Softening the light edge created by a cone???

I´m a noob at this so excuse my inexperience. This setup is composed of bits and pieces of reading things up and trial and error but after several attempts to improve the look of this I have hit a wall.

I´m trying to make the perimeter of the cone look more defuse, soft, as if the light were dissipating. Presently (as shown in the image) the contour is very defined.

How can I work this to create the effect I mention?

thanks in advance to all for the help.

A few days ago a tutorial covering exactly this (how to create a faded light cone) was published… for free:

I´ll check it out further later after work but at a glance looks very cool. Meanwhile I managed to get the ramp to control the width of the light but it leaves a black contour on the outside of the cone.

I tried to find a way to make a selective color transparent on a color ramp but didn’t find how to do it.

thanks for the help!