<figure><img src="image_32.png" /></figure>

**Fig. 30** Top: ROSINA-COPS total neutral number density (solid line) measured at Rosetta and the subspacecraft latitude (dashed line) as a function of time. Bottom: Ionospheric density as a function of time. The period shown is 2014 October 17–18. The blue (red) curves correspond to the calculated plasma density assuming photoionization alone (photoionization and electron-impact ionization). The vertical spread of these curves corresponds to the range of ion outflow velocity considered, spreading from 400 m/s (top boundary) to 700 m/s (bottom boundary). The RPC-MIP electron density is shown with large, violet dots. The RPC-LAP electron density is shown with small green dots, assuming an electron temperature of 7.5 eV (light green). Due to a different operation mode, there is no RPC-LAP electron density available between 07:00 and 08:30 UT on 2014 October 18. The subsolar latitude was 40° and Rosetta was in the solar terminator plane. From Galand et al. (2016), Fig. 15

over the most outgassing hemisphere (Galand et al. 2016). A dependence in $r^{-1}$ of the plasma density was observed (Galand et al. 2016), as predicted by the model (see Fig. 29).

In contrast, the plasma number density over the southern, winter hemisphere during pre-perihelion is dominantly produced through electron-impact ionisation (Galand et al. 2016; Heritier 2018). If only the photo-ionisation contribution is taken into account, the modelled plasma density largely underestimates the observed plasma density (see 2014 October 18 in Fig. 30). The observed electron flux is more intense over the winter hemisphere than over the summer hemisphere. This intensification over-compensates the weaker neutral density over the winter hemisphere; as a result, the plasma density was found to be higher over the winter hemisphere than over the summer hemisphere (see Fig. 30).

*   **During post-perihelion, quiet solar conditions:** As the solar activity decreased over the course of the escort phase, the photo-ionisation frequency at a given heliocentric distance is lower pre-compared with post-perihelion; the relative importance of photo-ionisation compared with electron-impact ionisation decreases. The observed plasma density at post-perihelion is higher in the summer/autumn (southern) hemisphere compared with the winter/spring (northern) hemisphere. The strong electron fluxes over the winter/spring hemisphere did not compensate for the weaker neutral density (Heritier et al. 2018), as it did during pre-perihelion. The multi-instrument analysis was applied during the return from the cometary tail excursion in April 2016. The very good agreement between the observed and modelled plasma density demonstrates the robustness of the model over a large range of cometocentric distances up to 80 km (Heritier et al. 2018).

*   **During solar events:** A Co-rotating Interaction Region (CIR, see also Sect. 2.4) hit comet 67P over several solar rotations in summer 2016 (Hajra et al. 2018a). The multi-instrument analysis was applied to the disturbed cometary environment in July and August 2016. The relative importance between photo-ionisation and electron-impact was found to be highly variable, with the latter sometimes largely dominating the former and increasing by one order of magnitude during quiet and disturbed times. The very good agreement
<figure><img src="image_33.png" /><figcaption>**Fig. 31** Top: Time series of the ROSINA-COPS measured neutral number density (full line) and cometocentric distance of the spacecraft (dashed line). Middle: Time series of the photo-ionisation frequency $v^{hv}$ (blue curve) and total ionisation frequencies ($v^{hv} + v^{e-}$) (red dots). Seasonal variations are colour coded in the top panel with pink for spring (northern hemisphere) and yellow for autumn (southern hemisphere). Bottom: Time series of the RPC-MIP measured electron number density (pink dots), smoothed using a 5-minute average (purple) and RPC-LAP derived total ion densities (green). Simplified modelled ionospheric densities (Eq. (9)) using photo-ionisation only (blue) and both photo-ionisation and electron-impact ionisation (red), assuming outflow velocity from 400 m/s (upper bound) to 700 m/s (lower bound). The solar wind dynamic pressure as predicted by the Tao et al. (2005) model is plotted in green (middle panel) to illustrate the effect of the CIR impact. From Heritier et al. (2018), reproduced with permission ©ESO</figcaption></figure>

between the observed and modelled plasma densities attests that the enhancement seen in the plasma density during the CIR was driven by an increase in the electron-impact ionisation frequency (see Fig. 31), and was not due to a plasma compression driven by the increase in the solar wind dynamic pressure (Heritier et al. 2018; Hajra et al. 2018a).

* **At the end of the Rosetta mission:** Rosetta made a controlled landing on the nucleus' surface which offered the opportunity for taking the first-ever plasma measurements all the way down to the surface (Heritier et al. 2018). Along the descent which covered a large range of latitudes and longitudes over the northern, spring hemisphere, the multi-instrument analysis showed that electron-impact ionisation was the dominant source of the cometary plasma. However, the margin of errors was large due to large uncertainties in the gas bulk velocity. A refined approach was developed for which the ion bulk velocity is no longer constant, but equal to the expansion velocity of the adiabatic gas and varies from 400 m/s close to the surface to 800 m/s (terminal flow velocity) at a cometocentric distance of about 20 km. Apart from a slight overestimation when Rosetta was over the nucleus' neck, modelled plasma density from the refined approach agrees extremely well with the cross-calibrated RPC-MIP/RPC-LAP densities. The peak in the plasma density profile, predicted to be located at twice the apparent radius of the nucleus (see Sect. 2.2.4) is clearly apparent in the observed plasma density dataset.

In summary, the multi-instrument analysis of the plasma density developed for a local outgassing rate between $10^{25}$ and $10^{27}$ s$^{-1}$ (that is, less than 2–4 AU for comet 67P Heritier et al. 2018) and cometocentric distances close to the nucleus (< 100 km), has shown that the cometary plasma is produced through photo-ionisation of solar EUV radiation and electron-impact ionisation; the relative difference in the sources varies with season, hemisphere, solar
<figure><img src="image_34.png" /><figcaption>**Fig. 32** Schematic of the multi-instrument analysis applied to FUV emissions. From Stephenson et al. (2021), reproduced with permission ©ESO</figcaption></figure>

activity and solar events. The plasma is lost through transport. The ions are strongly coupled to the neutrals, as the region analysed is below or close to the ion exobase (Galand et al. 2016). The ions do not seem to suffer any significant acceleration, at least if there is any, it is limited and does not affect the cometary plasma density. Very close to the nucleus (a few km above the surface), the analysis is improved by taking into account the neutral expanded flow (Heritier et al. 2017b). The robust multi-instrument approach is a relevant tool not only for the analysis of the plasma source and loss, but also for the analysis of solar events, as shown with the example of the CIR events in summer 2016.

### 3.2.2 Multi-instrument Analysis of the FUV Emissions

To enhance the science return from the Alice FUV spectrometer, a multi-instrument analysis has been applied to the observed FUV emissions from atomic hydrogen, oxygen, and carbon (Galand et al. 2020; Stephenson et al. 2021). This analysis combines gas, particle, and light measurements, taken simultaneously, from in situ and remote-sensing instruments onboard Rosetta, utilising a simple, physics-based model. The multi-instrument analysis has been applied to establish the source and identify the nature of the FUV emissions, as well as to provide further constraints on the composition of the neutral coma. The model focusses on dissociative excitation of cometary molecules by electron impact (see Sect. 2.5) which has been identified as a source of FUV emissions at comet 67P (e.g. Feldman et al. 2015, 2016, 2017). The brightness of an FUV emission line from electron impact is given by Eq. (15). As the analysis is focussing only on low outgassing rates ($Q < 2 \times 10^{26} \text{ s}^{-1}$), the differential flux, $J(E)$, of energetic electrons does not undergo any significant energy degradation in the coma and can be assumed to be constant throughout the column along the line of sight of the FUV spectrograph (Chaufray et al. 2017; Heritier 2018). As such, the simplified version Eq. (16) can be used to calculate the brightness of the modelled emissions.

A schematic outlining the multi-instrument analysis is shown in Fig. 32. The observed brightness from the Alice spectrograph is compared with the modelling brightness. The latter is derived from observations of the column density of the major neutral species along the line of sight and the differential flux of suprathermal electrons. By combining coincident in situ and remote-sensing measurements, uncertainty due to the variability of the neutral gas and electron flux is minimized.

This analysis has been applied to two different viewing geometries: nadir viewing and limb viewing. When viewing nadir, the composition and density of the neutral gas along the line of sight are well constrained as the major species do not have an extended source and the column of gas between the nucleus and the Rosetta spacecraft is coming from the
same region on the surface. Cases have been selected when the surface of the nucleus was in shadow, reducing contamination from solar flux reflected off the nucleus. It is possible to extrapolate from local measurements of total number density by ROSINA/COPS and neutral composition by ROSINA/DFMS (Balsiger et al. 2007), assuming a $1/r^2$ profile as observed (Hässig et al. 2015; Bieler et al. 2015b). Measurements from VIRTIS (Coradini et al. 2007) can also be used for deriving the column density of H$_2$O, CO, and CO$_2$.

For limb viewing, the column density of H$_2$O, CO, and CO$_2$ can be derived from observations by the sub-mm spectrograph, MIRO (Gulkis et al. 2007) and the infrared spectrometer VIRTIS. However, the column density of O$_2$ cannot be probed remotely with these instruments. It is also not possible to extrapolate it from in-situ composition measurements, as the neutral gas along the line of sight originates from many regions of the nucleus.

The emission frequency $v_l^X$, for a given neutral species $l$ and emission line $X$ is given by:

$$v_l^X = \int_{E_l^{th}}^{E^{Max}} \sigma_l^X(E) J^{e-}(E) dE \qquad (20)$$

where $\sigma_l^X$ is the emission cross-section of the emission line $X$ due to dissociative excitation of the molecular species $l$ by an energetic electron of energy $E$. A review of the relevant emission cross sections used is given in (Stephenson et al. 2021). $J^{e-}(E)$ is the suprathmal electron spectral flux, introduced already in Eq. (18) and corrected to the spacecraft potential as given in Eq. (19) (see Sect. 3.2.1). $E_l^{th}$ is the energy threshold for the dissociative excitation process (15–25 eV). $E^{max}$ is the maximum energy considered, typically around 200 eV for the observed RPC-IES spectral fluxes.

As well as emissions from dissociative excitation, photodissociation of cometary molecules generates emissions in the FUV. These are modelled as discussed in Stephenson et al. (2021). Measurements of the solar photon flux by TIMED/SEE orbiting the Earth is extrapolated to the position of 67P assuming a $1/r_h^2$ drop off, where $r_h$ is the heliocentric distance. As 67P and Earth were at most times out of solar phase during the Rosetta escort mission (except in February 2015), the TIMED/SEE measurements are taken from the same Carrington longitude as 67P for each observation. The neutral coma has been assumed to be optically thin, which again is only valid at large heliocentric distances.

From the multi-instrument analysis of nadir-viewing emissions, Galand et al. (2020) and Stephenson et al. (2021) established that dissociative excitation is the major source of FUV atomic emissions at large heliocentric distances (see Fig. 33a). This is true both over the northern, summer hemisphere where H$_2$O was the dominant outgassing species and over the southern, winter hemisphere where CO$_2$ played a larger role compared to water. The relative contributions of the neutral molecules to the emission lines are very different between the northern and southern hemispheres, for large heliocentric distances, but in both cases dissociative excitation by electron impact was the key driver of the emissions.

The multi-instrument analysis applied to limb-viewing observations showed that the variation in the FUV emission brightnesses is correlated with the variation in the electrons measured in situ at Rosetta (Figs. 33b and 33c; Galand et al. 2020; Stephenson et al. 2021). This demonstrated that the energetic electrons responsible for the FUV emissions are not produced locally, but rather have undergone a large-scale acceleration (see Sects. 2.3.2, 4.1 and Galand et al. 2020). This analysis has revealed the auroral nature of the FUV atomic emissions seen by Rosetta and the relevance of using OI 1356 Å as a remote-sensing tracer of solar wind electron variability.
<figure><img src="image_35.png" /><figcaption>**Fig. 33** (a) Comparison of modelled (black) and observed (magenta) atomic oxygen emissions for seven cases in the northern hemisphere of 67P with a nadir viewing. Measured and modelled points for a given date and time are offset for visibility. From Galand et al. (2020). (b) and (c) Comparison of modelled (solid lines) and observed (crosses) FUV emissions during a corotating interaction region at comet 67P on 4th Aug 2016. Each time interval of consecutive measurements is plotted in its own color to better distinguish them. Both from Stephenson et al. (2021), reproduced with permission ©ESO. Further atomic emission lines to those shown have been modelled in both of the above studies</figcaption></figure>

## 3.3 Numerical Models

By accompanying 67P for two years, the Rosetta orbiter provided a wealth of fresh new information during various stages of the comet's life, but as with all single-spacecraft missions, it could only be at one spot in time and space, and possibly the most intriguing plasma physics in the solar wind – comet interaction unfolded partially out of reach of Rosetta instruments. It makes the coupling of observational and modelling efforts a necessity. For instance, while Rosetta was close to the comet nucleus investigating the diamagnetic cavity (Sect. 4.6 and Goetz et al. 2016a,b; Henri et al. 2017; Hajra et al. 2018a), it was impossible to tell how the upstream solar wind variability influenced the cometary plasma environment (e.g. did a local or external physical mechanism cause the observed variability of the boundary of the diamagnetic cavity?).

Over the last decades the numerical methods used to advance theory and to analyse, interpret and predict measurements have been revolutionised. The increasing availability and expansion of computational resources has made possible the implementation of more precise and complete numerical models at larger spatial scales.

Numerical models in plasma physics, and by extension those to study the comet's interaction with the surrounding plasma environment, can be divided roughly into three broad numerical approaches (e.g. Ledvina et al. 2008): (1) models that treat all simulated plasma species as one or multiple fluids; (2) models that include some of the plasma species as (com-
<table><caption>**Table 5** Summary table for the most common numerical models and references to works that use them. $\Omega_{gi,e}$ are the gyroradii of the ions and electrons, respectively</caption><thead><tr><td>Model type</td><td>Applicable scale L</td><td>Examples</td></tr></thead><tbody><tr><td>Fluid</td><td>$L > \Omega_{gi} > \Omega_{ge}$</td><td>e.g. Huang et al. (2018)</td></tr><tr><td>Hybrid</td><td>$\Omega_{gi} > L > \Omega_{ge}$</td><td>e.g. Simon Wedlund et al. (2017), Lindkvist et al. (2018) and Koenders et al. (2016a)</td></tr><tr><td>Fully kinetic</td><td>$\Omega_{gi} > \Omega_{ge} > L$</td><td>e.g. Deca et al. (2019) and Gunell et al. (2019)</td></tr></tbody></table>

putational) particles, so-called ‘hybrid’ codes; (3) models that represent all plasma species using computational particles, so-called ‘fully kinetic’ codes. These categories are summarised in Table 5. Note that these categories are only one non-unique attempt to classify the numerical models used in cometary science. In reality, there is a wide spectrum of models often blending the borders we outlined above. Finally, there are some approaches that do not clearly fit in any of the three categories, such as test-particle or semi-analytical models, whose inputs are sometimes based on outputs of the other three categories.

Different numerical models provide different advantages and disadvantages. Typically, a less complete/self-consistent physical model translates into a lower computational burden, a more efficient use of computational resources. Some physical mechanisms or fully time-dependent simulations (as opposed to, e.g., a steady-state model with fixed neutral background atmosphere and solar wind conditions) might be almost impossible to implement in an efficient manner without losing self-consistency. This may be due to constraints on available computational resources, and the vast range of time-scales to be resolved (e.g., ions collisionally coupled to neutral gas less than $1 \text{ km s}^{-1}$ in speed, versus electron speeds of several $1000 \text{ km s}^{-1}$), or to a limited understanding of the underlying physics. In reality, the ‘amount’ of physics included in the model is always a compromise against the amount of available resources. Similarly, by enabling the study of a specific process or physical aspect in greater detail, 1-D and 2-D approaches vs 3-D approaches may bring valuable insights into the physics of cometary plasma environments at reduced cost. In the following paragraphs we attempt to give a brief overview of how numerical models, here mostly 3-D, have been applied in preparation to, during and after the Rosetta mission. We refer the reader to the complementary sections for a more in-depth discussion of the science covered in these works.

As Rosetta intended to accompany 67P throughout all outgassing stages of the comet, predicting the global structure of its plasma environment is key to understanding where to look for the most exciting science. Supported by several decades of experience investigating other comets and solar system bodies [e.g., Gombosi et al. 1996 describe mass-loading near comet 1P/Halley; Jia et al. 2008 model the effect of neutral jets during the Deep Space 1 Comet 19P/Borrelly flyby], (multi-fluid) MHD efforts have paved the way. Needing relatively little computational resources, they can resolve larger physical domains. For example, Huang et al. (2016) modelled a computational domain on the order of $10^6 \text{ km}$ to investigate the plasma and neutral gas environment of 67P near perihelion. The model extended the single fluid MHD model by Hansen et al. (2007), driven by the need to reproduce effects arising from the gyration of the cometary ions and the deflection of the solar wind protons (Rubin et al. 2014b,a, 2015).

The next step is to include ion dynamics self-consistently. This is achieved with kinetic hybrid models, where ions are treated as statistical macroparticles and electrons as a massless charge-neutralising MHD fluid, building on the knowledge accumulated on the plasma
environments of various solar system bodies, not necessarily cometary (see e.g. Bagdonat and Motschmann 2002; Kallio et al. 2006; Müller et al. 2011; Holmström 2013). More specifically driven by the Rosetta teams, recent improvements in cometary hybrid models include, e.g., more detailed models of photoionisation, solar wind charge exchange and electron ionisation processes and their respective effects on the creation of large-scale boundaries such as bow shock and cometopause regions (see Simon Wedlund et al. 2017, and Sect. 4.2), the ion dynamics of mass loading (Behar et al. 2016a), and analysis of the observed pickup ion energy spectra and shock-like structures (Lindkvist et al. 2018; Gunell et al. 2018; Alho et al. 2019, 2021). Hybrid approaches have also proven successful to investigate the effects of solar wind variability on the global structure of 67P's plasma environment (Koenders et al. 2013, 2015, 2016a; Alho et al. 2021), in particular during the weak and intermediate outgassing regimes. Comparing measurements with hybrid numerical simulations, Koenders et al. (2016b) studied the generation of low-frequency waves in the comet-solar wind interaction region, including the "singing comet waves" (see Sect. 2.3.7), showing how they arise from initial cometary pick-up ions perpendicular to the solar wind flow and along the IMF direction, triggering a modified ion-Weibel instability. In the most recent iterations of these models, extended boundary conditions (to include mass-loading, charge-exchange and ion productions over the large upstream region extending up to millions of km in the subsolar direction) as well as asymmetric outgassing driven by the nucleus illumination have been included (Koenders et al. 2013; Alho et al. 2021). Structures that are possible to describe with these models without much loss of ion scale physics include for example bow shock and ion collisionopause down to the diamagnetic cavity and the ambipolar electric field (see Sects. 2.3.2, 4.2, 4.6, and 4.5).

Modelling both electron and ion species as particles, fully kinetic approaches are in the-
ory able to present the most complete physical model. However, it comes at a significant
computational cost, restricting present-day global simulations to 67P's plasma environment
during its weakly and moderately active periods. Using four plasma species (solar wind
protons and electrons; cometary water ions and electrons), Deca et al. (2017) concluded
that the dynamical interaction of a weakly outgassing comet is representative of a four-fluid
coupled system and they were able to identify the origins of the warm and suprathermal
electron distributions observed by Rosetta. Global particle-in-cell simulations disentangled
the convoluted observed electron distributions and showed that the ambipolar electric field
temporarily traps and accelerates electrons near the comet without the need for wave-particle
or turbulent heating mechanisms (Divin et al. 2020; Sishtla et al. 2019). This also leads to
the mechanism responsible for the far-ultraviolet aurora identified at comet 67P (Galand
et al. 2020). As no collisions are included, the strict applicability of the method is as yet
confined to low-activity comets and/or regions far from the nucleus. Nevertheless, consid-
ering the limited size of the collisional domain at 67P (see discussions on exobase and
collisionopause in Sects. 2.3.5 and 4.5), the particle-in-cell results can be expected to well
represent the comet-solar wind interaction during the Rosetta mission.

A second set of fully kinetic models focused on the plasma environment of the Rosetta spacecraft itself. For example, Johansson et al. (2020) analysed the charging behaviour of Rosetta and Wattieaux et al. (2020) characterised the response of the RPC-MIP instrument to different electron populations. A similar study for RPC-ICA was performed by Bergman et al. (2020). All are crucial to aid our interpretation of the in situ plasma measurements, which in turn are dependent on the spacecraft charging and the local plasma environment (disturbed by the spacecraft, including solar arrays, booms and the relative position of the instruments). Finally, note that a fully kinetic description for the complex electron dynamics can provide an effective electron closure relation and identify where an isotropic single-electron fluid Ohm's law approximation can be used, and where it fails (Deca et al. 2019).
<figure><img src="image_36.png" /><figcaption>**Fig. 34** Illustration of the boundaries formed by the interaction of the solar wind with the coma that have been observed during spacecraft flybys of comets. All of these boundaries are thought to be permanent features of the interaction when the outgassing rate is high enough. The grey shaded region is the portion of the comet solar wind interaction explored by Rosetta between 2015 May and December</figcaption></figure>

The latter can then be used as input for less computationally demanding numerical approaches.

As mentioned above, there are a multitude of numerical approaches that do not clearly fit in any of the categories outlined above. Most prominently in these group are semi-analytical models and test-particle codes. The latter have been successful to characterise, e.g., the solar wind ion cavity (Behar et al. 2017) and suprathelial electrons near the nucleus of comet 67P (Madanian et al. 2016). Direct simulation Monte Carlo methods have been used to characterise the observed non-uniformity of the cometary neutral coma (Bieler et al. 2015b; Fougere et al. 2016a; Combi et al. 2020).

# 4 Large Scale Structures

The interaction of the solar wind with comets is unique compared to how the solar wind interacts with unmagnetized planetary atmospheres. This is because the high neutral outgassing rate of comets and the free expansion of the atmosphere causes this interaction to begin at great distances from the comet through the process of mass loading of the solar wind. The result is large scale structures in the form of boundaries, regions, and electric fields that have been observed by spacecraft flybys of comets and by Rosetta during its extended escort of 67P. Boundaries observed by a spacecraft at a comet can be permanent features, solar wind and interplanetary magnetic field (IMF) boundaries, or small-scale transient features created by instabilities or waves (Cravens 1989). Figure 34 illustrates the relative positions of the boundaries discussed in the following sections.

## 4.1 Electric Fields

Large scale plasma phenomena can usually be described using a fluid model. The main assumption needed is that the characteristic scale size of the phenomenon being investigated
<figure><img src="image_37.png" /><figcaption>**Fig. 35** Illustration of the electric fields in the inner part of the coma of a comet that has not developed a diamagnetic cavity. From (Gunell 2020)</figcaption></figure>

is much larger than an ion gyroradius. On smaller scales, either concerning physics such as the formation of pick-up ring distributions or where the characteristic gradients in the system are smaller than an ion gyroradius, electric fields become important. The same is true in the absence of a background magnetic field, as e.g. in the diamagnetic cavity.

When a comet plasma cloud is small compared to a pick up ion gyroradius, ions may be locally unmagnetised. Locally produced ions will move along the solar wind electric field on these scales. We know from conservation of momentum and observations that the solar wind will be deflected in the direction opposite to the cometary ions (see also Sect. 2.3.1 and Behar et al. 2016b, 2018b; Broiles et al. 2015). To understand the local plasma dynamics on this scale, it is usually helpful to look at the solar wind electric field in the local comet reference frame. The same is true for planet systems that are small compared to the pick up ion gyroradius such as Mars, where a plume of pick up ions is seen along the solar wind electric field direction (Dong et al. 2015).

Another important electric field comes into play when the newly added ions are no longer just a small perturbation to the solar wind flow. The newly born ions and electrons move in different directions along and against the solar wind electric field, so if the solar wind cannot easily displace the accumulating charges along the field line a polarisation electric field will build up, preventing further charge accumulation (Brenning et al. 1991; Nilsson et al. 2018). In particular this electric field arises in the case of unmagnetised ions and magnetised electrons, as was typically the case at comet 67P during the Rosetta mission. This is illustrated in Fig. 35, where $E_{pol}$ shows the polarisation electric field. The effect of the polarisation electric field has been modelled for barium release experiments (Brenning et al. 1991), a model later adapted to the situation at comet 67P (Nilsson et al. 2018). Gunell et al. (2019) further studied the role of the polarisation electric field using electrostatic PIC simulations. Such small scale plasma clouds with polarisation electric field effects have also been discussed based on MAVEN observations from Mars (Halekas et al. 2016). One prediction of the model is a significant anti-Sunward flow of the pick up ions, rather than along the inferred solar wind electric field direction. This is in agreement with observations
(Nilsson et al. 2015b, 2017). One can regard it as that the frozen-in electrons drag the ions with them, an interpretation also used by Dubinin et al. (1993) describing a similar situation in the magnetotail of Mars.

A simple model of the polarisation electric field (Nilsson et al. 2018) predicts that the electric field should be quite uniform inside the cometary plasma cloud. If so, the energy spectra of cometary ions moving along the electric field can directly be related to the distance between the measurement and the production region of the ions. The energy spectra can thus be used to remotely probe the plasma cloud structure. Nilsson et al. (2018) suggested that an abrupt increase of fluxes at energies above 1 keV could be related to the bow shock. Such a remote detection of the large scale bow shock close to perihelion was later reproduced in a hybrid model by Alho et al. (2019). The shape of the energy spectra thus reflects how the production of ions changes with distance, and abrupt changes in the energy spectra corresponds to abrupt changes in either production or the electric and magnetic fields and associated ion transport.

As the cometary plasma cloud grows larger and denser, the solar wind electric field is more efficiently shielded from the interior of the plasma cloud (Nilsson et al. 2018). Locally produced pick up ions are then less accelerated, possibly explaining the lower ion energies observed inside the comet magnetosphere around perihelion (Nilsson et al. 2017). This effect occurs at similar times and in regions where collisions also start to play a more significant role (see also Sect. 4.5). The stronger shielding of the solar wind electric field should however not lead to any clear boundary in the plasma, and accelerated ions are still present, just at lower energies.

Closer to the nucleus newborn, hot photoelectrons and a strong density gradient give rise to a significant ambipolar electric field accelerating ions radially outward (Odelstad et al. 2018; Berčič et al. 2018) ($E_{ambi}$ in Fig. 35). In a sense this is similar to the polarisation electric field, with the hot photoelectrons dragging the ions with them. However, while the radially directed ambipolar field is caused by the electrons having a higher temperature than the ions, the polarisation field is a secondary field caused by electrons and ions moving in different directions as a result of the solar wind convective electric field. Figure 35 illustrates the directions of the three different contributions to the electric field and the different scales of electron and ion gyroradii, which causes the charge separation behind the polarisation electric field. The presence of several distinct electron populations also means that the polarisation electric field accelerates some electrons inward (Madanian et al. 2017; Deca et al. 2017). The main source of hot electrons is believed to be photoelectrons due to EUV ionisation and secondary electrons due to electron impact ionisation, but additional heating is needed to explain the highest observed electron temperatures (see Sect. 2.3.3).

Rosetta observations showed that low energy ions observed close to the nucleus are moving away from the nucleus with a velocity well above that of the neutral gas (Odelstad et al. 2018). The Rosetta observations were made also well inside the collisionopause illustrated in Fig. 34, (see also Sect. 4.5). The ions can thus attain a speed of typically 2 to 4 km/s also inside the collisionopause, which in turn affects the collision cross section which is energy dependent and thus also the position of the collision dominated region (Mandt et al. 2019).

Rosetta observations also showed that electrons in the inner coma exhibit an excess of their suprathmal component as compared to what is expected from local production of photo electrons (Broiles et al. 2016a; Myllys et al. 2019), which result from inward electron acceleration by this ambipolar electric field (Madanian et al. 2017; Deca et al. 2017).

In the Rosetta observations, the most common flow direction for cometary ions with an energy below about 60 eV as measured by RPC-ICA (Berčič et al. 2018; Nilsson et al. 2017) was a radial outflow in $Y_{CSEQ}-Z_{CSEQ}$ plane with a significant anti-Sunward component. This
represents a combination of the influence of the polarisation electric field (anti-Sunward) and the ambipolar electric field (radial expansion). Note that the energy limit given here is after acceleration by the typically negative spacecraft potential (Odelstad et al. 2017) which means that the typical ion energy range when compensating for the spacecraft potential (Bergman et al. 2020) was in the energy range typically up to about 40 eV.

Other regions where quasi-stationary electric fields may be important are at sharp boundaries. Of the main boundaries shown in Fig. 34 the bow shock (Sect. 4.2) and the diamagnetic cavity (Sect. 4.6) are the ones most likely to exhibit electric field signatures.

In a coma the ambipolar electric field (see also Sect. 2.3.2) is present as soon as electron collisions are low enough to allow for a hot electron component. Ambipolar acceleration has been observed inside the diamagnetic cavity (Odelstad et al. 2018). At the diamagnetic cavity boundary, which is rather sharp at about 25 km width (Goetz et al. 2016a; Neubauer 1988), further transients can be expected due to the discontinuity of the mobility of electrons and ions from the field-free to the magnetised region outside the cavity. Studies of this are ongoing, but the effect of a sometimes abruptly changing spacecraft potential is yet to be fully taken into account for the interpretation of Rosetta data (Masunaga et al. 2019; Bergman et al. 2020; Johansson et al. 2020).

## 4.2 Bow Shock

Shocks form in a plasma flow upstream of obstacles, if the relative velocity of the plasma and the obstacle exceeds the characteristic speed of waves in the plasma. The compressional wave which forms in front of the obstacle steepens when more plasma comes in from upstream (see for example, Balogh and Treumann 2013; Burgess and Scholer 2015). A multitude of instabilities and wave modes are possible. Typically though, bow shocks grow from fast magnetosonic waves in the supermagnetosonic solar wind. The dissipation that causes heating of the solar wind as it passes the shock is caused by secondary instabilities leading to waves on smaller and faster scales, involving both ions and electrons.

Early theory showed that hydrodynamic (Biermann et al. 1967) and magnetohydrodynamic (Flammer and Mendis 1991) models of mass-loading break down already when the fraction of incorporated cometary ions reach a few per cent, unless a discontinuity corresponding to a bow shock is introduced. The agreement between these models and observations of the bow shock of the highly active comet 1P/Halley is reasonable (Neubauer et al. 1986).

Mass-loading slows down the solar wind upstream of the shock, leading to a lower Mach number than in the undisturbed solar wind or at planetary bow shocks. The magnetosonic Mach numbers of the Giotto bow shock crossings of comet 1P/Halley were computed by Coates et al. (1990) and were found to be between 1.1 and 1.8 inbound and between 1.6 and 1.7 outbound. This would make the shock marginally supercritical, but criticality also depends on the shock normal angle to the magnetic field (Balogh and Treumann 2013). One would in any case expect cometary shocks to have more subcritical properties than the bow shocks at planets. Subcritical shocks rely more on dissipation at the shock itself, whereas supercritical shocks reflect a significant fraction of the solar wind particles back upstream, which leads to instabilities, wave growth, and dissipation of energy in the foreshock region. In a single fluid MHD description, shocks fulfil the Rankine-Hugoniot conditions. In a multi-component plasma these conditions need to be modified (Motschmann et al. 1991b,a), and the different ion species behave differently. This changes further when kinetic effects are included (Fahr and Siewert 2015).

Comet bow shocks are more diffuse and wide than the bow shocks known from planets. This was found when the International Cometary Explorer (ICE) spacecraft flew by comet
21P/Giacobini-Zinner in 1985 (Smith et al. 1986). Bame et al. (1986) observed that the transitions were smooth and gradual in magnetic field and particle observations, but the wave instrument on ICE measured sharp boundaries where the wave activity increased in the same way as at planetary bow shocks, and an intense broadband spectrum of waves indicative of energy dissipation was found (Scarf et al. 1986b). As expected for shocks, the width of the bow shock was not proportional to the distance to the comet for comets 21P/Giacobini-Zinner and 1P/Halley. The widths were approximately the same, (3–4) × 10⁴ km, whereas the cometocentric distance to the shock differed by an order of magnitude. It was 1.27 × 10⁵ km at comet 21P/Giacobini-Zinner and 1.15 × 10⁶ km at comet 1P/Halley (Neubauer et al. 1986). The results obtained by the two Vega spacecraft were similar to those of Giotto (Gringauz et al. 1986a). Both Vega 2 and Giotto passed through a quasi-parallel shock on the outbound legs of their flybys (Galeev et al. 1986; Coates 1995).

The observations of comet 26P/Grigg-Skjellerup, visited by the Giotto spacecraft in 1992, yielded similar results with sharp transitions in both field and waves when the spacecraft was outbound. On the inbound leg only the wave measurements showed a sharp transition, while the increase in magnetic field was gradual (Neubauer et al. 1993b). It was later seen in models and observations at comet 67P/Churyumov-Gerasimenko that bow shocks can be very asymmetric at intermediate cometary outgassing rates. The outgassing rate at comet 26P was estimated to $6.7 \times 10^{27} \text{ s}^{-1}$ (Neubauer et al. 1993b), which is similar to comet 67P at perihelion and above the outgassing rate during the infant bow shock observations at comet 67P (see the outgassing rates in Fig. 3 in Sect. 2.1.1). This would place comet 26P between comet 67P and comets 21P/Giacobini-Zinner and 1P/Halley both in terms of outgassing rates and in bow shock symmetry. Asymmetries in bow shock thickness may also be caused by outgassing asymmetries as shown by simulations (Huang et al. 2016).

The last of the pre-Rosetta in situ bow shock observations happened in 2001 at comet 19P/Borelly. The Deep Space 1 spacecraft detected a bow shock $1.47 \times 10^5$ km from the nucleus (Richter et al. 2011). The observed magnetic compression ratio was 2.5, and the magnetic field fluctuations were seen to increase as the spacecraft moved into the region downstream of the shock.

Before Rosetta arrived at comet 67P, simulations predicted that the standoff distance of the bow shock would be a few thousand kilometres (Koenders et al. 2013, 2015). Simon Wedlund et al. (2017) performed a series of hybrid simulations in which first only photo-ionisation was included and then also electron impact ionisation and charge-exchange processes. The result was that with each addition of an ionisation process, the bow shock moved farther upstream up to a maximum standoff distance of more than 6000 km. Rosetta ventured out to a cometocentric distance of about 1500 km during its dayside excursion in September 2015. Given that this distance was much below the predicted standoff distance, it was no surprise that the bow shock was not found, and it was thought that Rosetta had not observed the bow shock at all during the mission (Mandt et al. 2016; Simon Wedlund et al. 2017). In fact the magnetic field strength did not decrease significantly even at 1500 km (as compared to 100 km), indicating that Rosetta was not near the bow shock, where lower field values are expected (Goetz et al. 2017). Recently, the non-detection of a bow shock was vindicated by Alho et al. (2021) who took into account a more realistic asymmetric outgassing based on the semi-empirical model of Hansen et al. (2016) and an extended mass-loading boundary condition (see also Sect. 3.3). These authors estimated with a kinetic hybrid plasma model that the bow shock subsolar standoff distance was increased by a factor 2 to 3 with respect to non-asymmetric outgassing conditions, reaching about 18,000 km for 67P around perihelion. They showed also that simulated pickup ion observations deep in the coma display spectral features in energy that may be interpreted with the simulations as the presence of
<figure><img src="image_38.png" /><figcaption>**Fig. 36** The infant bow shock at comet 67P. In the left-hand panel the red circles mark the position of comet 67P on each of the 152 days on which shocked solar wind plasma was observed (Goetz et al. 2020a). The second panel shows the magnetic flux density magnitude in a hybrid simulation of the infant bow shock. The light blue circle marks the position of the nucleus. The three panels on the right-hand side show from the top: the energy spectrum of the light ions, the electron energy spectrum, and the components and magnitude of *B* as observed by the Rosetta spacecraft (Gunell et al. 2018). The vertical light blue and purple lines mark when the spacecraft entered and exited the region with shocked plasma in an infant bow shock encounter. From (Gunell 2020)</figcaption></figure>

shock-like structures far upstream of the spacecraft. Both asymmetric outgassing and IMF clock angle were found to drive these spectral features.

The dayside excursion took place when the comet was close to perihelion, and the simulations mentioned above all concerned conditions corresponding to a comet near perihelion. However, far away from the Sun, the comet has only a very thin atmosphere, and its size is smaller than the proton gyroradius (~10³ km for a solar wind proton in the comet frame of reference and a 4 nT magnetic field). Hence, one would not expect a comet to have a bow shock at large heliocentric distances. Between the no-shock situation far away from the sun and the fully developed shock at perihelion, the bow shock forms. Lindkvist et al. (2018) performed hybrid simulations of comet 67P, comparing two different ionisation rates. In the simulation with the lower ionisation rate, a very asymmetric “shock-like structure” formed, extending far into the *z* < 0 plane in CSE coordinates. In the CSE coordinate system the *z* axis is parallel to the convection electric field of the solar wind. The purpose of the simulations by Lindkvist et al. (2018) was to study energy conversion at the comet. It was found that the shock-like structure acts as an electromagnetic generator in the same way as Earth’s bow shock. In a generator $\vec{E} \cdot \vec{J} < 0$ and energy is transferred from the particles to the fields. The shock-like structure also has the other properties of a collisionless shock, a rapidly increasing magnetic field, and a slowing down and heating of the solar wind, to the extent it can be modelled with the available resolution and in a hybrid simulation that does not include electron physics.

Gunell et al. (2018) found that under specific circumstances heated protons could be detected near the nucleus. Because of the similarity of these observations with numerical simulations, they introduced the concept of a highly asymmetric and unstable “infant bow shock” to explain the presence of these protons. Goetz et al. (2020a) performed a statistical study of the complete data set for the whole mission, and found that this shocked solar wind plasma had been observed on 152 days.

Figure 36 shows a summary of these observations. The left-hand panel shows where along the comet orbit the observations took place. The first occurrence was at a heliocentric
distance just below 3 AU. When the comet got closer than 1.7 AU from the Sun the infant bow shock sightings ceased. This is consistent with the bow shock moving outward and sunward as the outgassing and ionisation increased, and Rosetta was then no longer in the region with shocked plasma. The infant bow shock returned after perihelion. It is seen in Fig. 36 that the bow shock sightings are shifted somewhat toward larger heliocentric distances on the outward leg of the comet’s journey when the outgassing rate was higher (Hansen et al. 2016). It was found by Goetz et al. (2020a) that the infant bow shock is seen more often at intermediate outgassing rates.

The middle panel of Fig. 36 shows the magnitude of $\vec{B}$ in the $x-z$ plane in a hybrid simulation, where the $x$ axis is directed toward the Sun and the $z$ axis parallel to the solar wind electric field. It is seen how the infant bow shock extends far into the negative $z$ half plane and how the magnetic field increases at the shock, and continues to oscillate on the downstream side. On the right-hand side of Fig. 36 are three panels showing an example of Rosetta crossing the infant bow shock. Here, the spacecraft moves with respect to the infant bow shock because the shock turns due to a change in the solar wind magnetic field direction. This also changes the direction of the electric field, and hence of the $z$ axis in the middle panel of Fig. 36. An example of when this happened is marked by the light blue vertical line in Fig. 36 (see Gunell et al. 2018, for a detailed description).

An infant bow shock can be seen in figures from the simulation by Koenders et al. (2016a) although at the time it was not called by that name. The simulation was used to model the close flyby of comet 67P on 28 March 2015. Rosetta was close to the nucleus and the infant bow shock farther out, which is why it was not observed that day. Edberg et al. (2016b) studied the impact of corotating interaction regions on comet 67P, but they also found another feature. Edberg et al. (2016b) describe it thus: “On 24 December 2015, when the magnetic field orientation has changed, the solar wind flux is decreased and the suprathelial electrons increased significantly. It is possible that these signatures also indicate the crossing of a plasma boundary, which builds up as the solar wind dynamic pressure increases.” This can now be identified as one of the first encounters of the infant bow shock and it is part of the infant bow shock database used in the statistical study by Goetz et al. (2020a).

Since the Rosetta spacecraft was located downstream of the bow shock when the comet was less than 1.7 AU from the Sun, no in situ observations could be made for a considerable length of time. A method for remote detection of a bow shock was suggested by Nilsson et al. (2018), who observed that if cometary ions are accelerated by a constant electric field, the energy at which they reach the spacecraft is proportional to the distance to the place where they were created by ionisation. The ion energy spectrum is therefore determined by the $1/r^2$ slope of the ionisation source. Nilsson et al. (2018) applied this method to Rosetta data from 16 June 2015 at approximately 1.4 AU and found the $1/r^2$ relationship to hold up to an energy of ~1 keV, which corresponded to a distance of 4000 km, and they predicted that that was the position of the bow shock. The method has been evaluated by simulations, which yield consistent results (Alho et al. 2019).

The physics of collisionless shocks is complicated, and it involves a number of different types of waves on both large and small scales. A complete understanding of it would require both observations and computer simulations that treat both electrons and ions kinetically and resolves all relevant scales (Balogh and Treumann 2013). At comets the situation is complicated further by the presence of several ion species, and also the neutral atmosphere has a significant influence at least for some regimes. The way forward from an observational point of view is to make simultaneous measurements at multiple points in space as in the upcoming Comet Interceptor mission (Snodgrass and Jones 2019), which will make a fast fly-through of a cometary plasma. To obtain a truly detailed view of the bow shock of a comet
<figure><img src="image_39.png" /><figcaption>**Fig. 37** Analytical trajectories of solar wind protons, Sun to the right and upstream magnetic field directed upward, in the same plane. Around the nucleus at the centre, a region is created in which solar wind ions cannot penetrate. According to the model, these trajectories simply scale with the activity and the heliocentric distance. From Behar et al. (2018a), reproduced with permission ©ESO</figcaption></figure>

one would need a multi-spacecraft mission that accompanies the comet over an extended period of time (Goetz et al. 2021). The possibility of learning about cometary bow shocks by conducting laboratory experiments here on Earth is discussed briefly in Sect. 3.1.3.

## 4.3 Solar Wind Ion Cavity

From May to December 2015, that is to say, several months before and after perihelion, Rosetta was in a region which was mostly free from solar wind ions – the solar wind ion cavity (Nilsson et al. 2017; Behar et al. 2017). Mass loading of the solar wind leads to magnetic pileup (see Sect. 4.4) and the increased field causes deflection of solar wind ions. On large scales and for a low-to-medium outgassing activity, we have reviewed in Sect. 2.3.1 the theoretical and observational understanding of the ion dynamics within the coma. What happens closer to the nucleus, or similarly when the comet draws closer to the Sun? Still considering the electric field as mostly characterised by its motional component, we can further characterise the local ion dynamics, given the ion densities and the magnetic field strength. Using simple analytical models for these, a semi-analytical model of the global dynamics of solar wind protons for a given heliocentric distance can be derived (Behar et al. 2018a), and results in the trajectories shown in Fig. 37. The trajectories shown are monoenergetic test particles moving in a magnetic field proportional to $r^{-2}$. Other magnetic field models are discussed in Sect. 4.4. We find a solar wind deflected in the direction opposite to the upstream electric field, as previously discussed in Sect. 2.3.1, resulting in an asymmetrical flow.
One of the main aspects of this model is the resulting inner-region in which solar ions cannot penetrate: the solar wind ion cavity. Previous cometary missions did observe a region free of solar wind ions, for more active comets, close to the Sun. At 67P, Rosetta observations showed increasingly deflected solar wind ions, and when the deflection reached values of 90° and more, they were observed more scarcely, with lower densities. They finally disappeared from the observations, to reappear after perihelion (Behar et al. 2017), a result seen in Fig. 11 of Sect. 2.3.1, first and second upper rows. Close to the ion cavity, protons were observed with very large deflections, before disappearing from the data.

The deflection angle estimated by the model could be compared to observed deflections, on the time scale of the mission, or of one of the two excursions, namely the night-side excursion (Behar et al. 2018a). These successfully estimated deflection angles within an extended region of the coma validate the way the solar wind gyrates within the coma, being repelled from the inner-most region – the ion cavity – through this global kinetic interaction.

With a more careful look and during the time the probe was within the solar wind ion cavity, some protons were observed during the dayside excursion, which brought the spacecraft to the very boundary of the solar wind ion cavity at 800 km, simultaneously with the interaction between the coma and a CME (Edberg et al. 2016a).

Simon Wedlund et al. (2019b) posed the question of whether charge exchange between solar wind ions and cometary neutrals could be responsible for the decrease in solar wind ion flux that is observed when the spacecraft enters the solar wind ion cavity.

The solar wind ion cavity and the diamagnetic cavity are two different structures, with different spatial scales, involving very different physics. While the ions are deflected and diverted from the solar wind cavity, electrons keep advecting the magnetic field deeper within the ion cavity (Deca et al. 2017). As a result, the diamagnetic cavity is entirely independent and almost always within the ion cavity.

While the solar wind ions are excluded from the solar wind ion cavity, the solar wind magnetic field and pick up ions created upstream permeate the region downstream of the solar wind ion cavity boundary until the diamagnetic cavity boundary. Williamson et al. (2020) looked at the momentum flux continuity and plasma pressure balance over the Rosetta mission. They found the pressure on both sides of the solar wind ion cavity boundary to be approximately equal, as can be expected. The pick up ion momentum flux inside the solar wind ion cavity contributes the anti-sunward momentum flux of the solar wind outside. Essentially the pick up ions replace the solar wind ions. A further aspect of this was reported by Nilsson et al. (2020) who noted that the pick up ions just outside the boundary as well as inside the solar wind ion cavity were deflected in a similar manner to the solar wind. The pick up ions were moving against the inferred solar wind electric field direction. This is consistent with these ions carrying the momentum into the solar wind ion cavity and providing momentum to newborn ions inside the cavity. The description of the deflected solar wind in Sect. 2.3.1 holds here as well, with the pick up ions gyrating around the common centre of mass of the pick up ions and the locally born cold ions. The solar wind ion cavity boundary is thus not a significant boundary in terms of energy and momentum flux from the solar wind to the inner part of the coma.

## 4.4 Magnetic Field Structure and Tail

The interaction of the IMF carried by the solar wind and an outgassing comet leads to the formation of an induced magnetosphere through mass loading. The neutral gas coming from the cometary nucleus gets ionized and picked up by the IMF. This mass loading of the solar wind will slow it down and a simple 1D MHD model, presented by Biermann et al. (1967)
<figure><img src="image_40.png" /><figcaption>Fig. 38 Radial magnetic field profile for the two models as applied to comet 67P/Churyumov-Gerasimenko. From Goetz et al. (2017), Fig. 1</figcaption></figure>

and Flammer and Mendis (1991), can give an analytic solution of the solar wind velocity by combining the continuity, momentum and energy equations (see also Goetz et al. 2017):

$$u_x(x) = 2(f+1)(M(x) + \rho_{\infty}u_{\infty}) \times \left[ (f+2)\rho_{\infty}u_{\infty}^2 \pm \sqrt{(f+2)\rho_{\infty}^2 u_{\infty}^4 - 4(f+1)(M(x) + \rho_{\infty}u_{\infty})\rho_{\infty}u_{\infty}^3} \right], \quad (21)$$

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 which is given by:

$$M(x) = \int_{-\infty}^{x} \frac{m_c Q v_0}{4\pi u_n r^2} dr, \quad (22)$$

which is the integrated column density from the Haser (1957) model, with $Q$ the outgassing rate, $m_c$ the cometary ion mass and $u_n$ the outflow velocity of the neutrals and $v_0$ is the photoionisation frequency. The source is expected to emit radially symmetrically, and thus a $r^{-2}$ fall off of the neutral density. The magnetic field is then simply given by:

$$B_y(x) = \frac{u_{x\infty} B_{y\infty}}{u_x(x)}, \quad (23)$$

with $B_{y\infty}$ the magnetic field of the solar wind. This description has a problem for the location $x_l$ where $u_x(x_l)$ becomes complex and the magnetic field $B_y(x) \to \infty$ and the bow shock is created (see Sect. 4.2). A solution to the problem of the flow behind the shock was given by Galeev et al. (1985), when one assumes there is cooling of the plasma through charge exchange at a rate of $\alpha$ (for details, see also Goetz et al. 2017). This then results in a finite magnetic field behind the shock, as shown in Fig. 38.

With this 1D model one can get the magnetic field magnitude in the cometasheath along the Sun-comet line, but it does not describe the 2D/3D structure of the induced magnetosphere. The model needs to be adapted in that the mass loading source falls off radially away
<figure><img src="image_41.png" /><figcaption>Fig. 39 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 aberrated Parker spiral angles. From Volwerk et al. (2019), reproduced with permission ©ESO</figcaption></figure>

from this line. This means that the mass loading further away is less, and thus the braking of the solar wind and IMF will be less. Thereby, the magnetic field will be draped around the active nucleus, as described by Alfvén (1957).

In order to describe the actual situation at a comet, the dynamics of the IMF need to be incorporated. The IMF is usually split-up into four or six sectors, in which the radial component of the magnetic field changes sign. Thereby, differently directed magnetic field will be draped around the active nucleus. Depending on flow velocity of the magnetoplasma and the diffusion time of the magnetic field through the plasma, there can then be a layering of these field lines in front of the nucleus, creating “nested draping.” This was first observed during the flybys of comet 1P/Halley by VEGA 1 (Riedler et al. 1986) and Giotto (Raeder et al. 1987). Indeed, for the Giotto flyby, Raeder et al. (1987) were able to find the corresponding regions during ingress and egress, showing the actual “onion layers” of the draped magnetic field.

The flybys of comet 1P/Halley took less than 30 minutes, and thus the magnetic picture that was obtained of the upstream region was a snapshot. This was quite different for the dayside excursion of the Rosetta spacecraft at comet 67P/Churyumov-Gerasimenko. In this case the spacecraft took an upstream excursion of ~20 days up to a distance of ~1500 km from the nucleus. Volwerk et al. (2019) determined the cone angle of the magnetic field during the excursion, shown in Fig. 39 as a function of distance from the nucleus. In the case of nested draping, the cone angle, defined as:

$$ \theta_{co} = \tan^{-1} \left\{ \frac{\sqrt{B_y^2 + B_z^2}}{B_x} \right\}, \qquad (24) $$

where $\theta_{co} = 0°$ is purely sunward directed field and $\theta_{co} = 180°$ purely anti-sunward. In Fig. 39 it is clear that the cone angle switches between small values, below the aberrated Parker spiral (Parker 1958) (green lines), to large values above the aberrated Parker spiral. Through the motion of the comet an aberration of ~15° is created. So, indeed, during the outbound leg there are three regions of differently directed magnetic field. On the inbound leg there is a change in direction at $R \approx 1400$ km, which demarks a region that did not exist at that location during the inbound leg. This means that the draping moves faster towards the nucleus than the spacecraft is moving. This is called “dynamic draping.”
This means that the upstream structure of the magnetic field looks slightly different depending on the velocity of the spacecraft, the static picture that is obtained from a fast flyby is put into perspective by the slow upstream excursion.

Closer to the active nucleus there is another draping effect that needs to be taken into account. Koenders et al. (2016a) showed that the draping of the magnetic field close to the comet at intermediate gas production rates was mainly in the anti-direction of the solar wind convective electric field. This is caused by Newton's second law; the newly created ions are accelerated in the direction of the convective electric field, and as a reaction the solar wind ions will move in the opposite direction (see also Broiles et al. 2015), dragging along the frozen in magnetic field. This was observed on 28 March 2015 (see Koenders et al. 2016a, Fig. 2) when Rosetta had a closest approach of ~ 15 km. Naturally, this effect starts to become very important when the pick-up density starts to become similar to the solar wind density.

Following the mass-loaded field lines further downstream the cometary ion tail is reached, where the field lines stretch behind the comet, creating a double lobed (induced) magnetotail as described by Alfvén (1957). The first evidence for this magnetotail structure was given by the ICE spacecraft, on 11 September 1985, when it crossed the tail of comet 21P/Giacobini-Zinner at distance of ~ 10⁴ km (Smith et al. 1986).

Slavin et al. (1986, Fig. 1) showed the magnetic field super-imposed on a ground-base image of the comet in a band around the H₂O⁺ 7025 Å line. Before the bow shock crossing there are small variations in the magnetic field vectors, pointing sunward, with a strength varying up to 10 nT. After the bow shock is crossed, the magnetic field is much stronger and pointing anti-sunward, decreasing in strength as ICE moves towards Z'_{CSE} = 0. Near Z'_{CSE} ≈ 1000 km, the field is very weak, and then turns sunward again, and increases in strength. The field decreases in strength again towards the bow shock and after exiting the field is first anti-sunward and then returns sunward again like before the encounter. This encounter clearly showed the double lobed draped magnetic field of the induced magnetotail.

The second investigation of the tail region of a comet was performed by Rosetta at comet 67P/Churyumov-Gerasimenko. In this case the spacecraft moved up to ~ 1000 km down tail of the nucleus in the period from 24 March until 10 April 2016 and only the very near-region was studied (Volwerk et al. 2018). In order to study the draping of the field, the cone-angle θ_{co} was calculated. Volwerk et al. (2018) showed that the peak in the cone angle is between 60° and 80°, which means that the “draped” magnetic field is more cross tail than along the Sun-comet-line as one would expect.

The explanation for the “cross-tail” direction of the magnetic field can be found in the deflected solar wind magnetic field (Koenders et al. 2016a) as discussed above. The observations in the tail show that this deflected field is transported to the downstream side of the comet, and then eventually stretches out to the more regular tail structure.

Around apoapsis, for R ≥ 500 km, the clock angle, defined as:

$$ \phi_{\text{cl}} = \tan^{-1} \left\{ \frac{B_z}{B_y} \right\}, \qquad (25) $$

showed unexpected behaviour. In Fig. 6 of Volwerk et al. (2018) the unwrapped clock angle is presented, and it shows a continuously increasing angle $\phi_{cl}$. Even when the spacecraft turns around at apoapsis $\phi_{cl}$ increases, which means that RPC-MAG is measuring a traveling rotational wave along the magnetic field. Using the frequency of the wave and the velocity of Rosetta outbound ($\omega_h \approx 5.65°/h$, $v_{ros} \approx 1.3$ m/s) and inbound ($\omega_h \approx 5.83°/h$, $v_{ros} \approx 3$ m/s), a phase velocity of the wave was found of $v_h \approx 136$ m/s. This behaviour of the clock angle
is not present in the solar wind, and thus must be from cometary origin. However, with an average magnetic field of $B_m \approx 10$ nT, this velocity does not correspond to the Alfvén velocity, nor does the gyro frequency correspond to that of any major species.

## 4.5 Collisionopauses

A collisionopause is a boundary in the comet-solar wind interaction region where collisions first become important inside of the boundary (Mendis et al. 1986; Cravens 1989, 1991). Cravens (1991) outlined various types of collisionopause for both ions and electrons depending on the collision processes involved. To date, three boundaries have been observed by spacecraft at comets that have been proposed to be collisionopause boundaries: the cometopause (Gringauz et al. 1986b; Gombosi 1987; Coates 1997), the cometary ion collisionopause (Mandt et al. 2016, 2019), and the electron exobase (Henri et al. 2017). Two of the three boundaries are illustrated in Fig. 34. The electron exobase is observed in the region near the boundary of the diamagnetic cavity (Fig. 44).

Since a collisionopause is the location where collisions between plasma and neutrals dominate the plasma dynamics (Mendis et al. 1986), this boundary is similar to an exobase of an atmosphere, or the boundary used in aeronomy where collisions dominate the dynamic of the gas. Therefore, we can estimate the location of a collisionopause in a similar manner to how the exobase location is determined. An exobase is located where the ratio of the mean free path to the scale height, is equal to one. In the case of a collisionopause, the plasma mean free path, $\lambda$, is estimated as

$$ \lambda = \frac{1}{(n_n \sigma_c)}, \qquad (26) $$

where $n_n$ is the local neutral density and $\sigma_c$ is the momentum transfer cross-section of the relevant collision. According to Edberg et al. (2015) the plasma scale height at 67P observed between August 2014 and February 2015 was equal to the distance from the comet, $r$. More generally, Beth et al. (2019) showed that the plasma density asymptotically follows $\sim 1/r$, and therefore the scale height is $\sim r$. Assuming that this scale height is effective for the duration of the Rosetta mission during which the outgassing rate was high enough to form collisionopause boundaries, we can estimate the location of a collisionopause as the point where the distance from the comet is equal to the plasma mean free path. Taking into account that $n_n \propto r^2$, we can derive the mean free path to be

$$ \lambda = r = n_{s/c} \sigma_c r_{s/c}^2, \qquad (27) $$

where $r_{s/c}$ and $n_{s/c}$ are the spacecraft cometocentric distance, and the locally measured neutral density. This expression is equal to Eq. (29), if the relevant cross-section is that of electron-neutral collisions.

There are several sources of uncertainty when attempting to predict the location of a collisionopause, the greatest of which is the momentum transfer cross-section. These cross-sections depend on the composition of the ions and neutrals as well as the energy of the ions and electrons (Johnson et al. 2008), and are in general poorly understood (Mandt et al. 2019). When evaluating spacecraft flybys of comets, Itikawa and Mason (2005) assumed that the electron-neutral momentum transfer cross-section was $\sim 5 \times 10^{-16}$ cm$^2$ for 5 eV electrons, while Mendis et al. (1986) estimated the ion-neutral cross-section to be between $2 \times 10^{-15}$ cm$^2$ for solar wind protons and $8 \times 10^{-15}$ cm$^2$ for mass loaded solar wind with a bulk composition of $H_2O^+$. Mandt et al. (2019) conducted a review of cross sections for
reactions between water ions and water neutrals and showed that the energy-dependence of these cross sections means that the energy of the mass loaded solar wind ion flow determines the location of a cometary ion collisionopause boundary. However, based on the detailed analysis of solar wind ion cross sections by Simon Wedlund et al. (2019), the assumption of cross sections for the solar wind and cometary neutrals of ~2 × 10⁻¹⁵ cm² for solar wind protons is reasonable.

**The cometopause** is described as the boundary where the ion composition in the solar wind ion flow changes from predominantly solar wind ions ($H^+, He^{2+}$) to predominantly cometary ions ($O^+, OH^+, H_2O^+, H_3O^+, \text{etc.}$) (Gringauz et al. 1986b; Gombosi 1987; Coates 1997). Some have disputed the existence of this boundary (Rème et al. 1994), while others suggest that it is a permanent feature (Gringauz and Verigin 1991; Sauer et al. 1995). The cometopause at previous comet flybys was characterized by a decrease in electron velocity and temperature, an increase in ion densities and deflection of ions (Rème et al. 1988; Cravens 1989). It is thought to be the beginning of the magnetic pileup region (d'Uston et al. 1988). The question remains whether the cometopause could be a collisionopause from ion-neutral charge transfer reactions such as $H_2O_{\text{fast}}^+ + H_2O \rightarrow H_2O_{\text{fast}} + H_2O^+$ as proposed by Cravens (1989). Based on the cross section for this reaction and the production rate of $6 \times 10^{27} \text{ s}^{-1}$ measured by MIRO during the dayside excursion (Mandt et al. 2016), Rosetta should have crossed the cometopause before crossing the cometary ion collisionopause, which had a larger cross section. As shown in Fig. 34, the observed crossings of the cometopause for Giotto at 1P/Halley and 26P/Grigg-Skjellerup were at a much greater distance from the nucleus than the cometary ion collisionopause, and thus the location of the cometopause based on spacecraft flyby observations is well outside of the region explored by Rosetta, which agrees with ion composition observations made during high outgassing periods (Behar et al. 2017). Therefore, it is not likely that the cometopause is a collisionopause as speculated previously.

**The cometary ion collisionopause** was first observed by Giotto at 1P/Halley (Schwenn et al. 1988; Altwegg et al. 1993) and later by Deep Space 1 at 19P/Borrelly (Young et al. 2004), but was not identified as a boundary until after Rosetta observations detected and characterised this boundary at 67P (Mandt et al. 2016, 2019). Observations made by RPC-IES between January 2015 and February 2016 showed the formation of two regions based on ion energies: an inner and an outer region. These regions were separated by a boundary that appeared at times to be sharp, and at other times to be broad as illustrated in Fig. 40. The inner region is characterised by low energy ions that appear at an energy near the value of the spacecraft potential, which can be seen in panels (a) and (c) of Fig. 40, while the outer region is characterised by relatively high energy ions that RPC-ICA shows to be water-group ions (Nilsson et al. 2015a,b; Behar et al. 2016b). Their high energy suggests that they are cometary ions that have been picked up in the solar wind flow. The boundary was first detected in April 2015, when the solar wind disappeared from the RPC-IES ions and the energy of the water group ions began to vary between the value of the spacecraft potential and values above 50 eV. This variability was at times related to the spacecraft distance from the comet, but at other times may have been due to changes in solar wind dynamic pressure based on models extrapolating measurements made at Earth to the Rosetta location (Mandt et al. 2016). Over time, the outer region was observed less often than the inner region and by the end of July 2015 Rosetta remained mostly in the inner region. The next time that Rosetta moved into the outer region was during the dayside excursion that took place in September and October 2015, at which time the spacecraft travelled from within 300 km of the nucleus out to 1500 km from the nucleus and then back. During the excursion, Rosetta crossed the boundary and remained outside of the boundary for a couple of days as shown
<figure><img src="image_42.png" /><figcaption>**Fig. 40** Observations of crossings of the ion-neutral collisionopause during the excursion to 1500 km in September and October 2015. The bar at the top of the figure indicates whether the spacecraft was in the inner (black) or the outer (red) region. In the outer region ions with energies greater than 50 eV are observed (panel a). Ion energies in the inner region are observed at the spacecraft potential (panel c), which varied between 0 and -20 V. The boundary between the two regions appears in some crossings to be sharp, such as on 15 October, while at other points to be broad. The sharp boundary crossings likely appear to be sharp because the solar wind dynamic pressure increased due to an event such as a CIR or CME, causing the boundary to move across the spacecraft (see Mandt et al. 2016, for details). From Mandt et al. (2019), reproduced with permission ©ESO</figcaption></figure>

Fig. 40, thus confirming that the boundary is a permanent feature rather than a transient one. The electron densities were enhanced in the inner region while the magnetic field magnitude was reduced. This boundary was located well outside of the diamagnetic cavity (Goetz et al. 2016b).

It is valuable at this point to compare the Rosetta observations during the dayside excursion with observations made at 1P/Halley, 26P/Grigg-Skjellerup, and 19P/Borelly. We illustrate in Fig. 41 total ion or electron density, the ion velocity, and the ratio of mass 19 to 18 ions for these four mission observations. The cometary ion collisionopause observed by Rosetta strongly resembles a drop in ion velocity observed by Giotto at 1P/Halley (Schwenn et al. 1988) in a region described as an ion pileup region (Balsiger et al. 1986). The Giotto observations of the mass 19/18 ratio shown in the bottom panel of Fig. 41 demonstrate that $H_3O^+$ became the dominant ion species in the ion pileup region (Balsiger et al. 1986; Schwenn et al. 1988). This is indicative of a reaction taking place in this region forming $H_3O^+$ from $H_2O^+$. Based on the observations shown in panels (a) and (b) of Fig. 40 it appears that the ions begin to pile up inside of the point where we identify the cometary ion collisionopause with the shaded region. Inside of this, panel (a) shows that the ion densities decrease well inside of this boundary, possibly indicating the electron exobase, or the electron cooling boundary, where ion loss rates due to electron recombination will increase as a result of electron cooling.
<figure><img src="image_43.png" /><figcaption>**Fig. 41** Comparison of plasma observations as a function of the distance from the nucleus scaled by the production rate ×10⁻²⁷ as observed by Rosetta during the dayside excursion, Giotto during flybys of 1P/Halley (Altwegg et al. 1993) and 26P/Grigg-Skjellerup (Goldstein et al. 1994) and Deep Space 1 during the flyby of 19P/Borrelly (Young et al. 2004). The top panel shows the total ion number density for the flybys and the Rosetta electron density. The centre panel illustrates the ion bulk velocity, and the bottom panel shows the ratio of ions with mass 19 (H₃O⁺) to ions with mass 18 (mostly H₂O⁺ with some uncertain contribution from NH₄⁺). The horizontal dashed lines in the centre panel represent the estimated bulk velocities for RPC-IES observations of collisionopause crossings after correcting for spacecraft charging effects. The shaded regions indicate where Rosetta, DS1, and Giotto at 1P/Halley crossed into a similar range of velocities indicating crossing of the cometary ion collisionopause. The ion velocities at 26P/GS did not show an indication of crossing of this boundary. From Mandt et al. (2019), reproduced with permission ©ESO</figcaption></figure>

**The electron exobase** is the electron-neutral collisionopause (Mandt et al. 2016). It is also referred to as the electron cooling boundary (Eriksson et al. 2017; Henri et al. 2017), because it is the boundary outside of which electrons are no longer collisional. As with the cometary ion collisionopause, this boundary is not sharp but is instead a region of gradual transition. This is complicated by the fact that electrons may be cooled within the electron exobase, but cold electrons are found everywhere in the plasma environment. This is because of transport of electrons (Gilet et al. 2020). Evaluation of Rosetta observations show that this boundary is located near the diamagnetic cavity boundary (see Fig. 34) (Henri et al. 2017). For a more detailed discussion see Sect. 4.6 and 2.3.5.

We described here three possible collisionopause boundaries. The boundary closest to the nucleus would be the electron exobase, which is located near the diamagnetic cavity that is shown in Fig. 34. This Figure shows that observations have placed the cometary ion collisionopause farther from the nucleus than the diamagnetic cavity and that the cometopause is expected to be even farther away.

## 4.6 Diamagnetic Cavity

When Biermann et al. (1967) suggested the mechanism of mass-loading of the solar wind at a comet (see Eq. (21)), one of the outcomes of the model was the deceleration of the solar
wind until the velocity eventually reached zero somewhere upstream of the comet. Although the magnetic field was not included in the early models, it became clear that the magnetic field was tied to the solar wind (electrons) and thus would also come to a stop. With the assumption that a comet nucleus is not magnetised, the consequence of this would be the formation of a field-free diamagnetic cavity around the densest part of the cometary ion cloud around the nucleus.

The Active Magnetospheric Particle Tracer Experiment (AMPTE) in 1984–1986 enabled the first observations of such a region. The experiment consisted of three spacecraft, one of which was equipped with Barium and Lithium canisters that could be released in the magnetosheath of Earth’s magnetosphere or in the solar wind. The expanding gas and its impact on the plasma was then monitored by the spacecraft and ground-based observations (Valenzuela et al. 1986; Luehr et al. 1986; Haerendel et al. 1986; Rodgers et al. 1986). Just after the release of the Barium canister a region of zero-field could be observed for about a minute. This was the first evidence that addition of a gas cloud to a plasma can expel the magnetic field entirely from a certain region.

The advent of comet 1P/Halley then brought a number of flybys of the comet, of which ESA's Giotto spacecraft achieved the lowest altitudes, with a closest approach of ~600 km. As predicted, this was well within the bounds of the diamagnetic cavity and Neubauer et al. (1986) reported on magnetic field measurements while crossing into a field-free region at ~5000 km. Just outside the diamagnetic cavity Neubauer (1987) showed that a magnetic pile-up region similar to that at Mars or Venus exists, with maximum field strengths around 65 nT. This measurement presented the only detection of the diamagnetic cavity at a comet up until the new measurements by Rosetta.

In preparation for the Rosetta mission a number of simulations were used to constrain the diamagnetic cavity size and plasma parameters. Single fluid MHD simulations predict the diamagnetic cavity where ion-neutral friction equals magnetic pressure, which is at about $r = 50$ km, where the plasma velocity is also very close to zero. Multi-fluid MHD simulations show that an asymmetric outgassing profile (higher density on sunward side) extends the cavity further out on the sunward side (Huang et al. 2016). Furthermore, Kelvin-Helmholtz instabilities of the boundary can develop perpendicular to $\vec{B}$ (Rubin et al. 2012, 2015). The simulations also show that the solar wind only vanishes close to the diamagnetic cavity boundary (DCB). Hybrid simulations by Koenders et al. (2015) can confirm many of the MHD findings, but add more information in terms of ion dynamics. For example, they show a clear separation of solar wind ion cavity and diamagnetic cavity. Some accelerated cometary ions are visible even inside the diamagnetic cavity. Similar to Kelvin-Helmholtz instabilities, there are density filaments propagating along the boundary, however, these are not visible in the magnetic field, but that is attributable to numerical effects (high numerical diffusion for simulation stability) (Koenders et al. 2015). In summary, the diamagnetic cavity at comet 67P was expected to be observable only close to perihelion (±2 months) and was rather small with a radius of around 50 km. Due to navigational constraints of the Rosetta spacecraft, the altitude of the spacecraft during those months had to be raised to several hundred km (see Sect. 3.1) and thus an in-situ detection of the diamagnetic cavity was thought to be unlikely.

However, as reported in Goetz et al. (2016a,b) clear signatures of a magnetic field free region could be observed at 67P by Rosetta. It should be noted here, that the offset of the magnetometer was in the order of a couple of nT and thus in the initial data, the field was not observed as zero, instead the signatures were recognisable by a conspicuous absence of all field fluctuations that are predominant in the magnetic field around 67P close to perihelion
<figure><img src="image_44.png" /><figcaption>**Fig. 42** RPC observations of the plasma from 30 July 2015. From top to bottom: ICA heavy ions (high time resolution mode and negative spacecraft potential in black), IES ions, IES electrons, MIP spectra, plasma density from LAP and MIP, magnetic field, cone and clock angle of the magnetic field. The white line on the IES electrons indicates the summed flux over the 80–120 eV interval. The horizontal magenta bars mark the time that Rosetta was measuring inside the diamagnetic cavity. *e1* and *e2* mark the times of two density enhancements in the diamagnetic cavity</figcaption></figure>

(see Sect. 2.3.7). Assuming the field to be zero in the cavity has served as a good way to recalibrate the instrument, but on the other hand the exact field value in the cavity is only constrained to ±3 nT per component (Goetz et al. 2016a). Over 700 separate events have been reported since, between April 2015 and February 2016. This corresponds to heliocentric distances below 2 AU (2.4 AU) inbound (outbound) and gas production rates above $10^{27}$ s⁻¹ (Goetz et al. 2016a; Goetz 2019).

Figure 42 shows a series of cavity signatures observed by the RPC instruments on 30 July 2015, close to perihelion. The spacecraft was 180 km from the nucleus ($\vec{r}_{CSEQ}$ = (0, 80, 150) km). The quick succession of events already illustrates a peculiarity of the Rosetta measurements: Rosetta is a slow spacecraft, so whenever the spacecraft enters the diamagnetic cavity it is attributed to the boundary moving (not the spacecraft). These events illustrate typical behaviour of the plasma. The plasma outside is characterised by a series of asymmetric, steepened waves which are visible in the magnetic field, as well as in the MIP plasma density and the ICA heavy ion energy spectra (Stenberg Wieser et al. 2017; Hajra et al. 2018b). The signature of these steepened waves is mirrored in the magnetic field at the boundary of the diamagnetic cavity where the decrease is always less steep than the increase when Rosetta leaves the cavity (Goetz et al. 2016a). The magnetic field is oriented mostly along the x-axis (cone angle $\phi$ = 90°) whereas the clock angle $\theta$ varies more frequently. The magnetic field direction can flip when traversing a cavity (Goetz et al. 2016b). This is in accordance with the nested draping shown in Sect. 4.4. The IES ion measurements in this interval do not show much variation due to inopportune pointing. The electron spectra show
little variation, except for a dropout in electrons of energies between ~60 eV to ~200 eV. Even with poor temporal resolution this decrease is visible in the summed electron flux. Nemeth et al. (2016) and Madanian et al. (2017) speculated that this signature was due to the inability of field-aligned electrons to penetrate the diamagnetic cavity boundary. Madanian et al. (2020) calculated electron pitch angle distributions and found that the electrons in this energy range become increasingly field aligned as they enter the DCB. Inside the cavity, the unmagnetised plasma density has been shown to scale very well with the neutral density (Henri et al. 2017). The typical plasma density observed along Rosetta's trajectory close to perihelion is ~1000 cm⁻³, about a factor 1.5–2 higher outside the cavity (Hajra et al. 2018b).

The absence of the magnetic field also influences the wave environment, for example Gunell et al. (2017a) found ion-acoustic waves near the DCB and speculated that a current close to the boundary would be necessary to generate the waves. Other ion-acoustic waves are thought to be transmitted Lower hybrid waves (Madsen et al. 2018). For more details, see Sect. 2.3.7.

Although the unmagnetised plasma is observed to be quiet within the diamagnetic cavity (Henri et al. 2017), isolated events of dense plasma are sporadically observed. Two such events are marked e1 and e2 in Fig. 42. Hajra et al. (2018a) found that these plasma enhancements are not associated to neutral gas density fluctuations, but that both their structure and density are instead very similar to the steepened wave structures outside the diamagnetic cavity. They conclude that these blobs of plasma originate outside the cavity and are probably transmitted through the DCB. The scale length is 100–800 km, thus larger than the cavity itself, indicating it should be a global enhancement of the plasma density within the diamagnetic cavity (Hajra et al. 2018a).

These plasma enhancements are also visible in the ion spectra as higher energy and fluxes (Masunaga et al. 2019). Their properties are similar to the ion energy enhancements associated with the steepened waves, although they occur a factor of 10 less inside the cavity. They occur more frequently at lower gas production rates. The ion velocity is tailward and slightly radial. This affirms that the plasma can probably penetrate the DCB.

The shape and size of the diamagnetic cavity at 67P are hard to constrain, because only one point of measurement exists and in order to detect the diamagnetic cavity, the boundary needs to move and cannot be in a stationary state. Thus, models are needed to provide context. Historically, the problem of diamagnetic cavity formation has been viewed as a game of pressures: the magnetic pressure outside of the cavity needs to be balanced by another pressure on the inside. For the AMPTE artificial comet, it was determined that the gas pressure of the electrons in the added plasma was enough to balance the upstream magnetic pressure (Luehr et al. 1988). However, with the measurements by Giotto, it became clear that the situation there was somewhat different. Neither the electron pressure nor the ion dynamic pressure changed significantly at the diamagnetic cavity boundary (Cravens 1986). Thus a new mechanism had to be found to explain why the magnetic field was unable to diffuse into the diamagnetic cavity. Cravens (1987) presented a model in which the ion-neutral drag was proposed as that mechanism:

$$ \frac{\partial}{\partial r} \left( \frac{B^2}{2\mu_0} \right) = \rho_i k_{in} n_n (\vec{u}_i - \vec{u}_n)_r \quad (28) $$

Several assumptions were made: first, photochemical equilibrium was assumed and second, the ion velocity was set to zero in the integration region. These assumptions are thought to be valid at comet 1P/Halley where large neutral densities due to the high gas production
<figure><img src="image_45.png" /><figcaption>**Fig. 43** Left: Occurrence of cavity measurements over the spacecraft-comet distance in electron collision lengths. Right: spacecraft-comet distance over gas production rate (derived from in-situ measurements and a Haser model). The colour scale gives the dwell time of the spacecraft over the entire Rosetta comet phase, and the blue points mark the points at which a cavity was detected</figcaption></figure>

rate imply that the ions are efficiently coupled to the neutrals and do not move far between being created and annihilated by recombination. With this model the magnetic field in the boundary region could be calculated dependent on $r$ and matched reasonably well with the measured profile. The diamagnetic cavity size was predicted to be 4400 km, which also fit well with the measurements.

The sheer number of diamagnetic cavity crossings at 67P is useful to constrain the dependence of the diamagnetic cavity size and shape, depending on a variety of parameters. Goetz et al. (2016a) found that the size increases with gas production rate and, similar to simulations as well as observations at 1P/Halley, that the boundary is highly unstable. An instability is necessary to explain the quick succession of events as shown in Fig. 42 as well as the magnetic field orientation outside of the diamagnetic cavity. An elliptical shape with overlaying boundary oscillation fits the boundary normal distribution. All in all, the size of the diamagnetic cavity was much larger than expected, up to 400 km instead of just 50 km according to simulations and the models based on ion-neutral friction.

Henri et al. (2017) examined the plasma density inside the DCB in more detail and found that the size of the diamagnetic cavity scales very well with the electron exobase (or electron collisionopause), meaning that more cavities are detected when the spacecraft is close to the region where the electrons are more efficiently coupled to the neutrals (see also Sect. 2.3.2 and Fig. 43). The distance of Rosetta can be defined in terms of electron collision length scales:

$$r_{en} = r/(n_n r^2 \sigma_{en}). \qquad (29)$$

It is therefore possible that the mechanism that keeps the magnetic field at bay is related to the electron neutral collisions. As a way to explain the quiet and uniform plasma inside the diamagnetic cavity they also suggested that an instability such as a Rayleigh-Taylor instability could move the boundary quite rapidly. A four-fluid Hall MHD simulation shows that the introduction of the Hall term induces an asymmetry in the diamagnetic cavity size perpendicular to the upstream magnetic field and finds small regions of low magnetic field that are detached from the diamagnetic cavity that are possibly caused by reconnection (Huang et al. 2018). These regions could also be interpreted as protrusions from a global structure, similar to instabilities.

Modelling the diamagnetic cavity size at 67P based on the ion-neutral friction model gave satisfactory results if the maximum field in the pile-up region is chosen such that the observations fit the model (Nemeth et al. 2016; Timar et al. 2017; Madanian et al. 2017;
Nemeth 2020). This is unexpected, because this model (first derived by Cravens 1987) makes assumptions that do not apply at comet 67P: According to Beth et al. (2019) photochemical equilibrium does not hold in the coma at 67P, because transport is also important for the ion processes close to the cavity (see also Sect. 2.2.4). This can be shown by comparing the observed ion and neutral gas velocities. If the ion velocity is larger than the neutral velocity, this means that the ions have been accelerated and transport plays a role, and the ion-neutral collisions cannot sufficiently cool the ions. Unfortunately, reliable observations of slow ions are difficult with Rosetta, because of an often negative spacecraft potential (Odelstad et al. 2015; Bergman et al. 2020). Nonetheless, Odelstad et al. (2018) and Vigren et al. (2017) used independent methods to find that the ion velocity close to the diamagnetic cavity is 2–4 km/s with values on the lower edge of that range inside the diamagnetic cavity. As for the density, the ion velocity has a much higher variability outside of the cavity and decreases with cometicentric distance. From wake effects it can also be deduced that the bulk plasma flow is radial and supersonic. An ion velocity higher than the neutral velocity is in direct contradiction with the assumption that ions and neutrals are collisionally coupled and thus in direct contradiction with the model suggested by Cravens (1987). Vigren and Eriksson (2017) showed that such a discrepancy can be explained by low collision rates due to low neutral gas densities and propose that an ambipolar electric field (see also Sect. 4.1) can accelerate ions to the observed velocities. Fuselier et al. (2016) also pointed out that the unexpected H₂O⁺/H₃O⁺ ratio can be explained by an ambipolar field inside the diamagnetic cavity. It should also be noted that the definition of the collisionopause as a sharp boundary that separates a region where neutrals and ions are coupled from a region where they are not coupled is inappropriate, since collisions are a process that occurs on length scales comparable with the diamagnetic cavity size (Vigren and Eriksson 2019). As of now, it is unclear which process is responsible for deterring the magnetic field from diffusing into the diamagnetic cavity.

The inner coma is often dominated by warm electrons from photoionisation, but inside the diamagnetic cavity a second, colder ($< 0.1$ eV) population is found (Gilet et al. 2017; Odelstad et al. 2018; Engelhardt et al. 2018a). The cold electrons occur more frequently near the electron exobase and where the neutral gas is densest (e.g. due to asymmetric outgassing). The same ambipolar field that accelerates the ions retards the electrons and couples them more efficiently to the neutral gas via collisions. However, the appearance of cold electrons is also related to the direction of the convective electric field outside the diamagnetic cavity (Edberg et al. 2019a). The cold electrons are preferentially detected in the $-E_{conv}$ hemisphere, the same applies for the diamagnetic cavity (see also Sect. 2.3.2).

Figure 44 is an attempt at summarising the shape of and magnetic field and electron environment at the diamagnetic cavity. Although Rosetta observations of the diamagnetic cavity have added greatly to our understanding of the innermost coma, many open questions remain: What is the pressure balance at the boundary and what part does the changing plasma environment play in the movement of the DCB? How are electrons and ions cooled and/or accelerated in and near the cavity? What is the origin of the asymmetry in the in- and outbound crossing of the boundary? How are plasma enhancements transmitted trough the boundary and inside the diamagnetic cavity? Addressing these questions probably requires a multi-point measurement of the diamagnetic cavity, its boundary and upstream plasma conditions (Goetz et al. 2021).
<figure><img src="image_46.png" /><figcaption>**Fig. 44** Sketch of the diamagnetic cavity at comet 67P. The magnetic field (green) is draped around the cavity and solar wind electrons (sw e⁻) are moving along the field lines. Rosetta is located at the terminator, the most common configuration during the mission. Ion velocities are indicated in dark purple, with the accelerated ions outside the cavity moving anti-sunward and the newborn ions moving radially outward. The ambipolar electric field (white) is confined to the cavity. The cold (blue) and warm (red) ion populations are indicated as well. The light red background indicates the presence of warm electrons in the entire inner coma. The ion-neutral collisionopause is shown in black dashed lines</figcaption></figure>

# 5 Conclusions and Outlook

## 5.1 Conclusions

The plasma environment of comet 67P represents a new frontier in cometary plasma science. Due to the smaller outgassing rate compared to previously visited comets and the long mission duration, the Rosetta mission covered a new area in parameter space. At the comet, there are two plasma sources: the solar wind (mostly protons and electrons) and the cometary plasma, made up of heavy ions (mostly water) and electrons. Their densities mainly depend on heliocentric distance, though they are sometimes influenced by transient events, such as CIRs or cometary outbursts. The presence of these ions and electrons in the plasma stems from an equilibrium between sources (ionisation) and losses. The major net ionisation mechanisms are electron impact ionisation and photo-ionisation, with their relative importance changing over the two years covered by the Rosetta mission close to the nucleus. At larger cometocentric distances usually not explored by Rosetta, charge-exchange mechanisms are expected to play a prime role. The major plasma loss processes are transport and dissociative electron-ion recombination. Contrary to other cometary environments which are denser in their closest approach to the Sun, the outward transport of newborn ions remains an important process even near perihelion. FUV emissions can be used as a diagnostic tool for the neutral composition of the coma, electron-impact processes (including ionisation) and recombination processes. OI 1356 Å can be used to monitor the solar wind electrons beyond 2 AU from the Sun. Due to the large ion gyroradii compared to the size of the plasma environment, the kinetic behaviour of ions plays an important role for both the solar wind and cometary ions and can lead to pronounced asymmetries in large-scale structures. Several populations of electrons of different origin are present in the coma. Whereas solar wind
electrons are typically warm (around 10 eV), at large heliocentric distances (low outgassing) they are accelerated by an ambipolar electric field in the vicinity of the nucleus and reach energies of a few tens of eV responsible for ionisation and excitation of the cometary neutrals. Newborn cometary electrons are also warm (around 10 eV), although some of them undergo cooling through, most likely, collisions with cometary neutrals. This yields a colder electron population, even at large heliocentric distances (3–4 AU from the Sun) when the outgassing is low and electrons were not anticipated to be coupled to neutrals.

In order to distribute momentum and energy throughout the plasma environment, waves are excited at all activity stages, and observed in the magnetic field, electric field, and plasma density measurements with periods ranging from milliseconds up to tens of minutes. Transients in the solar wind and outgassing rate influence the interaction on time scales of hours to days.

The Rosetta mission has enabled major advances in cometary plasmas. It was equipped with a range of plasma, field, gas, and spectral instruments and orbited the comet for over two years. This made it possible to study the evolution of the plasma processes as activity increased until perihelion and decreased again afterwards. In addition, laboratory measurements of reaction rates and emissions are integral to delivering input for models, both analytical and numerical. While it is impossible to recreate the large-scale structures of the cometary plasma, laboratory experiments on smaller scales can give valuable insight into plasma processes. Numerical models are also a powerful tool to interpret and complement the observations. However, models and their input need to be chosen carefully to ensure they are suitable to the situation. Unfortunately, no model can adequately treat both large and small scales alike.

Large-scale structures span scales above or at the gyroradius of the cometary ions and can be used to identify distinct regions, with different properties, in the plasma environment. A classical bow shock, as known from earlier cometary missions, was not observed at 67P due to trajectory constraints, but there is evidence of the existence of a bow shock in the ion spectra. An infant bow shock, an asymmetric structure that could be a precursor of a real bow shock, was detected. Deflection of solar wind ions as a result of mass-loading creates a solar wind ion cavity, a region devoid of solar wind ions that is persistent at high gas production rates. Picked up ions continue to carry the momentum into the solar wind ion cavity.

Large-scale electric fields include the convective, ambipolar and polarization electric field. They affect both the ions and electrons, and are important for instabilities and wave generation. The magnetic field is draped around the inner coma, often in a nested field pattern that was also observed at other comets. The draping follows the direction of the deflected solar wind, even in the near-nucleus tail. A diamagnetic cavity, a region devoid of any magnetic field, was observed hundreds of times and was found to be larger than expected. The boundary of this region is highly unstable. Cold electrons are always observed in the cavity, while electrons from the solar wind cannot enter. The magnetic field is close to zero in the diamagnetic cavity and magnetic field oscillations cease. Rosetta was always outside of the electron collisionopause, the region where electrons couple efficiently with neutrals assuming radial transport, but it observed the ion-neutral collisionopause on multiple occasions.

Figure 45 is an attempt to summarise and overview the different key plasma processes described above. It shows the most important particle trajectories, fields and phenomena for the three activity stages as defined in the introduction (Sect. 1). Note that electric fields and most waves were not included, because they are summarised in Figs. 35 and 18. It becomes clear that comets are exposed to a wide range of scenarios. As they move around in the
**Fig. 45** Sketch of the plasma environment at 67P at three different activity stages as defined in Sect. 1. Note that the sketch is in a CSE system, aligned with the magnetic and convective electric fields and that the cross-sections are different for the three panels. While the structures are approximately to scale with respect to each other for the low and medium activity cases. The high activity case is not to scale with regards to the other stages and the scale is approximately logarithmic with respect to the radial distance to the nucleus

<figure><img src="image_47.png" /><figcaption>(a) low activity</figcaption></figure>

<figure><img src="image_48.png" /><figcaption>(b) medium activity</figcaption></figure>

<figure><img src="image_49.png" /><figcaption>(c) high activity</figcaption></figure>
solar system, the plasma conditions change as well as the activity of the comet. This gives rise to a plethora of different processes, whose importance is changing with the changing conditions. As an example, far from the Sun (low activity, panel a), solar wind ions and electrons penetrate deeply into the tenuous atmosphere where they can give rise to auroral emissions from the soft X-rays to the FUV. The intermediate case (panel b) is characterised by the beginnings of large-scale structures like the infant bow shock and magnetic field draping which are asymmetric due to the gyroradius effects of the ions. Closer to the Sun (panel c), an unstable diamagnetic cavity is formed and cold electrons dominate close to the nucleus, near the electron exobase. The solar wind ions are not able to penetrate the inner coma anymore and there is evidence for a classical bow shock upstream of the solar wind ion cavity. Comets therefore cover an extensive part of parameter space and present an excellent laboratory to study large scale structures as well as small scale interactions.

## 5.2 Open Questions

Many questions pertaining to cometary plasma environments still remain open, we provide here a non-exhaustive list of questions directly related to the new results from Rosetta:

* How do waves and wave-particle interactions affect the cometary plasma?

* What are the exact plasma distribution and ion composition (up to 50 amu) with respect to cometocentric distance (in 3D), and how does it vary in time? Qualitative and global quantitative measurements have been made with Rosetta, but systematic quantitative in situ surveys need to be made to understand the detailed ion-neutral physico-chemistry of the coma.

* Why is there evidence for ion acceleration at 67P within the cavity but not at 1P/Halley?

* What is the plasma balance near perihelion around the diamagnetic cavity?

* What is the impact of electric field acceleration and dust charging on the plasma balance and vice versa?

* What is the energy distribution of electrons below the spacecraft potential?

* How are dissociative electron-impact emissions (e.g., OI 6300 Å and OI 1356 Å) affected by the near nucleus coma environment near perihelion?

* How do nested draping and dynamic draping relate to each other, is a true pile-up of nested fields created or is this just a result of a snapshot flyby?

* What is the large-scale structure of the ion tail? How do the Rosetta near-tail and the ICE far-tail combine to one general structure?

* How do kinetic aspects of the ion dynamics around a low-to-medium activity comet continuously evolve towards a more fluid behaviour at high outgassing activity, close to the Sun?

* To what extent are the position and shape of the solar wind ion cavity dictated by macroscopic ion kinetic dynamics (see Fig. 37) and by loss of solar wind density through charge exchange?

* What is the combined effect of the polarisation and ambipolar electric fields?

* What is the speed of the bulk of low energy ions accelerated by the ambipolar electric field near the nucleus?

* How can we describe the shape and size of the bow shock, depending on outgassing and ionisation?

* What are the processes behind energy conversion at the bow shock and how can we make predictions based on outgassing and ionisation?

* Is there a force balance at the diamagnetic cavity boundary, and if so what forces are involved? What is the shape and stability of the boundary?
* Is the cometopause a physical boundary or a gradual transition in the composition of the cometary ions?

* Cold electrons have been observed even when the predicted electron collisionopause is below the surface. What is the process to cool newborn, warm electrons?

* What is the role of (quiet) solar wind dynamics in the inner coma dynamics?

These questions can be addressed by spacecraft missions (Goetz et al. 2021), but also simulations (see Sect. 3.3) and laboratory measurements (see Sect. 3.1.3).

## 5.3 Outlook

It is clear that the philosophical strive to improve our knowledge of the physical processes in the plasma at the comet, and more generally natural plasma over a full range of collisionality levels, requires space missions that provide data directly from the source. Goetz et al. (2021) outline open questions and propose mission concepts that would be able to (partially) answer them. By far the most complete mission profile is that of a dedicated multi-spacecraft mission to study a comet's plasma environment. Following a comet as it makes its way through the solar system, while exploring simultaneously the plasma environment at multiple points with a full suite of plasma and fields, energetic particle, and gas and remote-sensing instruments would afford the opportunity to answer most of the currently open questions.

A somewhat more limited mission concept is that of piggy-backing one or more dedicated plasma spacecraft on a mission exploring the nucleus, e.g. a sample return or lander mission. This would allow for a separation of the nucleus centred instruments that usually prefer smaller cometocentric distances and the plasma centred instruments that would require larger variations in cometocentric distances. The advantage is a reduction in mission cost, while losing some of the multi-point capabilities that come with a full plasma mission profile.

Other, smaller experiments based on similar concepts as AMPTE, i.e. creating ion clouds in or near Earth's magnetosphere, could also help understand microscopic processes like collisionality and pick up in a large scale system. This has the advantage of close proximity to Earth, but cannot address the questions on larger dynamics in a comet's plasmasphere.

A first step in this direction is ESA's Comet Interceptor mission (Snodgrass and Jones 2019), which will intercept a dynamically new comet with three spacecraft sometime in the 2030s. Since this mission will be a fast flyby with multi-point measurements of the magnetic field (though not of the plasma), it will give a valuable snapshot of the environment of a dynamically new object and will provide valuable clues as to the asymmetry of structures in the plasma. However, by its nature, Comet Interceptor will not be able to explore the evolution of the plasma environment, and will only cover one part of the enormous parameter space to be explored at comets. After the Giotto and Rosetta missions, Comet Interceptor is a promising next step to pave the way of multi-point, larger-class missions for exploring the exciting, challenging, and enriching plasma environment around comets, which has still so much to reveal.

### Acronyms

* 67P Comet 67P/Churyumov-Gerasimenko

* ACAP As close as possible

* AMPTE Active Magnetospheric Particle Tracer Experiment

* AU Astronomical unit

* CIR Corotating interaction region

* CME Coronal mass ejection
<table>
  <tr>
    <td>COSAC</td>
    <td>Cometary Sampling and Composition experiment</td>
  </tr>
  <tr>
    <td>CSE</td>
    <td>Comet-Sun electric field frame</td>
  </tr>
  <tr>
    <td>CSEQ</td>
    <td>Comet-centred solar equatorial coordinate system</td>
  </tr>
  <tr>
    <td>DCB</td>
    <td>Diamagnetic cavity boundary</td>
  </tr>
  <tr>
    <td>DR</td>
    <td>Dissociative recombination</td>
  </tr>
  <tr>
    <td>DS1</td>
    <td>Deep Space 1</td>
  </tr>
  <tr>
    <td>EI</td>
    <td>Electron impact</td>
  </tr>
  <tr>
    <td>ENA</td>
    <td>Energetic neutral atom</td>
  </tr>
  <tr>
    <td>ESA</td>
    <td>European Space Agency</td>
  </tr>
  <tr>
    <td>EUV</td>
    <td>Extreme ultraviolet</td>
  </tr>
  <tr>
    <td>FUV</td>
    <td>Far ultraviolet</td>
  </tr>
  <tr>
    <td>GIADA</td>
    <td>Grain Impact Analyser and Dust Accumulator</td>
  </tr>
  <tr>
    <td>HR</td>
    <td>High resolution</td>
  </tr>
  <tr>
    <td>ICE</td>
    <td>International Comet Explorer</td>
  </tr>
  <tr>
    <td>ICME</td>
    <td>Interplanetary coronal mass ejection</td>
  </tr>
  <tr>
    <td>IMF</td>
    <td>Interplanetary magnetic field</td>
  </tr>
  <tr>
    <td>LAICA</td>
    <td>Lyman Alpha Imaging Camera</td>
  </tr>
  <tr>
    <td>LHDI</td>
    <td>Lower hybrid drift instability</td>
  </tr>
  <tr>
    <td>LR</td>
    <td>Low resolution</td>
  </tr>
  <tr>
    <td>MAVEN</td>
    <td>Mars Atmosphere & Volatile Evolution</td>
  </tr>
  <tr>
    <td>MHD</td>
    <td>Magnetohydrodynamics</td>
  </tr>
  <tr>
    <td>MIRO</td>
    <td>Microwave Instrument for the Rosetta Orbiter</td>
  </tr>
  <tr>
    <td>NAVCAM</td>
    <td>Navigation camera</td>
  </tr>
  <tr>
    <td>OSIRIS</td>
    <td>Optical, Spectroscopic and Infrared Remote Imaging System</td>
  </tr>
  <tr>
    <td>PA</td>
    <td>Photo absorption</td>
  </tr>
  <tr>
    <td>PDS</td>
    <td>Planetary Data System</td>
  </tr>
  <tr>
    <td>PHIDRATES</td>
    <td>Photoionization/dissociation rates</td>
  </tr>
  <tr>
    <td>PI</td>
    <td>Photo ionisation</td>
  </tr>
  <tr>
    <td>PIC</td>
    <td>Particle in cell</td>
  </tr>
  <tr>
    <td>PIU</td>
    <td>Plasma Interface Unit</td>
  </tr>
  <tr>
    <td>PROCYON</td>
    <td>Proximate Object Close Flyby with Optical Navigation</td>
  </tr>
  <tr>
    <td>PSA</td>
    <td>Planetary Science Archive</td>
  </tr>
  <tr>
    <td>QDB</td>
    <td>Quantemol database</td>
  </tr>
  <tr>
    <td>ROMAP</td>
    <td>Rosetta magnetometer and plasma monitor instrument</td>
  </tr>
  <tr>
    <td>ROSINA</td>
    <td>Rosetta Orbiter Spectrometer for Ion and Neutral Analysis</td>
  </tr>
  <tr>
    <td>ROSINA-COPS</td>
    <td>ROSINA-Comet Pressure Sensor</td>
  </tr>
  <tr>
    <td>ROSINA-DFMS</td>
    <td>ROSINA-double focusing magnetic mass spectrometer</td>
  </tr>
  <tr>
    <td>RPC</td>
    <td>Rosetta Plasma Consortium</td>
  </tr>
  <tr>
    <td>RPC-ICA</td>
    <td>RPC-Ion Composition Analyser</td>
  </tr>
  <tr>
    <td>RPC-IES</td>
    <td>RPC-Ion and Electron Sensor</td>
  </tr>
  <tr>
    <td>RPC-LAP</td>
    <td>RPC-Langmuir probe instrument</td>
  </tr>
  <tr>
    <td>RPC-MAG</td>
    <td>RPC-Magnetometer</td>
  </tr>
  <tr>
    <td>RPC-MIP</td>
    <td>RPC-Mutual Impedance Probe</td>
  </tr>
  <tr>
    <td>RPWI</td>
    <td>Radio & Plasma Wave Instrument</td>
  </tr>
  <tr>
    <td>STR</td>
    <td>Star Tracker</td>
  </tr>
  <tr>
    <td>SWCX</td>
    <td>Solar wind charge exchange</td>
  </tr>
  <tr>
    <td>SWI</td>
    <td>Solar wind impact ionisation</td>
  </tr>
  <tr>
    <td>TIMED</td>
    <td>Thermosphere Ionosphere Mesosphere Energetics and Dynamics</td>
  </tr>
  <tr>
    <td>TIMED/SEE</td>
    <td>TIMED/Solar EUV Experiment</td>
  </tr>
</table>
<table><tr><td>UT</td><td>Universal time</td></tr><tr><td>UV</td><td>Ultraviolet</td></tr><tr><td>VDF</td><td>Velocity distribution function</td></tr><tr><td>VIRTIS</td><td>Visible and InfraRed Thermal Imaging Spectrometer</td></tr><tr><td>WAC</td><td>Wide Angle Camera</td></tr></table>

**Acknowledgements** Part of this work was inspired by discussions within International Team 402: “Plasma Environment of Comet 67P after Rosetta” at the International Space Science Institute, Bern, Switzerland. The authors thank the entire team behind ESA’s Rosetta mission and those that analysed the data and published the scientific results that are reviewed here. This work was supported in part by NASA Solar System Exploration Research Virtual Institute (SSERVI): Institute for Modeling Plasmas, Atmosphere, and Cosmic Dust (IMPACT), and the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. J.D. gratefully acknowledges support from NASA’s Rosetta Data Analysis Program, Grant No. 80NSSC19K1305. C.G. is supported by an ESA Research Fellowship. K.E.M. acknowledges support from NASA RDAP 80NSSC19K1306. Work at Umeå University was supported by the Swedish National Space Agency, grant 108/18. The work by CSW is supported by the Austrian Science Fund (FWF) under project N32035-N36. A.D. is supported by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”, grant 20-1-2-18-1. M.R. was funded by the State of Bern and the Swiss National Science Foundation (200020_182418). The work by M.G. was supported by the STFC of the UK under grant ST/N000692/1 and by ESA under contract number 4000119035/16/ES/JD. Work at CNRS was supported by CNES.

## Declarations

**Competing Interests** The authors declare no competing interests.

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