Astigmatism correction with an adaptive quadrupole and an expander lens for electron accelerators

Astigmatism is a type of aberration in beam optics which causes asymmetry in transverse coordinates. This asymmetric beam often shows an elliptical profile instead of circular, which may cause differences between the major and minor ellipse axes diameters and ellipse azimuth angle. In this research work, a novel astigmatism correction system is proposed for electron accelerators with a minimum number of electromagnetic lenses. An adaptive quadrupole lens is designed by coaxially locating two quadrupoles 45 degrees apart from each other. The focusing and defocusing axes and the azimuth angle of the resultant adaptive quadrupole are determined adaptively by the vector sum of created magnetic fields of two coaxially located quadrupoles. The adaptive quadrupole lens is placed on the common focal point of two solenoids as part of an expander lens. In this way, the focal points of the major and minor axes of an elliptical beam are slightly changed from the common focal point of the expander. This act helps to increase the minor axis diameter of the electron beam while decreasing the major one, resulting in a circular profile. Both a 2D beam trajectory model in MATLAB and a 3D Particle Accelerator simulation with Computer Simulation Technology (CST) tool show that the proposed method successfully corrects the astigmatism having any elliptical parameters for a sample electron beam.