I found it very difficult to get a nice Stargate effect made in pI, because of the way the event horizon ripples. It's a very 3D effect, though some of the filters in After Effects can probably replicate it pretty easily.
You can try creating a circular emitter that only shoots particles inward. Start them out a dark blue, and make them turn light blue as they reach the center of the circle. Turn on intense so they glow as they overlap, to create that bright spot in the center of the ring.