Ideal distortion-less bending of a focused non-paraxial electron beam

In specific applications, where electron beam is required to be bent after passing through the focusing optics, the beam spot on the target is distorted due to asymmetry introduced by the bending. For complete elimination of the above distortion, a circularly asymmetric initial velocity distribution of electrons that move in a radially decreasing magnetic field (i.e. index of field gradient=1) is proposed. The expression is quantitatively exact for beams with any angle of bending even when paraxial condition is not satisfied i.e. beam cross-sectional diameter is comparable with the radius of curvature of bending. Modified expression for the case, when kinetic energy of the electrons increases due to time-varying field during its motion through the bending magnetic field is also given as a result of which complexity of the magnetic field design (for strong focusing) can be avoided. Finally, a numerical model of electron gun is utilized to compare the results of proposed model.