Simulator for trajectories of charged particles in electric fields? I am looking for a numerical simulation program which computes the trajectory of a charged particle moving in an electric field.
The electric field should be numerically determined by determining a geometry of charged conductors with defined electric potentials. In particular the following simple example should be possible:

In contrast to the picture above the program should work numerically with the "correct" inhomogenous electric field and not work with the simple infinite plate approximation.
The program should be free and run on linux, windows or via a browser interface.
 A: You may have a look at agros2d which could simulate electrostatic fields determined by various boundary conditions and then charged particles in the electric field. A similar case as you mentioned in your question is demonstrated in this video.
Maybe the simulation library Kassiopeia from the Katrin experiment might also do what you want, but I didn't try it so far (in particular didn't try to reproduce your parallel plate example).
A: Simion
Directly from the product website: 

SIMION is a software package primarily used to calculate electric fields and the trajectories of charged particles in those fields when given a configuration of electrodes with voltages and particle initial conditions, including optional RF (quasistatic), magnetic field, and collisional effects. In this, SIMION provides extensive supporting functionality in geometry definition, user programming, data recording, and visualization. It is an affordable but versatile platform, widely used for over 30 years to simulate lens, mass spec, and other types of particle optics systems.


The software is on version 8. It is not free, with the cheapest being a 1-year “academic” license at 350 USD. There is  a free trial version, though it’s quite limited.
There are older versions of the software out there, but they certainly aren’t legally useable without permission and I would never advocate for using a cracked copy of software no matter how old it is.
A: There is CST program by Dassault systems that have a particle solver.
https://www.3ds.com/products-services/simulia/products/electromagnetic-simulation/particle-dynamics-solutions/
maybe particle accelerator solver could help for your thing
