For satellites above the safe altitude, an estimate of the probability of an encounter may be obtained by assuming the orbital phase is randomly distributed — as might be the case, for example, if the satellites were launched at random times, without coordination with the SPS. It is found that the chance of an encounter reaches a maximum just above the safe altitude, then drops off quite rapidly. It is possible for a satellite in an orbit of altitude 1200 km and inclination 28.5° to have about one chance in 2000 of an encounter with the beam to a given temperate-zone rectenna, during its first day of operation. Once an encounter has occurred (or the orbital position has been otherwise determined) , predicting future encounters is a deterministic problem, apart from stochastic orbit perturbations. It may be possible to choose the orbit altitude and phase so that encounters with a given beam occur very rarely, if at all. The problem becomes more complex if multiple satellites and/or multiple SPS installations are considered. On average, it appears that, if large numbers of satellites (c.100) are in orbits of moderate altitude (500 to 5000km) and moderate inclination, one of them will pass through the beam to a given temperate-zone rectenna about once a month. Conversely, if there are large numbers (c.100) of randomly-scattered rectennas, a typical low satellite might expect to meet one of their power beams about once a month. Because of the decrease in encounter probability with altitude, there does not at present appear to be any serious risk of encounters with power beams by a vehicle in low-thrust transfer from LEO to GEO. Measures which might be taken to reduce the frequency or minimize the effects of beam/satellite encounters include the following: i. Rectennas could be prohibited within 2° of the equator, in order to avoid frequent beam encounters by equatorial satellites. ii. Rectennas could be built at as high latitudes as economically and geographically possible, in order to minimize interference with low satellites in orbits of moderate inclination. iii. Where mission objectives and launch penalties permit, the use of the lowest possible inclination for sensitive satellites could be encouraged. iv. Satellites could often be designed to withstand passage through the microwave beam (where, at higher altitudes, the flux density may be several hundred mW/cm2), although it could be argued that the extra costs thus incurred should be borne by SPS operators. v. The power beam could be designed for rapid on-off switching or defocus (in times of a second or two), to minimize outages if it must be shut down to avoid damage to an approaching satellite. Continuous power to the utility grid could be ensured by modest energy-storage capacity at the rectenna, which may well be available to compensate for other, considerably longer outages.
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