# Spacecraft Charging Simulations of Probe B1 of Comet Interceptor during the Cometary Flyby

S. Bergman, Y. Miyake, S. Kasahara, F. L. Johansson, P. Henri

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S. Bergman, Y. Miyake, S. Kasahara, F. L. Johansson, P. Henri. Spacecraft Charging Simulations of Probe B1 of Comet Interceptor during the Cometary Flyby. The Astrophysical Journal, 2023, 959, 10.3847/1538-4357/ad0ce5. insu-04379375

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# Spacecraft Charging Simulations of Probe B1 of Comet Interceptor during the Cometary Flyby

S. Bergman<fnref n="1" />, Y. Miyake<fnref n="2" />, S. Kasahara<fnref n="1" />, F. L. Johansson<fnref n="3" />, and P. Henri<fnref n="4" />,<fnref n="5" />

Received 2023 September 11; revised 2023 November 9; accepted 2023 November 14; published 2023 December 15

## Abstract

Comet Interceptor will be the first mission to make a flyby of a long-period or interstellar comet. After launch, the spacecraft will wait at the Sun-Earth Lagrange point L2 for a yet-to-be-discovered comet to appear. The mission comprises three spacecraft: One main spacecraft, A, developed by ESA, and two subprobes, B1 and B2, developed by JAXA and ESA, respectively. All spacecraft will carry plasma instruments for a three-dimensional sampling of the cometary plasma environment. The plasma measurements will likely be affected by the spacecraft potential and by particles emitted from the spacecraft surface. In this work, we use the Spacecraft Plasma Interaction Software and the ElectroMagnetic Spacecraft Environment Simulator to make particle-in-cell simulations of the spacecraft-plasma interactions of probe B1 in different environments during the cometary flyby. This is done for two production rates of the target comet and two relative flyby velocities of the probe. At low flyby velocities, the spacecraft potential varies from 9 V in the solar wind to -5 V in the inner coma for a comet similar to comet 67P/Churyumov-Gerasimenko. For a comet similar to 1P/Halley, the potential is slightly less negative in the inner coma due to the more effective collisional cooling of the electrons in the environment. At high flyby velocities, secondary electron emissions from neutral gas impacts dominate the currents, charging the probe to positive potentials in most of the studied environments.

Unified Astronomy Thesaurus concepts: Comets (280); Space plasmas (1544)

## 1. Introduction

Several space missions have visited comets in the past. Since the very first cometary encounter in 1985, when the International Cometary Explorer (ICE; e.g., Brandt et al. 1985) visited comet 21P/Giacobini-Zinner, several successful missions have studied these remnant solar system bodies. The comets that have been studied in detail are comet 1P/Halley (hereafter Halley) and comet 67P/Churyumov-Gerasimenko (hereafter 67P). Comet Halley was visited by several spacecraft during its apparition in 1986; the European Space Agency's (ESA's) Giotto spacecraft (Reinhard 1986), the Russian Vega-1 and Vega-2 spacecraft (Sagdeev et al. 1986), and the Japanese Sakigake and Suisei spacecraft (Hirao & Itoh 1987) all made flybys at varying distances from the nucleus. The closest encounter was made by Giotto, with a closest approach of ~600 km. Comet 67P was the first comet to be studied for a long period of time when it was followed by ESA's Rosetta mission (Glassmeier et al. 2007) during the years 2014-2016. Rosetta provided measurements from when the comet was weakly active further away from the Sun to the more active case around perihelion.

All these previous missions studied short-period comets, i.e., comets that have already approached the Sun several times and hence have undergone significant alterations of their surface properties since formation. The new Comet Interceptor mission

(Snodgrass & Jones 2019) will be the first mission to target a long-period and, ideally, pristine comet. The spacecraft is planned to be launched in 2029 to the Sun-Earth Lagrange point L2, where it will wait for a yet-to-be-discovered target to appear. Comet Interceptor will comprise three spacecraft: One main spacecraft A (ESA) and two subprobes B1 (JAXA) and B2 (ESA) which will be deployed before the encounter. This will, for the first time, allow multipoint measurements of the cometary environment. The three spacecraft will make flybys at different distances from the nucleus; spacecraft A has a nominal closest approach of 1000 km, while probes B1 and B2 will make closer encounters with a nominal closest approach of 850 and 400 km, respectively.

All spacecraft will carry instruments dedicated to studying the plasma environment of the comet. The cometary plasma environment is characterized by a large interaction region, created by the gravitationally unbound atmosphere. The neutral particles in the coma get ionized through photoionization, electron impact ionization, and charge-exchange reactions (Galand et al. 2016; Simon Wedlund et al. 2017; Heritier et al. 2018), and start interacting with the solar wind. Mass loading (e.g., Szegö et al. 2000) causes the solar wind to decelerate and/or get deflected (e.g., Formisano et al. 1990; Behar et al. 2016), and as a result a bow shock is formed (see, e.g., review by Coates 1995), provided that the cometary activity is high enough (e.g., Simon Wedlund et al. 2017; Alho et al. 2019, 2021). Closer to the nucleus, the cometopause is defined as the boundary where the composition transitions from being dominated by solar wind to cometary plasma. For comet Halley, the cometopause was identified in Vega-2 data as a

<figure><img src="image_2.png" /></figure>

Original content from this work may be used under the terms of the [Creative Commons Attribution 4.0 licence](https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

<footnote n="1">¹Department of Earth and Planetary Science, Graduate School of Earth and Planetary Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan; sbergman@eps.s.u-tokyo.ac.jp</footnote>

<footnote n="2">²Graduate School of System Informatics, Kobe University, Kobe, Japan</footnote>

<footnote n="3">³European Space Agency, European Space Research and Technology Centre, Noordwijk, The Netherlands</footnote>

<footnote n="4">⁴Laboratoire de Physique et Chimie de l'Environnement et de l'Espace, CNRS, Orléans, France</footnote>

<footnote n="5">⁵Laboratoire Lagrange, Observatoire de la Côte d'Azur, Université Côte d'Azur, CNRS, Nice, France</footnote>
<figure><img src="image_2.png" /></figure>

# Spacecraft Charging Simulations of Probe B1 of Comet Interceptor during the Cometary Flyby

S. Bergman<fnref n="1" />, Y. Miyake<fnref n="2" />, S. Kasahara<fnref n="1" />, F. L. Johansson<fnref n="3" />, and P. Henri<fnref n="4" />,<fnref n="5" />

Received 2023 September 11; revised 2023 November 9; accepted 2023 November 14; published 2023 December 15

## Abstract

Comet Interceptor will be the first mission to make a flyby of a long-period or interstellar comet. After launch, the spacecraft will wait at the Sun-Earth Lagrange point L2 for a yet-to-be-discovered comet to appear. The mission comprises three spacecraft: One main spacecraft, A, developed by ESA, and two subprobes, B1 and B2, developed by JAXA and ESA, respectively. All spacecraft will carry plasma instruments for a three-dimensional sampling of the cometary plasma environment. The plasma measurements will likely be affected by the spacecraft potential and by particles emitted from the spacecraft surface. In this work, we use the Spacecraft Plasma Interaction Software and the ElectroMagnetic Spacecraft Environment Simulator to make particle-in-cell simulations of the spacecraft-plasma interactions of probe B1 in different environments during the cometary flyby. This is done for two production rates of the target comet and two relative flyby velocities of the probe. At low flyby velocities, the spacecraft potential varies from 9 V in the solar wind to -5 V in the inner coma for a comet similar to comet 67P/Churyumov-Gerasimenko. For a comet similar to 1P/Halley, the potential is slightly less negative in the inner coma due to the more effective collisional cooling of the electrons in the environment. At high flyby velocities, secondary electron emissions from neutral gas impacts dominate the currents, charging the probe to positive potentials in most of the studied environments.

Unified Astronomy Thesaurus concepts: Comets (280); Space plasmas (1544)

## 1. Introduction

Several space missions have visited comets in the past. Since the very first cometary encounter in 1985, when the International Cometary Explorer (ICE; e.g., Brandt et al. 1985) visited comet 21P/Giacobini-Zinner, several successful missions have studied these remnant solar system bodies. The comets that have been studied in detail are comet 1P/Halley (hereafter Halley) and comet 67P/Churyumov-Gerasimenko (hereafter 67P). Comet Halley was visited by several spacecraft during its apparition in 1986; the European Space Agency's (ESA's) Giotto spacecraft (Reinhard 1986), the Russian Vega-1 and Vega-2 spacecraft (Sagdeev et al. 1986), and the Japanese Sakigake and Suisei spacecraft (Hirao & Itoh 1987) all made flybys at varying distances from the nucleus. The closest encounter was made by Giotto, with a closest approach of ~600 km. Comet 67P was the first comet to be studied for a long period of time when it was followed by ESA's Rosetta mission (Glassmeier et al. 2007) during the years 2014-2016. Rosetta provided measurements from when the comet was weakly active further away from the Sun to the more active case around perihelion.

All these previous missions studied short-period comets, i.e., comets that have already approached the Sun several times and hence have undergone significant alterations of their surface properties since formation. The new Comet Interceptor mission

(Snodgrass & Jones 2019) will be the first mission to target a long-period and, ideally, pristine comet. The spacecraft is planned to be launched in 2029 to the Sun-Earth Lagrange point L2, where it will wait for a yet-to-be-discovered target to appear. Comet Interceptor will comprise three spacecraft: One main spacecraft A (ESA) and two subprobes B1 (JAXA) and B2 (ESA) which will be deployed before the encounter. This will, for the first time, allow multipoint measurements of the cometary environment. The three spacecraft will make flybys at different distances from the nucleus; spacecraft A has a nominal closest approach of 1000 km, while probes B1 and B2 will make closer encounters with a nominal closest approach of 850 and 400 km, respectively.

All spacecraft will carry instruments dedicated to studying the plasma environment of the comet. The cometary plasma environment is characterized by a large interaction region, created by the gravitationally unbound atmosphere. The neutral particles in the coma get ionized through photoionization, electron impact ionization, and charge-exchange reactions (Galand et al. 2016; Simon Wedlund et al. 2017; Heritier et al. 2018), and start interacting with the solar wind. Mass loading (e.g., Szegö et al. 2000) causes the solar wind to decelerate and/or get deflected (e.g., Formisano et al. 1990; Behar et al. 2016), and as a result a bow shock is formed (see, e.g., review by Coates 1995), provided that the cometary activity is high enough (e.g., Simon Wedlund et al. 2017; Alho et al. 2019, 2021). Closer to the nucleus, the *cometopause* is defined as the boundary where the composition transitions from being dominated by solar wind to cometary plasma. For comet Halley, the cometopause was identified in Vega-2 data as a

<figure><img src="image_3.png" /></figure>

Original content from this work may be used under the terms of the [Creative Commons Attribution 4.0 licence](https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

<footnote n="1">¹Department of Earth and Planetary Science, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan; sbergman@eps.s.u-tokyo.ac.jp</footnote>

<footnote n="2">²Graduate School of System Informatics, Kobe University, Kobe, Japan</footnote>

<footnote n="3">³European Space Agency, European Space Research and Technology Centre, Noordwijk, The Netherlands</footnote>

<footnote n="4">⁴Laboratoire de Physique et Chimie de l'Environnement et de l'Espace, CNRS, Orléans, France</footnote>

<footnote n="5">⁵Laboratoire Lagrange, Observatoire de la Côte d'Azur, Université Côte d'Azur, CNRS, Nice, France</footnote>
rather sharp boundary (Gringauz et al. 1986), which was shown to coincide with the collisionopause for charge exchange (Gombosi 1987). For the less active comet 67P, the situation was more complicated. A region completely free of solar wind ions, called the *solar wind ion cavity*, was identified in Rosetta data (Behar et al. 2017; Nilsson et al. 2017). Mass loading also causes the interplanetary magnetic field to get draped around the nucleus (Alfvén 1957), and closest to the nucleus a magnetic-field-free region, called the *diamagnetic cavity*, is formed. The diamagnetic cavity has been observed at both comet Halley (e.g., Neubauer et al. 1986) and comet 67P (e.g., Goetz et al. 2016). Illustrations of the cometary magnetosphere can be found in, for example, Goetz et al. (2022).

Both spacecraft A and probe B1 of Comet Interceptor will carry an ion sensor, allowing two-point measurements of the ion populations of both the solar wind and those of cometary origin. Furthermore, all three spacecraft will carry a magnetometer, making it possible to make a three-dimensional mapping of plasma boundaries. Spacecraft A will also carry a suite of other plasma instruments, including ion, electron, and ENA sensors. This can give unprecedented spatial information about the cometary plasma environment.

The plasma measurements will, however, likely be affected by the spacecraft potential. Due to interactions with the surrounding environment the surface of a spacecraft acquires an electrostatic potential, that can be either positive or negative (e.g., Garrett 1981; Whipple 1981). The resulting potential is determined by the properties of the surrounding plasma, the level of solar ultraviolet (UV) radiation exposing the spacecraft, the properties of the spacecraft surface, and, in some cases, the properties of the neutral environment. In dense plasma environments, the spacecraft tends to acquire negative potentials due to high fluxes of electrons to the surface. In less dense environments when the spacecraft is in sunlight, the surface instead charges positive due to photoemission. In some environments secondary electron emission (SEE) also affects the potential. When Rosetta visited comet 67P, the spacecraft was commonly charged to a negative potential of -10 to -20 V (Odelstad et al. 2017). The reason for this substantially negative potential was exposed positively biased conductors on the solar panels attracting cold electrons from the environment (Johansson et al. 2020). When Giotto encountered comet Halley the spacecraft potential was not measured directly. However, from sampled ion spectra the potential was estimated to vary from around 0 V inside of the diamagnetic cavity to +16 V outside (Krankowsky et al. 1986; Schwenn et al. 1987). For Vega-1 and Vega-2 the spacecraft potential was determined from data collected by Langmuir probes and electric field sensors. It was shown to be around +3 V in the outer coma for both spacecraft, and around +0.5 to +2 V at closest approach (Grard et al. 1985; Pedersen et al. 1986). In addition, when ICE visited comet 21P/Giacobini-Zinner, the spacecraft potential was low around closest approach (less than 0.8 V; Zwickl et al. 1988).

Another reason for the significantly different spacecraft potentials acquired by Rosetta compared to the flyby missions is likely the very different velocity of the spacecraft with respect to the comet. Rosetta was orbiting comet 67P at a very low relative velocity of ~1 ms⁻¹, while Giotto, Vega-1 and Vega-2, and ICE had relative flyby velocities of 68, 78, and 21 km s⁻¹, respectively. These high flyby velocities resulted in large amounts of SEE from impacts by neutral particles, positively charging these spacecraft (e.g., Thiemann et al. 1986; Grard et al. 1988).

Spacecraft charging causes issues for plasma measurements. For example, the negative potentials of Rosetta distorted the low-energy ion measurements made by the ion spectrometer on this spacecraft. The positive ions were accelerated toward the spacecraft prior to detection, changing their travel direction in the vicinity of the spacecraft (Bergman et al. 2020a, 2020b). This severely complicated the analysis of the plasma, e.g., inside the diamagnetic cavity. Comet Interceptor will likely suffer from spacecraft charging effects, and hence an estimate of the spacecraft potential acquired during the cometary flyby is crucial to maximize the scientific outcome of the plasma measurements.

In this study, we use the Spacecraft Plasma Interaction Software (SPIS; Thiebault et al. 2019) to simulate the surface charging of probe B1 of Comet Interceptor in different regions of the cometary plasma environment. Since the target comet is unknown, we run the simulations for two production rates of the comet and for two relative flyby velocities of the spacecraft. We also use the ElectroMagnetic Spacecraft Environment Simulator (EMSES; Miyake & Usui 2009) to study charging effects which have not yet been implemented in SPIS.

## 2. Simulation Software

### 2.1. SPIS

SPIS (Thiebault et al. 2019) is an electrostatic particle-in-cell (PIC) solver that simulates the interactions between a spacecraft and the surrounding plasma. It provides information on the spacecraft potential, the resulting currents to and from the spacecraft surface, as well as the potential field and distribution of particles around the spacecraft. The spacecraft geometry and simulation volume are represented using an unstructured finite element mesh, where the mesh resolution can be adapted and increased in regions of the volume where a higher resolution is necessary. The properties of the surface materials of the spacecraft are defined from a catalog of pre-defined materials, where the material properties also can be modified if needed. To model differential charging, the spacecraft structure is defined as an electrical circuit with several electrical nodes connected through resistors, capacitors, or voltage generators. For this work, SPIS versions 6.0.4 and 6.1.0 are used.

#### 2.1.1. Maxwell-Boltzmann Approximation for the Electrons

To reduce the computational load and the statistical noise of the simulation, the electrons can in some cases be modeled using a Maxwell-Boltzmann approximation instead of a full PIC treatment. The electrons are then assumed to be in equilibrium with the potential according to the Boltzmann relation:

$$n_e(\phi) = n_{e,\infty} \exp\left(-\frac{q\phi}{k_B T_e}\right), \quad (1)$$

where $n_{e,\infty}$ is the electron density at infinity (i.e., in the undisturbed plasma), $\phi$ is the potential, and $T_e$ is the electron temperature. This approximation is valid when the spacecraft potential is repulsive (i.e., negative) and no potential barriers exist in the simulation volume. The advantage of this approach is that the numerical noise introduced by a limited number of PIC particles is removed. Furthermore, when the electrons are treated as PIC the entire simulation volume has to be meshed with cells smaller than half the Debye length ($\lambda_D$) of the
rather sharp boundary (Gringauz et al. 1986), which was shown to coincide with the collisionopause for charge exchange (Gombosi 1987). For the less active comet 67P, the situation was more complicated. A region completely free of solar wind ions, called the *solar wind ion cavity*, was identified in Rosetta data (Behar et al. 2017; Nilsson et al. 2017). Mass loading also causes the interplanetary magnetic field to get draped around the nucleus (Alfvén 1957), and closest to the nucleus a magnetic-field-free region, called the *diamagnetic cavity*, is formed. The diamagnetic cavity has been observed at both comet Halley (e.g., Neubauer et al. 1986) and comet 67P (e.g., Goetz et al. 2016). Illustrations of the cometary magnetosphere can be found in, for example, Goetz et al. (2022).

Both spacecraft A and probe B1 of Comet Interceptor will carry an ion sensor, allowing two-point measurements of the ion populations of both the solar wind and those of cometary origin. Furthermore, all three spacecraft will carry a magnetometer, making it possible to make a three-dimensional mapping of plasma boundaries. Spacecraft A will also carry a suite of other plasma instruments, including ion, electron, and ENA sensors. This can give unprecedented spatial information about the cometary plasma environment.

The plasma measurements will, however, likely be affected by the spacecraft potential. Due to interactions with the surrounding environment the surface of a spacecraft acquires an electrostatic potential, that can be either positive or negative (e.g., Garrett 1981; Whipple 1981). The resulting potential is determined by the properties of the surrounding plasma, the level of solar ultraviolet (UV) radiation exposing the spacecraft, the properties of the spacecraft surface, and, in some cases, the properties of the neutral environment. In dense plasma environments, the spacecraft tends to acquire negative potentials due to high fluxes of electrons to the surface. In less dense environments when the spacecraft is in sunlight, the surface instead charges positive due to photoemission. In some environments secondary electron emission (SEE) also affects the potential. When Rosetta visited comet 67P, the spacecraft was commonly charged to a negative potential of -10 to -20 V (Odelstad et al. 2017). The reason for this substantially negative potential was exposed positively biased conductors on the solar panels attracting cold electrons from the environment (Johansson et al. 2020). When Giotto encountered comet Halley the spacecraft potential was not measured directly. However, from sampled ion spectra the potential was estimated to vary from around 0 V inside of the diamagnetic cavity to +16 V outside (Krankowsky et al. 1986; Schwenn et al. 1987). For Vega-1 and Vega-2 the spacecraft potential was determined from data collected by Langmuir probes and electric field sensors. It was shown to be around +3 V in the outer coma for both spacecraft, and around +0.5 to +2 V at closest approach (Grard et al. 1985; Pedersen et al. 1986). In addition, when ICE visited comet 21P/Giacobini-Zinner, the spacecraft potential was low around closest approach (less than 0.8 V; Zwickl et al. 1988).

Another reason for the significantly different spacecraft potentials acquired by Rosetta compared to the flyby missions is likely the very different velocity of the spacecraft with respect to the comet. Rosetta was orbiting comet 67P at a very low relative velocity of ~1 ms⁻¹, while Giotto, Vega-1 and Vega-2, and ICE had relative flyby velocities of 68, 78, and 21 km s⁻¹, respectively. These high flyby velocities resulted in large amounts of SEE from impacts by neutral particles, positively charging these spacecraft (e.g., Thiemann et al. 1986; Grard et al. 1988).

Spacecraft charging causes issues for plasma measurements. For example, the negative potentials of Rosetta distorted the low-energy ion measurements made by the ion spectrometer on this spacecraft. The positive ions were accelerated toward the spacecraft prior to detection, changing their travel direction in the vicinity of the spacecraft (Bergman et al. 2020a, 2020b). This severely complicated the analysis of the plasma, e.g., inside the diamagnetic cavity. Comet Interceptor will likely suffer from spacecraft charging effects, and hence an estimate of the spacecraft potential acquired during the cometary flyby is crucial to maximize the scientific outcome of the plasma measurements.

In this study, we use the Spacecraft Plasma Interaction Software (SPIS; Thiebault et al. 2019) to simulate the surface charging of probe B1 of Comet Interceptor in different regions of the cometary plasma environment. Since the target comet is unknown, we run the simulations for two production rates of the comet and for two relative flyby velocities of the spacecraft. We also use the ElectroMagnetic Spacecraft Environment Simulator (EMSES; Miyake & Usui 2009) to study charging effects which have not yet been implemented in SPIS.

## 2. Simulation Software

### 2.1. SPIS

SPIS (Thiebault et al. 2019) is an electrostatic particle-in-cell (PIC) solver that simulates the interactions between a spacecraft and the surrounding plasma. It provides information on the spacecraft potential, the resulting currents to and from the spacecraft surface, as well as the potential field and distribution of particles around the spacecraft. The spacecraft geometry and simulation volume are represented using an unstructured finite element mesh, where the mesh resolution can be adapted and increased in regions of the volume where a higher resolution is necessary. The properties of the surface materials of the spacecraft are defined from a catalog of pre-defined materials, where the material properties also can be modified if needed. To model differential charging, the spacecraft structure is defined as an electrical circuit with several electrical nodes connected through resistors, capacitors, or voltage generators. For this work, SPIS versions 6.0.4 and 6.1.0 are used.

#### 2.1.1. Maxwell-Boltzmann Approximation for the Electrons

To reduce the computational load and the statistical noise of the simulation, the electrons can in some cases be modeled using a Maxwell-Boltzmann approximation instead of a full PIC treatment. The electrons are then assumed to be in equilibrium with the potential according to the Boltzmann relation:

$$n_e(\phi) = n_{e,\infty} \exp\left(-\frac{q\phi}{k_B T_e}\right), \quad (1)$$

where $n_{e,\infty}$ is the electron density at infinity (i.e., in the undisturbed plasma), $\phi$ is the potential, and $T_e$ is the electron temperature. This approximation is valid when the spacecraft potential is repulsive (i.e., negative) and no potential barriers exist in the simulation volume. The advantage of this approach is that the numerical noise introduced by a limited number of PIC particles is removed. Furthermore, when the electrons are treated as PIC the entire simulation volume has to be meshed with cells smaller than half the Debye length ($\lambda_D$) of the
plasma, which is not necessary when the Maxwell–Boltzmann approximation is used.

Since SPIS v6.1.0, additional low-noise distributions have been introduced in SPIS. In this study, we make use of the kinetic Maxwell–Boltzmann approximation (Jorba Ferro 2018). This approximation is similar to the usual Maxwell–Boltzmann approximation, but uses a better modeling of the density and temperature variations with a temperature computation assuring that the energy is conserved in an attractive potential. Hence, this approximation can be used also for positive potentials.

## 2.2. EMSES

EMSES (Miyake & Usui 2009, 2016; Miyake et al. 2020) is, similarly to SPIS, a PIC code, however with the implementation of a full electromagnetic treatment. The spacecraft and simulation volume are described by an ordinary structured grid, with the possibility to include thin elements using an immersed boundary element approach. The spacecraft surface can be modeled as a perfect conductor or insulator. Even though the surface modeling capabilities of EMSES is limited compared to SPIS, EMSES is more versatile in modeling the interactions with the surface. Particle emission is controlled by the user by defining the particle flux and distribution of the emitted particles. As a result, different types of secondary emissions can be defined, while SPIS is limited to emissions by impacting electrons and protons. In this study, we utilize these features of EMSES to study secondary electron and ion emissions from impacting neutral particles.

# 3. Setup of SPIS Simulations

## 3.1. Spacecraft Model

The spacecraft model used for the SPIS simulations is shown in Figure 1(a). The main body is modeled as a box with dimensions 0.4 × 0.3 × 0.2 m with the hydrogen imager (HI), narrow-angle camera (NAC), wide-angle camera (WAC), and cometary ion mass spectrometer (CIMS) added as cylinders with appropriate dimensions. The probe will contain a dust shield for protection during the cometary encounter, which is also included in the model. The solar arrays are modeled with dimensions of 0.02 × 0.26 × 0.5 m. Finally, a boom with a length of 1.5 m containing the magnetometer (MAG) at the end is included. The coordinate system is defined as in Figure 1, with the z-axis pointing in the direction of the boom, the y-axis pointing along the symmetry axis of CIMS, and the x-axis completing the right-handed system.

Black kapton is used as surface material for the main body, the dust shield, the boom, CIMS, and MAG. For the cameras (HI, NAC, and WAC), aluminum is used. The solar panels are assumed to be conductive for the main simulations with the front plane (i.e., the side illuminated by sunlight) covered with indium tin oxide and the back plane with black kapton. However, the case of nonconductive solar panels is also investigated for a few environments (see Section 5.5).

The location of the spacecraft with respect to the comet and the Sun is illustrated in Figures 1(b)–(c). For all simulations, the comet is located in the +x direction. For all flyby simulations (i.e., all simulations except the solar wind case; see Section 3.3), the ram side is in the +z direction. For the solar wind simulation the ram side is in the +x direction. Probe B1 will make the flyby at an angle of 45° to the orbital plane of the comet. For all simulated environments except the solar wind

case, the Sun is hence located at −R cos(45°)ŷ + R sin(45°)ŷ, where R is the heliocentric distance. In the solar wind, the Sun will be located in the +z or −z direction, but the precise configuration has at the time of this study not been decided. We set the Sun direction to +z in this environment. Changing the direction to −z is expected to have a minor influence on the results.

The solar arrays can be rotated around the y-axis. For all environments except the solar wind case, the solar arrays are oriented as in Figure 1(a). The front plane is looking in the −x direction. For the solar wind simulation, the solar arrays are rotated by 90° so that the front plane is looking in the +z direction (Figure 1(b)).

## 3.2. Simulation Volume

The simulation volume in SPIS is a sphere with dimensions 8 × 8 × 8 m. In environments where extensive wakes are formed, the simulation volume is extended in the corresponding direction to capture the wake. The resolution of the mesh is 1–2 cm at the spacecraft and successively increased to the external boundary, where the resolution is set to 0.5λ<sub>D</sub> or 0.5 m in cases where λ<sub>D</sub> > 1 m.

## 3.3. Plasma Model

We simulate the spacecraft potential in different plasma environments that the probe is expected to encounter during the cometary flyby. Since the target comet and its production rate (Q) is unknown, we run simulations for two different comets: One with a lower production rate, corresponding to comet 67P around perihelion (Q = 3.5 × 10<sup>28</sup> s<sup>−1</sup>; Hansen et al. 2016), and one higher, similar to comet Halley at the Giotto encounter (Q = 6.9 × 10<sup>29</sup> s<sup>−1</sup>; Krankowsky et al. 1986). We also run one simulation for the solar wind, where average solar wind conditions are used. The heliocentric distance is 1 au in all simulations. The magnetic field is not expected to affect the charging of the spacecraft in any of the considered environments (e.g., Holmberg 2020), and has hence been excluded. In Table 1 the plasma parameters used for each simulated environment are listed. Details are given in the following sections.

### 3.3.1. 67P-like Comet

For a 67P-like comet, we run simulations for the diamagnetic cavity, the solar wind ion cavity, and the cometopause region. We base the major part of our model on measurements made by Rosetta.

The diamagnetic cavity boundary of comet 67P was detected at a cometocentric distance (r) of less than 400 km (Goetz et al. 2016), meaning that probe B1 will likely not enter the diamagnetic cavity in the case of a 67P-like comet, provided that the closest approach is 850 km. However, the closest approach distance will likely vary with the production rate, and we therefore simulate the expected spacecraft potential also in the diamagnetic cavity. In the simulations, r is set to 200 km. We use a plasma density (n) of 1000 cm<sup>−3</sup> (Henri et al. 2017). In the inner coma, the warm newborn electrons are cooled due to collisions with neutrals. The Langmuir probes (RPC-LAP; Eriksson et al. 2007) and the mutual impedance probe (RPC-MIP; Trotignon et al. 2007) of Rosetta detected two electron populations in the inner coma: One warm population with a temperature T<sub>e,w</sub> of ~5 eV, and one cold population with
plasma, which is not necessary when the Maxwell–Boltzmann approximation is used.

Since SPIS v6.1.0, additional low-noise distributions have been introduced in SPIS. In this study, we make use of the kinetic Maxwell–Boltzmann approximation (Jorba Ferro 2018). This approximation is similar to the usual Maxwell–Boltzmann approximation, but uses a better modeling of the density and temperature variations with a temperature computation assuring that the energy is conserved in an attractive potential. Hence, this approximation can be used also for positive potentials.

## 2.2. EMSES

EMSES (Miyake & Usui 2009, 2016; Miyake et al. 2020) is, similarly to SPIS, a PIC code, however with the implementation of a full electromagnetic treatment. The spacecraft and simulation volume are described by an ordinary structured grid, with the possibility to include thin elements using an immersed boundary element approach. The spacecraft surface can be modeled as a perfect conductor or insulator. Even though the surface modeling capabilities of EMSES is limited compared to SPIS, EMSES is more versatile in modeling the interactions with the surface. Particle emission is controlled by the user by defining the particle flux and distribution of the emitted particles. As a result, different types of secondary emissions can be defined, while SPIS is limited to emissions by impacting electrons and protons. In this study, we utilize these features of EMSES to study secondary electron and ion emissions from impacting neutral particles.

# 3. Setup of SPIS Simulations

## 3.1. Spacecraft Model

The spacecraft model used for the SPIS simulations is shown in Figure 1(a). The main body is modeled as a box with dimensions 0.4 × 0.3 × 0.2 m with the hydrogen imager (HI), narrow-angle camera (NAC), wide-angle camera (WAC), and cometary ion mass spectrometer (CIMS) added as cylinders with appropriate dimensions. The probe will contain a dust shield for protection during the cometary encounter, which is also included in the model. The solar arrays are modeled with dimensions of 0.02 × 0.26 × 0.5 m. Finally, a boom with a length of 1.5 m containing the magnetometer (MAG) at the end is included. The coordinate system is defined as in Figure 1, with the z-axis pointing in the direction of the boom, the y-axis pointing along the symmetry axis of CIMS, and the x-axis completing the right-handed system.

Black kapton is used as surface material for the main body, the dust shield, the boom, CIMS, and MAG. For the cameras (HI, NAC, and WAC), aluminum is used. The solar panels are assumed to be conductive for the main simulations with the front plane (i.e., the side illuminated by sunlight) covered with indium tin oxide and the back plane with black kapton. However, the case of nonconductive solar panels is also investigated for a few environments (see Section 5.5).

The location of the spacecraft with respect to the comet and the Sun is illustrated in Figures 1(b)–(c). For all simulations, the comet is located in the +x direction. For all flyby simulations (i.e., all simulations except the solar wind case; see Section 3.3), the ram side is in the +z direction. For the solar wind simulation the ram side is in the +x direction. Probe B1 will make the flyby at an angle of 45° to the orbital plane of the comet. For all simulated environments except the solar wind

case, the Sun is hence located at −R cos(45°)ŷ + R sin(45°)ŷ, where R is the heliocentric distance. In the solar wind, the Sun will be located in the +z or −z direction, but the precise configuration has at the time of this study not been decided. We set the Sun direction to +z in this environment. Changing the direction to −z is expected to have a minor influence on the results.

The solar arrays can be rotated around the y-axis. For all environments except the solar wind case, the solar arrays are oriented as in Figure 1(a). The front plane is looking in the −x direction. For the solar wind simulation, the solar arrays are rotated by 90° so that the front plane is looking in the +z direction (Figure 1(b)).

## 3.2. Simulation Volume

The simulation volume in SPIS is a sphere with dimensions 8 × 8 × 8 m. In environments where extensive wakes are formed, the simulation volume is extended in the corresponding direction to capture the wake. The resolution of the mesh is 1–2 cm at the spacecraft and successively increased to the external boundary, where the resolution is set to 0.5λ<sub>D</sub> or 0.5 m in cases where λ<sub>D</sub> > 1 m.

## 3.3. Plasma Model

We simulate the spacecraft potential in different plasma environments that the probe is expected to encounter during the cometary flyby. Since the target comet and its production rate (Q) is unknown, we run simulations for two different comets: One with a lower production rate, corresponding to comet 67P around perihelion (Q = 3.5 × 10<sup>28</sup> s<sup>−1</sup>; Hansen et al. 2016), and one higher, similar to comet Halley at the Giotto encounter (Q = 6.9 × 10<sup>29</sup> s<sup>−1</sup>; Krankowsky et al. 1986). We also run one simulation for the solar wind, where average solar wind conditions are used. The heliocentric distance is 1 au in all simulations. The magnetic field is not expected to affect the charging of the spacecraft in any of the considered environments (e.g., Holmberg 2020), and has hence been excluded. In Table 1 the plasma parameters used for each simulated environment are listed. Details are given in the following sections.

### 3.3.1. 67P-like Comet

For a 67P-like comet, we run simulations for the diamagnetic cavity, the solar wind ion cavity, and the cometopause region. We base the major part of our model on measurements made by Rosetta.

The diamagnetic cavity boundary of comet 67P was detected at a cometocentric distance (r) of less than 400 km (Goetz et al. 2016), meaning that probe B1 will likely not enter the diamagnetic cavity in the case of a 67P-like comet, provided that the closest approach is 850 km. However, the closest approach distance will likely vary with the production rate, and we therefore simulate the expected spacecraft potential also in the diamagnetic cavity. In the simulations, r is set to 200 km. We use a plasma density (n) of 1000 cm<sup>−3</sup> (Henri et al. 2017). In the inner coma, the warm newborn electrons are cooled due to collisions with neutrals. The Langmuir probes (RPC-LAP; Eriksson et al. 2007) and the mutual impedance probe (RPC-MIP; Trotignon et al. 2007) of Rosetta detected two electron populations in the inner coma: One warm population with a temperature T<sub>e,w</sub> of ~5 eV, and one cold population with
<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 1.** (a) The spacecraft model used for the SPIS simulations. (b) Illustration of the location of the spacecraft with respect to the comet and the Sun in the solar wind simulation. (c) Same as panel (b), but for the flyby simulations.</figcaption></figure>

a temperature $T_{e,c}$ below 0.1 eV (e.g., Eriksson et al. 2017; Gilet et al. 2020; Wattieaux et al. 2020). The cold-to-total electron density ratio was shown by Gilet et al. (2020) and Wattieaux et al. (2020) to be between 60% and 90%. For our simulations, we set the amount of cold electrons to 70% of the total density in the diamagnetic cavity. Since the thermal velocity is much larger than the bulk velocity for both the cold and warm electrons, the bulk velocity is set to zero with no impact on the results. For the ions, the bulk velocity ($v_i$) is set to $4 \text{ km s}^{-1}$ radially away from the nucleus (e.g., Odelstad et al. 2018; Bergman et al. 2021) and the temperature ($T_i$) to 0.1 eV (Galand et al. 2016).

The nominal closest approach will likely be located in the solar wind ion cavity for a 67P-like comet. We use $n = 300 \text{ cm}^{-3}$ for this region, in agreement with measurements by RPC-MIP and RPC-LAP of Rosetta during the dayside excursion. The amount of cold electrons in this region is uncertain. The cold-to-total density ratio is expected to decrease with $r$, but RPC-MIP has difficulties determining the ratio when it is <30% (Wattieaux et al. 2020). Likely, it is between 0% and 50% in the solar wind ion cavity. For the simulations, we assume that no cold electrons are present, but investigate the influence of a higher abundance of cold electrons in Section 5.3. For the ions, $T_i = 0.1$ eV and $v_i = 4 \text{ km s}^{-1}$ in the radial direction.

The definition of the cometopause has varied between different studies and comets. In this work, we define the cometopause as the boundary of the solar wind ion cavity. Around perihelion, Rosetta never exited the solar wind ion

cavity, not even during the dayside excursion when $r$ was up to ~1500 km. Hence, there are no measurements from Rosetta available for this region. RPC-LAP and RPC-MIP typically measured $n$ below $100 \text{ cm}^{-3}$ during the dayside excursion, and we choose $n = 50 \text{ cm}^{-3}$ for the cometopause simulations. We assume that all cometary electrons are warm with $T_{e,w} = 5$ eV. $T_i$ for the cometary ions is set to 1 eV and $v_i$ to $11 \text{ km s}^{-1}$ (Nilsson et al. 2020). We also include the solar wind in this simulation, where average conditions are used. The cometopause region involves a complex interaction between the solar wind and the cometary particles with significant deflection and pick-up (Behar et al. 2017; Nilsson et al. 2020). However, for the simulations we assume that the solar wind is flowing radially away from the Sun while the cometary ions are flowing radially away from the nucleus. As a result, the location of the wake likely differs from the real case, but we expect the influence on the spacecraft potential to be small.

### 3.3.2. Halley-like Comet

For a Halley-like comet, we run simulations for the diamagnetic cavity, the electron exobase, and the magnetic pile-up region. As much as possible, the plasma model is based on measurements made by Giotto. Unfortunately, Giotto could not make measurements of the cold electrons, and therefore the electron temperatures and the cold-to-total density ratios are instead based on models.

The diamagnetic cavity boundary of comet Halley was detected at $r \sim 4000$ km (Neubauer et al. 1986), and hence
<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 1.** (a) The spacecraft model used for the SPIS simulations. (b) Illustration of the location of the spacecraft with respect to the comet and the Sun in the solar wind simulation. (c) Same as panel (b), but for the flyby simulations.</figcaption></figure>

a temperature $T_{e,c}$ below 0.1 eV (e.g., Eriksson et al. 2017; Gilet et al. 2020; Wattieaux et al. 2020). The cold-to-total electron density ratio was shown by Gilet et al. (2020) and Wattieaux et al. (2020) to be between 60% and 90%. For our simulations, we set the amount of cold electrons to 70% of the total density in the diamagnetic cavity. Since the thermal velocity is much larger than the bulk velocity for both the cold and warm electrons, the bulk velocity is set to zero with no impact on the results. For the ions, the bulk velocity ($v_i$) is set to $4 \text{ km s}^{-1}$ radially away from the nucleus (e.g., Odelstad et al. 2018; Bergman et al. 2021) and the temperature ($T_i$) to 0.1 eV (Galand et al. 2016).

The nominal closest approach will likely be located in the solar wind ion cavity for a 67P-like comet. We use $n = 300 \text{ cm}^{-3}$ for this region, in agreement with measurements by RPC-MIP and RPC-LAP of Rosetta during the dayside excursion. The amount of cold electrons in this region is uncertain. The cold-to-total density ratio is expected to decrease with $r$, but RPC-MIP has difficulties determining the ratio when it is <30% (Wattieaux et al. 2020). Likely, it is between 0% and 50% in the solar wind ion cavity. For the simulations, we assume that no cold electrons are present, but investigate the influence of a higher abundance of cold electrons in Section 5.3. For the ions, $T_i = 0.1$ eV and $v_i = 4 \text{ km s}^{-1}$ in the radial direction.

The definition of the cometopause has varied between different studies and comets. In this work, we define the cometopause as the boundary of the solar wind ion cavity. Around perihelion, Rosetta never exited the solar wind ion

cavity, not even during the dayside excursion when $r$ was up to ~1500 km. Hence, there are no measurements from Rosetta available for this region. RPC-LAP and RPC-MIP typically measured $n$ below $100 \text{ cm}^{-3}$ during the dayside excursion, and we choose $n = 50 \text{ cm}^{-3}$ for the cometopause simulations. We assume that all cometary electrons are warm with $T_{e,w} = 5$ eV. $T_i$ for the cometary ions is set to 1 eV and $v_i$ to $11 \text{ km s}^{-1}$ (Nilsson et al. 2020). We also include the solar wind in this simulation, where average conditions are used. The cometopause region involves a complex interaction between the solar wind and the cometary particles with significant deflection and pick-up (Behar et al. 2017; Nilsson et al. 2020). However, for the simulations we assume that the solar wind is flowing radially away from the Sun while the cometary ions are flowing radially away from the nucleus. As a result, the location of the wake likely differs from the real case, but we expect the influence on the spacecraft potential to be small.

### 3.3.2. Halley-like Comet

For a Halley-like comet, we run simulations for the diamagnetic cavity, the electron exobase, and the magnetic pile-up region. As much as possible, the plasma model is based on measurements made by Giotto. Unfortunately, Giotto could not make measurements of the cold electrons, and therefore the electron temperatures and the cold-to-total density ratios are instead based on models.

The diamagnetic cavity boundary of comet Halley was detected at $r \sim 4000$ km (Neubauer et al. 1986), and hence
<table><caption>**Table 1**
Plasma Parameters of the Simulated Environments</caption><thead><tr><th colspan="8">Solar Wind</th></tr><tr><th>Plasma region</th><th>r (km)</th><th>λ<sub>D</sub> (m)</th><th>Population</th><th>n (cm<sup>-3</sup>)</th><th>T (eV)</th><th>ν (km s<sup>-1</sup>)</th><th>e<sup>-</sup> modeling approach</th></tr></thead><tbody><tr><td rowspan="2">Solar wind</td><td rowspan="2">...</td><td rowspan="2">8.9</td><td>Electrons</td><td>7</td><td>10</td><td>450</td><td>PIC</td></tr><tr><td>Ions (H<sup>+</sup>)</td><td>7</td><td>10</td><td>450</td><td>PIC</td></tr><tr><th colspan="8">67P-like Comet</th></tr><tr><th>Plasma region</th><th>r (km)</th><th>λ<sub>D</sub> (m)</th><th>Population</th><th>n (cm<sup>-3</sup>)</th><th>T (eV)</th><th>ν (km s<sup>-1</sup>)</th><th>e<sup>-</sup> modeling approach</th></tr><tr><td rowspan="4">Cometopause</td><td rowspan="4">2000</td><td rowspan="4">2.3</td><td>Cometary electrons</td><td>50</td><td>5</td><td>0</td><td>PIC</td></tr><tr><td>Solar wind electrons</td><td>7</td><td>10</td><td>450</td><td>PIC</td></tr><tr><td>Cometary ions (H<sub>2</sub>O<sup>+</sup>)</td><td>50</td><td>1</td><td>11</td><td>PIC</td></tr><tr><td>Solar wind ions (H<sup>+</sup>)</td><td>7</td><td>10</td><td>450</td><td>PIC</td></tr><tr><td rowspan="2">Solar wind ion cavity (CA)</td><td rowspan="2">850</td><td rowspan="2">1.0</td><td>Warm electrons</td><td>300</td><td>5</td><td>0</td><td>PIC</td></tr><tr><td>Ions (H<sub>2</sub>O<sup>+</sup>)</td><td>300</td><td>0.1</td><td>4</td><td>PIC</td></tr><tr><td rowspan="3">Diamagnetic cavity</td><td rowspan="3">200</td><td rowspan="3">0.09</td><td>Warm electrons</td><td>300</td><td>5</td><td>0</td><td>Small vol. PIC/M-B</td></tr><tr><td>Cold electrons</td><td>700</td><td>0.1</td><td>0</td><td>Small vol. PIC/M-B</td></tr><tr><td>Ions (H<sub>2</sub>O<sup>+</sup>)</td><td>1000</td><td>0.1</td><td>4</td><td>PIC</td></tr><tr><th colspan="8">Halley-like Comet</th></tr><tr><th>Plasma region</th><th>r (km)</th><th>λ<sub>D</sub> (m)</th><th>Population</th><th>n (cm<sup>-3</sup>)</th><th>T (eV)</th><th>ν (km s<sup>-1</sup>)</th><th>e<sup>-</sup> modeling approach</th></tr><tr><td rowspan="3">Magnetic pile-up</td><td rowspan="3">135 000</td><td rowspan="3">0.83</td><td>Warm electrons</td><td>20</td><td>20</td><td>0</td><td>PIC</td></tr><tr><td>Cold electrons</td><td>80</td><td>1</td><td>0</td><td>PIC</td></tr><tr><td>Ions (H<sub>2</sub>O<sup>+</sup>)</td><td>100</td><td>10</td><td>20</td><td>PIC</td></tr><tr><td rowspan="3">Electron exobase</td><td rowspan="3">10 000</td><td rowspan="3">0.10</td><td>Warm electrons</td><td>20</td><td>20</td><td>0</td><td>Small vol. PIC/Kinetic M-B</td></tr><tr><td>Cold electrons</td><td>5980</td><td>1</td><td>0</td><td>Small vol. PIC/Kinetic M-B</td></tr><tr><td>Ions (H<sub>2</sub>O<sup>+</sup>)</td><td>6000</td><td>1</td><td>0</td><td>PIC</td></tr><tr><td rowspan="3">Diamagnetic cavity (CA)</td><td rowspan="3">850</td><td rowspan="3">0.05</td><td>Warm electrons</td><td>40</td><td>10</td><td>0</td><td>Small vol. PIC/M-B</td></tr><tr><td>Cold electrons</td><td>1960</td><td>0.1</td><td>0</td><td>Small vol. PIC/M-B</td></tr><tr><td>Ions (H<sub>2</sub>O<sup>+</sup>)</td><td>2000</td><td>0.1</td><td>1</td><td>PIC</td></tr></tbody></table>

the closest approach of probe B1 is expected to be well within this region in the case of a Halley-like comet. The collisional cooling of the electrons is expected to be very efficient in the inner coma, and we assume that 98% are cold with $T_{e,c} = 0.1$ eV (Körösmezey et al. 1987; Gan & Cravens 1990). We also include a suprathermal component with $T_{e,w} = 10$ eV (Gan & Cravens 1990). In total, $n = 2000 \text{ cm}^{-3}$ (Gan & Cravens 1990; Altwegg et al. 1993). For the ions, $T_i = 0.1$ eV and $v_i = 1 \text{ km s}^{-1}$ (Schwenn et al. 1987; Altwegg et al. 1993).

Giotto detected an ion pile-up outside of the diamagnetic cavity, at $r \sim 10,000$ km, where $n$ suddenly increased to $\sim 6000 \text{ cm}^{-3}$ (Schwenn et al. 1987; Altwegg et al. 1993). This was by some studies (e.g., Gan & Cravens 1990; Häberli et al. 1996) interpreted as the electron exobase, where an increase in the electron temperature would reduce the recombination rate, which in turn would cause a density increase. In the simulations, $T_{e,c}$ is increased to 1 eV and the suprathermal $T_{e,w}$ to 20 eV in this region, according to the modeling results by Gan & Cravens (1990). $n$ is 5980 cm$^{-3}$ and 20 cm$^{-3}$ for the cold and suprathermal components, respectively. For the ions, $T_i = 1$ eV and $v_i = 0 \text{ km s}^{-1}$ (Schwenn et al. 1987; Altwegg et al. 1993).

Finally, we study the spacecraft potential in the magnetic pile-up region. A magnetic pile-up boundary was identified in data from Giotto at $r \sim 135,000$ km, where the magnetic field strength suddenly increased by a factor of $\sim 3$ (Neubauer et al. 1986; Mazelle et al. 1989). In this region, $n$ was around $100 \text{ cm}^{-3}$ (Altwegg et al. 1993), and we assume that 20% of the electrons are suprathermal with $T_{e,w} = 20$ eV (Gan & Cravens 1990). For

the cold electrons, we use $T_{e,c} = 1$ eV. For the ions, $T_i = 10$ eV and $v_i = 20 \text{ km s}^{-1}$ radially away from the nucleus (Altwegg et al. 1993).

### 3.4. Electron Modeling

The electrons are modeled as PIC in all SPIS simulations. Even though the Maxwell-Boltzmann approximation (see Section 2.1.1) is advantageous in that it can significantly reduce the noise level and computational load, it is not ideal for our application. The dust shield acts as a barrier in front of the probe, which the electrons tunnel through when a Maxwell-Boltzmann approximation is used. As a result, the electron density gets unrealistically large behind the dust shield and the electron current is overestimated. However, a full PIC treatment causes computational issues for cases with a short Debye length due to the required mesh resolution. For those cases, we have to considerably reduce the simulation volume for the full PIC simulation, which means that the wakes are not fully captured. Those simulations we also run with the full volume using a Maxwell-Boltzmann approximation for comparison and verification. The modeling approach used for each case is listed in Table 1.

### 3.5. Spacecraft Relative Flyby Velocity

The relative flyby velocity of the spacecraft ($v_{s/c}$) is expected to be in the range $10-70 \text{ km s}^{-1}$. At high $v_{s/c}$, impacts by
<table><caption>**Table 1**
Plasma Parameters of the Simulated Environments</caption><thead><tr><th colspan="8">Solar Wind</th></tr><tr><th>Plasma region</th><th>r (km)</th><th>λ<sub>D</sub> (m)</th><th>Population</th><th>n (cm<sup>-3</sup>)</th><th>T (eV)</th><th>ν (km s<sup>-1</sup>)</th><th>e<sup>-</sup> modeling approach</th></tr></thead><tbody><tr><td rowspan="2">Solar wind</td><td rowspan="2">...</td><td rowspan="2">8.9</td><td>Electrons</td><td>7</td><td>10</td><td>450</td><td>PIC</td></tr><tr><td>Ions (H<sup>+</sup>)</td><td>7</td><td>10</td><td>450</td><td>PIC</td></tr><tr><th colspan="8">67P-like Comet</th></tr><tr><th>Plasma region</th><th>r (km)</th><th>λ<sub>D</sub> (m)</th><th>Population</th><th>n (cm<sup>-3</sup>)</th><th>T (eV)</th><th>ν (km s<sup>-1</sup>)</th><th>e<sup>-</sup> modeling approach</th></tr><tr><td rowspan="4">Cometopause</td><td rowspan="4">2000</td><td rowspan="4">2.3</td><td>Cometary electrons</td><td>50</td><td>5</td><td>0</td><td>PIC</td></tr><tr><td>Solar wind electrons</td><td>7</td><td>10</td><td>450</td><td>PIC</td></tr><tr><td>Cometary ions (H<sub>2</sub>O<sup>+</sup>)</td><td>50</td><td>1</td><td>11</td><td>PIC</td></tr><tr><td>Solar wind ions (H<sup>+</sup>)</td><td>7</td><td>10</td><td>450</td><td>PIC</td></tr><tr><td rowspan="2">Solar wind ion cavity (CA)</td><td rowspan="2">850</td><td rowspan="2">1.0</td><td>Warm electrons</td><td>300</td><td>5</td><td>0</td><td>PIC</td></tr><tr><td>Ions (H<sub>2</sub>O<sup>+</sup>)</td><td>300</td><td>0.1</td><td>4</td><td>PIC</td></tr><tr><td rowspan="3">Diamagnetic cavity</td><td rowspan="3">200</td><td rowspan="3">0.09</td><td>Warm electrons</td><td>300</td><td>5</td><td>0</td><td>Small vol. PIC/M-B</td></tr><tr><td>Cold electrons</td><td>700</td><td>0.1</td><td>0</td><td>Small vol. PIC/M-B</td></tr><tr><td>Ions (H<sub>2</sub>O<sup>+</sup>)</td><td>1000</td><td>0.1</td><td>4</td><td>PIC</td></tr><tr><th colspan="8">Halley-like Comet</th></tr><tr><th>Plasma region</th><th>r (km)</th><th>λ<sub>D</sub> (m)</th><th>Population</th><th>n (cm<sup>-3</sup>)</th><th>T (eV)</th><th>ν (km s<sup>-1</sup>)</th><th>e<sup>-</sup> modeling approach</th></tr><tr><td rowspan="3">Magnetic pile-up</td><td rowspan="3">135 000</td><td rowspan="3">0.83</td><td>Warm electrons</td><td>20</td><td>20</td><td>0</td><td>PIC</td></tr><tr><td>Cold electrons</td><td>80</td><td>1</td><td>0</td><td>PIC</td></tr><tr><td>Ions (H<sub>2</sub>O<sup>+</sup>)</td><td>100</td><td>10</td><td>20</td><td>PIC</td></tr><tr><td rowspan="3">Electron exobase</td><td rowspan="3">10 000</td><td rowspan="3">0.10</td><td>Warm electrons</td><td>20</td><td>20</td><td>0</td><td>Small vol. PIC/Kinetic M-B</td></tr><tr><td>Cold electrons</td><td>5980</td><td>1</td><td>0</td><td>Small vol. PIC/Kinetic M-B</td></tr><tr><td>Ions (H<sub>2</sub>O<sup>+</sup>)</td><td>6000</td><td>1</td><td>0</td><td>PIC</td></tr><tr><td rowspan="3">Diamagnetic cavity (CA)</td><td rowspan="3">850</td><td rowspan="3">0.05</td><td>Warm electrons</td><td>40</td><td>10</td><td>0</td><td>Small vol. PIC/M-B</td></tr><tr><td>Cold electrons</td><td>1960</td><td>0.1</td><td>0</td><td>Small vol. PIC/M-B</td></tr><tr><td>Ions (H<sub>2</sub>O<sup>+</sup>)</td><td>2000</td><td>0.1</td><td>1</td><td>PIC</td></tr></tbody></table>

the closest approach of probe B1 is expected to be well within this region in the case of a Halley-like comet. The collisional cooling of the electrons is expected to be very efficient in the inner coma, and we assume that 98% are cold with $T_{e,c} = 0.1$ eV (Körösmezey et al. 1987; Gan & Cravens 1990). We also include a suprathermal component with $T_{e,w} = 10$ eV (Gan & Cravens 1990). In total, $n = 2000 \text{ cm}^{-3}$ (Gan & Cravens 1990; Altwegg et al. 1993). For the ions, $T_i = 0.1$ eV and $v_i = 1 \text{ km s}^{-1}$ (Schwenn et al. 1987; Altwegg et al. 1993).

Giotto detected an ion pile-up outside of the diamagnetic cavity, at $r \sim 10,000$ km, where $n$ suddenly increased to $\sim 6000 \text{ cm}^{-3}$ (Schwenn et al. 1987; Altwegg et al. 1993). This was by some studies (e.g., Gan & Cravens 1990; Häberli et al. 1996) interpreted as the electron exobase, where an increase in the electron temperature would reduce the recombination rate, which in turn would cause a density increase. In the simulations, $T_{e,c}$ is increased to 1 eV and the suprathermal $T_{e,w}$ to 20 eV in this region, according to the modeling results by Gan & Cravens (1990). $n$ is 5980 cm$^{-3}$ and 20 cm$^{-3}$ for the cold and suprathermal components, respectively. For the ions, $T_i = 1$ eV and $v_i = 0 \text{ km s}^{-1}$ (Schwenn et al. 1987; Altwegg et al. 1993).

Finally, we study the spacecraft potential in the magnetic pile-up region. A magnetic pile-up boundary was identified in data from Giotto at $r \sim 135,000$ km, where the magnetic field strength suddenly increased by a factor of $\sim 3$ (Neubauer et al. 1986; Mazelle et al. 1989). In this region, $n$ was around $100 \text{ cm}^{-3}$ (Altwegg et al. 1993), and we assume that 20% of the electrons are suprathermal with $T_{e,w} = 20$ eV (Gan & Cravens 1990). For

the cold electrons, we use $T_{e,c} = 1$ eV. For the ions, $T_i = 10$ eV and $v_i = 20 \text{ km s}^{-1}$ radially away from the nucleus (Altwegg et al. 1993).

### 3.4. Electron Modeling

The electrons are modeled as PIC in all SPIS simulations. Even though the Maxwell-Boltzmann approximation (see Section 2.1.1) is advantageous in that it can significantly reduce the noise level and computational load, it is not ideal for our application. The dust shield acts as a barrier in front of the probe, which the electrons tunnel through when a Maxwell-Boltzmann approximation is used. As a result, the electron density gets unrealistically large behind the dust shield and the electron current is overestimated. However, a full PIC treatment causes computational issues for cases with a short Debye length due to the required mesh resolution. For those cases, we have to considerably reduce the simulation volume for the full PIC simulation, which means that the wakes are not fully captured. Those simulations we also run with the full volume using a Maxwell-Boltzmann approximation for comparison and verification. The modeling approach used for each case is listed in Table 1.

### 3.5. Spacecraft Relative Flyby Velocity

The relative flyby velocity of the spacecraft ($v_{s/c}$) is expected to be in the range $10-70 \text{ km s}^{-1}$. At high $v_{s/c}$, impacts by
<table><caption>**Table 2**
Parameters Used for the Expected SEE from Neutral Impacts at $v_{s/c}$ = 70 km s$^{-1}$</caption><thead><tr><th></th><th colspan="3">Solar Wind</th></tr></thead><tbody><tr><td>Plasma region</td><td>$n_n$ (m<sup>-3</sup>)</td><td>$J_{SEE}$ (Am<sup>-2</sup>)</td><td>Solar flux amplification factor</td></tr><tr><td>Solar wind</td><td>...</td><td>...</td><td>...</td></tr><tr><td></td><td colspan="3">67P-like Comet</td></tr><tr><td>Plasma region</td><td>$n_n$ (m<sup>-3</sup>)</td><td>$J_{SEE}$ (Am<sup>-2</sup>)</td><td>Solar flux amplification factor</td></tr><tr><td>Cometopause</td><td>6.8 &times; 10<sup>11</sup></td><td>1.5 &times; 10<sup>-3</sup></td><td>100</td></tr><tr><td>Solar wind ion cavity (CA)</td><td>3.8 &times; 10<sup>12</sup></td><td>8.5 &times; 10<sup>-3</sup></td><td>557</td></tr><tr><td>Diamagnetic cavity</td><td>6.9 &times; 10<sup>13</sup></td><td>1.5 &times; 10<sup>-1</sup></td><td>10 164</td></tr><tr><td></td><td colspan="3">Halley-like Comet</td></tr><tr><td>Plasma region</td><td>$n_n$ (m<sup>-3</sup>)</td><td>$J_{SEE}$ (Am<sup>-2</sup>)</td><td>Solar flux amplification factor</td></tr><tr><td>Magnetic pile-up</td><td>5.2 &times; 10<sup>8</sup></td><td>1.2 &times; 10<sup>-6</sup></td><td>0.08</td></tr><tr><td>Electron exobase</td><td>4.8 &times; 10<sup>11</sup></td><td>1.1 &times; 10<sup>-3</sup></td><td>70</td></tr><tr><td>Diamagnetic cavity (CA)</td><td>7.5 &times; 10<sup>13</sup></td><td>1.7 &times; 10<sup>-1</sup></td><td>11 038</td></tr></tbody></table>

neutral particles will cause large amounts of SEE and secondary ion emission (SIE), as already observed, for example, during the flybys of comet Halley (e.g., Thiemann et al. 1986; Grard et al. 1988). In many environments, these emissions will dominate the currents to and from the spacecraft. If $v_{s/c}$ is as low as 10 km s$^{-1}$, the energy of the impacting particles will on the other hand be too low to cause significant SEE and SIE. We therefore study two different cases: One with a low $v_{s/c}$ of 10 km s$^{-1}$ and one with a high $v_{s/c}$ of 70 km s$^{-1}$.

### 3.5.1. Simulation Setup at $v_{s/c}$ = 70 km s$^{-1}$

SEE and SIE from neutral impacts have not been implemented in SPIS. Therefore, we approximate SEE at high flyby velocities by enhancing the photoemission from the spacecraft surfaces exposed to neutral impacts.

The SEE current density, $J_{SEE}$, generated by neutral impacts is given by

$$J_{SEE} = v_{s/c} n_n e Y_e, \qquad (2)$$

where $n_n$ is the neutral density, $e$ is the elementary charge, and $Y_e$ is the electron yield at the impact energy.

Schmidt & Arends (1985) determined the value of $Y_e$ for the Giotto spacecraft from laboratory measurements. $Y_e$ for different impacting particle species at the relative flyby velocity of Giotto (68 km s$^{-1}$) was determined for different target materials. For impacting water molecules, which can be assumed to dominate the gas environment around the comet, $Y_e$ varying between 0.1 and 0.2 was obtained, where the lower value was obtained from a surface of space-weathered gold and the higher from space-weathered aluminium. For this work, we use $Y_e = 0.2$.

The neutral densities are obtained from the Haser model (Haser 1957), given by

$$n_n(r) = \frac{Q}{4\pi v_n r^2} e^{-r/(v_n \tau)}, \qquad (3)$$

where $v_n$ is the radial expansion velocity of the neutral gas (assumed to be 1 km s$^{-1}$; Gulkis et al. 2015) and $\tau$ is the photochemical lifetime (77,000 s for water molecules).

In Table 2, calculated values of $n_n$ and the corresponding value of $J_{SEE}$ for the simulated environments are listed. To achieve these values of $J_{SEE}$ in SPIS, an extra Sun is added in the ram direction with adapted solar flux to achieve a photoemission level corresponding to $J_{SEE}$. The solar flux amplification factors for this extra Sun compared to a standard Sun are listed in Table 2. Although not directly comparable due to material differences, the calculated values of $J_{SEE}$ are in reasonable agreement with the current densities from secondary emissions measured by Giotto and Vega during the flybys of comet Halley (Grard et al. 1988). For example, measurements made by Giotto indicate current densities around 0.1–1 Am$^{-2}$ in the inner coma, agreeing well with the value used for the diamagnetic cavity in the current study.

We assume that the secondary electrons are described by a Maxwellian distribution with temperature 2 eV (Schmidt & Arends 1985).

No appropriate way of approximating SIE in SPIS has been found. For most of the studied environments this is an acceptable omission as the ion yield is expected to be one order of magnitude lower than the electron yield (Schmidt & Arends 1985). In the innermost coma the potential is, however, overestimated, which is investigated further in Section 5.1 using EMSES.

# 4. Results

## 4.1. Solar Wind

The spacecraft potentials ($U_{s/c}$) obtained for all environments are summarized in Table 3. For the solar wind, $U_{s/c}$ is 8.9 V. This value is in good agreement with simulation results obtained in the solar wind around 1 au for other missions, e.g., Solar Orbiter and Parker Solar Probe (Guillemant et al. 2013). It also agrees with measurements made by Rosetta (Odelstad et al. 2017). The current balance is shown in Figure 2. As expected, the photoelectron current is the dominating current in this environment. It is balanced by the same photoelectrons being attracted back to the spacecraft, as the spacecraft charges positively.
<table><caption>**Table 2**
Parameters Used for the Expected SEE from Neutral Impacts at $v_{s/c}$ = 70 km s$^{-1}$</caption><thead><tr><th></th><th colspan="3">Solar Wind</th></tr></thead><tbody><tr><td>Plasma region</td><td>$n_n$ (m<sup>-3</sup>)</td><td>$J_{SEE}$ (Am<sup>-2</sup>)</td><td>Solar flux amplification factor</td></tr><tr><td>Solar wind</td><td>...</td><td>...</td><td>...</td></tr><tr><td></td><td colspan="3">67P-like Comet</td></tr><tr><td>Plasma region</td><td>$n_n$ (m<sup>-3</sup>)</td><td>$J_{SEE}$ (Am<sup>-2</sup>)</td><td>Solar flux amplification factor</td></tr><tr><td>Cometopause</td><td>6.8 × 10<sup>11</sup></td><td>1.5 × 10<sup>-3</sup></td><td>100</td></tr><tr><td>Solar wind ion cavity (CA)</td><td>3.8 × 10<sup>12</sup></td><td>8.5 × 10<sup>-3</sup></td><td>557</td></tr><tr><td>Diamagnetic cavity</td><td>6.9 × 10<sup>13</sup></td><td>1.5 × 10<sup>-1</sup></td><td>10 164</td></tr><tr><td></td><td colspan="3">Halley-like Comet</td></tr><tr><td>Plasma region</td><td>$n_n$ (m<sup>-3</sup>)</td><td>$J_{SEE}$ (Am<sup>-2</sup>)</td><td>Solar flux amplification factor</td></tr><tr><td>Magnetic pile-up</td><td>5.2 × 10<sup>8</sup></td><td>1.2 × 10<sup>-6</sup></td><td>0.08</td></tr><tr><td>Electron exobase</td><td>4.8 × 10<sup>11</sup></td><td>1.1 × 10<sup>-3</sup></td><td>70</td></tr><tr><td>Diamagnetic cavity (CA)</td><td>7.5 × 10<sup>13</sup></td><td>1.7 × 10<sup>-1</sup></td><td>11 038</td></tr></tbody></table>

neutral particles will cause large amounts of SEE and secondary ion emission (SIE), as already observed, for example, during the flybys of comet Halley (e.g., Thiemann et al. 1986; Grard et al. 1988). In many environments, these emissions will dominate the currents to and from the spacecraft. If $v_{s/c}$ is as low as 10 km s$^{-1}$, the energy of the impacting particles will on the other hand be too low to cause significant SEE and SIE. We therefore study two different cases: One with a low $v_{s/c}$ of 10 km s$^{-1}$ and one with a high $v_{s/c}$ of 70 km s$^{-1}$.

### 3.5.1. Simulation Setup at $v_{s/c}$ = 70 km s$^{-1}$

SEE and SIE from neutral impacts have not been implemented in SPIS. Therefore, we approximate SEE at high flyby velocities by enhancing the photoemission from the spacecraft surfaces exposed to neutral impacts.

The SEE current density, $J_{SEE}$, generated by neutral impacts is given by

$$J_{SEE} = v_{s/c} n_n e Y_e, \quad (2)$$

where $n_n$ is the neutral density, $e$ is the elementary charge, and $Y_e$ is the electron yield at the impact energy.

Schmidt & Arends (1985) determined the value of $Y_e$ for the Giotto spacecraft from laboratory measurements. $Y_e$ for different impacting particle species at the relative flyby velocity of Giotto (68 km s$^{-1}$) was determined for different target materials. For impacting water molecules, which can be assumed to dominate the gas environment around the comet, $Y_e$ varying between 0.1 and 0.2 was obtained, where the lower value was obtained from a surface of space-weathered gold and the higher from space-weathered aluminium. For this work, we use $Y_e = 0.2$.

The neutral densities are obtained from the Haser model (Haser 1957), given by

$$n_n(r) = \frac{Q}{4\pi v_n r^2} e^{-r/(v_n \tau)}, \quad (3)$$

where $v_n$ is the radial expansion velocity of the neutral gas (assumed to be 1 km s$^{-1}$; Gulkis et al. 2015) and $\tau$ is the photochemical lifetime (77,000 s for water molecules).

In Table 2, calculated values of $n_n$ and the corresponding value of $J_{SEE}$ for the simulated environments are listed. To achieve these values of $J_{SEE}$ in SPIS, an extra Sun is added in the ram direction with adapted solar flux to achieve a photoemission level corresponding to $J_{SEE}$. The solar flux amplification factors for this extra Sun compared to a standard Sun are listed in Table 2. Although not directly comparable due to material differences, the calculated values of $J_{SEE}$ are in reasonable agreement with the current densities from secondary emissions measured by Giotto and Vega during the flybys of comet Halley (Grard et al. 1988). For example, measurements made by Giotto indicate current densities around 0.1–1 Am$^{-2}$ in the inner coma, agreeing well with the value used for the diamagnetic cavity in the current study.

We assume that the secondary electrons are described by a Maxwellian distribution with temperature 2 eV (Schmidt & Arends 1985).

No appropriate way of approximating SIE in SPIS has been found. For most of the studied environments this is an acceptable omission as the ion yield is expected to be one order of magnitude lower than the electron yield (Schmidt & Arends 1985). In the innermost coma the potential is, however, overestimated, which is investigated further in Section 5.1 using EMSES.

# 4. Results

## 4.1. Solar Wind

The spacecraft potentials ($U_{s/c}$) obtained for all environments are summarized in Table 3. For the solar wind, $U_{s/c}$ is 8.9 V. This value is in good agreement with simulation results obtained in the solar wind around 1 au for other missions, e.g., Solar Orbiter and Parker Solar Probe (Guillemant et al. 2013). It also agrees with measurements made by Rosetta (Odelstad et al. 2017). The current balance is shown in Figure 2. As expected, the photoelectron current is the dominating current in this environment. It is balanced by the same photoelectrons being attracted back to the spacecraft, as the spacecraft charges positively.
<figure><img src="image_6.png" /><figcaption>**Figure 2.** Balance of currents to and from the spacecraft surface for the solar wind simulation.</figcaption></figure>

## 4.2. Relative Flyby Velocity of 10 km s⁻¹

For a 67P-like comet, $U_{s/c}$ varies from 2.2 V at the cometopause to -4.7 V in the solar wind ion cavity (see Table 3). The potential is -4.5 V in the diamagnetic cavity, i.e., almost the same as in the solar wind ion cavity. The density of warm electrons is the same in both cases while the cold electrons cannot reach the spacecraft in the diamagnetic cavity (see, e.g., Figures 3(e)-(f) and Figures 4(g)-(i)), resulting in similar $U_{s/c}$. $U_{s/c}$ is slightly less negative in the diamagnetic cavity due to the higher ion density and hence larger ion current in this region. Note, though, that $\lambda_D$ is much smaller in the diamagnetic cavity due to the cold electrons, resulting in different potential structures around the spacecraft, as illustrated in Figure 5. This has important implications for plasma measurements (e.g., Bergman et al. 2020b).

The current balance for each environment is shown in Figure 6. For a 67P-like comet, the main balancing currents in all environments are the warm electron current and the photoelectron current, with a small influence from the SEE current from electrons.

In the diamagnetic cavity, the result shown in Table 3 is obtained from a full PIC simulation, but where the simulation volume is reduced to $2 \times 2 \times 2.7$ m due to computational limitations. For comparison, we also run a simulation with the full simulation volume where the electrons are modeled using a Maxwell-Boltzmann approximation. The resulting value of $U_{s/c}$ for the latter case is -5.2 V. A comparison of the charge density of the different particle populations around the spacecraft is shown in Figures 3 and 4. As expected, $U_{s/c}$ is more negative in the Maxwell-Boltzmann case due to the enhanced electron density behind the dust shield, visible in Figure 4(f). Apart from this, the charge density of particles around the spacecraft is similar for the two setups, verifying that the full PIC simulation yields reasonable results even though the full wakes are not captured. It furthermore validates the general performance of the Maxwell-Boltzmann approximation.

For a Halley-like comet, $U_{s/c}$ is 1.1 V in the magnetic pile-up region, -3.4 V at the electron exobase, and -0.1 V in the diamagnetic cavity. The reason for the less negative potential in the diamagnetic cavity compared to the 67P case is the more effective cooling of the electrons in the inner coma of a Halley-like comet. At the electron exobase, $U_{s/c}$ is naturally more negative than in the diamagnetic cavity due to the higher electron density and temperature.

<table><caption>**Table 3**
Spacecraft Potential Simulation Results</caption><tbody><tr><th colspan="3">Solar Wind</th></tr><tr><td></td><td colspan="2">U<sub>s/c</sub> (V)</td></tr><tr><td>Solar wind</td><td colspan="2">8.9</td></tr><tr><th colspan="3">67P-like Comet</th></tr><tr><td></td><td colspan="2">U<sub>s/c</sub> (V)</td></tr><tr><td></td><td>v<sub>s/c</sub> = 10 km s<sup>-1</sup></td><td>v<sub>s/c</sub> = 70 km s<sup>-1</sup></td></tr><tr><td>Cometopause</td><td>2.2</td><td>8.7</td></tr><tr><td>Solar wind ion cavity (CA)</td><td>-4.7</td><td>8.4</td></tr><tr><td>Diamagnetic cavity</td><td>-4.5</td><td>&lt;14.9<sup>a</sup></td></tr><tr><th colspan="3">Halley-like Comet</th></tr><tr><td></td><td colspan="2">U<sub>s/c</sub> (V)</td></tr><tr><td></td><td>v<sub>s/c</sub> = 10 km s<sup>-1</sup></td><td>v<sub>s/c</sub> = 70 km s<sup>-1</sup></td></tr><tr><td>Magnetic pile-up</td><td>1.1</td><td>1.2</td></tr><tr><td>Electron exobase</td><td>-3.4</td><td>-0.5</td></tr><tr><td>Diamagnetic cavity (CA)</td><td>-0.1</td><td>&lt;22.0<sup>a</sup></td></tr></tbody></table>

**Note.**

The results for the diamagnetic cavity and the electron exobase have been obtained using a full PIC simulation but with a smaller simulation volume: $1.6 \times 1.6 \times 2.6$ m for the diamagnetic cavity and $2.0 \times 2.0 \times 2.7$ m for the electron exobase. As for the 67P-like case, we also run simulations with the full simulation volume using a Maxwell-Boltzmann or kinetic Maxwell-Boltzmann approximation for the electrons. For the diamagnetic cavity, $U_{s/c}$ is slightly more negative (-0.17 V instead of -0.15 V) when a Maxwell-Boltzmann approximation is used, similarly to the 67P-like case. For the electron exobase we use the kinetic Maxwell-Boltzmann approximation, resulting in a slightly less negative potential of -3.1 V.

## 4.3. Relative Flyby Velocity of 70 km s⁻¹

For a 67P-like comet, the spacecraft is positively charged to 8-9 V in all simulated environments except the diamagnetic cavity. For a Halley-like comet, the influence from SEE is not

<footnote>a This value should be treated as an upper limit as it is likely overestimated due to the exclusion of SIE; see Section 5.1.</footnote>
<figure><img src="image_7.png" /><figcaption>**Figure 2.** Balance of currents to and from the spacecraft surface for the solar wind simulation.</figcaption></figure>

## 4.2. Relative Flyby Velocity of 10 km s⁻¹

For a 67P-like comet, $U_{s/c}$ varies from 2.2 V at the cometopause to −4.7 V in the solar wind ion cavity (see Table 3). The potential is −4.5 V in the diamagnetic cavity, i.e., almost the same as in the solar wind ion cavity. The density of warm electrons is the same in both cases while the cold electrons cannot reach the spacecraft in the diamagnetic cavity (see, e.g., Figures 3(e)–(f) and Figures 4(g)–(i)), resulting in similar $U_{s/c}$. $U_{s/c}$ is slightly less negative in the diamagnetic cavity due to the higher ion density and hence larger ion current in this region. Note, though, that $\lambda_D$ is much smaller in the diamagnetic cavity due to the cold electrons, resulting in different potential structures around the spacecraft, as illustrated in Figure 5. This has important implications for plasma measurements (e.g., Bergman et al. 2020b).

The current balance for each environment is shown in Figure 6. For a 67P-like comet, the main balancing currents in all environments are the warm electron current and the photoelectron current, with a small influence from the SEE current from electrons.

In the diamagnetic cavity, the result shown in Table 3 is obtained from a full PIC simulation, but where the simulation volume is reduced to $2 \times 2 \times 2.7$ m due to computational limitations. For comparison, we also run a simulation with the full simulation volume where the electrons are modeled using a Maxwell–Boltzmann approximation. The resulting value of $U_{s/c}$ for the latter case is −5.2 V. A comparison of the charge density of the different particle populations around the spacecraft is shown in Figures 3 and 4. As expected, $U_{s/c}$ is more negative in the Maxwell–Boltzmann case due to the enhanced electron density behind the dust shield, visible in Figure 4(f). Apart from this, the charge density of particles around the spacecraft is similar for the two setups, verifying that the full PIC simulation yields reasonable results even though the full wakes are not captured. It furthermore validates the general performance of the Maxwell–Boltzmann approximation.

For a Halley-like comet, $U_{s/c}$ is 1.1 V in the magnetic pile-up region, −3.4 V at the electron exobase, and −0.1 V in the diamagnetic cavity. The reason for the less negative potential in the diamagnetic cavity compared to the 67P case is the more effective cooling of the electrons in the inner coma of a Halley-like comet. At the electron exobase, $U_{s/c}$ is naturally more negative than in the diamagnetic cavity due to the higher electron density and temperature.

<table><caption>**Table 3**
Spacecraft Potential Simulation Results</caption><thead><tr><th></th><th colspan="2">Solar Wind</th></tr><tr><th></th><th colspan="2">U<sub>s/c</sub> (V)</th></tr></thead><tbody><tr><td>Solar wind</td><td colspan="2">8.9</td></tr><tr><th colspan="3">67P-like Comet</th></tr><tr><th></th><th colspan="2">U<sub>s/c</sub> (V)</th></tr><tr><th></th><th>v<sub>s/c</sub> = 10 km s<sup>-1</sup></th><th>v<sub>s/c</sub> = 70 km s<sup>-1</sup></th></tr><tr><td>Cometopause</td><td>2.2</td><td>8.7</td></tr><tr><td>Solar wind ion cavity (CA)</td><td>-4.7</td><td>8.4</td></tr><tr><td>Diamagnetic cavity</td><td>-4.5</td><td>&lt;14.9<sup>a</sup></td></tr><tr><th colspan="3">Halley-like Comet</th></tr><tr><th></th><th colspan="2">U<sub>s/c</sub> (V)</th></tr><tr><th></th><th>v<sub>s/c</sub> = 10 km s<sup>-1</sup></th><th>v<sub>s/c</sub> = 70 km s<sup>-1</sup></th></tr><tr><td>Magnetic pile-up</td><td>1.1</td><td>1.2</td></tr><tr><td>Electron exobase</td><td>-3.4</td><td>-0.5</td></tr><tr><td>Diamagnetic cavity (CA)</td><td>-0.1</td><td>&lt;22.0<sup>a</sup></td></tr></tbody></table>

**Note.**

The results for the diamagnetic cavity and the electron exobase have been obtained using a full PIC simulation but with a smaller simulation volume: $1.6 \times 1.6 \times 2.6$ m for the diamagnetic cavity and $2.0 \times 2.0 \times 2.7$ m for the electron exobase. As for the 67P-like case, we also run simulations with the full simulation volume using a Maxwell–Boltzmann or kinetic Maxwell–Boltzmann approximation for the electrons. For the diamagnetic cavity, $U_{s/c}$ is slightly more negative (−0.17 V instead of −0.15 V) when a Maxwell–Boltzmann approximation is used, similarly to the 67P-like case. For the electron exobase we use the kinetic Maxwell–Boltzmann approximation, resulting in a slightly less negative potential of −3.1 V.

## 4.3. Relative Flyby Velocity of 70 km s⁻¹

For a 67P-like comet, the spacecraft is positively charged to 8–9 V in all simulated environments except the diamagnetic cavity. For a Halley-like comet, the influence from SEE is not

<footnote>a This value should be treated as an upper limit as it is likely overestimated due to the exclusion of SIE; see Section 5.1.</footnote>
<figure><img src="image_7.png" /><figcaption>**Figure 3.** The resulting charge density of ions (panels (a)–(b)), warm electrons (panels (c)–(d)), and cold electrons (panels (e)–(f)) when a Maxwell-Boltzmann approximation is used for the electrons (panels (a), (c), and (e)) compared to a full PIC simulation, but with a smaller simulation volume (panels (b), (d) and (f)). The plasma model used is the diamagnetic cavity case for a 67P-like comet and $v_{s/c} = 10$ km s$^{-1}$. A cut in the x-z plane is shown. Note that the ions are modeled as PIC in both simulations.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Figure 3.** The resulting charge density of ions (panels (a)–(b)), warm electrons (panels (c)–(d)), and cold electrons (panels (e)–(f)) when a Maxwell-Boltzmann approximation is used for the electrons (panels (a), (c), and (e)) compared to a full PIC simulation, but with a smaller simulation volume (panels (b), (d) and (f)). The plasma model used is the diamagnetic cavity case for a 67P-like comet and $v_{s/c} = 10$ km s$^{-1}$. A cut in the x-z plane is shown. Note that the ions are modeled as PIC in both simulations.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Figure 4.** The resulting charge density of ions (panels (a)–(c)), warm electrons (panels (d)–(f)), and cold electrons (panels (g)–(i)) along the x-axis (panels (a), (d), and (g)), y-axis (panels (b), (e), and (h)) and z-axis (panels (c), (f), and (i)) when a Maxwell-Boltzmann approximation is used for the electrons (dark gray line) compared to a full PIC simulation, but with a smaller simulation volume (orange line). The plasma model for the case shown is the diamagnetic cavity case for a 67P-like comet and $v_{s/c} = 10$ km s⁻¹. Note that the ions are modeled as PIC in both simulations.</figcaption></figure>

as large in the magnetic pile-up region and at the electron exobase. The magnetosphere of a Halley-like comet is much larger than that of a 67P-like comet, and hence the density of neutral particles is lower in these two regions.

In the diamagnetic cavity, $U_{s/c}$ is more positive than in the other environments for both comets. These values are, however, likely overestimated since SIE has not been considered (see Section 5.1). These values should therefore be treated with care and only considered as upper limits of probable $U_{s/c}$ acquired by the probe.

The results for the environments with a short $\lambda_D$ have been obtained using full PIC simulations with the smaller simulation volumes presented in Section 4.2.

The current balance for all simulated environments is shown in Figure 7. The SEE current from neutrals is clearly dominating in most environments.

# 5. Discussion

## 5.1. Secondary Ion Emission

Due to limitations in the current implementation of SPIS, SIE is not included in the simulations. This results in an overestimation of $U_{s/c}$ at a high flyby velocity. In this section, we use EMSES to estimate the influence of SIE. We do this for one of the considered environments, the solar wind ion cavity of a 67P-like comet. We use a simplified model of the spacecraft where only the main spacecraft body (excluding the instruments and the dust shield), the solar panels, and the boom are included. For computational reasons, the dimensions of the solar panels are increased to $0.04 \times 0.3 \times 0.6$ m. This should not significantly affect the result in cases where SEE and SIE from neutrals are dominating, considering the direction of the impacting flow. The whole surface is assumed to be perfectly conducting.
<figure><img src="image_9.png" /><figcaption>**Figure 4.** The resulting charge density of ions (panels (a)–(c)), warm electrons (panels (d)–(f)), and cold electrons (panels (g)–(i)) along the x-axis (panels (a), (d), and (g)), y-axis (panels (b), (e), and (h)) and z-axis (panels (c), (f), and (i)) when a Maxwell-Boltzmann approximation is used for the electrons (dark gray line) compared to a full PIC simulation, but with a smaller simulation volume (orange line). The plasma model for the case shown is the diamagnetic cavity case for a 67P-like comet and $v_{s/c} = 10$ km s⁻¹. Note that the ions are modeled as PIC in both simulations.</figcaption></figure>

as large in the magnetic pile-up region and at the electron exobase. The magnetosphere of a Halley-like comet is much larger than that of a 67P-like comet, and hence the density of neutral particles is lower in these two regions.

In the diamagnetic cavity, $U_{s/c}$ is more positive than in the other environments for both comets. These values are, however, likely overestimated since SIE has not been considered (see Section 5.1). These values should therefore be treated with care and only considered as upper limits of probable $U_{s/c}$ acquired by the probe.

The results for the environments with a short $\lambda_D$ have been obtained using full PIC simulations with the smaller simulation volumes presented in Section 4.2.

The current balance for all simulated environments is shown in Figure 7. The SEE current from neutrals is clearly dominating in most environments.

# 5. Discussion

## 5.1. Secondary Ion Emission

Due to limitations in the current implementation of SPIS, SIE is not included in the simulations. This results in an overestimation of $U_{s/c}$ at a high flyby velocity. In this section, we use EMSES to estimate the influence of SIE. We do this for one of the considered environments, the solar wind ion cavity of a 67P-like comet. We use a simplified model of the spacecraft where only the main spacecraft body (excluding the instruments and the dust shield), the solar panels, and the boom are included. For computational reasons, the dimensions of the solar panels are increased to $0.04 \times 0.3 \times 0.6$ m. This should not significantly affect the result in cases where SEE and SIE from neutrals are dominating, considering the direction of the impacting flow. The whole surface is assumed to be perfectly conducting.
<figure><img src="image_9.png" /><figcaption>**Figure 5.** The resulting potential field around the spacecraft in the solar wind ion cavity ($\lambda_D=1.0$ m, $U_{s/c} = -4.7$ V) and the diamagnetic cavity ($\lambda_D=0.09$ m, $U_{s/c} = -4.5$ V) for a 67P-like comet at $v_{s/c} = 10$ km s$^{-1}$. The same potential surfaces are shown in both cases, corresponding to a potential of -4.0, -3.5, -3.0, -2.5, -2.0, -1.5, -1.0, and -0.5 V.</figcaption></figure>

First, to verify the performance of the two simulation softwares, we run comparative simulations in both SPIS and EMSES where only SEE (and not SIE) is included. The simpler spacecraft geometry is used also in SPIS, where silver is used as surface material to mimic a perfect conductor. The obtained spacecraft potential is 8.3 V using SPIS and 8.8 V using EMSES, which is considered to be a reasonable agreement.

We then include SIE in the EMSES simulation, assuming $O^+$ ions with a temperature of 2 eV. The ion yield is one order of magnitude smaller than the electron yield, in agreement with the results by Schmidt & Arends (1985). The resulting spacecraft potential is 8.0 V, i.e., less than 1 V lower compared to the case without SIE. For all simulation cases where $J_{SEE}$ is equal to or less than the studied case, we expect the influence of SIE to be less than 1 V, which is negligible for our applications. However, for the two diamagnetic cavity cases we expect the uncertainty to be larger. In these environments, the SEE current is dominant enough for $U_{s/c}$ to be determined by the value where close to all emitted secondary electrons are attracted back to the spacecraft. As a result, this value is very sensitive to the electrons in the high-energy tail of the emitted distribution. Since the amount of electrons in the tail is small, even a rather small SIE current is able to balance these electrons and shift $U_{s/c}$ by several volts. Therefore, the values of $U_{s/c}$ reported for the diamagnetic cavity only represent an upper limit of probable potentials.

Also important to mention is that SIE has an influence on the potential field around the spacecraft. A positive potential barrier of ~13 V is developed in front of the spacecraft (about 2–3 cm from the spacecraft surface) in the EMSES simulation

where SIE is included (see Figure 8). Similar effects were also observed by Thiemann et al. (1986). This potential barrier is important to take into account when, for example, studying the influence on particle measurements, but a more detailed investigation is outside the scope of the current study. We leave this as a topic for future work.

## 5.2. Temperature of Secondary Electrons

At high flyby velocities, $U_{s/c}$ is very sensitive to the temperature of the secondary electrons (e.g., Zhang et al. 2023). Not much can be found in the literature about the value of this parameter at neutral impacts, so for this study we use the standard photoemission temperature of 2 eV, somewhat supported by Schmidt & Arends (1985). However, this value is highly uncertain and might not be valid for black kapton. Measurements from the Cassini spacecraft’s Grand Finale indicate temperatures of 0.1–0.6 eV for secondary electrons (Johansson et al. 2022), one order of magnitude lower than the value used in this study. If the temperature is reduced to 0.2 eV in our simulation in the solar wind ion cavity, $U_{s/c}$ is reduced from 8.4 to 0.8 V. Hence, for all environments where the SEE current is dominating, $U_{s/c}$ can be as much as one order of magnitude lower if the temperature is reduced by one order of magnitude. All values presented for a high flyby velocity should hence be treated as upper limits. Previous flyby missions to comets reported lower potentials in the inner coma of 0–2 V (Grard et al. 1985; Krankowsky et al. 1986; Pedersen et al. 1986; Schwenn et al. 1987; Zwickl et al. 1988), possibly indicating a lower temperature of the secondaries in agreement
<figure><img src="image_10.png" /><figcaption>**Figure 5.** The resulting potential field around the spacecraft in the solar wind ion cavity ($\lambda_D=1.0$ m, $U_{s/c} = -4.7$ V) and the diamagnetic cavity ($\lambda_D=0.09$ m, $U_{s/c} = -4.5$ V) for a 67P-like comet at $v_{s/c} = 10$ km s$^{-1}$. The same potential surfaces are shown in both cases, corresponding to a potential of -4.0, -3.5, -3.0, -2.5, -2.0, -1.5, -1.0, and -0.5 V.</figcaption></figure>

First, to verify the performance of the two simulation softwares, we run comparative simulations in both SPIS and EMSES where only SEE (and not SIE) is included. The simpler spacecraft geometry is used also in SPIS, where silver is used as surface material to mimic a perfect conductor. The obtained spacecraft potential is 8.3 V using SPIS and 8.8 V using EMSES, which is considered to be a reasonable agreement.

We then include SIE in the EMSES simulation, assuming $O^+$ ions with a temperature of 2 eV. The ion yield is one order of magnitude smaller than the electron yield, in agreement with the results by Schmidt & Arends (1985). The resulting spacecraft potential is 8.0 V, i.e., less than 1 V lower compared to the case without SIE. For all simulation cases where $J_{SEE}$ is equal to or less than the studied case, we expect the influence of SIE to be less than 1 V, which is negligible for our applications. However, for the two diamagnetic cavity cases we expect the uncertainty to be larger. In these environments, the SEE current is dominant enough for $U_{s/c}$ to be determined by the value where close to all emitted secondary electrons are attracted back to the spacecraft. As a result, this value is very sensitive to the electrons in the high-energy tail of the emitted distribution. Since the amount of electrons in the tail is small, even a rather small SIE current is able to balance these electrons and shift $U_{s/c}$ by several volts. Therefore, the values of $U_{s/c}$ reported for the diamagnetic cavity only represent an upper limit of probable potentials.

Also important to mention is that SIE has an influence on the potential field around the spacecraft. A positive potential barrier of ~13 V is developed in front of the spacecraft (about 2–3 cm from the spacecraft surface) in the EMSES simulation

where SIE is included (see Figure 8). Similar effects were also observed by Thiemann et al. (1986). This potential barrier is important to take into account when, for example, studying the influence on particle measurements, but a more detailed investigation is outside the scope of the current study. We leave this as a topic for future work.

## 5.2. Temperature of Secondary Electrons

At high flyby velocities, $U_{s/c}$ is very sensitive to the temperature of the secondary electrons (e.g., Zhang et al. 2023). Not much can be found in the literature about the value of this parameter at neutral impacts, so for this study we use the standard photoemission temperature of 2 eV, somewhat supported by Schmidt & Arends (1985). However, this value is highly uncertain and might not be valid for black kapton. Measurements from the Cassini spacecraft’s Grand Finale indicate temperatures of 0.1–0.6 eV for secondary electrons (Johansson et al. 2022), one order of magnitude lower than the value used in this study. If the temperature is reduced to 0.2 eV in our simulation in the solar wind ion cavity, $U_{s/c}$ is reduced from 8.4 to 0.8 V. Hence, for all environments where the SEE current is dominating, $U_{s/c}$ can be as much as one order of magnitude lower if the temperature is reduced by one order of magnitude. All values presented for a high flyby velocity should hence be treated as upper limits. Previous flyby missions to comets reported lower potentials in the inner coma of 0–2 V (Grard et al. 1985; Krankowsky et al. 1986; Pedersen et al. 1986; Schwenn et al. 1987; Zwickl et al. 1988), possibly indicating a lower temperature of the secondaries in agreement
<figure><img src="image_10.png" /><figcaption>**Figure 6.** Balance of currents to and from the spacecraft surface for environments corresponding to (a) a 67P-like comet at the cometopause, (b) a 67P-like comet in the solar wind ion cavity, (c) a 67P-like comet in the diamagnetic cavity, (d) a Halley-like comet in the magnetic pile-up region, (e) a Halley-like comet at the exobase and (f) a Halley-like comet in the diamagnetic cavity. $v_{s/c}$ = 10 km s⁻¹ in all cases.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Figure 6.** Balance of currents to and from the spacecraft surface for environments corresponding to (a) a 67P-like comet at the cometopause, (b) a 67P-like comet in the solar wind ion cavity, (c) a 67P-like comet in the diamagnetic cavity, (d) a Halley-like comet in the magnetic pile-up region, (e) a Halley-like comet at the exobase and (f) a Halley-like comet in the diamagnetic cavity. $v_{s/c}$ = 10 km s⁻¹ in all cases.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Figure 7.** Same as Figure 6, but for $v_{s/c}$ = 70 km s⁻¹.</figcaption></figure>

with the values reported by Johansson et al. (2022). Further laboratory studies are necessary to constrain the value of this parameter for different materials.

### 5.3. Cold Electrons

One uncertainty to the analysis at a low flyby velocity arises from the unknown or highly variable amount of cold electrons in the inner coma of a 67P-like comet. In the solar wind ion

cavity, the cold-to-total density ratio is likely in the range 0%–50%. In this study, we assume it to be 0%. If we instead set it to 50%, the resulting value of $U_{s/c}$ is –1.0 V. The uncertainty introduced to $U_{s/c}$ is hence about 3 V. In the diamagnetic cavity, the variable amount of cold electrons (60%–90%; Gilet et al. 2020) is expected to affect the potential in a similar manner. At a high flyby velocity this uncertainty is not important, since the electron current is dominated by the SEE current.
<figure><img src="image_12.png" /><figcaption>**Figure 7.** Same as Figure 6, but for $v_{s/c}$ = 70 km s⁻¹.</figcaption></figure>

with the values reported by Johansson et al. (2022). Further laboratory studies are necessary to constrain the value of this parameter for different materials.

### 5.3. Cold Electrons

One uncertainty to the analysis at a low flyby velocity arises from the unknown or highly variable amount of cold electrons in the inner coma of a 67P-like comet. In the solar wind ion

cavity, the cold-to-total density ratio is likely in the range 0%–50%. In this study, we assume it to be 0%. If we instead set it to 50%, the resulting value of $U_{s/c}$ is –1.0 V. The uncertainty introduced to $U_{s/c}$ is hence about 3 V. In the diamagnetic cavity, the variable amount of cold electrons (60%–90%; Gilet et al. 2020) is expected to affect the potential in a similar manner. At a high flyby velocity this uncertainty is not important, since the electron current is dominated by the SEE current.
<table><caption>**Table 4**
Spacecraft Potential Simulation Results in the Case of Nonconductive Solar Panels</caption><thead><tr><th rowspan="2"></th><th colspan="2">U<sub>s/c</sub> (V)</th></tr><tr><th>Ground</th><th>Solar Panels (Front Plane)</th></tr></thead><tbody><tr><td>Solar wind</td><td>6.5</td><td>12.8</td></tr><tr><td>67P-like comet, solar wind ion cavity, v<sub>s/c</sub> = 10 km s<sup>-1</sup></td><td>-13.4</td><td>-1.5</td></tr><tr><td>67P-like comet, cometopause, v<sub>s/c</sub> = 70 km s<sup>-1</sup></td><td>9.3</td><td>4.6</td></tr></tbody></table>

## 5.4. Attenuation of EUV Flux

Measurements by RPC-LAP on Rosetta indicate an attenuation of the solar EUV flux around perihelion by as much as 50% (Johansson et al. 2017). Possibly, this is caused by nano-sized dust grains far away from the nucleus. This is not accounted for in this study. However, we analyze the resulting uncertainty for a 67P-like comet at a low flyby velocity in the solar wind ion cavity by rerunning the simulation with the EUV flux set to 50% of the original value. The resulting value of $U_{s/c}$ is -7.9 V, about 3 V more negative than the original result. An uncertainty of similar magnitude is expected for the diamagnetic cavity. Similarly, the results obtained for a Halley-like comet are expected to be slightly more negative in the case of EUV attenuation. Again, this effect is not important for a high flyby velocity.

## 5.5. Nonconductive Solar Panels

For this work, the front plane of the solar panels is assumed to be covered with indium tin oxide. However, at the time of this study the final design of the probe has not been fully determined, and there is a possibility that the solar panels will not be covered by conductive layers. We therefore investigate the influence of nonconductive solar panels for a few selected environments, where the surface material of the front plane is assumed to have the properties of solar cells. The results are summarized in Table 4. In the solar wind, the ground potential is now slightly less positive compared to the fully conductive case, while the front plane of the solar panels reaches a more positive potential of 12.8 V. In the solar wind ion cavity of a 67P-like comet, ground reaches a more negative potential of -13.4 V while the potential of the solar panels is -1.5 V at $v_{s/c} = 10$ km s$^{-1}$. At the cometopause at $v_{s/c} = 70$ km s$^{-1}$, the properties of the solar panels only have a minor effect on the spacecraft ground potential. Neither the front nor back plane of the solar panels are in the ram direction, and hence their contribution to the SEE current is minor. However, the potential of the front plane of the solar panels is determined by the electron and photoelectron currents, and is hence less positive. Similar results are expected for the other environments at a high flyby velocity where the SEE current is dominating: A minor influence on the ground potential but a less positive charging of the solar panels.

## 5.6. Influence on Plasma Measurements

The spacecraft potentials obtained in this study will likely affect the low-energy ion measurements made by CIMS on probe B1, at least at low flyby velocities. Bergman et al. (2020a) showed that the directional information of the data is significantly distorted when the energy of the measured ions at infinity is less than $|2qU_{s/c}|$, where $q$ is the charge of the ions. CIMS can measure energies down to ~10 eV/q, corresponding to an energy of ~5 eV/q at infinity when $U_{s/c} = -5$ V. We can

<figure><img src="image_12.png" /><figcaption>**Figure 8.** Resulting potential profiles along the z-axis obtained with EMSES at a high flyby velocity. For the blue line only SEE is included, while the gray line shows the result when also SIE is included. The environment corresponds to a 67P-like comet in the solar wind ion cavity.</figcaption></figure>

hence expect a distortion of the data at the lowest energies, especially in the inner coma of a 67P-like comet. The distortion will be even worse in the case of nonconductive solar panels. Similar charging of spacecraft A would cause distortions of the low-energy plasma measurements made also by this spacecraft. A detailed analysis of the influence of the spacecraft potential on the plasma measurements will be a topic for a future study.

# 6. Conclusions

In this work, we studied the expected spacecraft potential of probe B1 of Comet Interceptor using PIC simulations. The potential was simulated in different plasma environments that the probe is expected to encounter during the cometary flyby. This was done for two different target comets: One with a production rate similar to comet 67P at perihelion ($Q = 3.5 \times 10^{28}$ s$^{-1}$), and one similar to comet Halley at the Giotto encounter ($Q = 6.9 \times 10^{29}$ s$^{-1}$). We studied the potential at two different relative flyby velocities of the probe, 10 and 70 km s$^{-1}$. We conclude the following:

1. In the solar wind, the probe acquires a positive potential of 8.9 V.

2. At $v_{s/c} = 10$ km s$^{-1}$, the probe acquires negative potentials of a few volts in the inner coma. For a 67P-like comet, the potential varies from 2.2 V at the cometopause to -4.7 and -4.5 V in the solar wind ion cavity and diamagnetic cavity, respectively. For a Halley-like comet, the more effective cooling of the electrons in the inner coma results in a less negative potential of -0.1 V in the diamagnetic cavity. Around the electron exobase, the potential decreases to
<table><caption>**Table 4**
Spacecraft Potential Simulation Results in the Case of Nonconductive Solar Panels</caption><thead><tr><th rowspan="2"></th><th colspan="2">U<sub>s/c</sub> (V)</th></tr><tr><th>Ground</th><th>Solar Panels (Front Plane)</th></tr></thead><tbody><tr><td>Solar wind</td><td>6.5</td><td>12.8</td></tr><tr><td>67P-like comet, solar wind ion cavity, v<sub>s/c</sub> = 10 km s<sup>-1</sup></td><td>-13.4</td><td>-1.5</td></tr><tr><td>67P-like comet, cometopause, v<sub>s/c</sub> = 70 km s<sup>-1</sup></td><td>9.3</td><td>4.6</td></tr></tbody></table>

## 5.4. Attenuation of EUV Flux

Measurements by RPC-LAP on Rosetta indicate an attenuation of the solar EUV flux around perihelion by as much as 50% (Johansson et al. 2017). Possibly, this is caused by nano-sized dust grains far away from the nucleus. This is not accounted for in this study. However, we analyze the resulting uncertainty for a 67P-like comet at a low flyby velocity in the solar wind ion cavity by rerunning the simulation with the EUV flux set to 50% of the original value. The resulting value of $U_{s/c}$ is -7.9 V, about 3 V more negative than the original result. An uncertainty of similar magnitude is expected for the diamagnetic cavity. Similarly, the results obtained for a Halley-like comet are expected to be slightly more negative in the case of EUV attenuation. Again, this effect is not important for a high flyby velocity.

## 5.5. Nonconductive Solar Panels

For this work, the front plane of the solar panels is assumed to be covered with indium tin oxide. However, at the time of this study the final design of the probe has not been fully determined, and there is a possibility that the solar panels will not be covered by conductive layers. We therefore investigate the influence of nonconductive solar panels for a few selected environments, where the surface material of the front plane is assumed to have the properties of solar cells. The results are summarized in Table 4. In the solar wind, the ground potential is now slightly less positive compared to the fully conductive case, while the front plane of the solar panels reaches a more positive potential of 12.8 V. In the solar wind ion cavity of a 67P-like comet, ground reaches a more negative potential of -13.4 V while the potential of the solar panels is -1.5 V at $v_{s/c} = 10$ km s$^{-1}$. At the cometopause at $v_{s/c} = 70$ km s$^{-1}$, the properties of the solar panels only have a minor effect on the spacecraft ground potential. Neither the front nor back plane of the solar panels are in the ram direction, and hence their contribution to the SEE current is minor. However, the potential of the front plane of the solar panels is determined by the electron and photoelectron currents, and is hence less positive. Similar results are expected for the other environments at a high flyby velocity where the SEE current is dominating: A minor influence on the ground potential but a less positive charging of the solar panels.

## 5.6. Influence on Plasma Measurements

The spacecraft potentials obtained in this study will likely affect the low-energy ion measurements made by CIMS on probe B1, at least at low flyby velocities. Bergman et al. (2020a) showed that the directional information of the data is significantly distorted when the energy of the measured ions at infinity is less than $|2qU_{s/c}|$, where $q$ is the charge of the ions. CIMS can measure energies down to ~10 eV/q, corresponding to an energy of ~5 eV/q at infinity when $U_{s/c} = -5$ V. We can

<figure><img src="image_13.png" /><figcaption>**Figure 8.** Resulting potential profiles along the z-axis obtained with EMSES at a high flyby velocity. For the blue line only SEE is included, while the gray line shows the result when also SIE is included. The environment corresponds to a 67P-like comet in the solar wind ion cavity.</figcaption></figure>

hence expect a distortion of the data at the lowest energies, especially in the inner coma of a 67P-like comet. The distortion will be even worse in the case of nonconductive solar panels. Similar charging of spacecraft A would cause distortions of the low-energy plasma measurements made also by this spacecraft. A detailed analysis of the influence of the spacecraft potential on the plasma measurements will be a topic for a future study.

# 6. Conclusions

In this work, we studied the expected spacecraft potential of probe B1 of Comet Interceptor using PIC simulations. The potential was simulated in different plasma environments that the probe is expected to encounter during the cometary flyby. This was done for two different target comets: One with a production rate similar to comet 67P at perihelion ($Q = 3.5 \times 10^{28}$ s$^{-1}$), and one similar to comet Halley at the Giotto encounter ($Q = 6.9 \times 10^{29}$ s$^{-1}$). We studied the potential at two different relative flyby velocities of the probe, 10 and 70 km s$^{-1}$. We conclude the following:

1. In the solar wind, the probe acquires a positive potential of 8.9 V.

2. At $v_{s/c} = 10$ km s$^{-1}$, the probe acquires negative potentials of a few volts in the inner coma. For a 67P-like comet, the potential varies from 2.2 V at the cometopause to -4.7 and -4.5 V in the solar wind ion cavity and diamagnetic cavity, respectively. For a Halley-like comet, the more effective cooling of the electrons in the inner coma results in a less negative potential of -0.1 V in the diamagnetic cavity. Around the electron exobase, the potential decreases to
−3.4 V. At larger distances from the nucleus, in the magnetic pile-up region, the potential is 1.1 V.

3. At $v_{s/c} = 70$ km s⁻¹, SEE from impacts by neutral particles dominates the currents to and from the spacecraft surface in the inner coma, resulting in positive potentials in most environments. For a 67P-like comet, the potential is 8–9 V in all studied environments except the diamagnetic cavity. For a Halley-like comet, the potential is 1.2 V in the magnetic pile-up region and −0.5 V at the electron exobase. In the diamagnetic cavity, the obtained potentials are likely overestimated since SIE was not considered.

4. The spacecraft potential acquired at $v_{s/c} = 70$ km s⁻¹ is very sensitive to the temperature of the secondary electrons. The temperature can be as much as an order of magnitude lower than the value used in this study (Johansson et al. 2022), which would decrease the spacecraft potential by an order of magnitude in cases where the SEE current is dominating. The values reported for a high flyby velocity should hence be treated as upper limits of probable potentials acquired by the probe. Further laboratory studies are necessary to constrain the temperature of the secondaries for different materials.

5. The solar panels were covered with a conductive layer of indium tin oxide in all simulations. If the solar panels are nonconductive, the ground potential at $v_{s/c} = 10$ km s⁻¹ is more negative or less positive than the values reported in this study. The potential of the solar panels is instead less negative or more positive. At $v_{s/c} = 70$ km s⁻¹ when the SEE current is dominating, the ground potential is insensitive to the material of the solar panels but the solar panels themselves obtain less positive potentials.

6. SIE causes a positive potential barrier in front of the probe at high flyby velocities, which is an interesting topic for a future study.

7. A new version of SPIS with improved capabilities to model secondary emissions is necessary to accurately study charging effects in dense environments at high relative velocities. This would not only be useful for Comet Interceptor, but also other missions making fast flybys through cometary and planetary environments.

## Acknowledgments

The work by S.B. is supported by the Japan Society for the Promotion of Science (postdoctoral fellowship for research in Japan). Y.M. acknowledges grant No. 20K04041 from the Japan Society for the Promotion of Science (JSPS), and support from the innovative High Performance Computing Infrastructure (HPCI; hp230015) and the Joint Usage/Research Center for Interdisciplinary Large-scale Information Infrastructures (JHPCN; jh230042) in Japan. We acknowledge the Spacecraft Plasma Interaction Network in Europe (SPINE) for the development of the SPIS software. The software is publicly available at https://www.spis.org/software/spis/. The simulation results presented in this paper are publicly available on Zenodo: doi:10.5281/zenodo.10083020 (Bergman et al. 2023). The authors would also like to acknowledge the whole Comet Interceptor team for their contributions to the mission.

## ORCID iDs

S. Bergman https://orcid.org/0000-0003-0673-2264

Y. Miyake https://orcid.org/0000-0001-6491-1012

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Gulkis, S., Allen, M., von Allmen, P., et al. 2015, *Sci*, 347, aaa0709

Häberli, R. M., Altwegg, K., Balsiger, H., & Geiss, J. 1996, *JGRA*, 101, 15579

Hansen, K. C., Altwegg, K., Berthelier, J.-J., et al. 2016, *MNRAS*, 462, S491

Haser, L. 1957, *BSRSL*, 43, 740

Henri, P., Vallières, X., Hajra, R., et al. 2017, *MNRAS*, 469, S372

Heritier, K. L., Galand, M., Henri, P., et al. 2018, *A&A*, 618, A77

Hirao, K., & Itoh, T. 1987, *A&A*, 187, 39

Holmberg, M. 2020, JUICE Spacecraft Charging Analysis, Tech. rep. JUI-EST-SYS-TN-026, European Space Agency

Johansson, F. L., Eriksson, A. I., Gilet, N., et al. 2020, *A&A*, 642, A43

Johansson, F. L., Odelstad, E., Paulsson, J. J. P., et al. 2017, *MNRAS*, 469, S626

Johansson, F. L., Vigren, E., Waite, J. H., et al. 2022, *MNRAS*, 515, 2340

Jorba Ferro, O. 2018, PhD thesis, Universite de Toulouse

Körösmezey, A., Cravens, T. E., Gombosi, T. I., et al. 1987, *JGR*, 92, 7331

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Miyake, Y., Miloch, W. J., Kjus, S. H., & Pécseli, H. L. 2020, *JGRA*, 125, e2019JA027379

Miyake, Y., & Usui, H. 2009, *PhPl*, 16, 062904

Miyake, Y., & Usui, H. 2016, *RaSc*, 51, 1905

Neubauer, F. M., Glassmeier, K. H., Pohl, M., et al. 1986, *Natur*, 321, 352

Nilsson, H., Wieser, G. S., Behar, E., et al. 2017, *MNRAS*, 469, S252

Nilsson, H., Williamson, H., Bergman, S., et al. 2020, *MNRAS*, 498, 5263

Odelstad, E., Eriksson, A. I., Johansson, F. L., et al. 2018, *JGRA*, 123, 5870

Odelstad, E., Stenberg-Wieser, G., Wieser, M., et al. 2017, *MNRAS*, 469, S568

Pedersen, A., Grard, R., Trotignon, J. G., et al. 1986, in Proc. 20th ESLAB Symp. on the Exploration of Halley’s Comet, Heidelberg, ed. M. Grewing, F. Praderie, & R. Reinhard (Berlin: Springer), 297

Reinhard, R. 1986, *Natur*, 321, 313

Sagdeev, R. Z., Blamont, J., Galeev, A. A., et al. 1986, *Natur*, 321, 259

Schmidt, R., & Arends, H. 1985, *P&SS*, 33, 667

Schwenn, R., Ip, W. H., Rosenbauer, H., et al. 1987, *A&A*, 187, 160

Simon Wedlund, C., Alho, M., Gronoff, G., et al. 2017, *A&A*, 604, A73

Snodgrass, C., & Jones, G. 2019, *NatCo*, 10, 5418

Szegő, K., Glassmeier, K.-H., Bingham, R., et al. 2000, *SSRv*, 94, 429

Thièbault, B., Mateo-Velez, J.-C., Forest, J., & Sarrailh, P. 2019, SPIS 6 User Manual
−3.4 V. At larger distances from the nucleus, in the magnetic pile-up region, the potential is 1.1 V.

3. At $v_{s/c} = 70$ km s⁻¹, SEE from impacts by neutral particles dominates the currents to and from the spacecraft surface in the inner coma, resulting in positive potentials in most environments. For a 67P-like comet, the potential is 8–9 V in all studied environments except the diamagnetic cavity. For a Halley-like comet, the potential is 1.2 V in the magnetic pile-up region and −0.5 V at the electron exobase. In the diamagnetic cavity, the obtained potentials are likely overestimated since SIE was not considered.

4. The spacecraft potential acquired at $v_{s/c} = 70$ km s⁻¹ is very sensitive to the temperature of the secondary electrons. The temperature can be as much as an order of magnitude lower than the value used in this study (Johansson et al. 2022), which would decrease the spacecraft potential by an order of magnitude in cases where the SEE current is dominating. The values reported for a high flyby velocity should hence be treated as upper limits of probable potentials acquired by the probe. Further laboratory studies are necessary to constrain the temperature of the secondaries for different materials.

5. The solar panels were covered with a conductive layer of indium tin oxide in all simulations. If the solar panels are nonconductive, the ground potential at $v_{s/c} = 10$ km s⁻¹ is more negative or less positive than the values reported in this study. The potential of the solar panels is instead less negative or more positive. At $v_{s/c} = 70$ km s⁻¹ when the SEE current is dominating, the ground potential is insensitive to the material of the solar panels but the solar panels themselves obtain less positive potentials.

6. SIE causes a positive potential barrier in front of the probe at high flyby velocities, which is an interesting topic for a future study.

7. A new version of SPIS with improved capabilities to model secondary emissions is necessary to accurately study charging effects in dense environments at high relative velocities. This would not only be useful for Comet Interceptor, but also other missions making fast flybys through cometary and planetary environments.

## Acknowledgments

The work by S.B. is supported by the Japan Society for the Promotion of Science (postdoctoral fellowship for research in Japan). Y.M. acknowledges grant No. 20K04041 from the Japan Society for the Promotion of Science (JSPS), and support from the innovative High Performance Computing Infrastructure (HPCI; hp230015) and the Joint Usage/Research Center for Interdisciplinary Large-scale Information Infrastructures (JHPCN; jh230042) in Japan. We acknowledge the Spacecraft Plasma Interaction Network in Europe (SPINE) for the development of the SPIS software. The software is publicly available at https://www.spis.org/software/spis/. The simulation results presented in this paper are publicly available on Zenodo: doi:10.5281/zenodo.10083020 (Bergman et al. 2023). The authors would also like to acknowledge the whole Comet Interceptor team for their contributions to the mission.

## ORCID iDs

S. Bergman https://orcid.org/0000-0003-0673-2264

Y. Miyake https://orcid.org/0000-0001-6491-1012

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