Got particle system. Can I occlude the particles when not being hit by directional light shaft?

Title pretty much says it all. I have a basic dust particle system but when I place it in the scene it is everywhere in my scene. I’d really like to be able to contain the viewing of the particle system to only when it is hit by the directional light shaft. Is this possible? or is their an alternative I could try. Pic attached shows my scene and the dilemma.

Thanks,
Scott.

Thanks,
Scott.