The electrification of wind-blown sand on Mars and its
implications for atmospheric chemistry

Jasper F. Kok1,2,* and Nilton O. Renno1,2
1
  Applied Physics Program, University of Michigan, Ann Arbor, MI, 48109, USA.
2
  Atmospheric, Oceanic, and Space Sciences, University of Michigan, Ann Arbor, MI,
USA.

ABSTRACT

   Wind-blown sand, or 'saltation,' creates sand dunes, erodes geological features, and
could be a significant source of dust aerosols on Mars. Moreover, the electrification of
sand and dust in saltation, dust storms, and dust devils could produce electric discharges
and affect atmospheric chemistry. We present the first calculations of electric fields in
martian saltation, using a numerical model of saltation that includes sand electrification,
plasma physics, and the adsorption of ions and electrons onto particulates. Our results
indicate that electric discharges do not occur in martian saltation. Moreover, we find that
the production of hydrogen peroxide and the dissociation of methane by electric fields are
less significant than previously thought. Both these species are highly relevant to studies
of past and present life on Mars.




                                                                                         1
1. Introduction
    Wind-blown sand, or 'saltation,' creates sand dunes and ripples, and causes wind
erosion [Bagnold, 1941]. Moreover, the impact of saltating sand particles on the ground
ejects dust aerosols into the atmosphere on both Earth and Mars [Shao, 2000; Almeida et
al., 2008], which greatly affects the climate of both planets [Shao, 2000; Renno and Kok,
2008].
    Wind-blown sand and dust storms on Earth produce electric fields (E-fields) ranging
from 1 to 200 kV/m [Schmidt et al., 1998; Renno and Kok, 2008]. These large E-fields
are produced by charge transfer during collisions between sand and/or dust particles and
between saltating sand and the surface [Renno and Kok, 2008]. The physical mechanism
that governs this charge transfer is poorly understood, but laboratory and field
experiments indicate that saltating sand particles charge negatively while the soil surface
charges positively [Schmidt et al., 1998; Kok and Renno, 2008; Renno and Kok, 2008].
    On Mars, electrification of wind-blown sand and dust storms could trigger electric
discharges [Eden and Vonnegut, 1973; Melnik and Parrot, 1998] and reduce the wind
stress required to lift particles from the surface [Kok and Renno, 2006]. Moreover, recent
studies suggest that large E-fields predicted in wind-blown sand and dust storms [Melnik
and Parrot, 1998; Farrell et al., 2003; Zhai et al., 2006] produce energetic electrons
[Delory et al., 2006] that catalyze the production of hydrogen peroxide [Atreya et al.,
2006], a strong oxidant hostile to life as we know it. Indeed, these studies suggest that the
atmosphere becomes supersaturated, causing hydrogen peroxide snow to precipitate onto
the surface [Atreya et al., 2006], which provides a possible explanation for the reactive
soil and the unexpected absence of organics at the Viking landing sites [Oyama et al.,
1977]. In addition, energetic electrons produced by strong E-fields are predicted to
dissociate methane [Farrell et al., 2006]. This is important because methane has been
detected on Mars and is a possible marker of biological activity [Formisano et al., 2004].
Both the production of hydrogen peroxide and the destruction of methane in martian
wind-blown sand and dust storms are thus highly relevant to studies of past and present
life on Mars.
    In the absence of direct measurements, most researchers have used laboratory
experiments and numerical models to investigate the generation of E-fields in martian
saltation and dust storms. Eden and Vonnegut [1973] reported that shaking a flask of sand
with CO2 at martian pressure produces electric discharges. The occurrence of electric
discharges in martian dust storms is also predicted by numerical studies [Melnik and
Parrot, 1998; Farrell et al., 2003; Zhai et al., 2006]. However, these numerical studies
have two important shortcomings. First, because the charge transfer between colliding
sand/dust particles is poorly understood, these numerical studies have used charging
models that are not constrained by either theory or experiments [Renno and Kok, 2008].
Second, these studies have neglected the effects of E-fields on atmospheric conductivity.
Fortunately, progress has recently been made on both these issues. Indeed, Delory et al.
[2006] developed a plasma physics model that accounts for the production of energetic
electrons by E-fields and the subsequent ionization of martian air, while we recently
developed an improved parameterization of sand/dust electrification that is constrained
by E-field measurements in saltation on Earth [Kok and Renno, 2008].
    In this Letter, we build on the studies of Delory et al. [2006] and Kok and Renno
[2008] and report the first calculations of E-fields in martian saltation. Our study is an



                                                                                           2
improvement over calculations of E-fields in dust storms [Melnik and Parrot, 1998;
Farrell et al., 2003; Zhai et al., 2006] for three reasons: (i) our parameterization of the
charge transfer between colliding sand/dust particles is constrained by measurements
[Kok and Renno, 2008], (ii) we account for the effects of E-fields on atmospheric
conductivity [Delory et al., 2006], and (iii) we account for the adsorption of ions and
electrons to particulates [Draine and Sutin, 1987; Jackson et al., 2008]. We find that
electric discharges are unlikely to occur in martian wind-blown sand, and that the
production of hydrogen peroxide and the dissociation of methane by E-fields are less
significant than previously thought.

2. Model description

   Our numerical model of saltation is described in detail in Kok and Renno [2008], and
explicitly simulates the motion, concentration, and electric charging of saltating sand.
Our model simulates saltation in the absence of suspended dust, as is representative of
saltation on dunes, and its predictions are in good agreement with measurements of the
particle mass flux and E-field in terrestrial saltation [Kok and Renno, 2008]. Here, we
apply our model to Mars and calculate the E-field in saltation as described in Kok and
Renno [2008]. We assume that saltating particles have diameters Dp = 100 μm and
density of 3000 kg/m3 [Claudin and Andreotti, 2006], and take the atmospheric pressure
(P) and temperature (T) as 627 Pa and 227 K. As described in more detail below, we
expand the model by including the effects of E-fields on atmospheric conductivity and
accounting for the adsorption of ions and electrons to particulates.

2.1 Limits to Electric Fields on Mars

   On Earth, sand and dust electrification can produce large E-fields [Renno and Kok,
2008] because air is a good insulator and the E-field at which electric discharges occur is
large (about 3 MV/m). The situation is quite different on Mars. There, E-fields are
limited by large increases in atmospheric conductivity when E-fields become sufficiently
large to ionize CO2 [Delory et al., 2006], and by electric discharges thought to occur at
~20-25 kV/m [Melnik and Parrot, 1998].
   The E-field at which the insulating properties of a gas break down and an electric
discharge occurs is described by the 'Paschen law' [Raizer, 1997; Fridman and Kennedy,
2004], and depends on the gas pressure and the distance of the "electrodes" (or centers of
charge) between which the discharge occurs,
                     BPT0 / T
         E br =                         ,                                     (1)
                C + ln (Pz cat T0 / T )
with C = ln[A / ln (1 / γ + 1)] . The constants A = 15 m-1Pa-1 and B = 350 Vm-1Pa-1 define
the Townsend ionization coefficient α (see page 56 in Raizer [1997]) at T0 = 293 K for a
CO2 atmosphere. We take the secondary Townsend ionization coefficient γ as 0.01
[Raizer, 1997; Fridman and Kennedy, 2004]. Note that equation (1) does not include the
effect of sand and dust on the breakdown E-field. In the case of negatively charged
saltating sand over a positively charged soil surface [Kok and Renno, 2008], the surface
represents the anode, but the cathode is not well defined. We approximate the distance



                                                                                              3
from the cathode to the anode by the height zcat below which 50 % of the charge on
saltating sand is contained. The results reported here are not sensitive to this
approximation. For typical martian saltation, we find zcat = 30 cm and Ebr = 43 kV/m,
which is significantly above the ~20-25 kV/m value at which larger-scale discharges in
dust storms are thought to occur [Melnik and Parrot, 1998].
   The second mechanism limiting the generation of E-fields in martian saltation and dust
storms is the increase in atmospheric conductivity due to ionization by energetic electrons
[Delory et al., 2006]. The conductivity of the near-surface martian atmosphere is due
mostly to mobile ions [Molina-Cuberos et al., 2002], and equals [e.g., Michael et al.,
2008]
        σ = e( K e n e + K − n − + K + n + ) ,                                   (2)
where e is the elementary charge, and Ke, K–, K+, ne, n–, and n+ are the mobilities and
number densities of free electrons and negative and positive ions, respectively. We take
the ‘background’ concentrations of electrons and ions to be ne,0 = 5×106 m-3 and n-,0 = n+,0
= 3×109 m-3 [Molina-Cuberos, 2001, 2002; Delory et al., 2006]. Charges in the martian
atmosphere decay due to the adsorption of electrons and ions of opposite polarity, which
is a complex process [Draine and Sutin, 1987; Michael et al., 2008]. However, the
conductivity defines the approximate time scale trel = ε 0 / σ , where ε0 is the electric
permittivity, with which charges in the martian atmosphere decay. A simplified
expression of this charge decay is thus
         q(t + Δt ) = q(t ) exp(− Δt / t rel ) ,                                 (3)
where q(t) is the charge of the particle (or the surface) at time t, and Δt is the model time
step. As the atmospheric conductivity increases, the charge relaxation time trel decreases,
thereby also decreasing the charge held by saltating particles and the soil surface.

2.2 Plasma Physics

   Electric fields on Mars are thus limited by the occurrence of electric discharges
(Equation 1) and by increases in atmospheric conductivity (equations 2 and 3). As
electrons are accelerated from the top cathode (the top of the saltation layer) towards
anode (the surface), they can ionize CO2 and produce additional free electrons, but can
also be absorbed through dissociative attachment to CO2 [Delory et al., 2006] and
collisions with saltating sand particles. The electron concentration in the saltation layer is
then approximately given by [Raizer, 1997; Delory et al., 2006; Jackson et al., 2008]
                      ⎧⎪ zcat ⎡    k ( z )N CO2 1                    ~ ⎤       ⎫⎪
        ne = ne,0 exp⎨ ∫ ⎢α ( z ) − da         − πD p2 nsalt ( z ) J ( z )⎥ dz ⎬ ,     (4)
                       ⎪⎩ 0 ⎣          vd (z )  4                         ⎦ ⎪⎭
where NCO2 is the CO2 number concentration, vd is the electron drift velocity and is
obtained from Figure 4a in Delory et al. [2006], nsalt is the concentration of saltating sand
                                                                              ~
particles as predicted by our saltation model [Kok and Renno, 2008], and J is the
normalized cross section for a collision occurring between an electron and a saltating
                                                                                    ~
sand particle. Since the sand particles are strongly negatively charged, we have J < 1,
following equation (3.5) in Draine and Sutin [1987] and using equation (1) in Jackson et
al. [2008] to obtain the electron temperature as a function of the E-field. Furthermore, we



                                                                                             4
obtain the dissociative attachment rate constant kda from Figure 4d of Delory et al.
[2006], who solve the electron energy distribution to find kda as a function of the E-field.
Finally, we use Figure 4b of Delory et al. [2006] to obtain the Townsend ionization
coefficient α, which describes the multiplication of electrons per unit length due to
ionizing collisions as the initial population (ne,0) is accelerated from the cathode to the
anode [Raizer, 1997; Fridman and Kennedy, 2004]. This electron population becomes
increasingly energetic as the E-field rises, and can produce positive ions (mainly CO2+)
through electron impact ionization, and negative ions (mainly O-) through dissociative
attachment [Delory et al., 2006]. The CO +2 ions quickly react with CO2, O2, and H2O to
form H3O+·(H2O)j with j ≥ 1, while O- ions attach to CO2, forming CO 3- , which is
hydrated to CO 3- ⋅ (H 2 O ) j [Molina-Cuberos et al., 2001, 2002]. The concentration of
negative ions in the saltation layer is then described by [Michael et al., 2008]
                        z
        dn − N CO2 ne cat                                n K E
              =          ∫ k da ( z )dz − n − n + k rec − − − surf ,          (5)
          dt      z cat 0                                   z cat
where NCO2 is the CO2 number concentration, and Esurf is the surface E-field. The first
term on the right-hand side denotes the production of negative ions through dissociative
attachment to CO2 [Delory et al., 2006], the second term describes the recombination of
positive and negative ions [Molina-Cuberos et al., 2002], and the final term accounts for
the adsorption of negative ions to the positively charged soil surface. We neglect other
processes that are insignificant compared to these ion loss processes, such as
photodetachment [Molina-Cuberos et al., 2001; Michael et al., 2007] and the attachment
of negative ions to the strongly negatively charged saltating grains [Draine and Sutin,
1987], and we neglect the transport of ions out of the saltation layer. Furthermore, we
take the ion recombination rate constant as krec = 1.5×10-13 m3sec-1 [Molina-Cuberos et
al., 2002], and calculate n– and n+ iteratively using n+ = n– + ne [Molina-Cuberos et al.,
2001] and dn– /dt = 0 in steady-state. We then use the ion and electron concentrations to
calculate the atmospheric conductivity using (2), with ion and electron mobilities derived
from equations (5) and (7) of Michael et al. [2008], assuming the dominant ions to be
H3O+·(H2O)3 and CO 3- ⋅ (H 2 O )2 [Molina-Cuberos et al., 2001, 2002].

3. Results and Discussion

   We implement the plasma physics processes discussed above in the numerical model
of saltation described in [Kok and Renno, 2008], and iteratively calculate the E-field, the
atmospheric conductivity, and the motion, charging, and concentration of saltating sand
until steady-state is reached. As on Earth [Kok and Renno, 2008], the E-field in martian
saltation peaks at the surface and decreases monotonically with height (inset of Figure 1).
On Mars, the rate of decrease of the E-field with height is less than on Earth because the
smaller gravitational and aerodynamic drag forces cause the saltation layer to be thicker
there [Almeida et al., 2008].
   As expected, the E-field in the saltation layer increases with wind speed (Figure 1).
The resulting increasingly energetic electron population starts dissociating CO2 (i.e.,
e + CO 2 → CO + O - ) at a few kV/m and ionizing CO2 (i.e., e + CO 2 → 2e + CO +2 ) at ~10
kV/m [Delory et al., 2006]. The resulting increase in the concentration of ions and


                                                                                               5
electrons with the E-field (Figure 2) enhances the atmospheric conductivity, which
neutralizes the charges on saltating particles and the surface (see equation 3), thereby
limiting further increases in the E-field. Indeed, we find that this negative feedback limits
the E-field in martian saltation to ~15–20 kV/m. This upper limit on the E-field in
martian saltation is relatively insensitive to uncertainties in model parameters and the
model methodology, because of the sharp dependence of the production rate of ions on
the E-field (see Delory et al. [2006], figure 4d).
   Since the maximum E-field of ~15-20 kV/m is significantly below the threshold of
~43 kV/m required to initiate electric discharges (see equation 1), we conclude that such
discharges are unlikely to occur in martian saltation. However, discharges might still
occur in dust devils and dust storms for several reasons. First, the E-field required to
precipitate discharges over larger scales in dust storms is lower (see equation 1).
Moreover, the abundant presence of particulate matter in dust storms likely lowers the
background concentration of ions and electrons [Eden and Vonnegut, 1973; Michael et
al., 2008], thereby increasing the charge relaxation time and thus the E-field. Finally,
large-scale discharges in dust storms could occur at a lower E-field than predicted by the
Paschen law (equation 1) through electron runaway breakdown [Gurevich et al., 1992].
    Recent studies have predicted that E-fields of 10-25 kV/m generate plasma conditions
that produce hydrogen peroxide and dissociate methane in large quantities [Delory et al.,
2006; Atreya et al., 2006; Farrell et al., 2006]. While we here indeed find that the E-field
in saltation can exceed 10 kV/m for large wind speeds, we also find that the concentration
of ions and electrons at such E-fields is much smaller than suggested by these previous
studies (Figure 2). The difference occurs because we expanded on these previous studies
and accounted for losses of ions and electrons due to adsorption to saltating sand and the
soil surface, as well as the loss of electrons from dissociative attachment to CO2. A
separate calculation shows that the large concentration of electrons and ions predicted by
following these previous studies [Delory et al., 2006; Atreya et al., 2006] are unlikely to
occur in saltation or dust storms, because the large conductivity of the resulting plasma
limits the E-field to values well below those necessary to maintain the plasma (Figure 3).
Indeed, the charging current necessary to maintain these plasma conditions is several
orders of magnitude larger than that produced by saltation (Figure 3). Since saltation
probably plays a key role in charge generation in dust storms and dust devils [Renno and
Kok, 2008], we expect the charging current in these phenomena to be of similar
magnitude as in saltation. We therefore conclude that the concentration of ions and
electrons in martian wind-blown sand, dust devils, and dust storms, is much smaller than
previously suggested [Delory et al., 2006; Atreya et al., 2006]. The production of
hydrogen peroxide and the dissociation of methane by E-fields in these phenomena are
thus probably less significant than previously thought [Atreya et al., 2006; Farrell et al.,
2006].

4. Conclusions

   We present the first numerical simulation of E-fields in martian saltation, and find that
E-fields are limited to ~15-20 kV/m. This upper limit is imposed by the rapid increase in
atmospheric conductivity as the E-field rises and probably prevents the occurrence of
electric discharges in martian saltation.



                                                                                           6
   Furthermore, our results show that chemical reactions catalyzed by E-fields in
saltation are not as important as previously thought [Atreya et al., 2006; Farrell et al.,
2006]. Indeed, we find that the plasma in which these reactions occur cannot be sustained
because its large conductivity limits the E-field to values well below that necessary to
maintain the plasma (Figure 3). Nonetheless, the concept of electro-chemical production
of oxidants in martian saltation and dust storms, possibly through electric discharges,
remains a possible explanation for the puzzling absence of organics from the martian soil
[Oyama et al., 1977; Atreya et al., 2006] and should be investigated further.

Acknowledgements

  We thank John Barker and Robert Sullivan for useful discussions, Shanna Shaked for
comments on the manuscript, and NSF and NASA for financial support through awards
ATM 0622539 and NNX07AM99G.




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Figures




Figure 1. Simulated average E-field between the anode (the surface) and the cathode (zcat
≈ 30 cm) in Martian saltation as a function of wind shear velocity, u* = τ / ρ a , where τ
is the wind shear stress directly above the saltation layer [Shao, 2000] and ρa is
atmospheric density. The inset shows the vertical profile of the E-field for a wind shear
velocity of 2.5 m/s. The results are obtained with the numerical model of saltation
described by Kok and Renno [2008], expanded with equations (2)-(5) to account for
plasma physics processes and charge relaxation.




                                                                                            10
Figure 2. Simulated concentration of electrons (left axis and red lines) and the
enhancement of the ion concentration over the background concentration (n-,0 = n+,0 =
3×109 m-3 [Molina-Cuberos et al., 2002]; right axis and blue lines) as a function of the
average E-field between the anode and the cathode. Solid lines with circles indicate
results from our numerical saltation model [Kok and Renno, 2008], for which the anode is
at the surface and the cathode is at the height zcat (see text). For E-fields of ~5-12 kV/m,
the electron concentration decreases because of dissociative attachment to CO2 and
adsorption to sand particles, whereas for larger E-fields the electron concentration
increases due to the generation of additional electrons through ionization of CO2 [Delory
et al., 2006]. Dashed lines indicate electron and ion concentrations calculated for a
homogenous E-field over a length of 0.5 m following Delory et al. [2006] and Atreya et
al. [2006]. That is, we use equations (4) and (5) to calculate the ion and electron
concentrations, but neglect the terms in these equations that account for losses of
electrons and the loss of ions to the soil surface.




                                                                                         11
Figure 3. Simulated charge relaxation time (left axis and red lines) and charge separation
current ( I = σE ) required to sustain the E-field (right axis and blue line) against the
relaxation of charge on saltating particles and the surface, as a function of the average E-
field between the anode and the cathode. Solid lines with circles indicate results from our
numerical saltation model [Kok and Renno, 2008] for which the anode is at the surface
and the cathode is at the height zcat (see text). Dashed lines indicate results following
Delory et al. [2006] and Atreya et al. [2006], as described in the caption of Figure 2.




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