I mean things like the Team Fortress 2 medic gun:
...or the Killzone: Shadow Fall anti-gravity effect:
How do these work?
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Typically the trick to this sort of effect is use of scrolling textures. Particles will often be involved but they are usually only an embellishment.
It is the case that effects like this are bespoke and although they share a similar starting point the final effect is always a result of tweaks and tinkering until the art director is happy.
To take the effect to its most basic however you have two elements: the geometry and the texture coordinates. The geometry defines the basic outline shape of the effect while the movement of the texture coordinates defines movement within the geometry (and of course the texture itself defines the shape of whatever is moving along the geometry).
So for example, if you wanted some sort of arcing energy gun, you could construct a camera facing triangle strip along a path from gun to target, and change the shape of the arc over time to give a sense of dynamism. You could then animate the texture coordinates so that the texture scrolls down the length of the beam to give the impression of movement from gun to target. Use alpha in the texture to soften the edges and give the illusion of pulses. This would obviously be a very basic effect but add another set of texture coords and you can start to build something that looks far more complicated than the sum of its parts.
As Mr. Beast say, these effects (like fire, auras, etc.) are usually made with particle systems.
A particle system simulate a lot (10-10000?) small elements emitted by a source, an that flow through a path. The path may be as complex as required.
Each particle is shown in the scene with a sprite. And may be improved with an animated texture, blending effects, or shaders.
For very simple auras, some games just use 3 axis-oriented quads with a amazing animated texture.
Following a youtube example of particle system. https://www.youtube.com/watch?v=a8uZUqIEsoI