(67) (68) at R=5. Figure 18 shows the product [[spi:math]] v at L [[spi:math]] R = 5 as a function of energy for various charged-particle species, where [[spi:math]] is the cross section for charge exchange and v is the velocity of the charged particle. The product [[spi:math]] v represents a probability of loss per unit time. Thus, we anticipate (for example) a lifetime ~ 300 sec for 10-keV protons at L [[spi:math]] R = 5, and a lifetime ~ 2000 sec for 100-keV He+ there. The lifetimes at L = R + 1 = 6 would be about 15 times longer, i.e., ~ 4500 sec for H+ and ~ 30000 sec for He+. These results suggest a more rapid than natural depletion of the ring current by charge exchange as a result of propulsion by neutral-hydrogen exhaust. Natural charge-exchange lifetimes for ring current ions are ~ 105 sec. The lifetimes estimated above require further interpretation because typical drift periods for 10-100 keV ions at L ~ 5 amount to ~ 104 sec to ~105 sec and thus exceed the estimated lifetimes. This means that results contingent on the drift average specified in (60) have direct applicability only on time scales of a drift period or longer. When the results suggest a lifetime much shorter than the drift period (as they do in several of the above examples), this should be taken to mean that the ions in question fail (with high probability) to survive their first transit through the neutral gas cloud. However, ions that have not yet entered the gas cloud will survive until they do enter it, i.e., up to a full drift period (depending on their 67 [[spi:math]] We estimate that the jet divergence is sin [[spi:math]] 1/14 and therefore that [[spi:math]]
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