Beam Particle System Questions

Today, I’ve learned that I am absolutely TERRIBLY when it comes to particle systems. I’ve got a couple of materials set up - I started off following this guide:

I’ve made my own modifications to keep it straight and a single beam (not doing the weird things like the 3 beams were doing), but I’m not entirely happy with the result - the beam is too wide, and I’m not sure how to control the regularity of the pulses on it.

My goals:

  1. Have a little “ball of light” at the end of the beam - I have a a texture that’s just a white radial gradient on a black background, but I’m not sure how to use it.

  2. (Perhaps) Animate the pulses so they move from source to target along the beam at a defined speed. Whether or not I do this is still in question - I’m aiming for a mobile platform, and I’m not sure how taxing this would be. I’m also not sure how difficult it would be.

If anybody could help me achieve these goals, it would be greatly appreciated. Thank you!