Beam deflection into a quadrant by a positionally stationary magnetic bending system

A system of postionally stationary magnets is analyzed for the continuously variable deflection of a 50 MeV electron beam. The system is composed of a collection of horizontal and vertical bending magnets, quadrupoles, and a final deflection magnet that is conical in shape and capable of deflections of plus or minus 50 degrees simultaneously in both horizonal and vertical planes. Throughout the system the beam is assumed to be focused by its own magnetic self-field, the electric self-field being neutralized by background ions. The motion of the beam in the externally applied magnetic fields may then be considered as single particle motion. The system of bending magnets and quadrupoles pre-conditions the beam by introducing the proper displacements and angles at the entrance to the final deflection magnet for momentum deviations up to plus or minus one percent. The displacements and angles are determined by the chromaticity of the final deflection and are a function of the bending angles in the two planes. The total system is then doubly achromatic in both planes. The preconditioning magnets are of standard accelerator beam transport design while the conical deflection magnet is of a design fashioned from a television deflection coil scaled up by about a factor of 10 in size