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Equations of Motion for a Collection of Paul-Trapped Particles

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.

Wolfgang Christian
Fri May 12 10:36:01 EDT 1995