Using a single fire movie (one for each test) as the sprite for the particles, in conjunction with the time sampling method called Random Play Once, this effect can be achieved.
This is a fairly simple particle system with no Aux particles. Just a good source video.
ReelSmart Motion Blur, from RevisionFX, was used to give some added motion blur – which really helps sell the effect.
JUST ADDED – 2 tests where a combo of Particular's Physics time factor and Twixtor are used together to slow some effects down.
Test created by Aharon Rabinowitz.
Learn more about Red Giant Trapcode Particular at: http://www.redgiantsoftware.com/products/all/trapcode-particular/
Learn More about Re:VisionFX ReelSmart Motion Blur at: http://www.revisionfx.com/products/rsmb/
Learn More about Re:VisionFX Twixtor at:http://www.revisionfx.com/products/twixtor/