I prefer the ring thing rather than this one sorry.
The point is that particles should be somehow random, elseway they create a "patter", wich is a bit odd.
If you want to have the rings, they should start very close to the firing point and then fade soon.
In the shots you made I haven't understood if they continuosly follow the shot, if not they are too far from the ship, and at this distance they should be almost faded out.
If it is impossible to make them the way I suggested, if they continuosly folllow the shot, they should be scratched away since they'll always look odd. At least you may try some small semivisible irregular rings (like the em cannon in the film "eraser", with shwarzenegger)