Gradient for Beam of Light

My first post...

I'm trying to get images for an animation in a tutorial.  The frames will consist of a moving LED beam.

I've got it working, but I'd like the gradient used for the beam to be more representative of the the actual light dispersion.  

The density of the gradient should fade from left to right, AND

the density of the gradient should fade as a function of the "off angle".  Brightest on the sensor pole immediately adjacent to the pole, and fading off as the angle get larger.  For example, 50% intensity at +-7 degrees.

That's what the actual radiation pattern of the LED is.  Decreasing with the square of the distance, and decaying to 1/2 intensity at +-7 degrees.  Having the graphic reflect something like the actual dispersion of light will help make some of the points of the tutorial more intuitive.

I think I should be able to get what I want with a gradient/mesh/transparency and or mesh fill.  Maybe combining multiple objects somehow.  But, I've played with all those tools and can't get what I want.

Ignoring the need to also  fade from left to right, I can get this using the fountain fill with linear gradient.  But, even this subset of the task isn't what I want.  The gradient is vertical, versus radial around the emitter point:

I tried elliptical gradient, but the gradient starts from the center of the object.  Maybe I could somehow combine and object with an elliptical gradient with its center over the emitter point source.  But, I couldn't figure out to do that.  I kept loosing the fill all together when I did virtual segment delete after combining the curves

I see a tutorial on how to do what I want in PhotoShop, so I'm about ready to give up and try that.  I'm not that skilled in CD, but much better in CD than PhotoShop, So I'd like to stick with CD since this is just a small piece of the graphics I need to do for the animation.

Any help would be greatly appreciated!