For the first phase, it is necessary to consider models of the exhaust jet. According to the SPS baseline concept review (U.S. NASA, 1978) the POTV engine assembly consists of two stages with 4 engines in the first stage and 2 engines in the second stage. Each engine has a mass flow rate F [[spi:math]] 104 kg/sec. Taking an averaging approach, one may assume as a working model an average total POTV exhaust rate F [[spi:math]] 310 kg/sec of H2O over an average exhaust cross-section of ~ 9 m at exit (average of 3 nozzles of 2 m diameter each). The exhaust speed is u ~ 4 km/sec. Once the exhaust leaves the nozzle it expands primarily isotropically away from the exhaust beam axis. Thermodynamically, this expansion is controlled by the temperature of the exhaust so that relatively more molecules have zero transverse speed and the abundance of molecules with higher transverse speeds fall off in a Gaussian fashion according to a thermal distribution. The proper treatment of the density distribution in such a thermally expanding jet in collisionless medium is by solution of the Boltzmann equation. The Boltzmann equation for the free expansion of a neutral gas with distribution function [[spi:math]] for a source distribution [[spi:math]] is given by: (1) Our source is a time-independent beam at the origin firing off exhaust molecules with speed v0 in the z-direction of a cylindrical coordinate system [[spi:math]]. A cylindrical system in velocity space [[spi:math]] is also used. The velocity distribution in the r-direction is assumed to be a Gaussian with a cut-off constant [[spi:math]]. We shall study the effect of this beam-spread constant [[spi:math]] upon the artificial auroral emission intensity. A properly 9 [[spi:math]
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