Since the response time of the Martian atmosphere is on the order of a second, the blowing of dust across the surface and dust particle collisions must continually build up negative charge in the dust devil in order to prevent rapid shielding of the space charge density. Additionally, negatively charged dust must be kept separate from positive charges, which are assumed to be mostly confined to the surface, if only the dust is charged negatively. This charge separation is assumed to occur through convective motion and possibly by gravitational settling of positive dust. The negative space charge density, by Gauss' Law, will give rise to an electric field. By Ohm's Law, an electric field in a finitely conducting medium gives rise to a current. For the lifetime of the dust devil, the persistence of the negative charge density supplies a continuous current source. In this way the dust devil-ground system can be thought of as a current generator. In contrast, in terrestrial thunderstorms the current generator is located entirely within the cloud. Colliding ice particles of different sizes acquire different charges [e.g., Baker and Dash, 1994], and these different charges are kept separated by convective motion and gravitational settling.
The strength of the current generator is given by Volland [1984] as
where
The subscripts "I" and "a" refer to values inside and outside the dust devil, respectively. This equation shows that the strength of the current source is proportional to the product of the charge content inside the cloud and the ambient conductivity inside the cloud. The conductivity inside the cloud is typically smaller than the conductivity of the ambient atmosphere due to the attachment of ions to dust particles. The effective charge of the dust devil as measured by an observer outside the dust devil, Qeff, is only a fraction of the total charge content of the dust devil, Qi. The strength of the current source is, therefore, equal to this effective charge divided by the relaxation time of the ambient atmosphere, t. In order to estimate the strength of the current source, we need to know how the conductivity inside the dust devil relates to the conductivity of the ambient atmosphere, which must be determined through measurements.
Some of this current flows into the dust devil from the ground. The direction of current flow is usually defined as the direction positive charge moves, in the same direction at the electric field. Since the dust cloud is negatively charged, the electric field and current flow from the surrounding environment to the dust devil. The dust devil, then, is, in effect, a current sink. However, since the conductivity increases exponentially with height, a significant part of the current flows from the ionosphere to the top of the dust devil. Volland [1984] and Tzur and Roble [1985] showed that a significant portion of the current created from the positive charge regions of terrestrial thunderstorms flows from the cloud top to the ionosphere due to the exponentially increasing atmospheric conductivity.
For a single current generator located in an atmosphere with an exponentially increasing conductivity a distance h above a perfectly conducting surface, the efficiency of the current generator to produce a global electric circuit depends on the ratio between the electric conductivity at the height h and the conductivity just above the ground. The fraction of the current flowing into the ionosphere is given by Volland [1984] as
Assuming a conductivity scale height of 10 km, only 20% of the total current flows from the ionosphere for smaller dust devils. For larger dust devils, the fraction approaches ½. However, these fractions have been calculated neglecting the effect of aerosols on the conductivity near the surface which would lower the ground conductivity in the numerator and increase the fraction of the current flowing from the ionosphere.
Now we can develop a picture for a nominal global electric circuit on Mars. On the day side, solar ultraviolet radiation liberates electrons from surface materials. These photoelectrons form negative ions which are distributed into the atmosphere by atmospheric motion. Additionally, winds blow mostly silicate dust across the surface, charging the dust particles negatively. Convective motion during the warmest part of the day forms dust devils and carries negative dust and ions a few kilometers into the atmosphere. A continuous supply of dust ensures a continuous space charge density for the lifetime of the storm. This negative space charge density creates electric fields which point from the ionosphere down to the dust devil and from the surface up. Negative ions pulled downward by the ground-to-dust devil electric field are hindered by lower conductivity near the surface in addition to the upward convective motion of the atmosphere. Positive ions in the lower atmosphere would contribute to a ground-to-dust devil current. Current flowing from the ionosphere down to the dust devil is not hindered by convection so that both downward flowing positive ions and upward moving negative ions contribute to the ionosphere-to-dust devil current.
If more current flows from the ionosphere than from the ground to the dust devil, this would have the net effect of giving the ionosphere a negative potential with respect to the surface. Therefore, in the steady state, charge would leak from the ground to the ionosphere due to a vertically upward fair weather electric field, in contrast to Earth's downward fair weather electric field. Additionally, this fair weather electric field would be reinforced by Grard's [1995] photoionization of the surface during the daytime.
The value of the potential difference between the ground and the ionosphere is given by
where all quantities are globally averaged. The globally averaged current, I, is related to the current flowing from the ionosphere to an individual dust devil times to number of dust devils occurring at any particular time. The value of the ionospheric current is highly uncertain. The charge content of a typical dust devil may be between 0.01 C and 10 C. Additionally, the ratio of the conductivity inside the dust devil to the ambient atmospheric conductivity is unknown. Finally, the ratio of the atmospheric conductivity just above the ground to that at the height of the negative charge center has only been simply estimated. Also, as in the case with Earth, there have been no global simultaneous observations of dust devils on Mars, so the number of current sources at any particular time is unknown. Therefore, even though we have a rough estimate for the global resistance, the globally integrated current, and, hence, the ground-ionosphere potential difference remain undetermined.
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Variations in the Martian Global Electric Circuit,
Conclusions, and References