Violation of Midplane Symmetry in Bending Magnets

Charged particle optics has traditionally been based on the concept of midplane symmetry. Accelerators, beamlines, and spectrometers are often midplane symmetric in their entirety. Departures from midplane symmetry are usually obtained by rotating midplane symmetric components about a longitudinal axis. Misalignments and magnet imperfections introduce non midplane symmetric components into a beam line. Vertical steering and correction of the effect of errors can be accomplished through the deliberate introduction of midplane symmetry violating components in bending magnets. We have worked out the equations of motion and derived the transfer matrix for bending magnets with small midplane symmetry violating field components. The solutions are linearized in the non midplane symmetric magnetic field components.