Is not too complicated, two particle emitters with long lastin particles, not too many though and not too slow either. The obvious tracer, the circle, the nurbs, and you got your system. Added some turbulence at the beginning so it starts spreading, then at the center added a rotation force, quite big with a sphere type falloff.
Background well you know a normal circular gradient in a layer layout adding a small turbulence or noise to it. Texture for system one, some cool v gradient with the color of your choice layered adding some noise turbulence similar to the background, quite big you barely see it but it determines quite a lot. Cloned it and tweaked colors for system two.
Some huge zenital softbox with a bit of blue in it. No shadows.
Two other softboxes one on the right casting shadows and a fill from the left with a small redish ink to it.
Ambien occlusion quite low.
Cell renderer disableing edges, allowing color, illumination and outline to cast with white.
Photoshop: curves, vignete, and then the light filter.