One can study various modes of light sail operation to see how it will perform. The parasitic reduction of perigee seems to be associated with acceleration in the direction of sunlight and requires more energy for insertion into a higher circular orbit. The following mode of operation prefers acceleration in the direction of sunlight. The attitude of the sail is directed as follows.
The relative change in the apogee of the sail increases with time but the perigee also decreases even if a small 10 second step is used in the calculation.
Again, more Δv is required to put the light sail into a circular orbit than for a ballistic transfer orbit. More time would be required to compensate for the loses when the Δv is in the proper direction orbit insertion.
If nature favors some modes of light sail operation over others the preferred mode would make the desired orbital changes in the least possible time. It may require a little R & D to determine the optimal solution. The rate of the gain in altitude at apogee is greatest for α=0 when the light sail moves in the direction of sunlight. If the drop in perigee isn't compensated for light sail won't climb out of the Earth's gravity well before it encounters atmospheric drag. So one will have to do the climb stepping from one circular orbit to a higher one.
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