Particle colouring shader for light

Hi there,

Had a good hunt but have been unable to work out how to even start doing this:

Basically, I have a texture being used with a linerenderer to render a laserbeam. The texture is white in the centre, and fades to grey on the sides.

I'm trying to come up with a way of tinting it, while retaining the white- effectively a shader that does the photoshop equivalent of colorize, or adds the colour additively if that makes sense? All of the tinting shaders seem to tint the white to become blue or red. The effect should look more or less like a lightsaber

I realize I could fake it by adding a white cylinder but would prefer it to be a simple shader on the line-renderer as this makes the scripting of it flickering etc a lot easier.