You just want one of the beam textures to move along the whole beam?
If so...
$Section:
+Width: 1
+Texture: [beam_1]
+RGBA Inner: 0 255 0 200
+RGBA Outer: 0 128 0 50
+Flicker: 0.1
+Zadd: 0.4
+Tile Factor: 10.0, 2
+Translation: 1.0
$Section:
+Width: 2
+Texture: [beam_2]
+RGBA Inner: 0 255 000 96
+RGBA Outer: 0 125 0 20
+Flicker: 0.8
+Zadd: 0.2
+Tile Factor: 10.0, 2
+Translation: -1.0
$Section:
+Width: 3
+Texture: [beam_3]
+RGBA Inner: 96 255 96 50
+RGBA Outer: 48 128 48 5
+Flicker: 0.0
+Zadd: 0.0
+Tile Factor: 100.0, 2
+Translation: -10.0
I just took this from one of Nukemod's beams. I think they do what you are thinking of. I'm not really sure how they work, all I know is that they do work (hopefully), so that might be something to go on.