A pulsed 'plasma broom' for dusting off surfaces on Mars

The fine dust particles are highly adherent to surfaces due to a combination of factors, such as electrification [12] (due to a high flux of UV radiation and low content of water vapors in the atmosphere or due to high electric fields during storms) and chemical composition (e.g. dust with a high ferric content is easily magnetized) [13]. In order to solve this dust contamination problem several approaches have been proposed each with its own benefits and disadvantages [14–22]. The cleaning efficiency varies largely depending on several factors, from the type of dust removal mechanism (electrical or mechanical) to its implementation and operation. Electrical approaches are contactless while mechanical ones seem to be affected by the triboelectric effect, the inherent charging of the dust particles by friction. In the first category an established dust removal technique consists in printing directly on the surface (insulating or dielectric) an electrostatic shield made of a fine conducting mesh-grid [18–20]. When charged dust particles adhere to the surface a high voltage is applied on the grid wires and the electrostatic force repels them off. The removal process takes a relatively long time, from minutes to several hours for an efficient surface cleaning. A second solution consists in the use of a precipitator to collect dust during the process of extracting oxygen, water or methane from the Martian atmosphere [21]. A tube provided with two electrodes produces a corona discharge when a high voltage is applied. The electric field drives electrostatically the charged dust to one electrode where it is trapped. Both methods become less efficient when the surface is covered with a thick layer of dust, and particularly for larger particles (e.g. in the mm range) for which electrical levitation becomes questionable due to the particles weight. It appears that lifting off large particles with electric fields is a major challenge of the electrical removal techniques.

In order to overcome this deficiency we propose a much more robust cleaning technique which seems to be very effective for a wide range of particle diameters (from microns to 1 mm and even beyond this size, thus including sand particles) and much more rapid compared to known methods. The removal of dust is based on a plasma jet produced in a pulsed discharge. A proof-of-principles demonstration is presented in the followings, by cleaning an array of PV cells heavily covered with dust and sand immersed in CO₂ at low pressure.

Mars atmosphere is composed mainly of CO₂ (95%), N₂ and Ar in small percentage (2.7% and 1.6%, respectively) and traces of O₂ and CO (each below $0.2 \%$) [23]. The atmospheric pressure at the planet surface varies between 3.5 and 7.5 Torr. Even at the reduced atmospheric pressure of the environment dust is susceptible to the drag force of the wind. The drag force exerted by a flowing gas on a small spherical dust grain is the well known Stoke formula ${F}_{{\rm{gas}}}=6\pi \rho \nu {r}_{{\rm{d}}}{v}_{{\rm{g}}}$ proportional to the gas density ρ and its kinematic viscosity ν, sphere radius r_d and gas flow speed v_g relative to the grain. By equating it with the weight of the particle ${m}_{{\rm{d}}}g$ one obtains a first order estimate of the threshold speed for detaching a grain from a surface. A more rigorous approach takes into consideration the adhesion force and the effect of the surface roughness [3, 4].

It is conceivable that if dust is transported and deposited by the force of wind gusts, it can also be removed from a surface by the same physical process. In fact self-cleaning of dust from solar panels and surfaces of rovers cruising on the surface of Mars has been well documented in numerous photographs. Such a phenomenon is called cleaning event [24]. Removal of dust from a surface by blowing gas can be effective if two conditions are met, according to the above formula: the speed and the density of the flowing gas are large enough to provide a strong lift off force to the microparticles. Such studies have been conducted in gas at low pressure similar to the Martian atmosphere [4]. At sub-atmospheric pressure a viable alternative to a gas jet is to produce a plasma jet by ionizing the static gas and accelerating it in an electric field. Our proposed cleaning method is based on this feature. The advantages of such a technique are multiple: the gas at the ambient low pressure is accelerated to supersonic speed (at several km s⁻¹) thus eliminating the need for compressed gas at high pressure, and since the pulsed discharge lasts for a short time (sub-millisecond) the drag force exerted by the plasma (the rate of momentum transfer) is high.

A typical device for producing dense pulsed plasma jets is the coaxial plasma gun. Plasmas produced between coaxial electrodes have been intensely investigated beginning with the late 60's with the goal of obtaining surplus energy from fusion reactions [25]. Later, their potential application in space propulsion has been recognized due to their high ion density and ejection speed resulting in a high thrust force [26]. In light of the new ambitions for human space exploration the interest for this type of discharge has been renewed recently since the magnetoplasmadynamic accelerator is one the most powerful form of electric propulsion [27]. The plasma wind force has been exploited in fusion applications related to the acceleration of microparticles to hypervelocities [28] or in removing dust floating inside a plasma reactor [29]. Hypervelocity dust particles can be used as a tool for diagnozing hot plasmas [30] or for quenching instabilities in tokamak plasmas [31].

The open circuit voltage of the clean PV cells was ${V}_{{\rm{oc}}0}^{(1/2)}=0.3\,{\rm{V}}$ when illuminating half a cell, ${V}_{{\rm{oc}}0}^{(1)}=0.6\,{\rm{V}}$ for one full cell, whereas for the array of all three cells connected in series ${V}_{{\rm{oc}}0}^{(3)}=1.4\,{\rm{V}}$. The cells were then thoroughly covered with a 1 mm layer of Martian simulant JSC Mars-1A as shown in figure 2(b) blocking completely the incident light on the cells, and insuring that ${V}_{{\rm{oc}}0}^{(i)}=0\,{\rm{V}}$ with i = 1/2, 1 and 3, respectively. The coaxial gun was mounted vertically, and centered above the cells depending on their arrangement. When operating with half a cell the other half was masked by an opaque tape. When operating with the full cell the coaxial gun was pointing towards the cell center while for the case of the three-cell array it was centered above the mid-cell. The coaxial gun was fired successively at regular time intervals of about 2 min, leaving sufficient time for charging up the capacitor. The voltage delivered by the individual cell or the cell array was monitored continuously and measured after each shot. The cleaning efficiency was inferred as the ratio ${E}^{(i)}={V}_{{\rm{oc}}({\rm{dusty}})}^{(i)}/{V}_{{{\rm{oc}}}_{0}}^{(i)}\,\times \,100( \% )$ after a series of shots, where ${V}_{{\rm{oc}}({\rm{dusty}})}^{(i)}$ is the voltage of the cell or of the cell array (i = 1/2, 1 and 3, respectively) with dust on its surface. The results are shown in figures 4(a)–(c) where measurements have been carried out for a half cell, a single cell and an array of three connected cells, respectively.

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The results for a single shot are as follows: ${E}^{(1/2)}=37$%–$18 \%$ (figure 4 (a)) and ${E}^{(1)}=18$%–$15 \%$ (figure 4 (b)) for the range of distances between 5 and 11.5 cm, respectively. At an intermediate distance of the above range, i.e. at 9 cm, ${E}^{(3)}=20 \%$ (figure 4(c)). After a few shots and at the closest distances, between 5 and 9 cm, ${E}^{(1/2)}\approx 99 \%$ which means that a total cleaning was rapidly obtained. For obtaining the same cleaning efficiency at 11.5 cm, 16 shots were required. We note that the number of shots increases exponentially with distance in order to obtain a complete surface cleaning. For the single cell ${E}^{(1)}\approx 99 \%$ after 6 to 8 shots at a distance between 5 and 9 cm, while at 11.5 cm about 18 shots were needed. In the case of three cells the efficiency increases slowly with the number of shots at distances of 8 and 9 cm, reaching a saturation value ${E}^{(3)}=80 \%$ after 20 shots. The partial cleaning obtained in the setup with three cells is expected as the side cells were not directly exposed to the plasma jet. However, the shock wave produced by the fast propagating plasma jet is reflected along the surface of the cells and entrained the dust particles in a sideways motion.

An alternative method for inferring the cleaning efficiency consists in weighing pre- and post-plasma exposure some samples whose surfaces were covered with dust. The coaxial gun muzzle was placed 1 cm far from each sample and the center axis of the plasma jet was at about 1.5 cm from the surface. In this case the plasma jet was parallel with the surface [36]. Several identical plates made of glossy cardboard with an area 29.61 cm² ($51.5\times 57.5$ mm²) were fully covered with dust simulant JSC Mars-1A. The mass of a cardboard plate was 1.1772 g. The mass of dust deposited on a sample varied between 0.4997 and 0.6029 g. The mass measurements were carried out with a high precision balance having an accuracy 10⁻⁴ g.

The use of the glossy cardboard demonstrates that the technique works with other types of surfaces as well and it gives an indication of the precise dust quantity that can be removed. Weight measurements with this accuracy are possible only within some limited mass ranges allowed by the high precision balance. The cardboard sheets are light whereas the PV cells are two heavy compared with the dust deposited on their surface.

The cleaning efficiency was measured considering the total weight of each sample including that of the dust: $E=[1-({M}_{{\rm{dusty}}}-{M}_{{\rm{clean}}})/{M}_{{\rm{dust}}}]\times 100\,( \% )$, where M_dusty and M_clean are the masses of the sample with and without dust, respectively, and M_dust is the initial mass of dust on the sample.

At 1 kV E increases with roughly 10%– $15 \%$ per shot, as shown in table 2. At 2 kV the first shot achieved $E=82.3 \%$, while for the next two shots E increased by $\approx 7 \%$. It should be noted that at 2 kV the released energy into the discharge is larger by a factor of 4 compared to the 1 kV shot. For 1.5 kV shots the efficiencies are approximately in-between those obtained at 1 and 2 kV.

One important feature of this cleaning technique is the use of a high voltage in the few kV range (only 1–2 kV) which implicitly requires a relatively low amount of stored energy. At 1 kV the 500 μF capacitor stored 250 J and given the peak value of the pulsed current obtained, the corresponding peak power was 7 MW. The goal was to use as little energy as possible and the trade-off is between choosing the charging voltage of the capacitor (or energy level) and the generation of sufficiently high discharge current at a given gas pressure in order to produce enough plasma thrust for pushing the dust particles.

Coaxial guns are known for electrode sputtering due to the high radial electric fields. An additional benefit of working at 1 kV is keeping the sputtered material at low levels as we found no significant contamination on the surface of the PV cells after many shots. It should be pointed out however that contamination due to electrode erosion is less of an issue for surfaces covered with a thick layer of dust since the detached material from the gun electrodes collides first with the dust particles, and thereafter with the surface.

Another aspect is that the electromagnetic noise associated with the flowing pulsed currents of only a few kA did not interfere with the proper functioning of the PV cells or other pieces of electronic equipment nearby. Cleaning of the solar panels can be achieved by mounting the coaxial plasma gun on a mobile robotic arm. Firing the plasma jet at an angle could guide the ejected dust along a controlled direction until all dust particles would eventually be pushed out of the cells surface.

A comparison between surfaces with different areas and having different cleaning efficiencies is not straightforward, as is the case of the PV cells and the cardboard sample used in the experiment. In order to make such a quantitative evaluation a new physical quantity is introduced: the CE which is defined as the cleaning efficiency multiplied by the area of the cleaned surface: ${\rm{CE}}=E( \% )\cdot {10}^{-2}\cdot {S}\,$ $({\mathrm{cm}}^{2})$. Basically, CE is the same when cleaning two different areas with 1 cm² and 2 cm² but with 100% and 50% efficiency, respectively.

The cleaning effectiveness is evaluated in the case of three consecutive shots (of figure 4) for half a PV cell, one full cell and three connected cells at 1 kV and 9 cm distance: ${\rm{CE}}=12.5,16.3$ and $23.8 \%$ cm², respectively. In the cases of the cardboard sample (for 1, 1.5 and 2 kV) the three consecutive shots produce the following values: ${\rm{CE}}=11.6,16.6$ and $29.6 \%$ cm², respectively. One can see that at 1 kV half of the PV cell ($E=93.5 \%$ and S = 13.34 cm²) is more effectively cleaned than the cardboard sample ($E=39.2 \%$ and S = 29.61 cm²). On the other hand, the cardboard sample is roughly as effectively cleaned at 1.5 kV ($E=61.2 \%$ and S = 29.61 cm²) as one full PV cell at 1 kV ($E=56.0 \%$ and S = 26.68 cm²).

Differences in the cleaning efficiencies can arise from the tribological properties of the surface. A direct determination of the friction coefficient has been carried out using a standard CSM ball-on-disc tribometer equipped with a 6 mm diameter saphire ball and set at 0.25 N applied force: for the PV cell ${\mu }_{{\rm{PV}}}=0.19\pm 0.02$ and for the glossy cardboard sample ${\mu }_{{\rm{cardboard}}}=0.04\pm 0.01$.

In order to asses the validity of this proposed cleaning technique from an energy budget point of view, an estimate of the consumed energy for cleaning a given area relative to the solar energy produced by the same area is evaluated. We consider here solar cells with an area 83 cm², similar with that of the three connected PV cells of our experiment. The total peak irradiance at the surface of Mars varies largely depending on sun elevation, amount of dust in the atmosphere, seasonal variation and direct and diffusive irradiation. An average value is however provided by Haberle et al in [37] for the Viking Lander 1 site: 3 kW h m⁻² per day. With state of the art triple junction GaAs solar cells having a 30% efficiency, as those produced for space applications, a total electrical solar power of 900 W h m⁻² per day can be obtained, which is equivalent to 3.24 MJ m⁻² or 324 J cm⁻². A PV array with an area 83 cm² would therefore produce  26.9 kJ daily. If 20 shots will be used to clean this array then 5 kJ will be needed (at 250 J per shot corresponding to 1 kV shots) which represents about 18.6% of the daily energy production rate. With this amount of energy only 5 shots will be possible at 2 kV, but in this case the removal efficiency is also higher. The operation of the coaxial gun seems therefore feasible. However this situation is not encountered often because strong dust storms which would completely burry the solar cells in sand are not produced on a daily base, and therefore a thorough cleaning of the solar cells would be performed once every period.

The operation of our coaxial gun with prefilled gas at a few torr can be well described by the snow plow model [38]. In this approach a thin plasma sheath is formed at the back of the electrodes and travels along the gun axis as an ionization shock waves towards the front end of the gun. Numerical simulations carried out for the parameters of our experiment have produced results consistent with the measurements, i.e. the plasma plume speed in the range of 1–5 km s⁻¹ and peak discharge currents of 6–12 kA [39]. This regime is different from the deflagration operation mode induced by puffing gas inside the coaxial gap with electrodes biased at tens of kV [40].

In order to characterize the ejected plasma the speed of the plume has been imaged with an ICCD camera. Figure 5 shows the sequence of images (a)–(f) recorded at different moments from the time zero of the discharge current. The average plasma plume speed was 1.4 ± 0.2 km s⁻¹ obtained at 1 kV and 5 Torr, and is a factor of 5 larger than the sound speed in CO₂ (∼285 m s⁻¹). For 1.5 kV the speed of the plasma jet was 1.6 ± 0.3 km s⁻¹ while at 2 kV it was 1.9 ± 0.3 km s⁻¹. The rapidly expelled plasma jet from the gun nozzle shown in figures 5(a) and (b) is pushing against the inert gas and creates a shock wave observed in figures 5(c) and (d). The shock wave is moving axially and expands transversally as seen in the images (e) and (f) of figure 5. It is the collision of the shock wave and its sideways expansion that impinges upon the dust particles situated on the PV cells at several centimeters from the gun axis. However, the dust which is relatively far positioned and interacts little with the plasma is not affected and stays on the surface as seen in figure 2(c) where a dust layer in the shape of a ring is not removed.

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In the pressure range 1–5 Torr the discharge current had a peak value of 7 kA at 1 kV and 14 kA at 2 kV, while the discharge period was approximately 350 μs, as shown in figure 6(a). The peak electron temperature was found to be ${T}_{{\rm{e}}}\simeq 10$–12 eV while the peak electron density was ${n}_{{\rm{e}}}\simeq 7\times {10}^{20}$ m⁻³–10²¹ m⁻³ for 1 kV shots, as shown in figures 6(b) and (c), respectively. In the case of 2 kV shots ${T}_{{\rm{e}}}\simeq 11$–14 eV, while ${n}_{{\rm{e}}}\simeq {10}^{21}$ –$2\times {10}^{21}$ m⁻³. For shots at 1.5 kV ${T}_{{\rm{e}}}\simeq 10$–13 eV, and ${n}_{{\rm{e}}}\simeq 9\times {10}^{20}$ –$1.5\times {10}^{21}$ m⁻³. While the ion temperature has not been measured, it is supposed that the ions are cold (${T}_{{\rm{i}}}\ll 1$ eV) and the ion heat flux to the surface is negligible. The mean free path of CO₂ molecules at 5 Torr is $\approx 12\,\mu {\rm{m}}$ while the Debye length for the measured plasma parameters is ${\lambda }_{{\rm{D}}}\approx 0.6\mbox{--}0.9\,\mu {\rm{m}}$.

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The plasma drag force exerted on a spherical dust particle by an ionized gas is [28, 41]:

$$\begin{eqnarray}&&{F}_{{\rm{plasma}}}=2\pi {r}_{{\rm{d}}}^{2}{k}_{B}{T}_{{\rm{i}}}{n}_{{\rm{i}}}{G}_{0}(s),\end{eqnarray} \tag{ 4 }$$

where

$$\begin{eqnarray*}&&{G}_{0}(s)=\left({s}^{2}+1-\displaystyle \frac{1}{4{s}^{2}}\right){\rm{erf}}(s)+\left(s+\displaystyle \frac{1}{2s}\right)\displaystyle \frac{\exp (-{s}^{2})}{\sqrt{\pi }}\end{eqnarray*}$$

and

$$\begin{eqnarray*}&&s=\sqrt{\displaystyle \frac{{m}_{{\rm{i}}}{v}_{{\rm{p}}}^{2}}{2{k}_{B}{T}_{{\rm{i}}}}},\end{eqnarray*}$$

${k}_{B}{T}_{{\rm{i}}}$ is the ion temperature (in our case T_i =  0.025 eV), n_i is the ion density (n_i = n_e), and v_p is the plasma jet speed. The force is numerically simulated and shown in figure 7. It takes into account the collisional ion drag which depends on the plasma jet speed, the plasma density and the dust radius and mass. Since the dust particles are much larger than the plasma screening length (${r}_{{\rm{d}}}\gg {\lambda }_{{\rm{D}}}$) the orbital ion drag force which arises from the long range Coulomb interactions of ions with a charged dust particle is neglected [42]. In fact ${\lambda }_{{\rm{D}}}\lt 1\,\mu {\rm{m}}$ and ${r}_{{\rm{d}}}\geqslant 5\,\mu {\rm{m}}$ for 99% of the dust inventory, as shown in table 1.

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The plasma drag force F_plasma relative to the dust weight ${m}_{{\rm{d}}}g$ is evaluated for the following plasma jet densities: ${n}_{{\rm{i}}}=7\times {10}^{20}$, $1.5\times {10}^{21}$ and $2\times {10}^{21}$ m⁻³. Also the dust weight has been considered on Earth and on Mars where the gravitational acceleration is about 2.6 times lower.

On Earth, for the smallest dust particle with a diameter of 1 μm ${F}_{{\rm{plasma}}}/{m}_{{\rm{d}}}g$ is $\approx {10}^{8}$ and $\approx {10}^{10}$ for the lowest and highest plasma densities considered, respectively. As the diameter of the dust grain increases up to 1 mm, the ratio of forces drops quickly to $\approx 1.4\times {10}^{2}$ and $\approx 6.3\times {10}^{3}$, for the two cases. On Mars however, dust lift off by the plasma drag force seems to be much more effective. At the lowest plasma density and for the 1 mm dust grain, the plasma drag force is over 3 orders of magnitude higher then its weight ($\approx {10}^{3}$), while at the highest plasma density this ratio goes to $\approx 5.6\times {10}^{4}$. At the same time, for the 1 μm dust grain the force ratio is between $\approx {10}^{9}$ and 10¹¹, for these two plasma densities. Similar drag force ratios are observed when comparing the following two cases: the lowest plasma density (i.e. $7\times {10}^{20}$ m⁻³) and Mars gravity with the mid-value plasma density (i.e. $1.5\times {10}^{21}$ m⁻³) and Earth gravity. As a general remark we can assert that the plasma wind force is many orders of magnitude larger than the dust weight in all discharge conditions that we tested, while for the largest dust grains it is sufficiently high in order to achieve a good surface cleaning.