Dust impacts on the spacecraft body generate clouds of ions and electrons through a process known as impact ionisation. An impact ionisation model suggested by Drapatz and Michel (1974) can be summarised as follows: Dust grains impacting onto the spacecraft at speeds that are supersonic in the target solid, i.e. faster than a few kilometres per second, produce a shock compression wave in the solid which shatters, vaporises and ionises the dust as well as the material of the target, where an impact crater forms. Free charges in the form of electrons and atomic and molecular ions are produced by thermal ionisation of the impact vapour. The initial ionisation is followed by recombination and thermalisation and a residual ionisation remains in the impact vapour. The amount of the residual ionisation can be derived from laboratory measurements of the charge production. An empirical relation describes the charge production Q, as a function of the dust mass m and speed v according to Q=ξ m^αv^β, where Q is given in Coulombs, the m in kilograms and v in kilometres per second. The exponents α and β are dimensionless and determined from experimental data. The constant ξ gives the proportionality and, as parameters α and β, it is dependent on both impactor and target composition. This impact ionisation model (see Drapatz and Michel, 1974) is in a good agreement with laboratory experiments in relatively thin targets, for speeds between the supersonic limit and some tens of kilometres per second. The model is based on the assumption that neutral vapour forms in the impact process and that it subsequently ionises because of its high temperature. Ionisation can also occur directly in the target where the propagating shock wave leads to a high-pressure high-temperature state so that the ejected target material is already ionised (see Hornung and Kissel, 1994). The properties of the vapour cloud are also depending on material composition and on the impact angle (Schultz et al., 2006). Moreover, the shock wave propagation in the target (spacecraft) and dust material produces not only vapour, but also solid fragments, and the fragment formation is predominant at smaller impact velocities (Jones et al., 1996). In summary, there is no theory that fully describes the charge production, sometimes also denoted as plasma production, that is caused by dust impacts on spacecraft. The following discussion uses the term impact cloud for the impact-generated electrons, ions and neutrals to avoid confusion with the surrounding plasma.

Figure 2The mass vs. velocity distribution of iron dust particles generated by the accelerator facility at the University of Colorado.

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Charge production is often determined empirically in dust accelerator facilities, in recent years at those of the University of Stuttgart (Mocker et al., 2011) and the University of Colorado (Shu et al., 2012) for the range of impact velocities shown in Fig. 2. The parameters to describe impact charge production derived from observations vary strongly for different impact materials; α has reported values between 0.7 and 1 while β has been measured between 2.5 and 6.2 (see for example Dietzel et al., 1973; Auer, 2001; Collette et al., 2014, and references therein). An often-used relationship for dust impacts on spacecraft is Q≈0.7 mv^3.5, which was reported for aluminium targets (McBride and McDonnell, 1999). It should be noted that the exponents also change for low impact energies (speeds below ∼1 km s⁻¹ and sizes below ∼10 nm). For low energy collisions, where fragments of significant sizes compared to the initial impactor survive, there may be surface effects such as capacitive contact charging (see for example John et al., 1980). The exponent also changes at high impact energies for speeds above ∼50 km s⁻¹ and dust sizes above ∼1 µm (Auer, 2001; Göller and Grün, 1989). Collette et al. (2014) measured the charge impact yield as a function of impact velocity for common materials used on spacecraft, and they point out the need for dedicated studies for impacts > 50 km s⁻¹. For very large impact energies, where the impactor gets completely vaporised, surface effects are negligible and the charge generation can be modelled through hydrodynamic theory (Hornung and Kissel, 1994). Moreover, there is a dependence of impact angle on the charge generation (Schulz and Sugita, 2006; Collette et al., 2014). Based on spectroscopic analysis of 4.7–5.6 km s⁻¹ impact flashes Sugita et al. (1998) find temperatures of about 4000 to 5000 K for the impact vapour cloud. Subsequent observations yield temperatures of 0.9 to 3 eV for impact speeds varying from 10 to 40 km s⁻¹ (Miyachi et al., 2008). Laboratory measurements find impact vapour ion temperatures of about 5 eV at 4 km s⁻¹ impact speed and > 10 eV at 20 km s⁻¹ (Collette et al., 2016).

Formation of the dust impact signal involves the dust impact process, the interaction of the impact cloud with the surrounding plasma and finally the detection by electric field measurement. At the most basic level, dust impacts on the spacecraft body generate clouds of free electrons and positive or negative ions. These charged particles are attracted to, or repulsed from, the spacecraft surface according to its electric potential relative to the surrounding ambient plasma. Charged particles from the impact cloud can be re-collected by the spacecraft or escape to free space and generate a transient deviation from the equilibrium spacecraft surface potential. The potential change can be positive or negative, e.g. escaping electrons generate a positive signal. Electrons are significantly faster than ions, and thus the signal generated by escaping electrons appears before the signal generated by escaping ions for the case when the spacecraft potential is not too large. The amplitude of the spacecraft potential deviation is given by the amount of escaped charges and by spacecraft capacitance. The spacecraft potential relaxes back to the equilibrium value via interaction with ambient plasma according to ${\mathrm{\Phi }}_{\mathrm{SC}}\sim e^{-t/\mathit{\tau }}$, where τ is a characteristic relaxation time (Meyer-Vernet, 1985).

Figure 3This figure sketches the impact process for a spacecraft that is slightly negatively charged (a), zero biased (b) and slightly positively charged (c). It is further described in the text and parameters given in Table 1.

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The different phases of the impact process for various spacecraft potentials (slightly positive, zero and slightly negative) are illustrated in Fig. 3. In the first phase (T1), at which the spacecraft is assumed to be in equilibrium potential, the impact occurs, and an impact cloud is generated (green). Some of the cloud particles may be re-collected. The second phase (T2) is characterised by electron escape and partial recollection depending on the target's potential, yielding an initial rise in signal strength (blue). The third phase (T3) is characterised by the ion escape, decreasing the spacecraft potential (red). The final phase (T4) is the relaxation phase when the spacecraft potential returns to the equilibrium value (orange). Individual time steps are summarised in Table 1 and sketched in Fig. 3. The ratio between escaping electrons and ions in phases T2 and T3 depend on the spacecraft potential. For example, more electrons than ions leave for a negatively charged spacecraft (Fig. 3a).

Table 1Explanation of impact process signal shape illustrated in Fig. 3.

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Electric field antennas can be operated as a dipole, where the voltage difference between two antenna booms is measured, or a monopole, where the voltage difference between an antenna boom and the spacecraft body is measured. It has been noted that the power spectral density of dust impact signals measured by monopole antennas is significantly larger than that measured by the dipole antennas (Meyer-Vernet, 1985; Tsintikidis et al., 1994; Meyer-Vernet et al., 2014), and this difference is attributed to the low sensitivity of a symmetric dipole antenna to dust impacts on spacecraft body. It is important to note that dust impact on a spacecraft body described by this model can be detected by the monopole electric field antenna as a potential drop between the spacecraft body and one antenna. A dipole configuration measuring electric field as a potential difference between two antennas can be utilised to detect a signal only when escaping electrons or ions influence the potential of one of the dipole antennas asymmetrically. The described model shows a strong dependence on the spacecraft potential. This can be compared with laboratory experiments for various polarities and sizes of bias voltage. A series of such measurement campaigns have been performed at the dust accelerator facility at the University of Colorado in order to aid the interpretation of signals collected in space. Collette et al. (2015) successfully identified different mechanisms of voltage signal generation on the antennas. The experiments performed by Nouzák et al. (2018) used a scale model of the Cassini spacecraft to investigate the differences between antennas operated in monopole vs. dipole modes. The results show that in the dipole mode the antennas are greatly insensitive to dust impacts occurring on the spacecraft and only impacts on the antennas generate clear signals. This study helped clarify the appropriate cross section to be used for calculating the density of dust populations encountered by the spacecraft (Ye et al., 2016b).

Figure 4Laboratory simulation of dust impacts on the Cassini model showing the impact signal detected by the antenna (E_U boom was bombarded) for different polarities and sizes of bias voltage. Different phases of dust impact signal are distinguished by colours (green – cloud generation, blue – electron escape, red – ion escape, orange – relaxation). The inserts show details of the pre-spikes (modified from Nouzák et al., 2018). The conditions in these laboratory measurements are comparable to a measurement in monopole configuration on the spacecraft.

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A few cases of impact events are shown in Fig. 4, derived from laboratory studies on a scaled-down Cassini model (Nouzák et al., 2018). Although the signals are measured in dipole configuration, since the dust impacts one of the dipole antennas, this configuration corresponds to monopole measurement when dust impacts the spacecraft body as described above. The laboratory experiment is performed in the vacuum chamber without ambient plasma. The relaxation process is simulated by discharge of the electronics circuit inside of the Cassini model.

Table 2Examples of signal development for different biases (spacecraft potential) shown in Fig. 4.

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Figure 4 shows different signal shapes measured in the Cassini laboratory simulation, and the signal development of the different stages are described for each case in Table 2:

• The signal shown in panel (a) is for a strongly negatively biased target potential. All electrons are repulsed from the spacecraft and all ions are recollected back to a strongly negatively biased target. The ion escape part (red) is not apparent in this case. The electron part (blue) is followed directly by relaxation (orange).

• Panel (b) describes the signal shape for a reduced negative target potential. The number of escaping ions increases with the reduction of the negative potential (panel b). The electron part (blue) is followed by the smaller ion part (red) and relaxation (orange). A kink appears between the ion part (red) and relaxation (orange); see Fig. 3a.

• Panel (c), describing the signal measured at an unbiased target, shows that similar numbers of electrons and ions escape. The amplitude of the electron part (blue) is similar to the ion part (red).

• Panel (d) shows the case of positively charged target. The number of escaping electrons is reduced and the ion part of the signal exceeds the electron one. This results in a bipolar signal where the first part is typically called “pre-spike” (Collette et al., 2015; Thayer et al., 2016). A larger number of escaping ions change the polarity of the signal.

• Panel (e) shows the signal for a higher positive target bias potential – the first (electron) part of the bipolar pulse is reduced with increasing positive target potential.

• Panel (f) shows a case of even higher positive bias. All electrons are re-collected in this case. The signal has no electron (blue) part and it has no “pre-spikes” in this case.

The shapes of all pulses measured in the laboratory for various biases can be explained by the model described above. It must be noted, however, that since electron and ion escapes are very fast processes (∼ µs), detection of a detailed structure of initial parts of pulses including “pre-spikes” thus requires fast electronics (sampling of the order of 100 kHz). Therefore, not all spacecraft are able to detect them, and a thorough inquiry into signal shapes using in situ data is difficult. The antenna signal can be also affected by the response of instrument electronics. For example, the transfer function of electronics can modify a shape and duration of the measured signal (Ye et al., 2019).

Detection of dust impacts with antenna measurements has recently been done in several space missions. In the following, we discuss the major findings related to dust detection from the respective missions.

5.1 STEREO

STEREO is a NASA mission that was launched on 26 October 2006, with the study of coronal mass ejections as the primary scientific goal. The mission consists of two twin spacecraft that orbit the Sun at around 1 AU, one trailing the Earth (STEREO B) while the other leads (STEREO A). The study of the STEREO/WAVES radio receiver data proved to be of great interest for dust studies. STEREO/WAVES measured the flux of sub-micrometre dust near 1 AU (Meyer-Vernet et al., 2009; Belheouane et al., 2012; Zaslavsky et al., 2012) and discovered a highly time-variable flux possible caused by nanometre-scale dust particles (Meyer-Vernet et al., 2009b). The nanodust impacts were observed frequently on both STEREO spacecraft as radio pulses on single monopole antennas. The physical mechanism that leads to their generation is not yet fully understood. The voltage was much higher on the antenna that was adequately located to be sensitive to impacts of prograde nanodust on each spacecraft (Meyer-Vernet et al., 2009b), which destabilised the photoelectron sheath of that antenna (Pantellini et al., 2012), producing a ratio between antenna voltages in agreement with the mechanism producing the pulses (Zaslavsky et al., 2012). The formation of the signal involves a transient local perturbation of the photoelectron equilibrium current on the antenna being close to the impact. The steps that lead to the antenna signals have been studied with plasma simulations and semi-empirically (see for example Pantellini et al., 2012; Meyer-Vernet et al., 2014; Zaslavsky, 2015). Kellogg et al. (2018) suggested that STEREO does not observe nanodust, but did not propose an alternative mechanism able to explain the observations. The larger dust impacts observed with STEREO/WAVES are observed with similar amplitudes at all three antennas. Based on STEREO/WAVES Zaslavsky (2015) proposed a model accounting for electric pulse generation by electron collection after an impact, linking the shape and amplitude of the electric signals to the dust and local plasma parameters. Figure 5 shows the model applied to typical impact clouds.

Figure 5Dust impact signals recorded by the STEREO/WAVES TDS on STEREO A, shown with black crosses, are shown in comparison to a fit with a semi-empirical model, discussed in the text, shown with red solid lines (from Zaslavsky et al., 2015).

5.3 MMS

The MMS mission consists of four Earth-orbiting spacecraft was launched in 2015 (Burch et al., 2016). While the missions are similar, the MMS electric field instruments differ just slightly from the Cluster ones. Each of the spacecraft is equipped with three pairs of electric field probes, two in the spin plane (120 m tip-to-tip) and one in the axial plane (29 m; Torbert et al., 2016). The electric field is measured in the dipole configuration in all three directions with sampling frequency up to 8 kHz (burst mode) and up to 256 kHz in wave burst mode. The main difference is that the instrument operates simultaneously also in the monopole configuration. The combination of dipole and monopole measurements provides complex information about the ambient electric field and the spacecraft potential, which can be used for the reliable identification of dust impacts. Solitary waves and other structures in the ambient plasma or electric field generate pulses simultaneously in both monopole and dipole configuration. On the other hand, changes in the spacecraft potential triggered by the dust impact generate identical pulses on all monopole antennas and no signal in the dipole configuration (electric field data). This allows us to reliably distinguish changes in the spacecraft potential from the other pulses as solitary waves (see Vaverka et al., 2018). A measurement with MMS, shown in Fig. 6, illustrates the different detections in monopole and dipole configuration.

Figure 6A potential signal of dust impact measured with MMS. Example of a typical event related to the change of the spacecraft potential observed in monopole configuration (a), the dipole measurements (b) with a lack of signal and the derived voltage pulse in (c) (see Vaverka et al., 2018).

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5.6 Cassini

The Cassini Radio and Plasma Wave Science (RPWS) instrument measures oscillating electric fields over the frequency range 1 Hz to 16 MHz and magnetic fields in the range 1 Hz to 12 kHz (Gurnett et al., 2004). The instrument uses three nearly orthogonal electric field antennas (E_u, E_v, E_w, each 10 m long and 2.86 cm in diameter) and three orthogonal magnetic search coil antennas. The E_u and E_v antennas are often used together as a dipole antenna and E_w and the spacecraft body as a monopole antenna (Gurnett, 1998), both sensitive to dust impacts. The south-polar plume of Enceladus was one of the top discoveries made by the Cassini mission. During the Enceladus plume crossing, besides dust impact signals, RPWS detected plasma oscillations induced by dust impacts, the frequencies of which are equal to the local plasma frequencies (Ye et al., 2014), which can be explained by a beam-plasma instability induced by the impact-produced electrons when their speed exceeds the thermal speed of the ambient plasma (Meyer-Vernet et al., 2017). Comparison of observations (Ye et al., 2014b) showed that the dust density profile measured by RPWS is consistent with that measured by the dedicated dust detector on board.

Cassini allowed for a comparison of measurements in dipole and monopole configuration. The difference is clearly seen in Fig. 7, which shows the electric power spectrum measured by the Cassini RPWS HFR receiver simultaneously in dipole (top) and monopole (bottom) mode in Saturn's E-ring at the first close approach of Enceladus (Meyer-Vernet et al., 2014). During the subsequent mission, the Wideband Receiver (WBR) of the RPWS instrument was switched from monopole mode to dipole mode at a ring plane crossing, so that the responses of these two antenna modes to dust impacts were compared, assuming the dust density and size distribution did not change across the ring plane (Ye et al., 2016a). Figure 8 shows an RPWS wave power spectrogram, which covers a 1 h period around a ring plane crossing on DOY 001, 2016. As the antenna mode switched from monopole to dipole at the ring plane at ∼10:30 UTC, the spectral power decrease was accompanied by a significant decrease in the negative impact rates (blue) and the polarity ratio jumping to ∼1. The spectral power is proportional to the product of impact rate and average voltage jump size squared (Meyer-Vernet, 1985). So, the difference in spectral power at the antenna switch could be due to either a lower impact rate or smaller average voltage pulse size, or both.

Figure 7From Meyer-Vernet et al. (2014): time-frequency electric power spectral density measured by Cassini/RPWS on 9 March 2005 in Saturn's E ring, in dipole (a) and monopole mode (b). The increase due to micron-sized dust impacts on the spacecraft only appears in monopole mode, whereas the dipole only measures the weaker plasma quasi-thermal and impact noise.

Figure 8Adapted from Figs. 4 and 5 of Ye et al. (2016b). RPWS wave power spectrogram around a ring plane crossing on DOY 001, 2016. The top panel shows the positive (red) and negative (blue) impact rates. The middle panel shows the impact signal polarity ratios with the moving averages (teal). At ∼10:30 UTC, the antenna used was switched from monopole to dipole, which was accompanied by a decrease in the spectral power and the polarity ratio jumping back to 1.

In Fig. 9, we show a comparison of the vertical dust density profiles measured by the RPWS WBR and the Cassini Cosmic Dust Analyzer (CDA) High Rate Detector (HRD) during the ring plane crossing on DOY 361, 2016. HRD uses polarised foils for dust detection and can measure high impact rates of particles bigger than a size threshold that depends on the impact speed (Srama et al., 2004). Discontinuities in the RPWS dust density profile are due to gain changes of WBR. The CDA data showed consistent peak densities of around 0.04 m⁻³ (threshold ∼0.8 µm) during the ring-grazing orbits, less than 1 order of magnitude higher than the RPWS dust density, which is within the uncertainty limit of the method (Ye et al., 2014). The density peak measured by RPWS is wider than that by CDA with a full-width half-maximum of 600–1000 km compared to 475 km for the latter (averaged profile shows a FWHM of 475 km). This difference is discussed in detail in Ye et al. (2018a). The E ring density structure based on RPWS measurements has been shown to be consistent as well with that revealed by optical observation (Ye et al., 2016a).

Figure 9Adapted from Fig. 4 of Ye et al. (2018a). Comparison of vertical dust density profiles of the Janus–Epimetheus ring measured by RPWS and CDA during the ring plane crossing on DOY 361, 2016. There is 1 order of magnitude of difference between the two results, which is within the uncertainty limit estimated for the RPWS measurement (Ye et al., 2014).

Ye et al. (2016b) compared the data collected with these two antenna setups and found that the wave power spectral density observed by the monopole antenna is ≈10 dB higher than that observed by the dipole antenna. This does not necessarily mean that the monopole antenna is more sensitive to individual dust impacts, because direct comparison of the waveforms observed by these two antennas showed that the sizes of the voltage jumps induced by dust impacts are comparable. Comparison of the impact rates showed that the monopole antenna detects ∼10 times more dust impacts than the dipole antenna. This difference in impact rates is roughly in line with the difference in the effective impact areas of the spacecraft body and the dipole electric antenna. Detailed analysis showed that the polarity ratio of the impacts detected by the dipole antenna changes with the projected area ratio of the dipole antenna elements (E_u and E_v) as the spacecraft rotates, providing strong evidence that the dipole mode primarily detects impacts on the antenna booms.

Cassini cruise measurements between 1 and 5 AU also enabled us to study the rise time of the impact ionisation pulses as a function of dust mass and of heliocentric distance (Meyer-Vernet et al., 2017), a quantity of great importance for future missions since it determines the frequency range and voltage amplitude for dust detection.

Many dust observations describe the dust flux near-Earth orbit; it can be estimated from meteor observations, crater statistics and measurements from spacecraft. Based on these sources, an empirical polynomial mass distribution was found (Grün et al., 1985; Ceplecha et al., 1998). Observations by the STEREO spacecraft allowed this distribution to be extended to smaller masses (Zaslavsky et al., 2012; Meyer-Vernet et al., 2009b; Malaspina et al., 2015). There is still an uncertainty, however, about the absolute flux values. Estimates of cosmic dust fluxes near 1 AU and onto Earth range over several orders of magnitude and are based on a number of different assumptions (cf. for example Nesvorný et al., 2011; Mann et al., 2011; Plane, 2012). There is even less known on the dust flux inside 1 AU and estimates are often based on extrapolation of the flux curve obtained near Earth and considering the major forces acting on dust particles (Mann et al., 2004): Large dust particles (“micron dust” m > 10⁻¹⁴ kg) are mainly influenced by gravity force and move in Keplerian orbits superimposed by a slow migration inward caused by the Poynting–Robertson effect. For dust with masses 10⁻¹⁹ kg < m < 10⁻¹⁴ kg (“beta meteoroids”) the radiation pressure force is comparable to the gravitation; when these small particles form, typically by collisions of larger dust, they move outward in hyperbolic orbits (Czechowski and Mann, 2007). For even smaller dust with m < 10⁻¹⁹ kg (nanodust) electromagnetic forces prevail, and they are deflected in a way that is similar to the pick-up process of ions that newly form in the solar wind (Mann et al., 2010).

The observational studies of scattered light and thermal emission from the dust are constrained by large contributions from dust near the Earth to the brightness because the observed brightness is an integrated signal along the line of sight (Mann et al., 2004). Since early infrared eclipse observations (MacQueen, 1968) showed irregularities in the slope of the corona brightness with varying distance from the solar limb, the possibility of dust rings existing around the Sun is discussed. Indeed, model calculations were made to show that dust rings can form for specific dust properties in the initial stage of dust sublimation when the dust size is reduced and the radiation pressure force increases with reduced dust size (Mukai and Yamamoto, 1979). The solar eclipse observations made over the years suggest, however, that the observed features can be explained without the existence of pronounced rings (Mann, 1992) and that the average dust properties in the inner heliosphere change over timescales of years (Kimura et al., 1997; Ohgaito et al., 2002). The spatial distribution of the dust that can be derived from the scattered light and thermal emission observations suggests that the dust number density increases with distance from the Sun, and in combination with the increasing orbital velocities this leads to increasing dust flux inversely proportional to the distance r from the Sun within or close to the ecliptic plane (Mann et al., 2004). The amount of dust above the solar poles and in orbits with high inclination is even less known (Mann et al., 2004). Recent white light observations from STEREO A (Stenborg and Howard 2017a, b) provide the shape of the F corona and inner zodiacal light from 5 to 24^∘ line-of-sight elongation and show its flattening to larger elongation. Closer analysis also showed that the flattening varied with spacecraft position, indicating an influence of the dust brightness near the spacecraft (Stenborg, et al., 2018; Stauffer et al., 2018), again showing the importance of considering the line-of-sight effects when analysing brightness observations.

While we can expect that the flux of large particles in the inner solar system increases proportionally to 1∕r, where r ist the distance from the Sun, it is difficult to predict the flux of smaller dust. Detailed trajectory calculations show that nanodust can be trapped in orbits with perihelia very close to the Sun instead of being ejected (Czechowski and Mann, 2010). Trapping conditions depend on a number of different parameters so that the nanodust flux outward can vary in time (Czechowski and Mann, 2010, 2012). The majority of nanoparticles and those that form at distances 0.2 AU from the Sun or larger are usually ejected outward. Figure 10 shows the velocity of nanoparticles that are ejected from circular orbit at 0.2 AU. While the particles gradually gain speed, one can see that in the inner solar system they still have a velocity close to that of the parent object. The trajectory of the largest particle shown in the figure with approximate radius 100 nm corresponds to a beta-meteoroid that is mainly influenced by radiation pressure force (Wehry and Mann, 1999) because it has a smaller value of surface charge to mass than the smaller particles. Figure 11 shows the velocity as a function of distance for the same range of parameters for the nanodust but when particles are released from initially highly elongated orbits. The orbital eccentricity and perihelion assumed for the model calculations presented correspond to the orbits of the Aquarid meteoroids and the nanoparticles are released at different locations of the orbit. One can see that their trajectories in the inner solar system strongly depend on the initial condition.

Figure 10Velocity as function of distance from the Sun for particles with $Q/m={\mathrm{10}}^{-\mathrm{4}}$, 10⁻⁵, 10⁻⁶ and 10⁻⁷ e∕m_p released from a circular orbit with the radius 0.2 AU near the ecliptic plane. Solid lines correspond to the focusing, and dashed to defocusing, magnetic field orientation (adapted from Mann et al., 2014).

Figure 11Velocities of small fragments released from Aquarid meteoroids as a function of the heliocentric distance. The velocities are calculated for dust with $Q/m={\mathrm{10}}^{-\mathrm{4}}$, 10⁻⁵, 10⁻⁶ and 10${}^{-\mathrm{7}}e/m_{\mathrm{p}}$. The ratio of surface charge to mass corresponds to sizes 3 nm, 10 nm and larger. The particles are released from the orbit of Aquarids at the perihelion (0.09 AU from the Sun, a), and at the distance 0.2 AU on the inbound (b) and outbound (c) parts of the orbit. From Czechowski and Mann (2018).

In addition to uncertainty of the dust trajectories, the dust production rate is hard to predict. The majority of dust particles smaller than micron size inside 1 AU are produced by fragmentation during collisions of larger dust particles. The dust formation by mutual collisions depends on the dust material compositions (Ishimoto and Mann, 1999; Mann and Czechowski, 2005); it varies with the dust velocities and it is for instance enhanced when coronal mass ejections push out nanoparticles (Czechowski and Kleimann, 2017). Sun grazing comets (cf. Jones et al., 2018) are another source of time variable dust flux. The nanodust flux can also vary due to other effects, like the variation of the source, e.g. when the dust flux is enhanced by a single collision event in the inner heliosphere, or due to the influence of the solar magnetic field structure (see Czechowski and Mann, 2012; Juhasz and Horanyi, 2013). While estimates are made for time-stationary conditions, current sheet crossings occur along the trajectories and, in addition, the magnetic field is time-variable. Coronal mass ejections also change the conditions, pushing large fractions of nanodust outward at speeds reaching 1000 km s⁻¹ (Czechowski and Kleimann, 2017).

From 10 years of STEREO A observations attributed to nanodust impacts several important properties can be obtained. The signal explained as nanodust is 10–100 times more frequent in a stream interaction region (SIR) or during interplanetary coronal mass ejections (ICMEs). The observed signals exhibited a periodicity due to the crossing by STEREO of the solar magnetic equator. A correlation with solar wind perturbations and periodicities corresponding to those of Mercury and Venus were also detected (Le Chat et al., 2015). These signals nearly disappeared on STEREO A around 2012 (Le Chat et al., 2013; Malaspina et al., 2015) when the heliosphere entered a defocusing configuration in which the nanodust coming from the inner heliosphere are pushed away from the solar magnetic equator, therefore possibly preventing their observation. Observations with the RPWS instrument on board Cassini between 1 and 5 AU have produced two further important properties of interplanetary nanodust. Firstly, the average nanodust flux measured at 1 AU was similar in order of magnitude to the average of the highly variable flux measured by STEREO when the heliosphere was in a focusing configuration (Schippers et al., 2014), and it decreased roughly as the inverse squared heliocentric distance (Schippers et al., 2015). Secondly, the nanodust fluxes were found to follow the variation in solar wind drift speed closely (Meyer-Vernet et al., 2017) as predicted by nanodust dynamics (Mann and Czechowski, 2012).

Finally, aside from providing information on dust in the inner heliosphere, it is also quite possible that the Parker Probe and Solar Orbiter missions will find more effects that dust particles have on the solar wind. Cosmic dust particles interact with the surrounding plasma through electric charge collection, the photoelectric effect (Mann et al., 2014) and destruction processes (sputtering, fragmentation, sublimation). Photoionisation, electron-impact ionisation and charge exchange quickly ionise the atoms and molecules in the solar wind (Mann and Czechowski, 2005) so that dust destruction generates pick-up ions. While those interactions do not affect solar wind measurable parameters much near 1 AU (Mann et al., 2010), conditions are possibly different near the Sun. Dust particles sublimate at bulk temperatures ∼1000–2000 K inside ∼10 solar radii (Mukai and Mukai, 1973; Mann et al., 2004; Mann and Murad, 2005). A fraction of dust material vaporises during collision (Mann and Czechowski, 2005). The effect of dust on the solar wind is also time-variable, as for instance the dust destruction rates due to sputtering increase during coronal mass ejections (Ragot and Kahler, 2003). The solar wind particles also change charge state by interaction with the dust surface or by passing through the particles (Mann et al., 2010; Minato et al., 2004). And some authors suggest that newly formed charged dust fragments generate features in the solar wind magnetic field (Connors et al., 2014; Lai et al., 2013, 2015).

The design of the radio and plasma waves instrument (RPW) on the ESA Solar Orbiter (Mueller and al., 2019) is similar to STEREO/WAVES instrumentation. The electric antenna system on RPW consists of a set of three identical antennas deployed from +Z axis and from the opposite corners of the spacecraft and can operate in dipole and monopole modes. RPW antennas consist each of a 1 m rigid deployable boom and a 6.5 m stacer deployable monopole, which has a 1.5 cm radius. The Time Domain Sampler (TDS) subsystem of the RPW instrument (Maksimovic et al., 2019) is designed to capture electromagnetic waveform snapshots at high cadence from 200 Hz to 200 kHz, resolving in particular voltage spikes associated with interplanetary dust impacts.

Figure 12Parker Solar Probe trajectory during first perihelion passage. Blue arrows indicate speed of spacecraft relative to the dust particles in circular orbit. Red arrows indicate the surface vector of the spacecraft heat shield. Figure courtesy of Calvinhac (2019).

Solar Orbiter will make observations of the Sun and in situ measurements from elliptic orbits coming as close as ∼60 solar radii (∼0.285 AU) to the Sun. The aphelia lie outside 0.8 AU for a large part of the 7-year nominal mission time during which orbital latitude reaches 25^∘. The long cruise phase of Solar Orbiter and the elongated spacecraft orbits with aphelia close to 1 AU provide the opportunity to study in detail the dust flux near 1 AU and to estimate the flux of sub-micrometre dust onto Earth, its time variation and its variation during part of a solar cycle.

The FIELDS instrument on Parker Solar Probe (Bale et al., 2016) combines magnetic and electric field measurements into a single, coordinated experiment. Four electric field antennas (2 m long, 3.18 mm diameter Niobium C-103 thin-walled tubes) are mounted at the base of the heat shield, and deploy in full sunlight out of the spacecraft wake, while a fifth antenna is mounted on the magnetometer boom in the umbra of the spacecraft. The sensor electric field signals are transferred to a Digital Fields Board (DFB), a Time Domain Sampler (TDS) and a Radio Frequency Spectrometer (RFS) for signal processing and digitisation. The DFB and TDS make rapid samples of waveforms with the highest sampling rate of 150 000 samples per second (DFB) and 2 000 000 samples per second (TDS), with an on-board selection of events to reduce bit rate. The low frequency (LF) part of the RFS is a dual channel digital spectrometer receiving inputs from the four first antennas, either in dipole or monopole mode, with a frequency range of 10 kHz to 2.4 MHz, allowing a relative frequency spacing of about 4.5 %.

Parker Solar Probe orbits the Sun in the ecliptic plane, making seven Venus gravity assist manoeuvres during the 7-year nominal mission duration, which will lessen its perihelia to less than 10 R_S, the closest any spacecraft has come to the Sun. In this way, the spacecraft will spend a total of 937 h inside 20 R_S, 440 h inside 15 R_S and 14 h inside 10 R_S (Fox et al., 2015). The surrounding plasma changes considerably along the spacecraft orbits (Bale et al., 2016). The orbital trajectory for the first orbit around the Sun is shown in Fig. 12.

Figure 13The estimated signals for impacts of 0.1 µm particles with speed 100 km s⁻¹ for spacecraft at different distance from the Sun. The charge production of the impact is assumed to be Q=30 pC. Estimate based on the Vaverka et al. (2017b) model.

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Our considerations suggest that both RPW and FIELDS measurements in monopole mode will be able to detect signals generated by dust impacts. Distinction between dust and other wave features needs to be considered based on the observational data. At present, we do not know the mass range of dust particles that will be detectable. As heliocentric distance decreases, the pulse's decay time will decrease faster than its rise time (Meyer-Vernet et al., 2017), eventually becoming smaller than the rise time, which will decrease the dust signal for large grains. The spacecraft charging and charged particle dynamics close to the Sun are expected to be considerably complicated by the presence of a potential barrier (sheath structure) due to strong photoemission (Ergun et al., 2010; Campanell, 2013) as well as by the presence of the thermal shield and non-conducting solar panels.

Figure 14The spacecraft potential change during dust impact for different values of the photocurrent. A typical value of photocurrent at 1 AU is 40 µA m⁻². While its influence on spacecraft potential is considerable, this is not for the change induced by impacts.

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Vaverka et al. (2017b) simulated pulses generated by dust impacts in various plasma environments using a simple numerical model. The spacecraft potential is calculated using orbital-motion-limited theory and the current generated by the dust impact is represented by a Gaussian function. We used this approach to simulate the spacecraft charging in the inner solar system. The rise time of the pulse was estimated according to Meyer-Vernet et al. (2017) for variable photoelectron sheaths. The rise time of the measured pulse is also affected by the response of the antenna electronics. These electronic effects were not taken into account in the model. This model also does not describe the detailed structure of the pulses including “pre-spikes” but only their general shapes, and it can be appropriate to estimate the conditions for dust impacts. Figure 13 shows estimated signals for impacts of 0.1 µm particles with speeds of 100 km s⁻¹ for spacecraft at different distances from the Sun. The top panel represents temporal evolution of the spacecraft potential and the bottom panel shows changes in the equilibrium potential. The charge production of the impact is assumed to be Q=30 pC according the equation presented in Sect. 2. The amplitude of the pulse is then proportional to the mass of the impinging grain and to its velocity with power between 2.5 and 6.2 (depends on materials). It is possible to see that the amplitude and duration of the pulses are reduced with decreasing distance from the sun. This fact means that the sensitivity of dust impact detection is smaller close to the sun. It is necessary to mention that the conditions for the orbital-motion-limited theory are not satisfied near the sun. The presence of the potential barrier created due to strong photoemission, described by Ergun et al. (2010) and Campanell (2013), strongly influences the spacecraft charging and charge dynamics. An interesting result is that the shape of the detected signal depends only weakly on the solar UV illumination, which leads to the photocurrent as shown in Fig. 14 for 1 AU from the sun. The increase or decrease in the solar activity, which varies the UV flux, influence the spacecraft potential but not so much the profile of the pulse generated by dust impacts.

A challenge in the data analysis will be to distinguish dust impact signals from other events. A comparison to dust measurements from other spacecraft at a similar distance from the Sun as Parker Probe and Solar Orbiter should be considered. BepiColombo equipped with the Mercury Dust Monitor (MDM, Nogami et al., 2010) and electric field antennas (PWI, plasma wave investigation; Kasaba et al., 2010) will in the near future study the dust environment near Mercury at 0.31 to 0.47 AU from the Sun. Though noise events are also considered an issue for those measurements, they offer an opportunity for simultaneous dust observations from several spacecraft so as to have a more reliable distinction of dust impacts and other events.

The data will be published for open access on the UiT Open Research Repository at https://doi.org/10.18710/LURI1R (Mann et al., 2019).

This paper was prepared during discussions of the ISSI team on dust impacts at the International space science institute in Bern, Switzerland. All authors contributed to the writing of this text in an open editing process and to the discussions that lead to the writing.

The authors declare that they have no conflict of interest.

This research has been supported by the Research Council of Norway (grant no. 262941), the Czech ministry of education youth and sport (grant no. LTAUSA 17066), NASA (grant no. 1415150) and CDAP (grant no. 14397000).

This paper was edited by Dominique Bockelee-Morvan and reviewed by Laila Andersson and one anonymous referee.