How to create the curved firework which is at the end of the Disney's movie-intro?
I am talking about this (video link): https://youtu.be/k9bUTfFF3_4?t=20
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You could create a long cylinder for your trail, with a big spherical head, give it the following modifiers: Subdivision Surface, Curve, Displace (to give it a bit of bumps), also give it a particle system with an icosphere as particle in order to make it emit sparks:
Here is the kind of material you can give to your trail: a mix between Emission and Transparent, with a Noise as factor, also give it gradient transparency on X so that it fades: