Abstract
This chapter discusses the theory of classic mechanics and describes the electron trajectories and aberrations in the generalized position and momentum representations and is derived by the Hamiltonian function and the canonical equations. This Hamiltonian approach may be regarded as canonical aberration theory and has several advantages. The chapter also discusses canonical aberration theory and canonical electron beam optics. A brief account of conventional aberration theory, using Lagrangian representation, in a rotationally symmetric electromagnetic system is also provided. Canonical aberration theory is discussed, using Hamiltonian representation, also in a rotationally symmetric electromagnetic system. Higher order aberration in a round lens is derived followed by higher order aberration in electromagnetic multipoles. The chapter also discusses canonical electron beam optics which is divided into three parts: (1) electron beam optics in round lenses; (2) electron beam optics in a combined system consisting of round, quadrupole and octopole lenses; and (3) electron beam optical computations in round electrostatic lenses.
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