et al._ (2018) performed laboratory experiments to study tail detachment
events. They used a laser-driven plasma which collides with a cylindrical
obstacle. Behind the obstacle detached tails are measured. At the same time
numerical simulations of this interaction were performed. However, it should
be noted that this was an unmagnetized interaction. The experiment showed that
an electrostatic field is created in the plasma when the density is high,
because of a temperature difference between the ions and the electrons. This
field leads the plasma ions to converge in a tail and move away form the
obstacle, giving the impression of a detached tail. The authors argue that
this is a viable process to explain a detached tail, because the physical
sizes related to cometary effects are shorter than the gyro radius of cometary
ions in the solar wind, invalidating an MHD approach.

##  3 Boundaries/Regions

###  3.1 Overview

Comet interactions with the solar wind begin at great distances from the comet
because the high neutral outgassing rate leads to mass-loading of the solar
wind (_Galeev and Sagdeev_ , 1988). Closer to the nucleus, this interaction
leads to the formation of large scale structures in the form of boundaries
that separate regions characterized by plasmas with differing parameters.
Prior to spacecraft flybys of comets, computer simulations of the solar wind
interaction with the comet predicted the existence of two permanent
boundaries: a bow shock and a contact surface (_Schmidt and Wegmann_ , 1982;
_Ip and Axford_ , 1982). These boundaries established three regions of comet-
solar wind interaction: an upstream region outside of the bow shock, a region
between the bow shock and contact surface termed the cometosheath, and a
diamagnetic cavity located between the contact surface and the nucleus. After
spacecraft made in situ observations during several flybys and the escort of
comet 67P by _Rosetta_ , several other boundaries were also observed: the
cometopause, an ion pileup boundary, and ion-neutral and electron-neutral
collisionopauses. Plasma interaction boundaries observed at a comet can be
permanent features, solar wind and interplanetary magnetic field boundaries,
or small-scale transient features created by waves or instabilities (_Cravens_
, 1989). Permanent features include shocks and collisionopause boundaries.
Shocks form when the relative velocity of the plasma and an obstacle, in this
case the cometary plasma, exceed the characteristic speed of waves in the
plasmas. As discussed in Sect. 3.5, a collisionopause forms when collisions
between neutrals and ions or electrons change characteristics of the plasma
such as composition or velocity (_Mendis et al._ , 1986; _Cravens_ , 1989,
1991). _Cravens_ (1991) outlined various types of collisionopause for both
ions and electrons depending on the collision processes and the reactions that
may occur, including ion-neutral charge transfer and ion-neutral chemistry.
Fig. 8 illustrates the boundaries that are discussed in this section. We
review here observations of five boundaries that were determined to be
permanent features (_Gringauz and Verigin_ , 1991).

###  3.2 Bow Shock

The bow shock is the location where the solar wind flow transitions from
supersonic to subsonic as a result of mass loading. Simulations predicted, and
spacecraft observations confirmed that this boundary would be broad and weak
compared to planetary bow shocks because the slowing of the solar wind begins
well upstream of the shock (see also Sect. 6). Spacecraft observations have
noted sudden changes in the plasma density and velocity across the bow shock
and an enhancement of the magnetic field (_Galeev and Sagdeev_ , 1988). The
detailed physics of the cometary bow shock formation and early modeling
efforts are described in Section 3 of _Ip_ (2004) while spacecraft
observations prior to _Rosetta_ are outlined in Section 4.1 of _Ip_ (2004).
_Rosetta_ ’s exploration of the plasma environment around 67P has
significantly advanced our understanding of cometary bow shocks for weakly
outgassing comets. Hybrid modeling of the comet found that including electron
impact ionisation and charge-exchange processes in addition to photo-
ionization increased the standoff distance of the bow shock along the Sun-
comet line by more than a factor of six, as illustrated in Fig. 9.
Furthermore, simulations also showed that asymmetric outgassing and
illumination driven outgassing can extend the standoff distance even further
(_Huang et al._ , 2016; _Alho et al._ , 2020). The _Rosetta_ spacecraft did
not travel far enough from the comet to cross the bow shock during outgassing
rates relevant to these simulations.

Figure 9: Illustration of how the simulated distance of the bow shock from the nucleus increases compared to simulations with only photo-ionization (PI) when the influence of electron-impact ionization (EI) and charge-exchange processes (CX) are included (Adapted from Fig. 11 in _Simon Wedlund et al._ (2017)). Number | Type | Example
---|---|---
R1 | Ion-neutral charge transfer | H2O${}_{\text{fast}}^{+}$ | + | H2O | $\rightarrow$ | H2O${}_{\text{fast}}$ | + | H2O+ |  |
R2 | Ion-neutral chemistry | H2O+ | + | H2O | $\rightarrow$ | H3O+ | + | OH |  |
R3 | Ionization | H${}_{\text{fast}}^{+}$ | + | H2O | $\rightarrow$ | H${}_{\text{fast}}$ | + | H2O+ | + | e-
R4 | Electron removal | O | + | H2O | $\rightarrow$ | O+ | + | H2O | + | e-
R5 | Ion-electron recombination | H3O+ | + | e- | $\rightarrow$ | OH | + | 2H |  |
R6 | Ion-ion coulomb interaction | H2O+ | + | H2O+ | $\rightarrow$ | H2O+ | + | H2O+ |  |
Table 1: Summary table of collisional processes that can take place in the
cometary plasma.

The greatest advantage of _Rosetta_ in advancing our understanding of cometary
bow shocks was thanks to the extended amount of time spent escorting the comet
around the Sun. This allowed detection of the bow shock as it began to form,
or an infant bow shock (_Gunell et al._ , 2018). Statistical analyses of the
full _Rosetta_ dataset showed that the spacecraft encountered the infant bow
shock multiple times between 3.0 and 1.7 AU inbound to the Sun and then again
outbound starting at around 1.8 AU (_Goetz et al._ , 2021b). Additionally, a
method for detecting the existence of a bow shock from inside the shock was
discovered. The energy of ions at the spacecraft location that were
accelerated by a constant electric field upstream of the spacecraft is
proportional to the distance from the place where the ions were initially
created. This was used to determine that a bow shock had formed at a distance
of $\sim 4000\,$km from the nucleus when the comet was 1.4 AU from the Sun
(_Nilsson et al._ , 2018). This was confirmed with hybrid simulations (_Alho
et al._ , 2019) that were later used to determine the spectral features in ion
energy that could indicate the presence of a bow shock upstream of the
spacecraft (_Alho et al._ , 2020). Similarly, a bimodal ion distribution found
in the environment of comet 1P/Halley indicated that ions produced before and
after the bow shock are observed as two distinct populations, indicating that
the acceleration history of the ions is preserved (_Thomsen et al._ , 1987).

Although we have learned a great deal about cometary bow shocks, we are
lacking observations that cover sufficient space and production rate to fully
understand the transition between an infant bow shock and a full shock as well
as the implications of asymmetric outgassing on the location and shape of the
bow shock. Future observations should include simultaneous measurements at
multiple points in space (_Snodgrass and Jones_ , 2019) and multi-spacecraft
missions over long time periods (_Götz et al._ , 2019), which should be
combined with simulations that treat electrons and ions kinetically resolving
all relevant scales (_Balogh and Treumann_ , 2013).

###  3.3 Cometopause

The concept of the cometopause is introduced in Section 4.3 of _Ip_ (2004),
which discusses ion properties inside of the bow shock over a wide distance
range. We have learned a great deal more from _Rosetta_ about the interaction
between the solar wind and the coma inside of the cometopause. We outline here
what new understanding we have gained about the cometopause and introduce new
regions and boundaries that were discovered by _Rosetta_.

The cometopause is described as the boundary where the ion composition changes
from predominantly solar wind ions to predominantly cometary ions (_Gringauz
et al._ , 1986; _Mendis et al._ , 1989; _Coates_ , 1997). Although some
dispute the existence of this boundary (_Rème et al._ , 1994), it was
determined by several researchers to be a permanent feature (_Gringauz and
Verigin_ , 1991; _Sauer et al._ , 1995). Several authors have proposed that
the cometopause is the location where collisions causing charge exchange
between solar wind protons and cometary neutrals become dominant (_Gringauz et
al._ , 1986; _Gombosi_ , 1987; _Cravens_ , 1989; _Ip_ , 1989), a form of
collisionopause boundary ((see Table 1) and 3.5). However, this is not an
appropriate explanation for the cometopause as explained in 3.5. Instead, as
theoretical simulations suggest, the cometopause is best explained by
deflection of solar wind protons (_Sauer et al._ , 1995). _Giotto_ observed
plasma flux deflection that indicated plasma flow forced around a comet
(_Perez-de Tejada_ , 1989), suggesting that the cometopause could be the
beginning of the solar wind ion cavity (see Sect. 3.4). Previous work stated
that _Rosetta’s_ instruments did not observe the cometopause (_Mandt et al._ ,
2016), but if this is the boundary of the solar wind ion cavity then it may
have been observed several times as it was forming (_Behar et al._ , 2017).
Further work is needed to better understand the physics of this region of the
cometosphere.

###  3.4 Solar wind ion cavity

From May to December 2015 _Rosetta_ was located in a region that was mostly
free from solar wind ions, a region termed the solar wind ion cavity (_Nilsson
et al._ , 2017; _Behar et al._ , 2017). This cavity was determined to have
formed as a result of the deflection of the solar wind ions by magnetic pileup
that results from mass loading of the solar wind. Prior to the disappearance
of the solar wind ions, the ion instruments observed deflection of the solar
wind that increased over time as shown in Fig. 10. When the ion deflections
were greater than 90 degrees, ion observations became less frequent and had
lower densities until they disappeared. Deflections were observed to be very
large near the boundary of the cavity, possibly in the region of the
cometopause. A simple analytical model that estimates the global dynamics of
solar wind protons for a given heliocentric distance provided strong agreement
with observed deflection angles during _Rosetta’s_ nightside excursion,
validating understanding of how the solar wind ions gyrate withing the coma
and how they are repelled from the inner-most region to form an ion cavity
(_Behar et al._ , 2018). Although the solar wind ions are deflected away from
the solar wind ion cavity, cometary ions picked up by the solar wind and the
solar wind magnetic field are still present even though the pickup ions are
deflected in a similar manner to the solar wind ions (_Nilsson et al._ ,
2020). The boundary also does not constitute a discontinuity in the momentum
budget, but just a change in the composition of the plasma flow (_Williamson
et al._ , 2020). _Edberg et al._ (2016a) showed that the impact of an ICME can
compress the solar wind ion cavity, indicating that the solar wind dynamic
pressure regulates the size of this region.

Figure 10: Observations of the increasing deflection of solar wind protons and
alpha particles as comet 67P approached the Sun from September 2014 to May
2015, the formation of the solar wind ion cavity between May and December
2015, and the decreasing deflection of solar wind ions as the comet moved away
from the Sun after December 2015 (adapted from Fig. 1 of _Behar et al._
(2017)).

###  3.5 Ion-neutral collisionopause

Collisions within an atmosphere or coma influence the dynamics and chemistry
of neutrals and ions. The term collisionopause is used to define a boundary
inside of which collisions play a dominant role. We describe in this section
ion-neutral collisionopause boundaries, and cover the electron-neutral
collisionopause in Sect. 3.6.

The location of an ion-neutral collisionopause is calculated in a manner
similar to determine the location of the exobase in aeronomy, or the study of
neutral atmospheres. In the case of a steady state atmosphere, the exobase is
the location is where the Knudsen number, or the ratio of the mean free path,
$\lambda$ to the scale height, is one.

$\displaystyle\lambda=\frac{1}{n_{n}\sigma}.$ (11)

where $n_{n}$ is the neutral density and $\sigma$ is the collision cross
section. In aeronomy, when determining the location of the neutral exobase the
cross-section is the species-specific neutral collision cross-section. This
means that each species has its own exobase. For an ion-neutral
collisionopause, the cross-section would be the collision cross-section for
the relevant ion species with water. In the coma, the neutral density,
$n_{n}$, as a function of distance from the comet can be approximated as

$\displaystyle
n_{n}(r)=n_{\text{s/c}}\left(\frac{r_{\text{s/c}}}{r}\right)^{2}$ (12)

where $r$ is the distance from the nucleus, $n_{s/c}$ is the density at the
spacecraft, and $r_{s/c}$ is the distance of the spacecraft from the nucleus.

The scale height is the distance over which the density of a neutral species
or the plasma reduces by a factor of $e$. _Rosetta_ observations suggested
that the plasma scale height at the location of _Rosetta_ when escorting 67P
could be approximated by the distance of the spacecraft from the comet, $r$
(_Edberg et al._ , 2015). Therefore the location of both ion-neutral and
electron-neutral collisionopause boundaries could be found by setting the mean
free path equal to the distance from the comet

$\displaystyle\lambda=r=n_{\text{s/c}}\sigma r_{\text{s/c}}^{2}$ (13)

In the case of _Rosetta_ , the neutral density was measured at the spacecraft
location, making this a reasonable equation to use for determining where a
collisionopause would be located based on local measurements. A
collisionopause distance can also be calculated by substituting for $n_{s/c}$
with the outgassing rate, $Q$, which is a function of $n_{s/c}$ and the
neutral outflow velocity, $v_{n}$

$\displaystyle Q=4\pi r^{2}n_{\text{s/c}}v_{n}$ (14)

_Cravens_ (1991) outlined various types of collisionopause for both ions and
electrons depending on the collision processes involved, which are outlined in
Table 1. Reactions of type R1 are charge transfer reactions where the charge
is transferred from a fast ($<300$ km/s) ion in the mass loaded solar wind
flow (e.g. H+ or H2O+) to a neutral travelling away from the comet at
velocities of $1\,$km/s or less. As a result of this reaction, the ion becomes
an energetic neutral, and the bulk velocity of the ions is reduced. Chemical
reactions like R2 not only reduce the bulk velocity of the ions, but also
alter the relative composition of the ion population. For example, in reaction
R2, a proton is transferred from H2O+ to H2O, creating an H3O+ ion, increasing
the bulk mass 19/18 ratio of the ion population. If H2O+ is fast it will end
as an energetic OH neutral while H3O+ will have the same energy as the
neutrals. Another chemical reaction that should be noted is the proton
transfer from H3O+ to NH3 producing NH${}_{4}^{+}$ in the dense coma (_Beth et
al._ , 2016). This reaction depends on the volume mixing ratio of NH3 in the
coma and would reduce the mass 19/18 ratio, countering the effect of producing
H3O+.

As outlined in _Mandt et al._ (2019), the collision cross-section is the
greatest source of uncertainty for calculating ion-neutral collisionopause
distances. In early studies, the ion-neutral cross-section was estimated to be
$2\times 10^{-15}\text{cm}^{2}$ for solar wind ions and $8\times
10^{-15}\text{cm}^{2}$ for mass loaded solar wind with a bulk composition of
$H_{2}O^{+}$ (_Mendis et al._ , 1986). We illustrate in the shaded blue region
of Fig. 11 the calculated location of the collisionopause throughout the
_Rosetta_ mission based on these cross-sections. Note that because the solar
wind ion cross-section is smaller than the cross-section for water ions, the
collisionopause location calculated with Eq. (13) for charge transfer of solar
wind ions will be closer to the nucleus than the collisionopause for picked up
cometary ions. _Rosetta_ made several observations of a boundary where the
bulk ion velocity transitioned between values greater than 10 km/s outside of
the boundary to velocities too low to measure directly because the ions were
seen at the value of the spacecraft potential that were interpreted to
represent a cometary ion collisionopause (_Mandt et al._ , 2016). However,
most of these observations were within the solar wind ion cavity (_Mandt et
al._ , 2016), meaning that the spacecraft was inside of the cometopause. This
demonstrates that the cometopause is not a collisionopause and is instead a
boundary formed as a result of deflection of the solar wind ions.

Figure 11: Calculated location of the cometary ion collisionopause (blue
shaded region) and the electron exobase (red dashed line) compared to the
distance of _Rosetta_ (black line) from the comet nucleus (gray shaded
region).

Furthermore, although the boundary was observed within the range of predicted
locations illustrated in the shaded blue region of Fig. 11, it appeared to
vary in distance depending on solar wind dynamic pressure (_Mandt et al._ ,
2016) similar to the cometopause (_Edberg et al._ , 2016a). Laboratory
measurements show that the cross-sections for reactions (R1) and (R2) depend
on the energy of the ions (_Lishawa et al._ , 1990; _Fleshman et al._ , 2012).
A comparison of these cross-sections as a function of energy with the
_Rosetta_ observations of cometary ion collisionopause crossings (_Mandt et
al._ , 2016), observations made by _Giotto_ at 1P/Halley (_Schwenn et al._ ,
1988; _Altwegg et al._ , 1993), and observations made by Deep Space 1 at
19P/Borelly (_Young et al._ , 2004) found that the collisionopause had been
observed at all three comets and appeared to form as a result of a combination
of reactions (R1) and (R2) (_Mandt et al._ , 2019).

Many questions remain about this region of the cometosphere and the role of
collisions in influencing the dynamics of cometary ions that have been picked
up by the solar wind. A greater understanding of cross sections is needed and
more observations of ion and neutral composition would be of high value.
Additionally, measurements of the electron temperatures are needed to
constrain the electron recombination rates in this region and inside of the
collisionopause.

###  3.6 Electron-neutral collisionopause

Collisions between electrons and neutrals in the coma will cool the electrons
to temperatures similar to the neutral gas temperature (_Eberhardt and
Krankowsky_ , 1995). The electron-neutral collisionopause, also called the
electron exobase, represents the boundary outside of which collisions do not
efficiently influence the electron temperatures. The location of the electron
exobase calculated using Eq. (13) and a cross-section of $5\times
10^{-16}\text{cm}^{2}$ is illustrated in Fig. 11. As shown here, _Rosetta_ was
not expected to cross inside of the electron exobase. However, additional
processes can enhance the electron collision rate, and thus electron cooling
can extend the location where electrons thermalize to the same temperature as
the neutrals beyond the calculated exobase location (_Henri et al._ , 2017).
These processes include rotational and vibrational cooling for electrons
orginating close to the nucleus where electrons pass through the densest gas
(_Engelhardt et al._ , 2018b), and possibly through an ambipolar electric
field either trapping electrons in the dense neutral region (_Madanian et al._
, 2016; _Vigren and Eriksson_ , 2019) or increasing the electron collision
cross-section by slowing their outward movement (_Engelhardt et al._ , 2018b).

At several points during the mission _Rosetta’s_ instruments observed a
population of cold electrons that at times made up as much as 90% of the
electron population (_Engelhardt et al._ , 2018b; _Gilet et al._ , 2020).
_Henri et al._ (2017) found a relationship between the location of the
electron exobase and the diamagnetic cavity boundary (DCB, Sect. 3.7). These
observations confirmed that electron cooling is more efficient than suggested
by the simple approximation shown in Eq. (13) and that a more comprehensive
cooling model is required to estimate the location of the electron exobase
(see also Sect. 2). Furthermore, because _Rosetta_ did not explore the coma at
a close enough distance to the nucleus, in situ measurements of the electron
neutral collisionopause are lacking. Future exploration of this region,
measuring the ion and neutral composition and the electron densities and
temperatures would be of high value.

###  3.7 Diamagnetic cavity

The mass-loading of the solar wind by cometary ions was predicted to
decelerate the solar wind until the velocity reached zero upstream of the
comet under high outgassing rates (_Biermann et al._ , 1967). Because the
solar wind magnetic field is tied to the solar wind plasma, the magnetic field
was predicted to come to a stop creating a magnetic field free region around
the nucleus (_Schmidt and Wegmann_ , 1982; _Ip and Axford_ , 1982). The first
confirmation that a diamagnetic cavity could form in the conditions provided
by a coma was during the Active Magnetospheric Particle Tracer Experiment
(AMPTE). The magnetic field briefly dropped to zero after release of a Barium
cloud, confirming the formation of a field-free region (_Luehr et al._ ,
1988). The boundary of this region was found to be where the electron thermal
pressure equalled the magnetic field pressure.

The _Giotto_ spacecraft flew close enough to comet 1P/Halley to pass within
the predicted region where the diamagnetic cavity was expected to exist. The
magnetic field measurements showed that the field magnitude dropped to and
remained at close to $0\,$nT around $5000\,$km from the comet nucleus. The
observations suggested that the boundary of the diamagnetic cavity was not
symmetric about the nucleus, and may have ripples across its surface
(_Neubauer_ , 1988). The position of the boundary was expected to be
determined by a balance of outward ion-neutral drag and inward magnetic
gradient forces (_Gringauz and Verigin_ , 1991; _Coates_ , 1997). Besides
Giotto at 1P/Halley, no other spacecraft directly observed the diamagnetic
cavity previous to the Rosetta mission. However, a decrease in HCO+ emissions
in the innermost coma of comet Hale-Bopp was speculated to be associated to
the diamagnetic cavity. As Hale-Bopp is much more active than 1P/Halley, the
diamagnetic cavity was predicted to be around $500000\,$km in size, which
coincided with a drop in emissions (_Womack et al._ , 1997). It should be
noted that in early works the solar wind ion cavity boundary and the
diamagnetic cavity boundary were identified to be in the same place. However,
Rosetta observations have clearly shown that the solar wind ion cavity is most
of the time much larger than the diamagnetic cavity. This is because the solar
wind ions are deflected upstream and the pick up ions take over the role of
the solar wind flow and carry the magnetic field into the inner coma where it
is eventually stopped at the diamagnetic cavity boundary.

Prior to the Rosetta mission, several modelling studies for 67P were conducted
to project the location of the diamagnetic cavity. Single fluid MHD
simulations predicted that the cavity would form around 50 km from the nucleus
within two months of perihelion, while multifluid simulations showed that the
boundary could be extended on the sunward side by an asymmetric outgassing
profile (_Huang et al._ , 2016). Hybrid simulations agreed with these results.
However, clear signatures of a magnetic field free region were observed at
distances as great as 400 km from the nucleus much earlier in the mission when
the comet was within 2 AU of the sun inbound and continued until the comet had
reached 2.4 AU from the Sun outbound (_Goetz et al._ , 2016a, 2018). In fact,
the diamagnetic cavity was crossed into by the spacecraft over 700 times,
indicating a highly variable boundary. The extension of the diamagnetic cavity
was shown to be dependent on the gas production rate, with higher gas
production rates leading to larger sizes of the diamagnetic cavity.

The ions inside the diamagnetic cavity are usually found to be quite constant
in density and velocity, except for sporadic enhancements (see below). The ion
velocity of the constant low velocity population is around $5-10\,$km/s
(_Bergman et al._ , 2021). This is significantly higher than the neutral gas
velocity ($\leq 1\,$km/s, _Hansen et al._ , 2016), which indicates that there
must be an acceleration mechanism for those ions. It is speculated that an
ambipolar field caused by the electron pressure gradient of the expanding
plasma accelerates these ions (_Vigren and Eriksson_ , 2019). At the same
time, the ions cannot collide frequently with the neutral gas, as that would
cause ion cooling and a reduction in velocity.

This is quite interesting since for comet 1P/Halley, the collisions between
neutral gas and ions were identified as the process that prevents the magnetic
field from diffusing or convecting into the diamagnetic cavity (_Cravens_ ,
1987). Therefore another process must be at play at comet 67P, but it is still
an open question which one it is.

A series of asymmetric, steepened waves were visible in the magnetic field and
plasma density outside of the boundary (_Goetz et al._ , 2016a; _Stenberg
Wieser et al._ , 2017; _Hajra et al._ , 2018; _Ostaszewski et al._ , 2020) and
in the shape of the boundary itself (_Goetz et al._ , 2016b). The unmagnetised
plasma density inside of the cavity scales well with the neutral density
(_Henri et al._ , 2017). Observations of dense plasma events when the
spacecraft was inside of the boundary (_Hajra et al._ , 2018; _Masunaga et
al._ , 2019) provided indications that plasma from outside of the diamagnetic
cavity boundary could possibly penetrate into the cavity.

The electron environment changes at the diamagnetic cavity boundary: electrons
in an energy range of $100-200\,$eV are ubiquitous outside of the diamagnetic
cavity, but depleted inside the diamagnetic cavity (_Nemeth et al._ , 2016).
These electrons probably originate from the solar wind (strahl electrons) and
are tied to the magnetic field. As the magnetic field decreases into the
diamagnetic cavity, the electrons are adiabatically transported and become
field aligned. Therefore, without a perpendicular component, they cannot cross
field lines and enter the diamagnetic cavity (_Madanian et al._ , 2020).

The relationship between observations of the electron exobase and the
diamagnetic cavity boundary (_Henri et al._ , 2017) suggest that the mechanism
determining the distance of the boundary from the nucleus is related to
electron neutral collisions and that the location of the boundary could change
quite rapidly as a result of instabilities. _Huang et al._ (2018) showed that
the introduction of a Hall term in an MHD multi-fluid model could also lead to
an extension of the diamagnetic cavity as well as the formation of filaments
extending away from the main diamagnetic cavity boundary, similar to an
instability as described above. In general, the _Rosetta_ observations were
unexpected and many questions remain about the mechanisms involved in forming
and determining the location of the dimagnetic cavity boundary. In particular,
the pressure balance at the boundary is not well understood, nor the role of
the changing plasma environment in the movement of the boundary. Why is there
evidence for ion acceleration at 67P within the cavity but not at 1P/Halley?
The processes that cool and/or accelerate electrons and ions in and near the
cavity are poorly known, as well as the process for transmitting plasma
enhancements through the boundary and inside the cavity. Finally, we do not
know the origin of the asymmetry in the in- and outbound crossing of the
boundary. Answering these questions would likely require multi-point
measurements of the diamagnetic cavity, its boundary, and the upstream plasma
conditions (_Goetz et al._ , 2018).

##  4 Waves

Figure 12: Examples of wave observations at comet 67P. Note that all panels
show timeseries, except for panel c) which displays a frequency spectrum for
better visibility. For descriptions see text. Credits: a) _Richter et al._
(2016), Annales Geophysicae; b) _Karlsson et al._ (2017), Geophysical Research
Letters; c) _Gunell et al._ (2017b), MNRAS; d) _Volwerk et al._ (2016),
Annales Geophysicae; e) _Stenberg Wieser et al._ (2017), MNRAS; f) _Odelstad
et al._ (2020), Journal of Geophysical Research

In general, waves in plasmas are oscillations in the properties of a coupled
system. Since any oscillations have to adhere to the plasma equations, wave
modes are discrete. Different approximations of the plasma will result in
different wave dispersion relations, thus it is important to always check the
underlying assumption of any approximation and make sure it is applicable to
the situation.

Usually, a plasma, which is initially in equilibrium, becomes unstable because
a source of free energy is added, at a comet, this source of free energy is
the presence of newly ionised cometary ions in the solar wind flow. _Goetz et
al._ (2017) found that, in general, the wave activity, or overall power
spectral density of the magnetic field at 67P, is modulated by the neutral gas
production rate, demonstrating that the addition of more ions leads to more
free energy that needs to be distributed in the plasma in order to reach
equilibrium again. This addition of free energy will induce wave-like
disturbances at a multitude of frequencies. Most of them are damped quickly
and only if the disturbances are at a frequency near a wave mode (e.g. ion
cyclotron mode) can a wave actually develop and propagate. Due to various
processes, the wave is dispersed and dissipated until the energy contained in
the original instability is evenly distributed. For a wave to be detectable by
instruments, its amplitude needs to be larger than the underlying thermal
fluctuations. In addition, plasma wave excitation and propagation depends on
the direction of the magnetic field.

Plasma waves in the cometary environment contribute to the heating and cooling
of the plasma and couple fields and particles as well as different particle
populations. Therefore the study of these waves is important in understanding
the energy and momentum transfer as well as the behaviour of particles in the
environment. Hereunder, the reader may find a list of waves that have been
detected at comets, with an emphasis on the new results from the _Rosetta_
mission to comet 67P.

##### Pick-up induced waves

If a cometary neutral is ionised in the solar wind, the resulting ion is
moving at a velocity of the negative of the solar wind velocity
($-v_{\text{sw}}$) in the solar wind frame of reference. It will therefore be
subject to the solar wind convective electric field

$E_{\text{conv}}=-\vec{v}_{\text{sw}}\times\vec{B}_{\text{IMF}},$ (15)

where $\vec{B}_{\text{IMF}}$ is the interplanetary magnetic field. Along with
the ion’s gyromotion in the magnetic field, this will lead to an $E\times
B$-drift. In velocity space, this motion describes a circle with the solar
wind ion velocity at its center. If ions are produced over a region greater
than the ion gyroradius the cometary ion distribution function will form a
full ring distribution, if the ions are produced over a region smaller than
the ion gyroradius, the ring distribution is only partial (see e. g. _Behar_ ,
2018). If the interplanetary magnetic field is parallel to the solar wind
velocity, the convective electric field is zero, and the cometary ions are not
accelerated. Then, they form a beam distribution in the solar wind frame of
reference. Both the beam and ring distribution coexist with the solar wind
beam distribution. Therefore, upstream of a comet, two ion distributions can
be used to approximate the situation: a ring-beam and a beam-beam
distribution. Both these distributions are unstable and give rise to wave
activity (e.g. _Coates et al._ , 1993).

These waves were detected at active comets and usually at high cometocentric
distances ($r_{c}>1000\,$km). In this regime, the large interaction region
allows for the ring distribution of the cometary ions to fully develop. This
was not the case for most of the _Rosetta_ mission, where the ion gyroradius
was larger or of the same order of magnitude as the size of the interaction
region. In the high activity case during the _Rosetta_ mission, the plasma
environment was larger than the ion gyroradius, but it was also inhomogeneous
at those length scales which prevents the ring distribution from developing.
Therefore a full, classical ring-beam distribution does not develop (_Nicolaou
et al._ , 2017). As a result none of the pick-up induced waves were observed
at 67P and most of the results pertaining to ring/ring-beam instabilities stem
from earlier works. For more information on those results, the reader is
referred to _Ip_ (2004).

##### Singing Comet Waves

These ultra low frequency (ULF) waves were first (and only) detected at comet
67P at low to medium gas production rates (_Richter et al._ , 2015; _Goetz et
al._ , 2020). The singing comet waves are characterized by large amplitude
magnetic field magnitude fluctuations in the frequency range of $10-100\,$mHz
and can be detected ubiquitously in the plasma environment of comet 67P for
gas production rates $Q<5\times 10^{26}\,$s-1. Figure 12a shows an example of
the magnetic field measurements from the two magnetometers of _Rosetta_ and
Philae. Their frequency is not correlated with the magnetic field magnitude
and it was therefore concluded that it was not due to an ion-cyclotron
resonance (for which the frequency correlates with the magnetic field). A new
mechanism for the generation of these particular waves was found: an unstable
cross-field current in the comet’s reference frame. At low gas production
rates, the cometary pickup ions have gyroradii much larger than the scale
length of the cometary environment ($10000$s km vs $100$s km) and therefore
the ions cannot complete a full ring distribution as it was seen at more
active comets with much larger cometary environments. Instead, they are
accelerated linearly along the electric field. Since all ions are moving in
the same direction, this constitutes a current that is parallel to the
convective electric field, but perpendicular to the magnetic field. Such a
configuration is unstable to the ion-Weibel instability and will produce
waves. This mechanism was investigated in hybrid simulations (_Koenders et
al._ , 2016b) and in an analytical model (_Meier et al._ , 2016). Although the
hybrid simulation suggests that the waves should be more ubiquitous in the
hemisphere that has a positive convective electric field, this cannot be seen
from data, where the waves are detected everywhere, without a preferential
location (_Goetz et al._ , 2020). This is not necessarily a contradiction,
because the waves could be generated in a region around the nucleus that is
larger than the distances covered by the measurements. There are some
indications that this is the case, e.g. from two-point measurements which
constrain the generation region to between $100\,$km and more than $800\,$km
in size, which is larger or of the same order than the measurement range (up
to $260\,$km in the interval covered by the study by _Volwerk et al._ , 2018).
But the exact extent of the generation region is as of yet unknown and
requires more investigation.

Two point measurements constrained the wavelength to $100$s km and found that
the length scale over which the wave trains are coherent is larger than $\sim
50\,$km (the separation of the two measurement points). This is easily seen in
the measurements (Figure 12a) where both magnetometers show the same wave
form, with only marginal deviation. The waves are compressional and, in
isolated occasions, also observable in the plasma density (_Breuillard et al._
, 2019). While a case study has found an anti-correlation of the wave
frequency with the plasma density, a statistical study covering several months
of observations could not confirm this correlation. Therefore the exact
relationship between the plasma density and the magnetic field remains an open
question.

##### Lower hybrid waves

While singing comet waves are mostly detected in the magnetic field
observations, electric field measurements also exhibit wave activity. Most
prominent among these signatures are waves in the lower hybrid frequency range
(a couple of Hz). This particular type of wave can transfer energy between
ions and electrons and is typically found in plasmas where the ions are not
magnetized, but the electrons are. If there are density gradients present in
such a plasma, a lower hybrid drift instability (LHDI) can occur and cause
lower hybrid waves (LHW) to grow.

The lower hybrid frequency $f_{\text{LH}}$ is defined as:

$f_{\text{LH}}=\frac{1}{2\pi}\sqrt{\frac{\omega_{\text{gi}}\,\omega_{\text{ge}}}{1+\frac{\omega_{\text{ge}}^{2}}{\omega_{\text{pe}}^{2}}}}\approx\frac{1}{2\pi}\sqrt{\omega_{\text{ge}}\,\omega_{\text{gi}}},$
(16)

where $\omega_{\text{gi}}$ and $\omega_{\text{ge}}$ are the ion gyrofrequency
and the electron gyrofrequency respectively and $\omega_{\text{pe}}$ is the
electron plasma frequency. At comet 67P, the approximation is usually
satisfied as the electron plasma frequency is typically much larger than the
electron gyrofrequency. Values for $f_{\text{LH}}$ are in the $1-20\,$Hz range
at 67P. Interaction of electrons with LH waves have been suggested as a
possible heating mechanism for the electrons, but no studies have attempted to
verify this.

Observations show that wave packets in the electric field are often observed
at plasma density gradients and with frequencies near those associated with
the lower hybrid wave (_Karlsson et al._ , 2017; _André et al._ , 2017). The
upper panel in Figure 12b shows the spacecraft potential, (a proxy for the
plasma density), during a plasma density gradient. The middle panel shows the
derived lower hybrid frequency, and the lower panel shows the electric field
measurements with the LH wave activity clearly visible. The amplitudes are
largest during the density gradient. Estimates of the LHDI criterion and model
results show that these observations are consistent with LH waves generated by
a LHDI and that the growth rate can be quite large so that the wave packets
can grow to significant amplitudes within a couple of seconds. The LHW can
also influence the plasma as a whole, by e.g. forcing the diamagnetic boundary
to oscillate slightly. This in turn can lead to a mode conversion, where LHW
that are generated at density gradients outside the diamagnetic cavity can be
converted to ion acoustic waves (IAW) that propagate in the unmagnetized
plasma of the diamagnetic cavity (_Madsen et al._ , 2018).

It should be noted that collisions can significantly inhibit wave growth as
they cool and slow down the electrons. Therefore, for dense plasmas such as
those encountered at comet 1P/Halley and at comet 67P close to perihelion
and/or very close to the nucleus are not favorable for LHW growth.

##### Ion acoustic waves

Ion acoustic waves (IAWs) are compressional waves in an unmagnetized plasma,
or in a plasma where the gyrofrequencies are lower than the wave frequency and
the gyroradii are larger than the wavelength. They have been observed at comet
1P/Halley’s foreshock (_Oya et al._ , 1986) and at the artificial comet AMPTE
(_Gurnett et al._ , 1985). The presence of IAW was reported at comet 67P at
multiple times during the _Rosetta_ mission, all in the plasma in the
innermost coma of 67P. IAWs can be observed in a range of frequencies, from
100s Hz up to the kHz range.

In order to verify that the observed waves are indeed IAW, calculations of the
dispersion relation using the observed ion and electron distribution function
as well as the measured plasma density can be used. Notably, all observations
were made in the inner coma, where a significant cold ion population exists
due to ion-neutral collisions. IAW grow if $T_{e}\gg T_{i}$, so that any wave
activity should be damped quickly in regions where ion cooling is
insignificant (_Gunell et al._ , 2017b). In the case that there are
accelerated water ions present, this population constitutes a beam-like part
of the ion population which makes the situation unstable and can lead to IAW
growth. In the absence of such a beam, a current driven instability can add to
the growth rates of the IAW. _Rosetta_ ’s close flyby of comet 67P made it
possible to observe the large scale current that is associated with the
magnetic field draping near the nucleus (_Koenders et al._ , 2016a) and the
wave signatures in that region. It was found that in the presence of this
current, IAW are produced, while outside of the region containing the current,
the waves are propagating away from the current and eventually damped (_Gunell
et al._ , 2021).

IAW were also detected inside the diamagnetic cavity, close to the DCB, but
not outside of it. Figure 12c shows the power spectral density of the current
(a proxy for the density) for short intervals inside (solid lines), outside
(dashed lines) and in the boundary (black line) of the diamagnetic cavity.
Clearly, the power spectral density is about two orders of magnitude higher
inside the diamagnetic cavity than it is outside. Here, again the dominance of
the cold ion population leads to the growth of the waves. However, an
additional current was speculated to be in place. Considering that the
diamagnetic cavity boundary is wavy, there might be a current closing through
the protruding parts of the diamagnetic cavity that drives the wave generation
(_Gunell et al._ , 2017a). Further studies and observations, ideally by
multiple spacecraft, are necessary to confirm this generation mechanism.
Through a combination of data analysis and modeling of dispersion relations,
the wave observations can be used to constrain the plasma parameters in the
generation region of the waves.

##### Mirror modes and magnetic holes

The pick-up process at the comet leads to the generation of a ring or ring-
beam distribution of the heavy ions. This distribution is unstable, and can
cause the generation of mirror-modes in a high-$\beta$ plasma. Mirror modes
are compressional, pressure equilibrium structures. They have large amplitudes
and do not propagate in the plasma, instead they are convected with the plasma
flow. Mirror modes have been observed at comet 1P/Halley and comet
21P/Giacobini-Zinner. _Volwerk et al._ (2014) found that at 1P/Halley that
changes in the dynamic pressure of the solar wind influenced the generation of
mirror-mode waves in the cometosheath, as well as outgassing rate changes.
Increased solar wind dynamic pressure compresses the magnetosheath and
inhibits the growth of mirror-modes, but increased outgassing will enhance ion
pick up and thereby assist the growth of mirror modes. _Schmid et al._ (2014)
showed evidence for the Bohm-type diffusion of mirror-modes as they move from
the source region further into the magnetosheath. The mirror-modes grow in
size over time as the high-frequency parts of the structures diffuse faster
than the low-frequencies.

Mirror modes have been observed in the pile-up region at comet 67P (_Volwerk
et al._ , 2016) with timescales of $100\,$s to $150\,$s which corresponds to
sizes of 10s of water ion gyroradii. Figure 12d shows an example of the
magnetic field measurements during a mirror mode wave train, the LAP current
(a density proxy) is added to show that density and magnetic field are out of
phase. Outside of the pile-up region, the timescale of the mirror modes is
smaller ($\sim 10$s) and the scale size is just a few water ion gyroradii.
These mirror mode signatures are more asymmetric with either the decrease or
increase of the field being steeper than the other side. The presence of
mirror modes indicates that there is a full ring/ring-beam distribution
present in the coma, i.e. that the water ions have had enough time to go
through an entire gyration before they reach the spacecraft in the inner coma.
The larger mirror mode structures are thought to be caused by the diffusion of
smaller scale mirror modes as they are convected through the coma, whereas the
asymmetry of the structure could be caused by the interaction of different
mirror modes.

Magnetic holes are thought to be a further development stage of these mirror
modes (_Winterhalter et al._ , 2000). They are omnipresent in the solar wind
(_Volwerk et al._ , 2020, 2021) and therefore should impact the pick-up and
pile-up processes in the coma. Magnetic holes were detected at 67P, inside and
outside of the solar wind ion cavity (_Plaschke et al._ , 2018), which
indicates that the magnetic field structures are moving into the coma along
with the electron fluid, while the solar wind ions are substituted by
accelerated cometary ions.

##### Steepened magnetosonic waves

Steepened magnetic field structures were first detected near the diamagnetic
cavity of comet 67P (_Goetz et al._ , 2016a). The diamagnetic cavity entry and
exit is also asymmetric, with the former being usually longer than the latter.

High time resolution observations of the low energy ion environment in the
inner coma showed periodic enhancements in the ion energy with a sharp
increased followed by a longer relaxation time, as illustrated in the upper
panel of Figure 12e. Some of this observed increase was due to the spacecraft
potential increase, but taking the spacecraft potential into account still
allows identification of the asymmetric structures in the measured ion energy
and flux (_Stenberg Wieser et al._ , 2017). The occurrence rate of these
structures was highest near the diamagnetic cavity.

The magnetic field observations (see lower panel of Figure 12e cover a larger
time span of the mission time, and therefore a larger study could be
performed. Using machine learning, over 70000 individual steepened wave
structures were detected in the magnetic field (_Ostaszewski et al._ , 2020).
More steepened waves occur when there is more mass-loading of the plasma,
which means that the peak in wave activity is around perihelion. During the
dayside excursion, the only time that _Rosetta_ left the innermost coma, the
number of wave detections decreased. There is no evidence that the occurance
of steepened waves is correlated to the solar wind parameters.

At high activity levels, the waves are steeper but have lower amplitudes, this