Figure  shows the composition of the three solar wind scenarios considered. The solar wind and CME compositions used here are based on the work of their Table 6 and contain 10 different species, including protons (H), helium ions (He), and the heavier species carbon (C), oxygen (O), nitrogen (N), iron (Fe), neon (Ne), magnesium (Mg), silicon (Si), and sulfur (S) ions. Generally, the solar wind is composed of a big fraction of protons, a small fraction of helium, and traces of the heavier species. The composition changes between 96 % H/4 % He for the slow solar wind and 98 % H/2 % He for the fast solar wind, with heavier species around 0.1 %. The composition of CMEs however is much more dominated by heavier species, 67 % H 30 % He, and 3 % heavier species. In addition to the plasma composition, the plasma speed and density are also different for each solar wind scenario. Table  summarizes the values that have been used for the solar wind as well as CME conditions within this study. It has to be noted that the composition, speed, and plasma density of the solar wind or CMEs are highly variable. The given values describe average conditions.

Sputtering is the impact process of an energetic ion or atom on a target and the subsequent removal of target atoms from its surface. The sputtering yield is the main parameter of the sputtering process itself. This yield denotes the number of target atoms sputtered by one incident ion and is a function of the ion's kinetic energy and the target's material properties e.g.and references therein.

For further analysis we have retrieved the sputtering yield for carbon, Fe0.4Mg0.6O, and astronomical silicate (MgFeSiO4) hit by nine different solar wind (SW) ions. For the Fe0.4Mg0.6O and silicate we have used the SRIM (Stopping and Range of Ions in Matter) package that derives the sputtering yields and also stopping powers and ranges of ions within compounds. For each solar wind scenario, the SRIM program has been initialized by the above-mentioned plasma composition and speed (energy/nucleii). In order to derive the sputtering yield for the dust species i for a given scenario, we summed up the sputtering yields for each atom j sputtered by solar wind ion k. 1Yi=∑j,kYi,j,k The index j denotes the target atoms Mg/Fe/Si/O for astronomical silicate and Fe/Mg/O for the Fe0.4Mg0.6O composition. The yields correspond to the atomic abundance ratios of the dust composition and the ion ratio of the solar wind composition. For the mono-atomic carbon case we have used the analytic formula from together with the experimentally fitted sputtering parameters and references cited within pages 45–46. The result of these calculations are sputtering yields for silicate, Fe0.4Mg0.6O, and carbon for the three different sputtering scenarios, i.e. slow SW/fast SW/CME. The individually derived yields can be found in the Supplement.

Figure  shows the results of the assessment, i.e. the sputtering yield as a function of ion species (H – sulfur S), for the three different materials. The given values are not absolute but prorated with solar wind ion composition present in fast and slow solar wind as well as CME conditions (Yi,k⋅ck; ck is the fractional abundance of ion k in the solar wind conditions; cf. Eq. , Table ). The highest sputtering yields are found for Fe0.4Mg0.6O material; the yields are somewhat smaller for silicate and are the lowest by far for carbon material. Figure  also shows that the sputtering yields strongly increase during CME conditions and that this is due to the sputtering by the heavy ions that are more abundant during CME than in the normal solar wind. Likewise, the higher abundance of He ions in the slow solar wind explains why sputtering yields are larger in the slow solar wind than in the fast solar wind.

The sputtering yields for carbon are significantly lower than for the silicate and Fe0.4Mg0.6O materials. In addition, Fig.  shows the strong enhancement of the sputtering yield in the case of CME conditions due to the higher abundance of heavier ion species. The higher abundance of He ions in the slow solar wind conditions is the reason for the higher sputtering yields compared to the fast solar wind. This is the case for all three dust components.

Absolute sputtering yields are listed in the Supplement. They depend on the target material and strongly vary with the mass of the sputtering ion. The yields for sputtering by iron ions are for instance 2 orders of magnitude higher than those for sputtering by protons, and this is so for all the target materials. Comparing the sputtering yields for the three different ion speeds considered, those for 300 km s-1 are the highest, those for 500 km s-1 are 20 % lower, and those for 800 km s-1 are 40 % lower.

To show the importance of heavy ion sputtering, especially during CME conditions, we have calculated the relative sputtering yield Yrk weighed with the plasma composition as follows: 2Yrk=ck⋅Yk∑ck⋅Yk. ck denotes the composition of the solar wind plasma as shown in Fig. . The weighted sputtering yield for the carbon target material is shown in Fig. , and the other target materials show similar results. One can see that the increase in heavy ions in CME, which is small in numbers, results in a much higher contribution of these ions to the sputtering yield; in turn we expect that this strongly influences sputtering efficiencies. Other works on sputtering have considered H and He as components of the fast and slow SW e.g. only. This is a valid simplification for general solar wind conditions. Our calculation shows that considering heavy ions barely influences the sputtering efficiency in the fast and slow SW.

The sputtering yields used in this study have only been derived by considering a normal impact of an ion onto the target particle and a resulting collision cascade governed by atomic forces within the target lattice. However, it has to be noted that the sputtering process is also heavily influenced by a number of additional parameters, which cannot be accounted for in this study. Eventual sputtering yield enhancement can occur due to high target temperatures , non-normal impact angle, ion charge state for sputtering of insulators , and a size dependence of the yield when considering nanometre-sized dust . All these processes might enhance the sputtering yield substantially. On the other hand, microscopic surface roughness can increase but also decrease the sputtering yield under certain circumstances, e.g. slant sputtering . In addition, we also do not consider composition change due to eventual implementation of solar wind ions into the dust or fractional depletion of a certain atom type within the dust. Due to a lack of quantitative information on these enhancement factors for our study, we use the conservative sputtering yields given by SRIM. As a consequence, our results provide an upper limit for dust sputtering lifetimes. We speculate that dust sputtering lifetimes could be 1 order of magnitude shorter when taking the microphysics of dust sputtering into account.

For the derivation of nanodust sputtering lifetimes, we follow the formalism given by . The mass loss rate from a surface through sputtering in the solar wind is given by the following: 3dmsputdt=-fSWYtotAmA.

Here, A is the cross section of the dust, fSW the solar wind ion flux, Ytot is the total sputtering yield of the target material, and mA is the mean mass of the sputtered atoms.

Under the assumption of constant composition and size-independent sputtering yield, the sputtering lifetime can be integrated from the sputtering mass loss rate of a circular surface exposed to the SW/CME plasma: 4tsput=4r0NAρfSWYtotM.

Here, r0 is the initial radius of the dust, NA is the Avogadro constant, and M and ρ are the molar mass and mass density of the sputtered material. For the solar wind flux fSW=np⋅vp the values from Table  have been used.

Figure  shows sputtering lifetimes of 1  nm dust at a distance of 1 AU from the Sun. Lifetimes for all three plasma conditions and the three different dust compositions are shown.

One can see that carbon nanodust survives longest among all three studied compositions; i.e. 1 nm dust survives 5000 d at 1 AU under CME conditions. Fe0.4Mg0.6O sputtering lifetimes are a factor of 20 shorter. The lifetimes of silicate are a factor of 60 shorter than the carbon sputtering lifetimes. These factors vary slightly with all solar wind conditions. When comparing the different solar wind conditions, CME sputtering lifetimes are the shortest. Sputtering lifetimes in the slow solar wind are 20-fold longer. The lifetimes for fast solar wind conditions are 20 times longer than the lifetimes in CME conditions. This behaviour varies a bit from one dust composition to the other. The short lifetimes in the CME scenario occur due to the presence of heavy ions in an overall denser plasma cloud. However, CMEs are distinct solar eruptions, and these sputtering conditions do not last longer than 1 or 2 d and occur only locally in the heliosphere. The given lifetimes of several tens of days and more at 1 AU for 1 nm dust make full destruction due to CME sputtering impossible. However, for the case of fast and slow SW, which is present within the heliosphere at all times, the sputtering lifetimes are close to 10 years in the case of silicate nanodust and 30 years for Fe0.4Mg0.6O nanodust.

The sputtering lifetime described in Eq. () is linear in initial dust particle radius and enables easy calculation of lifetimes for other dust sizes. In Fig.  we show the derived lifetimes of dust particles in the size range from 1 nm to 1 µm at the Earth's orbit.

Sub-micron dust particles at Earth's orbit have sputtering lifetimes that can reach several hundred thousands of days, i.e. thousands of orbital periods. For a better comparison, the sputtering lifetimes are plotted together with the collisional and Poynting–Robertson lifetimes given by . As mentioned above, only nanodust in the small size limit can be significantly removed by solar wind sputtering in reasonable timescales. For slow and fast solar wind conditions at 1 AU, we find that the sputtering lifetime of silicate particles smaller than 60 nm is clearly below their Poynting–Robertson and collision lifetime. That is also the case for Fe0.4Mg0.6O dust below 30 nm and carbon dust below 20 nm. We point out that for CME conditions at 1 AU we also find that the sputtering lifetime of silicate and Fe0.4Mg0.6O particles is well below the Poynting–Robertson and collision lifetime of the dust in the whole considered size interval of 1 to 1000 nm. In practice, this has no consequence because of the short time duration of CMEs. This situation changes when considering sputtering at shorter distances from the Sun, as the SW and CME plasma density increases.

For this approach we consider a SW plasma density following a power law with exponent -2: 5fSW(d)=fSW(1AU)d-2.

Here, the distance from the Sun d is given in astronomical units. The used exponent lies within the range of published values; e.g. report a value of -2.2±0.1. This value was found for the fast SW conditions which we are going to apply for the slow SW and CME conditions as well. Figure  shows the lifetime of 1 nm dust at distances from the Sun from 0.01 to 1 AU, derived for the three different SW scenarios and three dust materials. The high vulnerability of silicate to sputtering is visible here too as their solar wind sputtering lifetimes are in the range of the carbon's lifetimes for CME conditions.

As stated above, carbon is a very resistant material with respect to sputtering. Carbon dust with only 1 nm can survive several 10 d at 0.1 AU. Only in the case of sputtering within the CME conditions are the carbon sputtering lifetimes below the typical duration of a CME of 1–2 d within the shortest distances from the Sun.

From the mass loss rate (Eq. ) it is also possible to derive the erosion rate of a dust particle due to sputtering. This erosion rate, i.e. the shrinkage of dust per unit time (dr / dt), is also independent of dust size. 6drdt(d)=-fSW(d)M4NAρ For a distance of 0.1 AU, we derived the erosion rates of the three dust components for the three solar wind conditions in Table .

As the dust erosion rate (Eq. ) is independent of initial dust radius, the sputtering of dust larger than 1 µm can also be considered. For example, a silicate dust particle with a size of 10 µm has a 10 000-fold lifetime of a 1 nm dust grain. When assuming the dust is at a distance of 0.1 AU, the 1 nm dust survives 0.6 d under CME conditions; i.e. it will be destroyed by a single CME. A dust grain of 10 µm size has a lifetime of 6000 d under CME conditions. That means this can be hit by 3000 strong CMEs at a distance of 0.1 AU until it will be finally destroyed. Within our solar system, CME rates vary during a solar cycle. The rate can peak up to 400 per month during high solar activity and can be as low as 10 CMEs per month during solar minimum . When assuming a mean value of 100 CMEs per month, the duration a 10 µm particle can survive at 0.1 AU is at least 2.5 years. It has to be noted that this requires that the dust particle is hit by every CME ejected by the Sun. This seems to be unlikely due to the randomness of the CME propagation and its allocated size within the heliosphere. Another reason why the lifetime of bigger dust particles might be unrealistic is that during this period the dust size and its orbit change drastically. This leads to a different sputtering environment, and the assumption of a constant erosion rate breaks down.

As dust particles approach the vicinity of the Sun, their temperature increases drastically. To investigate the relevance of the sputtering process, the seemingly low nanodust sputtering lifetimes have to be compared to dust destruction by sublimation into free space.

Where pv is the vapour pressure of the dust material, Tdust is the temperature of the nanodust as a function of distance from the Sun d, and R is the universal gas constant. In Fig.  (orange lines and right y axis) the sublimation lifetime of 1 nm sized dust particles made of carbon, silicate, and Fe0.4Mg0.6O is shown again within the temperature range from 500 to 3000 K. As the vapour pressure of carbon is relatively low, the carbon nanodust has the longest sublimation lifetime. The oxides on the other hand have much shorter lifetimes. Astronomical silicate has slightly higher vapour pressure than Fe0.4Mg0.6O because of its SiO2 content.

As the vapour pressure is a very steep function of temperature, according to Eq. () the relationship is inversely translated to the sublimation lifetime. At temperatures below 1000 K the lifetimes of all different kinds of 1 nm dust are larger than 105 d. Nanodust with temperatures above 2500 K already have sublimation lifetimes below 10-5 d; these lifetimes are so short that the dust can be regarded as non-existent.

The next step will be the direct comparison of sublimation and sputtering lifetimes for nanodust within the near-Sun environment.

The results shown in Fig. a–c indicate a diverse influence of sublimation and sputtering on the nanodust environment near the Sun. The following remarks shall put the results into context for current and upcoming dust measurements near the Sun.

When dust particles approach the Sun, they heat up quickly and along with that the sublimation becomes the governing destruction process. One finding is that sublimation for nanodust is much less size dependent compared to the sputtering process. The derived sublimation lifetimes show that the governing parameters are the distance from the Sun, the resulting equilibrium temperature, and their composition.

The sputtering process on the other hand is much more size dependent but also shows distinct dependencies for dust composition and the increasingly harsh plasma environment near the Sun. Also, the type of plasma environment, i.e. slow or fast solar wind or CME impacts, present in the heliosphere plays an important role in the sputtering of nanodust. The importance of sputtering for the destruction of nanodust even at 1 AU can be seen in Fig. , where the dust sputtering lifetimes are well below the collisional and Poynting–Robertson lifetimes given by . The change in the nanodust population through sputtering can result in different dust fluxes at 1 AU than expected so far. Additional measurements and dust flux modelling are needed to verify this finding.

As the sputtering and sublimation of nanodust are important destruction processes near the Sun, it can also be expected that the nanodust population will change its composition when approaching the Sun. While nanodust particles probably have a diverse composition at 1 AU and further away, only the most durable nanodust can survive near the Sun. Our calculation allows the assumption that the majority of nanodust in close proximity to the Sun contains large fractions of carbon in comparison to Fe0.4Mg0.6O or silicate that are more likely sublimated or sputtered and not very abundant there. Quantitative statements on the abundance of different dust species also depend on their production rates near the Sun. Giving production rates for dust and nanodust made of different material is beyond the scope of this study.

Closer to the Sun, the nanodust population becomes even more variable under the influence of CME impacts. The sputtering lifetimes of nanodust under CME conditions are several orders of magnitude lower than for the solar wind conditions (Fig. ). Void zones for silicate nanodust in the small size limit are identified after the passage of a mature CME impact. This finding would impact the nanodust population locally and during certain times, especially at solar maximum conditions when CMEs are frequent (up to 400 per month ). This variability of the nanodust population might be quantified by impact measurements onboard Parker Solar Probe and Solar Orbiter, taking sputtering and also sublimation into account. Together with the onboard plasma and optical instruments, further constraints on the near-Sun nanodust population are possibly deducted.

The F-corona brightness at mid-infrared to visible wavelengths can be attributed to thermal emission from micron-sized dust particles . Recent WISPR observations on PSP show that F-corona intensity leaves its linearity around 17 solar radii (0.08 AU). These observations would support the existence of the predicted dust-free zones within the F corona . In Sect.  we have identified sputtering by CME impacts as a possible destruction process also for µm dust. From Fig. , we find that a 10 µm dust particle can be fully destroyed within 3 years at a distance of 0.1 AU from the Sun when struck by multiple CMEs (assuming around 100 CMEs per month) and under constant exposure to the solar wind.

In the end, it has to be noted that the given lifetimes are only valid for dust on near-circular orbits. Dust affected by sublimation or sputtering is subject to a constant reduction of its size, which will result in alteration of its present orbit. The given results only represent a general description of these destruction processes. However, conclusions on the impact of sputtering and sublimation on individual dust grains along their orbits cannot be drawn and are not the subject of this work.