Beam particle taper oddly shaped

I’m using a beam emitter to create a beam with a specific shape, wide at the beginning and narrowing down towards the end. I’ve set up source and target but the result looks odd - here’s the rough shape I’m going for:


I was expecting the Taper to do the job but the result is not smooth at all. Bumping up interpolation helps somewhat:


Material setup is as basic as it gets:


I’ve been fiddling with the tangents and a bunch of other settings but nothing got me closer to what I wanted. Did I misunderstand how it’s supposed to work?

How to achieve the effect described above - a beam starting out wide and tapering towards the end?
I know I could do it in the material but was wondering if there’s a way to do it in cascade.