We investigate the generation of charge due to collision between projectiles with sizes below

The variables in any experiment studying the impact of dust grains – be it of terrestrial, meteoric, interplanetary, or interstellar origin – span many orders of magnitude. By

Early experimental studies of impact ionization of micrometre-sized grains on metal surfaces were applied in designing highly sensitive micrometeor detectors; see e.g.

In a treatment of impact charging at speeds of up to some tens of km s

Motivated by the notions above, we propose in this paper a new charging theory for impact speeds below

The models of charging and fragmentation that constitute our novel approach are presented in Sect.

The current paper concerns itself in essence with the competition between the charging efficiency of two mechanisms: ionization and capacitive charging. The ionization mechanism is here represented by shock wave ionization – that compressibility in solids allows for high enough energy density for charges (electrons) to separate from their respective solids (nanoscale and microscale particles) when the impact speed is high enough. For this mechanism to take place, the particles need to impact a much larger bulk solid at speeds of several km s

In the sections below, we introduce the theoretical framework for our contact charging model based on fragmentation and capacitive charging as well as the theory of shock wave ionization with special emphasis on the low-velocity regime. We utilize our model on two slightly different types of projectile grains.

The motivation behind the model presented below and the approach for its utilization can be summarized as follows: at speeds comparable to or lower than the critical limit for significant deformation or cratering in a grain–surface collision – see e.g.

At speeds

Figure

Contact geometry for the charging model of capacitive contact charging. An incoming grain of size above

We employ the same parameterization of fragment size distribution in both the fragmentation-at-impact model (iron particles) and fragment-in-projectile model (ice particles containing meteoric smoke particles – MSPs), namely

Size distribution of parameterized MSP particles inside an ice particle of size 30 nm. Note that

The motivation for the current work is that at low-impact speeds

The fundamental mechanism behind contact charging as investigated here is a capacitive coupling between a particle and a surface over an effective separation

Material properties used in the calculation of contact charging yields for silver (Ag), iron (Fe), water ice, stainless steel (SS) and a meteoric smoke analogue (MSP).

It is recognized that impact ionization is a combination of mechanisms, each dominating for certain parts in a wide velocity range. In this paper, we take it as fact that the impact ionization will tend towards a volume ionization mechanism – as a consequence of a Thomas–Fermi model for electronic structure – as impact speeds exceed

The model of shock wave ionization does not, however, describe ionization for the entire velocity range below

For the high-velocity regime, the shock wave ionization model assumes that the ionization state freezes at some point during expansion of the impact cloud arising from impact

For the low-velocity regime,

In the following, we consider the situation where both target and projectile are conductive. This means, in simplified terms, that electrons can easily move between potential wells on the surface of the projectile and target and have time to equilibrate the charge within the collision time

In Sect.

The choice of default projectile grain size (30 nm) in the presented model results below may be motivated by it being typical for mesospheric icy dust grains usually encountered by sounding rockets. It is also among the smaller projectile sizes (see e.g. Fig. 2 in

We must also address the choice of limits in fragment size distributions and sensitivity to changes in the lower cut-off limit. In their treatment of collisional charging of interstellar grains,

Sensitivity of contact charge generation in an Fe-on-Ag collision to different values of the lowest allowed fragment sizes. Cut-off values are labelled in the legend.

In the following simulations, we have used iron as a projectile material and silver as a target material. This is due to experiments with this combination being done in the past both at the LASP dust accelerator

Figure

Simulation of contact charging of iron projectiles (

Although it is not the purpose or motivation of this work to explain the entire charging mechanism at low-impact speeds with fragmentational contact charging, we nevertheless have calculated a best fit of our model to experimental data with reasonable parameters. In Fig.

Simulation of contact charging of iron projectiles on a silver target. This simulation was a “best-fit” run, in which the fraction of charged fragments, yield pressure, and fragment size span was allowed to change. This shows the case for

Since many of the parameters used in our charge model are valid for bulk projectiles, the validity of extrapolating the model to sizes

It is technically challenging to set up laboratory experiments for studying low-impact velocities (

It is however possible to use sounding rockets to obtain a point measurement in the low size and speed range: typical sounding rockets utilized in upper atmosphere research operate at low speeds

As previously stated, we utilize the fact that dust grains in the mesosphere are contaminated with meteoric smoke – recondensed and agglomerated remnants of meteoric ablation. In Fig.

Contact charge yield of 30 nm ice particles with MSP impurities impacting on stainless steel. The shaded area shows possible yields for the case of a mixture of insulating and conducting particles.

In the following we attempt to simulate the current recorded by MUDD during a flight in the MAXIDUSTY campaign (Andøya Space Center, 30 June 2016). We assume the finding of

The rocket traversed a dust layer situated at

Measurements from the impact Faraday cup MUDD flown on the MXD-1 sounding rocket payload (red) and a best fit from simulation of contact charging (grey) using the fragmentation model described in Sect.

As presented in Sect.

To investigate the applicability of an SLS at speeds of the order of 1 km s

A first-order estimate of the mean diffusion distance of an impurity ion inside a cooling – i.e. solidifying – metal grain can be found by recognizing that the diffused area must be

We assume the particle has bulk properties, which is suitable for clusters of size of the order of 10 nm. The available volume from which ions can be released is then (denoting the grain radius

It is clear that we also require a parameterization of the temperature inside the expanding shock. For this purpose we utilize the fact that the relationship between the shock front velocity

In the following calculations of impurity ionization production, we have used the fact that the solidification temperature of nanoscale iron particles is 1000 K

Results from calculation of impurity (1 % potassium) charging using the Saha–Langmuir equation (blue, dashed) and fragmentation model described in this work. The solid red line shows the number of released

In Fig.

We summarize our result of low-velocity impact charging in Fig.

Comparison of specific yields from our contact charging model (dashed) to the Saha–Langmuir solution from

In Sect.

The number of

Based on recent observations by the Parker Solar Probe (PSP),

Another possible candidate for employment of our model on spacecraft data is secondary ejecta. Secondary ejecta, which are material from craters generated by dust impacts on the spacecraft body, have energies much lower than the impacting grains. Such secondary grains have been observed as stray light in optical images from e.g. STEREO

One impediment to utilizing our model on dust in space is that it may be difficult to determine its composition and structure. In consequence, the work function of the projectile material may be unknown and moreover size-dependent

The ESA Solar Orbiter (ESO) was launched in February 2020. Its orbit is different from PSP in that its perihelia are larger than

In this work we have investigated the production of charge in impacts of projectiles of iron and agglomerates of ice and meteoric smoke on a metal surface at speeds

In this Appendix we give a scaling relation for charge production by capacitive charging when employing a fragmentation model.

The available material from which fragments can form is given by the Hertzian deformation presented in Sect.

The largest possible spherical fragment (of volume

As contact charging scales with the cross section of fragments, we calculate the total surface area of all (discretely distributed) fragments:

Now we recall the scaling

This result is also intuitively reasonable, that since there are many more small particles than large ones, the surface area of the small particles contributes more to the total area and thus charge production. Moreover, we note that the sensitivity to the parameter

The data to reproduce the rocket measurements in Fig. 7 can be obtained from the UiT Open Research Repository at

The presented model was developed by TA with theoretical insights from IM. Calculations based on this were done by TA. IM, JV, LN and ÅF developed the discussion regarding relevance for spacecraft. TA prepared the manuscript, with contributions from all the co-authors.

The authors declare that they have no conflict of interest.

This work was supported by the Research Council of Norway through grant nos. 262941 and 275503. Jakub Vaverka and Libor Nouzak were supported by the Czech Science Foundation under project 20-13616Y. The publication charges for this article have been funded by a grant from the publication fund of UiT – Arctic University of Norway.

This research has been supported by the Norwegian Research Council (grant nos. 262941, 275503) and the Czech Science Foundation (grant no. 20-13616Y).

This paper was edited by Gunter Stober and reviewed by two anonymous referees.