Particle System Shape, how to make particle emit toward one point. (inverse cone)?

Hi, the shape "cone" of my particle system is facing the wrong way. So by default the cone has it's tip where the emitter point is and the goes broad the further away from this point it is.

I would like to have an emitter with starts broad and the particles fly towards eachother. A flipped cone shape. When resizing the cone, I'm only able to make the base larger to the point the cone looks like a circle as I can not make the base larger then the upper point.

Original cone: \/ Desired Cone: /\ (Particle Direction is Up. So in the desired cone they come together instead of going appart like in the original.

I hope the question is clear. How do I acchieve this?

Thanks for any hint.

Cheers Fred