causal arrival of the wave front at [[spi:math]], although the contribution of the Laguerre function must be taken into account. Hence, the key parameters in the problem are: (1) the ionospheric reflectance [[spi:math]], (2) the Alfven transit time [[spi:math]], and (3) the momentum transfer time characterized approximately by 1/ p. If the ionospheric reflec- tance approaches unity, i.e., [[spi:math]], the two contributions in (28) are of approximately equal strength and the Alfven wave velocity field switches sign as each subsequent reflection arrives at zi and there is no net wave energy dissipation, just beam energy redistribution into the magnetospheric plasma. The time constant for beam energy redistribution to the magnetosphere is the Alfven transit time [[spi:math]] if [[spi:math]], and is somewhat longer (perhaps a few transit times) if [[spi:math]] approaches unity. The momentum transfer time [[spi:math]] measures the time constant of beam energy transfer to the local plasma at the vicinity of the wave front. If [[spi:math]] there is very little reflected wave and only [[spi:math]] is important. For realistic mid-latitude ionospheres, [[spi:math]] so the only important time constants are [[spi:math]] and [[spi:math]]. Thus, it is of interest to examine the time constant [[spi:math]] for the COTV beam. By definition, [[spi:math]] (34) where mA is defined by (19). Thus, it is somewhat unfortunate that this important time constant is subjected to the uncertainties concerning the difference between sheet-source and distributed-source models of beam-magneto- sphere interactions discussed earlier. Recognition of this feature indicates that distributed-source models must be looked into in the future. In the case of an ion engine beam, mA is related to the exhaust flux FA and the beam speed 27
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