Charged particles flowing through a certain control volume are subject to forces exerted by some external E and B fields, as well as the fields due to the presence of the surrounding particles. A common method used in computer simulation of such a flow is to use a spatial grid. The values of the electric and magnetic fields due to the external effects, such as the accelerator grid used in ion engines, are calculated at the nodes of this grid. To these values are added the fields due to the motion of the plasma itself. The fields are then inerpolated onto the charged macro-particles using some weighing algorithm. The macro-particles are then moved according to the Newton-Lorentz relationship. After this, the whole cycle repeats, up to a specified number of time steps.

This process is demonstrated in the following animation:

The resolution of the spatial grid, as well as the number of particles used in the simulation determine the accuracy of the result. The grid resolution is often chosen to be the Debye Length, since the quasi-neutrality of plasma breaks down at scales smaller than this parameter. The simulation of a quasi-neutral plasma requires additional steps, and often provides no large difference in the accuracy of results, since most plasma analysis is concerned with the general flow properties, and not with the effects at minute scales. The physical properties of the macro-particles (i.e. mass or charge) are scaled such that the limited number of particles carries the same charge and mass as the studied plasma. Furthermore, the computational time can be reduced by simulating only one specie, such as the ions, and assuming that the electrons provide an uniform neutralizing background.