| Okay: for 1) I described something called a "plow sail" in Permanence. I don't explain it in that book, but it's a magsail that's used to deflect particles away from the cycler. In fact, since that action would decelerate it, it is a small, low-power interstellar ramjet. It harvests just enough hydrogen to keep itself at speed; its main function is to deflect particulates away from the cycler habitats.
One variant to this idea is to use cargo magsails from stars you've passed by: the magsail drops off its cargo at the cycler, and keeps accelerating on the beam for some time. Then it settles into a low-power mode a few light-minutes or hours ahead of the cycler. In that position, it provides deflection (you'd want to ionize the interstellar medium with a laser before deflecting it, according to some studies) and is decelerated until it either falls behind the cycler, or matches velocity with it. Depending on how long that takes, you either lose the sail (which is just a large loop of wire) or you attach a small hab to it and ride it down to the next system on your ring.
As to 2), I'm not talking about any specific type of particle beam. Many varieties are possible, from laser to microwave to neutral-beam to mesoparticle beam. Charged particle beams are the least likely to be useful, though. Because they are charged, such beams spread very rapidly. Electron beams dissipate in under a kilometer, typically. The solution, if you need charged particles, is to use a neutral beam, and ionize it just before it hits your magsail, using a laser.
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