The six-dimensional beam-beam interaction as developed in 1992 by Hirata, Moshammer, and Ruggiero has been extended to include linear coupled motion and an arbitrary crossing plane. The technique of symplectic mapping in the six-dimensional phase space, called synchrobeam mapping, is applied to investigate the beam-beam kick within a solenoid. A linear beam-beam model including coupling is discussed in detail, also in the framework of a six-dimensional symplectic dispersion formalism.
