Create a "pulse"/ring that expands but doesn't scale

I’m very new to Unity but I’m slowly starting to get the hang of the basic functions. However, I’m trying to make a simple 2D game where pressing a key (actually taping the screen as it’s a mobile game) creates a “pulse” or a ripple if you like, from the middle of the screen. Much like this game: - YouTube .

Now, my question is, how would I best go to create this effect? The most important thing is that the ring keeps it’s width constant while increasing the radius over time (exactly like the video above).

I’ve tried using a particle effect but that doesn’t really have the “solid” feel I want and I can’t seem to get a constant density so it looks thicker at the start and the gradually “disolves”. I’ve also tried importing a “torus” (ring) model from Blender and animate it in the Unity animator but that fails horribly as all I can animate is the scale which makes the ring thicker the larger it becomes (obviously).

It’s worth adding that I’ve got SpriteManager and iTween “ready” if need be but I haven’t used either much and couldn’t figure out a way to apply them to this problem.

Any advice is greatly apreciated.

Using the LineRenderer did the trick as syclamoth suggested as well as some help from this thread:

Thank you for the help.