Classification of eigenmodes in a side-coupled structure according to the space group representations

The geometric symmetry of an RF structure can be expressed by a group of symmetry operations that keep the configuration invariant. For a periodic structure, the geometric symmetry is described by a space group containing translations, reflections, and other operations. Eigenmodes in the structure can be classified according to the irreducible representations of the space group of the structure. In this paper, we apply this method to a side-coupled structure (SCS) which is widely used for proton accelerators.