The only time I ever used repulser beams was when I was playing against one of my friends, and I was pursuing a fighter-heavy strategy. He built a bunch of dedicated PDC ships and sent them after my fighters while his fleet hung back and waited to go after my defenceless carriers.
I ended up building a couple Repulser Ship and I sent those in just in front of my fighters. They knocked his PDC ships out of the way and my fighter squadrons raced through the gap and wasted his fleet. Sweetness.
