Mesher might work, did a quick test
- PF Source created, set to use a Box as its particle
- Mesher created with the PF Source in the Pick Object
- PF Source render properties set to not renderable
- Plane created, painted with a material that uses CoronaDistance in it - the Distance From is set to the Mesher object (here I just plugged that in to Self Illumination)
This will animate fine from what I can see. May be other options, here I was making the particles not show up in the render and just leaving the Mesher versions visible, but likely could make the Mesher ones invisible and the original particles left visible too. Not 100% sure that is the result you are looking for, but should let the target change based on the distance to the arrows I think.