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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, ). Real
physical systems
do not exhibit anything like the same level of statistical noise, since they generally
contain of order Avogadro's number () 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).

Richard Fitzpatrick
2006-03-29