Dust sputtering within the inner heliosphere: a modelling study

The aim of this study is to investigate through modelling how sputtering by impacting solar wind ions influences the lifetime of dust particles in the inner heliosphere near the Sun. We consider three typical dust materials, silicate, Fe0.4Mg0.6O, and carbon, and describe their sputtering yields based on atomic yields given by the Stopping and Range of Ions in Matter (SRIM) package. The influence of the solar wind is characterized by plasma density, solar wind speed, and solar wind composition, and we assume for these parameter values that are typical for fast solar wind, slow solar wind, and coronal mass ejection (CME) conditions to calculate the sputtering lifetimes of dust. To compare the sputtering lifetimes to typical sublimation lifetimes, we use temperature estimates based on Mie calculations and material vapour pressure derived with the MAGMA chemical equilibrium code. We also compare the sputtering lifetimes to the Poynting–Robertson lifetime and to the collision lifetime. We present a set of sputtering rates and lifetimes that can be used for estimating dust destruction in the fast and slow solar wind and during CME conditions. Our results can be applied to solid particles of a few nanometres and larger. The sputtering lifetimes increase linearly with the size of particles. We show that sputtering rates increase during CME conditions, primarily because of the high number densities of heavy ions in the CME plasma. The shortest sputtering lifetimes we find are for silicate, followed by Fe0.4Mg0.6O and carbon. In a comparison between sputtering and sublimation lifetimes we concentrate on the nanodust population. The comparison shows that sublimation is the faster destruction process within 0.1 AU for Fe0.4Mg0.6O, within 0.05 AU for carbon dust, and within 0.07 AU for silicate dust. The destruction by sputtering can play a role in the vicinity of the Sun. We discuss our findings in the context of recent Fcorona intensity measurements onboard Parker Solar Probe.

considered? Perhaps the authors can provide an estimate of the uncertainties on the results presented here when not considering these parameters....
The reviewer points on the not well known nature of the sputtering yield for dust grains. We have added a statement how the additional but rather unknown parameters within the sputtering yield may affect our results. 'Due to a lack of quantitative information on these enhancements 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 one order of magnitude shorter when taking the microphysics of dust sputtering into account.' ...Line 147: "ten orbital period"; it is orbital period of the dust? can you give the value in day or years as for the FeMgO nanodust?...
The reviewer is right and we have changed this cumbersome expression to 'ten years'.

Response to Reviewer #2
We would like to thank the reviewer for his or her substantial review of our manuscript. The overall positive appraisal of our work leaves us feeling grateful. In addition, the minor corrections to manuscript and especially the suggestions to the content by the reviewer are very much appreciated. All comments have found its way into the manuscript and will be addressed point by point below. We give thanks to the reviewer for this suggestion. This publication is indeed a very valuable reference and fits perfectly. We have added it to the manuscript.
We have changed the manuscript accordingly.
... Table 1: Perhaps you want to add two columns to give the (fractional ) abundance of He and heavies. ....
We thank the reviewer for the suggestion to add the abundances to the table and have done so. ...Line 91 ff: use italics for the formula symbols, same as in the formula.
We have changed the manuscript in accordance with the corrections by the reviewer.
... Figure 2: The absolute sputter yield is somewhat misleading, since only the sputter yield prorated to the solar wind ion abundance applies. Perhaps you plot the prorated sputter yield for all the solar wind ions, and sum curve that adds the yield contributions from H to Fe stepwise, thus showing their contributions. If you do that also for fast SW and CME you will get a very strong plot. ....
The reviewer is definitely correct about the absolute sputtering yield. We have replaced the old Figure 2 with a new Figure that shows in a stacked bar plot the solar wind composition prorated sputtering yield. We have also added a description of this new Sputtering yields are a function of solar wind ion itself, its fractional abundance (fast solar wind (fSW), slow solar wind (sSW) and CME), and its mean speed.
figure. However, we still mention the absolute sputtering yield as it is available in the supplemented material. The description of Figure 2 has been changed to: ' Figure 2 shows the results of the assessment, i.e. the sputtering yield as a function of ion species (H -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 (Y i,k · c k , c k is the fractional abundance of ion k in the solar wind conditions, cf. Eq. 1, Tab. 1). The highest sputtering yields are found for Fe 0.4 Mg 0.6 O material, the yields are somewhat smaller for silicate and are the lowest by far for carbon material. The Figure 2 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 then in the fast solar wind. ...Line 237: Write "... are larger than 10ˆ5 d." Remember the difference of drinking a great cup of tea, and drinking a large cup of tea.
We would like to thank the reviewer for identifying the typos and small mistakes in the text. We have corrected all the comments.
...Line 288ff: These arguments imply that the average composition of small grains changes when getting closer to the Sun. Maybe you want to elaborate on this argument. ....
The reviewer raises a valid point on the dust composition changes in the proximity of the Sun. We have added a short paragraph, which shortly discusses this point based on our model calculations. However, quantitative statements are not possible from our results.
'Our calculation allow the assumption that the majority of nanodust in the close proximity of the Sun is made of carbon. Fe 0.4 Mg 0.6 O and silicate dust is very likely sublimated or sputtered and not very abundant there. Quantitative statements on the abundance of different dust species depends also on their production rates near the Sun. Giving production rates for dust and nanodust made of different material are beyond the scope of this study.' ...Line 311: "the fragile nanodust" this is the first time this classification is presented. Does that imply that the nano-dust is not a solid, but small, grain, but more a composition of many grains loosely attached to each other? ....
The reviewer refers to a general point in dust science. There are different types of dust, on the one hand rock solid fragments of small solar system bodies and on the other hand fragile conglomerates of smaller parts that form a larger dust grain. In the case of nanodust, its structure can be assumed as clusters of atoms and molecules. In the case of atomic clusters the binding energy might be as larger as in solid grains. Molecular clusters are much weaker bound and the term 'fragile' might be used for these clusters.
Our intention using the term 'fragile' related to the short lifetimes of nanodust, so that a single CME might be enough to destroy a nanometersized dust grain. In addition, we did not aim to relate to the idea mentioned by the reviewer as our calculation does not cover this perspective of the dust and nanodust. For clarification, we have changed the term 'fragile' to 'small' within the manuscript.
...Line 324ff: Sublimation seems to be important around 0.1 AU. Shouldn't there be an optical singal if you would look at optical lines of sublimated material located at about 0.1 AU. Can you address this with Solar Orbiter or PSP? ...
The reviewer points out a good possibility for future research. PSP carries a Wide field visible light imager (WISPR) that is not able to do spectroscopic measurements. Solar orbiter on the other hand carries different spectrometers for the EUV-and X-rays. We have added the following paragraph to account for that idea.
'An additional possibility to characterize the composition of dust near the Sun is the detection of emission lines from sublimated dust atoms or ions. At 0.1 AU sublimation starts to be effective and might lead to layers of atomic species. Also collisional dust destruction can be a source of ions which might be visible near the sun (Mann et al. 2005). These ions might be detected optically from specific emission lines or using in-situ mass spectrometric measurements onboard spacecraft.' ...Line 341: Write "... distances from the Sun, i.e. 1 AU and further out.... We have implemented the correction.
Standard comment: Typo within the supplemented material This comment is to report a typo within the supplemented material.The supplemented material uploaded contains a typo within the sputtering yieldthe H ion for the silicate dust material (within supplement material.pdf and AstronomicalSilicate.txt): Old version: H,0.0059,0.0034,0.0030,0.0209,0.0109,0.0047,0.0040,0.0346,0.0103,0.0049,0.0391,0.0305 Correct version: H,0.0059,0.0034,0.0030,0.0209,0.0109,0.0047,0.0040,0.0346,0.0103,0.0049,0.0039,0.0305 The corrected value does neither change the results of the manuscript nor the findings.The figures of the manuscript do not change when using the corrected value. The original figures can still be used and the authors declare that no other changes has been made to manuscript. It was only barely visible during the production of the new Figure  2 (requested from reviewer 2). The new Figure 2 has been made using the correct value. To correct this typo, a new version of the supplemented material has been prepared which will be uploaded with the revised version of the manuscript. the :::::::::: Wide-Field :::::: Imager ::: for ::::: Solar ::::: Probe :::::::: (WISPR) : (Howard et al., 2019) onboard PSP include the F-corona that is produced by circumsolar dust. The observed corona intensity decreases with decreasing PSP distance from the Sun and this slope changes at 17 solar radii; dust depletion is mentioned as one of the possible explanations for this observation (Howard et al., 2019). While it seems established that a dust-free zone around the Sun forms because of within 10 solar radii (Mann et al., 2004). For dust destruction at larger distances, the sputtering process becomes important.
Parker Solar Probe (Fox et al., 2016) and Solar Orbiter (Müller et al., 2013) will help to quantify the dust component in the inner heliosphere with unprecedented detail. These spacecraft do not carry dedicated dust sensors, but can measure the dust component from the F-corona intensity as mentioned above and detect high velocity dust impacts on the satellite body using electric field sensors. The dust impacts are observed because they change the floating potential of the spacecraft for short  Sputtering, i.e., the emission of atoms from a surface due to the impact of energetic ions, occurs within the whole heliosphere as solar wind particles :::: ions hit dust particles. Sublimation of dust, i.e. the phase transition of a body due to absorption of solar radiation and subsequent increase of its vapour pressure, happens only when the equilibrium temperature exceeds the binding energy of the atoms in the dust structure.
Analysis of astronomical observations point to the existence of nanometer-sized dust particles in debris disks around other stars (e.g. ?). Theoretical considerations suggest that the nanodust is trapped under certain conditions in orbits around the Sun 50 (Czechowski and Mann, 2010;Stamm et al., 2019). While the trajectory of dust particles are influenced by the bombardment of solar energetic particles ::: ions : (Ragot and Kahler, 2003), our work concentrates on the survival of nanodust during passages of Coronal mass ejections (CME) and the solar wind. Czechowski and Kleimann (2017) carried out dust trajectory calculations within a CME scenario and find trapped as well as ejected nanodust trajectories. However, the vast amount of energetic plasma ejected during a CME does not leave the nanodust untouched. We investigate dust destruction by sputtering and consider the 55 conditions near the Sun, for which this process becomes important in comparison to the sublimation of dust particles.
This study is organized as follows: Section 2 introduces the solar wind and CME composition as well as plasma densities used in this study. This section also covers the sputtering process of dust within our solar system. Section 3 investigates the

Dust sputtering
Sputtering is the physical process of atom ejection from a solid through the bombardment of energetic ions (Behrisch and Eckstein, 2007). This process usually is performed within a laboratory environment where a cathode is bombarded with noble gas ions and the ejected cathode atom deposit and form high quality surfaces :::::::::::::::::::::::::: (see Greene, 2017, for a review). However, this process is also well known in the context of dust destruction for interplanetary (e.g. Mukai and Schwehm, 1981) and interstellar 65 dust grains (e.g. Barlow, 1978;Draine and Salpeter, 1979).
For the calculation of nanodust sputtering, we divide our study into three different sputtering scenarios. These are the slow solar wind conditions, fast solar wind conditions and CME conditions. In the following, the heliospheric conditions of these scenarios are discussed in detail. Subsequently, we introduce the calculation of the dust's sputtering lifetimes. This is followed by an analysis of dust sputtering at 1 AU and in the inner heliosphere. Figure 1 shows the composition of the three solar wind scenarios considered. The SW/CME composition used here is :::: solar ::::
For each solar wind scenario, the SRIM program has been initialized by the above discussed plasma composition and speed (energy/nucleii). In order to derive the sputtering yield for the dust species i : i for a given scenario, we summed up the sputtering 90 yields for each atom j : j sputtered by solar wind ion k. : k. : The index j : j denotes the target atoms Mg/Fe/Si/O for astronomical silicate and Fe/Mg/O for the Fe 0.4 Mg 0.6 O composition.
The yields correspond to the atomic ::::::::: abundance ratios of the dust composition and the ion ratio of the solar wind composition.
of these calculations are sputtering yields for silicate, Fe 0.4 Mg 0.6 O and carbon for the three different sputtering scenarios, i.e.
slow SW / fast SW / CME. The individually derived yields can be found in the supplemented material.

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For the derivation of nanodust sputtering lifetimes we follow the formalism given by Wurz (2012). The mass loss rate from a surface through sputtering in the solar wind is given by the following: Here, A : A : is the cross section of the dust, f SW the solar wind ion flux, Y tot the total sputtering yield of the target material and m A is the mean mass of the sputtered atoms.

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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: Here, r 0 is the initial radius of the dust, N A is the Avogadro constant, M and ρ are the molar mass and mass density of the sputtered material. For the solar wind flux f SW = n p · v p the values from Tab. 1 have been used.  One can see that carbon nanodust survives longest among all three studied composition, i.e. 1 nm dust survives 5000 days at 1 AU under CME conditions. Fe 0.4 Mg 0.6 O sputtering lifetimes are by 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 condition. When 160 comparing the different solar wind conditions, CME sputtering lifetimes are the shortest. Sputtering lifetime 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 condition.
This behavior 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, CME's are distinct solar eruptions and these sputtering conditions do not last longer than one or two days and occur only locally in the heliosphere. The given lifetimes of several ten 165 days and more at 1 AU for 1 nm dust make a full destruction due to CME sputtering not possible. However, for the case of fast and slow SW, which is present within the heliosphere at all times, the sputtering life times are close to ten orbital periods :::: years in the case of silicate nanodust and thirty years for Fe 0.4 Mg 0.6 O nanodust. 8 The sputtering lifetime described in Eq. 4 is linear in initial dust particle radius and enables easy calculation of lifetimes for other dust sizes. In Fig. 5 we show the derived lifetimes of dust particles in the size range from 1 nm to 1 µm at the Earth's Poynting-Robertson lifetime (τP R) are shown in black for comparison (data taken from Grün et al., 1985). 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 Grün et al. (1985). 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 175 and collision lifetime. That is also the case for Fe 0.4 Mg 0.6 O 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 Fe 0.4 Mg 0.6 O particles is well below 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 CME. This situation changes when considering sputtering at shorter distances from the Sun, as the SW and CME plasma density increases.

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For this approach we consider a SW plasma density following a power law with exponent minus two: Here, the distance from the Sun d is given in astronomical units. The used exponent lies within the range of published values, e.g. Maksimovic et al. (2005) report a value of -2.2±0.1. This values was found for the fast SW conditions which we are going to apply for the slow SW and CME conditions as well. Figure 6 shows the lifetime of 1 nm dust at distances from the Sun 185 from 0.01 AU 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. Sputtering 1nm dust CME fast SW slow SW As stated above, carbon is a very resistant material with respect to sputtering. Carbon dust with only 1 nm can survive several ten days at 0.1 AU. Only in the case of sputtering within the CME conditions the carbon sputtering lifetimes is below the typical 190 duration of a CME of 1-2 days within the shortest distances from the Sun.

-
From the mass loss rate (Eq.3) 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.
For a distance of 0.1 AU, we derived the erosion rates of the three dust components for the three solar wind conditions in Tab.

2.
As the dust erosion rate (Eq. 6) is independent of initial dust radius, the sputtering of dust larger than 1 micron can also be considered. For example a silicate dust particle with a size of 10 µm has a 10000 fold lifetime of a 1 nm dust grain. When slow SW conditions 9.3 · 10 −2 3.3 · 10 −2 5.4 · 10 −4 CME conditions 0.41 1.6 2.6 · 10 −2 assuming the dust is in at a distance of 0.1 AU the 1 nm dust survives 0.6 days 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 days under CME condition. That means this can be hit by 200 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 CME per month during solar minimum . When assuming a mean value of 100 CMEs per month, the duration a 10 µm 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 205 reason why the lifetime of bigger dust particles might be unrealistic is that during this period the dust size and its orbit changes 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 Sun their temperature increases drastically. To investigate the relevance of the sputtering process, the seemingly low nanodust sputtering lifetimes has to be compared to dust destruction by sublimation into free space.

Dust sublimation
The processes of sublimation, evaporation and condensation is usually described by Langmuir's equation of evaporation: A.
In case of sublimation, it describes the sublimated mass per time unit as a function of vapour pressure p v and temperature T : T : of the sublimating material. A is the whole surface of the dust and R :: R : is the gas constant. In the context of free space, 215 atoms leave the materials surface into the vacuum, while the adsorption of atoms onto surfaces can also occur under certain conditions, e.g. the resupply of Saturn E rings by the adsorption of Enceladus water vapour (e.g. Hansen et al., 2006). The sublimation of dust particles has been studied within different astrophysical context, e.g. protoplanetary systems (e.g. Duschl et al., 1996) and interstellar dust (e.g. Draine and Salpeter, 1979). For a self-consistent study, the sublimation of the same dust materials as in the sputtering part will be considered. In order to quantify the dust sublimation two parameters are needed, i.e. 220 dust temperature at certain distances from the Sun and the dust materials vapour pressure. For deriving the dust temperature we assume the equilibrium of absorbed solar radiation and re-emitted :::::: emitted : thermal radiation of the dust particle (Myrvang, 2018). The effect of dust cooling due to evaporation has been quantified to be only 10% of the re-emitted :::::: emitted : power (e.g. Schwehm, 1980), which we neglect in this study. Figure 7 shows the temperature of 1 nm dust particles made of carbon, silicate and Fe 0.4 Mg 0.6 O, for comparison the temperature of a black body is also shown. All nanodust is significantly hotter than a 225 blackbody, except for silicate near 1 AU which has similar equilibrium temperatures. Near the Sun, the dust temperatures of all materials exceed the black body. At 0.01 AU the Fe 0.4 Mg 0.6 O 1 nm dust is ≈ 700 K hotter than a black body, carbon 500 K and silicate 400 K. All three materials with a dust size of 1 nm are hotter than 3000 K near the Sun. The temperature change from 1 nm to 100 nm is below 100 K for each dust material (not shown). These temperatures have been derived using Mie theory and the refractive indices for carbon and astronomical silicate come from Li and Greenberg (1997). The refractive index for 230 FeO/MgO is from Henning et al. (1995), we have used the data for the Mg 0.6 Fe 0.4 O compound.
The second quantity for the description of sublimation is the vapour pressure. For the derivation of the vapour pressure for the oxides Fe 0.4 Mg 0.6 O and astronomical silicate we used the MAGMA code (Fegley Jr and Cameron, 1987;Schaefer and Fegley, 2004). The program is very flexible with regard to material composition and the derived vapour pressures have been checked with a vast number of experimental data. The MAGMA code has been used mainly for the change of planets 235 and planetesimals due to geological activity but also for the evaporation of meteoroids within the Earth's atmosphere (e.g. Schult et al., 2015). The MAGMA model is a multicomponent gas-melt chemical equilibrium code and is able to derive vapour pressures for mixtures of its base components (MgO, SiO 2 , FeO, CaO, Al 2 O 3 , Na 2 O, TiO 2 , K 2 O, ThO 2 , UO 2 , PuO 2 ). The results of the MAGMA model has been successfully compared to experimental work on the vapourisation of chondrite type material. The good performance of the MAGMA model encouraged us to use it in the context of dust sublimation near the Sun 240 as well. The vapour pressure for carbon was used from the literature (Leider et al., 1973;Lide, 2003). Figure 8 (blue lines and left y axis) shows the vapour pressure of all three materials in the temperature range between 500 and 3000 K. The exponential growth of the vapour pressure with temperature is a typical behaviour of all materials. Please pay attention to the comparably low vapour pressure of carbon compared to the oxides, this will have an impact on the dust lifetime. To derive the sublimation lifetime of nanometer sized dust particles, Eq. 7 is integrated using spherical geometry (Lamy, 1974): Where p v is the vapour pressure of the dust material, T dust is the temperature of the nanodust as a function of distance from the Sun d, and R : d, ::: and :: R : is the universal gas constant. In Fig. 8 (orange lines and right y axis) the sublimation lifetime of 1 nm 250 sized dust particles made of carbon, silicate and Fe 0.4 Mg 0.6 O, 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 hands have much shorter lifetimes. Astronomical silicate has slightly higher vapor pressure than Fe 0.4 Mg 0.6 O because of its SiO 2 content. the sublimation lifetime. At temperatures below 1000 K the lifetime of all different kinds of 1 nm dust are greater ::::: larger than 10 5 d. Nanodust with temperatures above 2500 K have already sublimation lifetimes below 10 −5 d, these lifetimes are so short that the dust can be regarded as non-existing.
The next step will be the direct comparison of sublimation and sputtering lifetime for nanodust within the near Sun environment.

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4 Implications for nanodust near the Sun In the earlier sections, it has been shown that sputtering and sublimation can be significant sinks for nanodust. The loss of nanodust due to solar wind sputtering increases with ion number density and ion mass (see :::: Fig. 2). The effect of sublimation however, is a steep function of dust temperature (see Sect.3). For the comparison of sputtering and sublimation of nanodust we have chosen the CME scenario. We find the shortest sputtering lifetimes for CME conditions, but the short duration of single 265 CMEs has to be taken into account.
The comparison of the lifetimes is done in the small size limit of the dust population, i.e. the sizes 0.2 nm, 1 nm, and 5 nm.
There is no experimental prove ::::::: evidence for the existence of sub nanometer dust. However, it will be hypothesized that these clusters of molecules exist. This assumption will help to better assess the importance of nanodust sputtering in this study.
Here, we compare the sputtering and sublimation lifetimes of the three different nanodust compositions, namely carbon,

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Fe 0.4 Mg 0.6 O and silicate nanodust. Figure 9 a) shows the sputtering and sublimation lifetimes of carbon dust. All lifetimes are compared to a duration of 2 days, which is used as the upper limit for the duration of a CME. In the case of carbon, which is a rather sturdy material, the nanodust can survive in the near proximity of the Sun. The sublimation of carbon nanodust within 2 days occurs at a distance of 0.03 AU from the Sun, that is because of carbon's comparably high evaporation temperature of 2600K at low pressures (Whittaker, 1978). However, the sputtering lifetime of carbon is longer than sublimation counterpart.

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The nanodust could withstand the sputtering of a CME to even shorter distances if it was not evaporated beforehand. When considering the duration of a CME the sputtering and sublimation of only the smallest nanodust are comparably. In the case of carbon nanodust we state that during a typical CME sputtering is not a relevant destruction process within the inner heliosphere.
The lifetimes of Fe 0.4 Mg 0.6 O dust for destruction by sublimation and sputtering are much shorter, see Fig. 9 Fig. 2) as carbon, a single CME cannot destroy nanodust by a single hit. A 1 nm Fe 0.4 Mg 0.6 O dust grain would be completely sputtered by a CME if it reached 0.1 AU but will sublimate earlier due to its high temperature.

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Regarding the sputtering and sublimation lifetime of silicate nanodust we find a different situation compared to the aforementioned compositions. The actual lifetimes of silicate nanodust are shown in Fig. 9 c). The sublimation lifetime of Silicate nanodust equals the two day period at distances from the Sun of around 0.15 AU. The complete sputtering of the silicate nanodust during a CME impact occurs at solar distances of 0.2 AU, 0.07 AU and 0.03 AU for the respective grain sizes 1 nm, 5 nm and 20 nm. We can conclude here that a region void of silicate nanodust forms after the passage of a single CME. This region 290 lies between 0.1 and 0.15 AU for the 1-3 nm dust, larger dust rather sublimates than being fully sputtered by a single CME. The existence of this sputtering region is due to the comparably low temperatures of silicate dust that leads to lower sublimation rates for the same distances as compared to the Fe 0.4 Mg 0.6 O dust that is destroyed by sublimation.

Discussion
The results shown in Fig. 9 (a-c) indicate a diverse influence of sublimation and sputtering on the nanodust environment near 295 the Sun. The following remarks shall put the results into a 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.

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The sputtering process on the other hand is much more size dependent but also show 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 play an important role for the sputtering of nanodust. The importance of sputtering for the destruction of nanodust even at 1 AU can be seen in Fig. 5 where the dust sputtering lifetimes are well below the collisional and Poynting-Robertson lifetimes given by Grün et al. (1985). The change of the nanodust population through 305 sputtering can result in different dust fluxes at 1 AU as expected so far. Additional measurements and dust flux modelling are needed to verify this finding.
Closer to the Sun, the nanodust population becomes even more variable under the influence of CME impacts. The sputtering 315 lifetimes of nanodust under CME conditions are several orders of magnitude lower than for the solar wind conditions (Fig. 6).
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 of Parker Solar Probe and Solar Orbiter taking sputtering and also sublimation into account.

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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 wavelength can be attributed to thermal emission from micron sized dust particles (Kimura and Mann, 1998). Recent WISPR observations on PSP (Howard et al., 2019) 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 325 zones within the F-corona (Lamy, 1974;Mann, 1992). In section 2.2 we have identified sputtering by CME impacts as a possible destruction process also for µm-dust. From Fig. 6, we find that a ten µm dust particle can be fully destroyed within three 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 330 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 subject of this work.

Conclusions
Interplanetary dust enters a harsh environment when approaching the proximity of our central star. Especially the fragile 335 :::: small : nanodust is prone to destruction through sputtering by the solar wind or sublimation near the Sun. Studies on dust destructions mechanisms near the Sun already showed that there are distinct regions dominated by sublimation and sputtering in the heliosphere (e.g. Mukai and Schwehm, 1981). This study has investigated dust sputtering during more extreme conditions of Coronal Mass ejection (CME) events. CME plasma in addition to its high number density contains a large fraction of heavy ions. We find that dust is sputtered most effectively in the CME case followed by sputtering within the slow solar wind.

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The weakest sputtering we find in the low-density plasma of the fast solar wind. However, the sputtering process is also very composition dependent. Carbon has been found to be more stable against sputtering than the silicate and Fe 0.4 Mg 0.6 O composition. The case of nanodust has been studied in more detail for sputtering and sublimation during a the passage of a single CME. Nanodust free zones can occur after two day CMEs for silicate (0.1 to 0.15 AU) but not for Fe 0.4 Mg 0.6 O and carbon.

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The implementation of sputtering and sublimation as destruction mechanisms needs to be included into dust flux models especially for the case of dust in the small size limit. Taking these processes into account is definitely important when considering the dust population near the Sun or other central stars. But also when considering dust trajectory modelling, the rough environment near stars lead to a shrinking of dust particles due to sublimation and sputtering. That leads to an increase of the often used charge to mass ratio of dust in these trajectory models for the small dust component. We expect that integrating the 360 change of the dust size together with its full equation of motion will lead to new insights of the nanodust population near central stars. A recent study by Shestakova and Demchenko (2018) derived the orbital evolution of µm dust within the sublimation zone and included the dust size reduction due to sublimation. They find either elongated dust trajectories after partial sublimation or trajectories leading to complete sublimation after spiralling further into the evaporation zone of the Sun. A future study which also takes the sputtering of dust into account will find deeper insight into the fate of nanodust near the Sun and during 365 the passage of a CME.
Variations in the F-corona intensity has usually been explained by the destruction of dust through sublimation or orbital changes (Lamy, 1974;Mann, 1992). The results of our work have shown that sputtering of micron sized dust during the passage of multiple CME can play a role in the explanation of dust free zones in the F-corona.
Furthermore, we also expect that standard solar wind conditions can lead to significant sputtering in timescales which are 370 shorter than the dynamical removal times of dust within intermediate distances from the Sun, i.e. 1 AU and greater ::::: further ::: out.
Nevertheless, further laboratory as well as theoretical research is necessary to pin point sputtering yields for small dust grains of various composition. At the moment, experimental, theoretical and modelling results of sputtering yields show a diverse picture where scientific consensus is missing.
Code and data availability. The derived sputtering yields, dust temperatures and vapor pressures are made available within the supplemented 375 material. The MAGMA code can be obtained from Bruce Fegley upon request.
Author contributions. C. Baumann carried out the calculations and wrote the initial manuscript. M. Myrvang contributed the dust temperatures near the Sun. C. Baumann and I. Mann conceived the idea of the work. All authors contributed to the finalization of the manuscript.