Reducing Rectenna Size of Power Sat Systems

The major issue with most microwave power transmission concepts is that due to the orbit the power satellites are parked in (geostationary), the beam is often diffused so much that a rectenna to receive it would have to be very large. One concept says it would have to be 14 kilometers wide, another 20 miles! Logically, decreasing the distance that the beam would have to travel would reduce the rectenna size. Perhaps having a receiving and refocusing satellite near low earth orbit would help to reduce the beam dispersal allowing for smaller rectenna sizes. High stratosphere, permanently aloft refocusing stations could focus the beam even more. The goal would be to reduce the minimum rectenna size to well under a kilometer in any dimension.