Discussion

Obviously, the ideas discussed above could be generalized in a fairly straight-forward manner to deal with the evolution of two and three-dimensional charged particle distributions. PIC codes have the advantage that they are reasonably straight-forward to write. Unfortunately, PIC codes also have a number of disadvantages. The first is that PIC codes suffer from high levels of statistical noise, since they generally only deal with a relatively small number of particles (typically, $\leq 10^6$). Real physical systems do not exhibit anything like the same level of statistical noise, since they generally contain of order Avogadro's number ($\sim 10^{24}$) of interacting particles. Another problem with PIC codes is that they do not handle charged particle collisions very well. The reason for this is that there are generally a large number of particles in each cell (for practical reasons), and the short range Coulomb fields of these particles tend to cancel one another out (recall that the electric field is only calculated at the cell vertices).