Page:Solar wind.djvu/6

order 10^-1 of the steady field. Acceleration of planetary photoions at low latitudes may occur in this case by a magnetic pumping mechanism (Alfvén and Falthammar, 1973), with the average ion velocity approaching the flow velocity $v_{0}$ according to the relation:

$v=v_{0}(1-e^{t/T})$

where t is the average time from creation of an ion in the flow, and $\tau$ is the characteristic acceleration time given by:

$\tau \cong (\Delta B/B)^{-2}T_{eye}$

with $\Delta B$ the average transverse field noise component, B the average field magnitude, and $T_{eye}=2\pi m/eB$ the cyclotron period of the ion species of mass, m. Calculation of the resulting average ion velocities at the equatorial terminator for He⁺ on Venus and O⁺ on Mars indicate that these ions have only been accelerated to a few percent of the flow velocity as they cross the terminator. Reduction of ionopause heights at the equator to achieve equality in equatorial and polar drag factors requires a reduction in effective equatorial obstacle radius relative to polar obstacle radius of 650 km for Venus and 250 km for Mars. In addition to this possible asymmetry in the ionopause height from pole to equator, there may be a difference in the height of the shock above the polar and equatorial ionopause boundaries caused by a difference in plasma compressibility. For flow around the ionopause in the equatorial plane, the steady field is nearly parallel to the flow velocity, and the compression and expansion of the plasma along the streamlines is not strongly affected by the magnetic field. Moreover, any transverse magnetic noise component will tend to isotropize the pressure, and instabilities in the flow with $v\|B$ will enhance this effect. The gas in this case should act as an ideal gas with ratio of specific heats $\gamma$ = 5/3. However, for flow over the poles, the streamlines are nearly orthogonal to the magnetic field along the flow tube, and compression and expansion of the plasma involves the magnetic pressure directly. In this case, the ratio $\gamma$ may be closer to 2. This difference in compressibility will cause a significant asymmetry in the shock altitudes from pole to equator even for a completely symmetry ionopause, and the ionopause height asymmetry described above will add to the total shock asymmetry.

The shock positions corresponding to several different Mach numbers for $\gamma$ = 5/3 and 2 have been calculated by Spreiter et al. (1966) for the Earth's magnetosphere, and are shown in figure 4. Direct scaling of this figure to Mars and Venus without inclusion of the ionopause height asymmetries shows that the shock distances at the terminator could differ from pole to equatorial terminator by 1000 km for Mars and 1500 km for Venus due to the compressibility effect alone. The subsolar shock distances extrapolated from the terminator shock distances could differ by 500 km for Mars and 750 km for Venus, leading to obstacle height estimates differing by 350 km for Mars and 500 km for Venus.

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