Matthew Fillingim
GPHYS 522
Final Paper
On Earth it is generally accepted that the global electric circuit is driven by thunderstorms [Wilson, 1920]. In this circuit model, thunderstorms act as electrical generators that drive currents upward. As a result, the upper atmosphere becomes positively charged with respect to Earth's surface. In the steady state, charge in the upper atmosphere leaks back to the ground through the finitely conducting atmosphere. Near Earth's surface, the atmospheric conductivity is large enough to dissipate any field on the order of minutes. Therefore, the average global electric field must be maintained by some almost continuous current source. For Earth, the dominant generator is believed to be thunderstorms [Krider and Roble, 1986]. Other sources also play a role in driving Earth's global electric circuit, but it is thought that thunderstorms are the dominant contributor.
How can knowledge of Earth's global electric circuit be applied to Mars? In order for a global electric circuit similar to Earth's to exist in the Martian atmosphere, a constant current source, or current generator must be located in a finitely conducting atmosphere. Over decades of visual observations by both orbiting spacecraft and landers, no thunderstorms have been detected on Mars. Most likely, the Martian environment is too dry and too cold for such phenomena to form. Therefore, alternate current sources must be found in order to drive the global electric circuit. Alternate current sources on Earth and their applications to the Martian environment will be investigated later. First, we will look at the possibility of the presence of a conducting atmosphere and some of the sources of atmospheric conductivity.
There are some significant differences between Earth's atmosphere and the Martian atmosphere. At the surface, atmospheric pressure on Mars is approximately 10 millibars, about 100 times less than that at Earth's surface. In Earth's environment, the 10 mbar level is at a height of 30 to 35 km. Similarly, the temperature of Earth's atmosphere at this altitude is approximately equal to the surface temperature on the day side of Mars, that is, about 250 K. For an ideal gas,
where P is the pressure, n is the number density of the gas, k is Boltzmann's constant (1.38 x 10-23 J/K), and T is the temperature. Since pressure and temperature are approximately equal, the atmospheric number density at the surface of Mars is approximately equal to that of Earth's atmosphere at 30 to 35 km, though the composition is different. We can conclude then that ion pair production rate due to cosmic rays is a few to 10 ion pairs per cubic centimeter per second depending upon solar activity [Viggiano and Arnold, 1995]. Since Mars does not have a strong global dipole magnetic field, this production rate does not change with latitude as it does in Earth's atmosphere [Volland, 1984].
Though ion pair production due to cosmic rays doesn't change with latitude, it does change over the course of a Martian year. At any location on the Martian surface, the atmospheric pressure varies by 20% or more over the course of a Martian year as a consequence of cyclic condensation of carbon dioxide at the winter pole and evaporation at the summer pole. There is a strong asymmetry between the behavior of the two hemispheres, due in part to the eccentricity of Mars' orbit and in part to systematic elevation differences between the two polar regions [Lewis, 1995]. Since the lower atmosphere is less dense, there is less pair production due to galactic cosmic rays. So we expect a yearly variation in atmospheric conductivity of ~20% superimposed on the eleven year solar cycle variation of roughly the same magnitude due to the Forbush decrease effect [Holzworth, 1995].
Within a few meters of the surface and up to about 100 meters, radioactive elements in the crust, mainly uranium, thorium, and their decay products, emit beta and gamma radiation which provides an additional source of ion pair production on Earth. Since the terrestrial planets have essentially the same bulk composition, this process almost certainly occurs near the Martian surface as well. At the surface of Earth, the ionization production rate is estimated to be ~10 cm-3 s-1 [Volland, 1984]. If we conclude that this should be about the order of magnitude expected at the surface of Mars, then the ionization rate due to cosmic rays is approximately equal to that due to radioactive crustal material at the ground level. Ionization due to radioactive isotopes would be expected to fall off very rapidly with altitude since the source material is confined to the lower surface of the atmosphere.
Due to the lack of a substantial ozone layer in the Martian atmosphere, an additional uniquely Martian source of ionization near the base of the atmosphere is the penetration of solar ultraviolet radiation to the surface. Ozone is a strong absorber of ultraviolet in the wavelength range from 200 nm to 300 nm (the Hartley continuum) [Chamberlain and Hunten, 1987]. The absence of ozone in the atmosphere of Mars allows photons with energies up to 6 eV (~200 nm and longer) to reach the surface. The work functions of many of the Martian surface minerals are between 4 and 5 eV [Grard, 1995]. Therefore, the surface minerals will emit photoelectrons due to incident solar ultraviolet radiation. Grard [1995] suggested that these free electrons attach themselves to ambient atmospheric molecules via a three-body process creating negative ions. This negative charge distribution above the positively charged surface yields an upward electric field at the surface on the order of 10-2 to 10-1 V/m by his estimates. Grard's [1995] estimates also suggested an atmospheric conductivity of 10-11 S/m near the surface, about three orders of magnitude greater that the conductivity of Earth's atmosphere near the surface, but approximately equal to the conductivity found in Earth's stratosphere. Given this conductivity, the response time of the lower Martian atmosphere, which is the ratio of the permittivity to the conductivity, is,
This vertically upward electric field would be rapidly shielded if there was not a continuous source of negative ions to the atmosphere supplied by photoelectrons created by solar ultraviolet radiation. Therefore, this effect is only important on the day side; this effect rapidly decays after sunset.
The upper most regions of Mars' atmosphere are ionized by solar extreme ultraviolet and X-rays creating an ionosphere. The ionospheric peak occurs at an altitude between 120 and 150 km with an electron number density on the order of 105 cm-3 [e.g., Kliore, 1992]. The main ambient ion at this altitude is O2+ [Hanson et al., 1977]. Mars' ionosphere is basically of the Chapman-layer type [Chamberlain and Hunten, 1987], and, thus, the physics of ion production and recombination is similar to that of the E-region of Earth's ionosphere.
Conductivity is directly proportional to the charged particle number density, n, and inversely proportional to the collision frequency of ions with neutrals, vni, i.e.,
where q is the electronic charge (1.6 x 10-19 C) and m is the mass of the charge carrier. The charged particle number density rapidly increases in the ionosphere up to the ionospheric peak while the neutral particle number density, and, hence, the collision frequency, continues to exponentially decrease with height due to hydrostatic equilibrium. Therefore, according to the above equation, the ionosphere forms a highly conductive layer at the top of the atmosphere.
Again, using the Earth as an analogy, the Martian surface conductivity may be on the order of 10-3 S/m, similar to that of Earth's surface [Volland, 1984]. However, Farrell et al. [1996] estimate that the surface conductivity could be as low as 10-8 S/m, still at least three orders of magnitude greater than the conductivity of the lower most atmosphere given by Grard [1995]. Therefore, we can conclude that the Martian atmosphere acts as a resistor between the conducting planetary surface at the bottom and the ionosphere at the top. So the leaky spherical capacitor model applied to Earth's global electrical circuit also seems to apply to the Martian environment.
Next: Variations in Conductivity with Height