A nonlinear Coulomb interaction term appears in the equations describing the
motions of a collection of Paul-trapped particles. A realistic description may also include a damping term which arises from collisions with a background gas
and/or from laser cooling. The motion of the ion in a collection of
**N** ions is given by:

where , , and are the
damping forces in the **x**-,
**y**-, and **z**- directions respectively, is the distance between
particles **j** and **i**, and is the unit vector pointing from
particle **j** to particle **i**.

Fri May 12 10:36:01 EDT 1995