Aberrations caused by mechanical misalignments in electrostatic quadrupole lens systems

Image aberrations resulting from small misalignments in quadrupole lenses multiplets have been analysed. Analytical formulas for the coefficients of the beam displacement, astigmatism and coma associated with misalignments in a general quadrupole lens system have been derived. Numerical computations of systems of three and four quadrupole lenses have also been carried out. The aberration figures obtained for systems with and without a mechanical defect are compared. The aberration coefficients that have been obtained can be used for estimating tolerance limits for lens misalignments.