I haven't done this myself so far, but I suspect the best way to go here might involve cycloid splines, blend mode cloners and Field Forces.
Searching around those terms I found this tutorial from Insydium.
Obviously, they are using their own particle system, but there is no reason to think the native one couldn't also do it... though I am probably not the best person to advise on the specifics of that; I don't have much experience in Cinema particles yet !
CBR