Can I add a particle distribution/density into a solvepde model of poisson's equation.

I have an electric field model (using pde toolbox), into which I have a stream of charged particles. I would like to add those particle's phi/E contributions to the volume. Can I somehow integrate that density distribution into my model?

I have x,y locations of all my particles, as well as discritized density in a Particle-in-Cell volume(2d)

Given the size of my (2d) volume Finite difference method is too computationally intensive.

Any thougts?

Thank you.