9. Simulation with Long-Ranged Potentials: Particles and Fields
In many cases the interparticle potential may be safely neglected beyond
a few particle diameters. Defining a cutoff distance ,
we may estimate the importance of the neglected
``tail'' of a potential by
If the decay of is slow, this integral may be non-negligible.
For example, the interaction between charged particles
decays only as , and any cutoff will introduce a considerable
error. Another instance is astrophysics, where the gravitational potential
reaches too far to permit a simple cutoff.
For ionic systems that are globally neutral the Ewald summation
method known from solid state physics may be invoked. In the case of
hot plasmas or gravitating systems the Particle-Mesh
methods are appropriate.