If we are receiving the FRBs, the focused beam must be pointed towards earth. So the spaceships with light sails must be headed in the direction of earth. Get ready for the invasion!
Only if they were aiming at where we are now, which doesn't make sense. They would have to aim the craft at where we are going to be in X years. X being the duration of the voyage.
Come to think of it, even if they were aiming directly at where we are now I would assume the light source would still be occulted regularly by everything between us and them.
Gotta remember, if we are seeing light intentionally or unintentionally, they pointed these sails to our current position, almost X years in the past. Where X is the distance in light-years.
You have two sails in concentric rings that are connected, with your craft attached to the outer ring. When you want to decelerate you disconnect the two rings and and tweak the reflection of the inner ring to be somewhat outward focused and give the inner ring a little push. As it moves forward the energy bouncing off the inner ring is directed backwards to the outer ring, which slows. As long as the inner ring reflect more energy backwards (and to the outer ring) than the outer ring is getting from your source the outer ring slows down. Really hard to describe, but easy to draw. First proposed by Robert L. Forward.
If you project a large magnetic field the extra-solar ionized gas (intergalatic, between stars) can exert a fair amount of drag.
A lot of people talk about bussard collector (magnetic scope for hydrogen/helium) to power fusion. But instead of collecting gas use it as a drag chute.
Well, it'll take them awhile to get here. There's still time to start putting rail-guns on asteroids for purely mining purposes, or giant laser arrays on Mercury - just for moving ships around of course.
