##### Periodicity

A periodic problem involves geometry that repeats itself after some distance along a vector. A linear accelerator is an example of such a structure. Both OM2p and OM3p support periodicity.

There are two separate attributes that are used as a pair to model periodic structures: Periodic Master and Periodic Slave . All model surfaces/edges along one periodic plane are given one attribute in the pair, and surfaces/edges on the second plane get the other. In OM3p (OM2p), the periodic slave must be assigned to a face (edge) that is the same size and shape as the face (edge) to which the periodic master has been assigned. For OM2p operating on a cylindrical coordinate system, the direction of periodicity must be parallel to the rotational axis.  In other words, periodic boundary conditions (PBCs) may only be applied to edges in the model that are perpendicular to the axis.  In 3D problems modeled with OM3p, the periodic axis can be in any direction, and PBCs are applied to faces that lie on two offset planes perpendicular to this direction.  Each pair of PBCs must have the same set number in the attribute label.

Application of PBCs enforces a specific phase advance in the electric field between the master and slave planes, of the form

where pm is any position on the master periodic surface and rp is the periodicity vector, or the vector that translates the master surface to the slave surface. You may set the Phase Advance in the simulation properties dialog box on the Solver tab. By default, the Phase Advance Count is set to zero. When using periodicity, you must define the relationship between master and slave by using a Count greater than or equal to one. If you want the solution on master and slave to have the same phase, use a Phase Advance Count of one, with Start (deg) equal to zero.